From de64f02ad3582308d9efa8682fd5b2cc25913ea6 Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 16 Nov 2023 09:38:01 +0100 Subject: [PATCH 001/142] Add test case --- test/Jamfile.v2 | 1 + test/scipy_issue_14901_ncf.cpp | 27 +++++++++++++++++++++++++++ 2 files changed, 28 insertions(+) create mode 100644 test/scipy_issue_14901_ncf.cpp diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 44c76058ba..34a3ce7779 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -896,6 +896,7 @@ test-suite distribution_tests : [ run git_issue_800.cpp ../../test/build//boost_unit_test_framework ] [ run git_issue_845.cpp ../../test/build//boost_unit_test_framework ] [ run scipy_issue_14901.cpp ../../test/build//boost_unit_test_framework ] + [ run scipy_issue_14901_ncf.cpp ../../test/build//boost_unit_test_framework ] [ run scipy_issue_15101.cpp ../../test/build//boost_unit_test_framework ] [ run scipy_issue_17146.cpp ../../test/build//boost_unit_test_framework ] [ run scipy_issue_17388.cpp ../../test/build//boost_unit_test_framework ] diff --git a/test/scipy_issue_14901_ncf.cpp b/test/scipy_issue_14901_ncf.cpp new file mode 100644 index 0000000000..0be7382695 --- /dev/null +++ b/test/scipy_issue_14901_ncf.cpp @@ -0,0 +1,27 @@ +// Copyright Matt Borland, 2023 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// See: https://github.com/scipy/scipy/issues/14901 + +#include +#include +#include "math_unit_test.hpp" + +#pragma STDC FENV_ACCESS ON + +int main() +{ + auto ncf1 = boost::math::non_central_f(1, 1, 1); + const auto cdf1 = boost::math::cdf(ncf1, 2); + + CHECK_ULP_CLOSE(cdf1, 1 - 0.5230393170884924, 20); + + if (std::fetestexcept(FE_INVALID) || std::fetestexcept(FE_DIVBYZERO)) + { + return 1; + } + + return boost::math::test::report_errors(); +} From d18964d5aa968cea0742c4bb0dad99a3f2e37f3f Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 16 Nov 2023 09:38:11 +0100 Subject: [PATCH 002/142] Check update of xterm for denom of 0 --- include/boost/math/distributions/non_central_beta.hpp | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/include/boost/math/distributions/non_central_beta.hpp b/include/boost/math/distributions/non_central_beta.hpp index 9266c9e576..944f1dc242 100644 --- a/include/boost/math/distributions/non_central_beta.hpp +++ b/include/boost/math/distributions/non_central_beta.hpp @@ -212,7 +212,10 @@ namespace boost } pois *= i / l2; beta -= xterm; - xterm *= (a + i - 1) / (x * (a + b + i - 2)); + if (a + b + i - 2 != 0) + { + xterm *= (a + i - 1) / (x * (a + b + i - 2)); + } } return sum; } From 8da51f2bde1767353f55d0a32e327f9e2951f2e8 Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 16 Nov 2023 11:26:15 +0100 Subject: [PATCH 003/142] Add test values from issue --- test/ccmath_ceil_test.cpp | 8 ++++++++ test/ccmath_floor_test.cpp | 8 ++++++++ 2 files changed, 16 insertions(+) diff --git a/test/ccmath_ceil_test.cpp b/test/ccmath_ceil_test.cpp index 9540ea99d6..b374e1035e 100644 --- a/test/ccmath_ceil_test.cpp +++ b/test/ccmath_ceil_test.cpp @@ -37,6 +37,14 @@ constexpr void test() static_assert(boost::math::ccmath::ceil(T(2.9)) == T(3)); static_assert(boost::math::ccmath::ceil(T(-2.7)) == T(-2)); static_assert(boost::math::ccmath::ceil(T(-2)) == T(-2)); + + constexpr T half_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits::max)() / 2)); + static_assert(half_max_ceil == (std::numeric_limits::max)() / 2); + assert(half_max_ceil == std::ceil((std::numeric_limits::max)() / 2)); + + constexpr T third_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits::max)() / 3)); + static_assert(third_max_ceil == (std::numeric_limits::max)() / 3); + assert(third_max_ceil == std::ceil((std::numeric_limits::max)() / 3)); } #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P) diff --git a/test/ccmath_floor_test.cpp b/test/ccmath_floor_test.cpp index aa907fab11..3662526d36 100644 --- a/test/ccmath_floor_test.cpp +++ b/test/ccmath_floor_test.cpp @@ -37,6 +37,14 @@ constexpr void test() static_assert(boost::math::ccmath::floor(T(2.9)) == T(2)); static_assert(boost::math::ccmath::floor(T(-2.7)) == T(-3)); static_assert(boost::math::ccmath::floor(T(-2)) == T(-2)); + + constexpr T half_max_floor = boost::math::ccmath::floor(T((std::numeric_limits::max)() / 2)); + static_assert(half_max_floor == (std::numeric_limits::max)() / 2); + assert(half_max_floor == std::floor((std::numeric_limits::max)() / 2)); + + constexpr T third_max_floor = boost::math::ccmath::floor(T((std::numeric_limits::max)() / 3)); + static_assert(third_max_floor == (std::numeric_limits::max)() / 3); + assert(third_max_floor == std::floor((std::numeric_limits::max)() / 3)); } #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P) From fe377373e472cc4441d2c7a2e7782ff119764645 Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 16 Nov 2023 11:26:41 +0100 Subject: [PATCH 004/142] Use identity function in floor if val >= 1/epsilon --- include/boost/math/ccmath/floor.hpp | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/include/boost/math/ccmath/floor.hpp b/include/boost/math/ccmath/floor.hpp index fa071e24ba..fb1dea34db 100644 --- a/include/boost/math/ccmath/floor.hpp +++ b/include/boost/math/ccmath/floor.hpp @@ -15,6 +15,7 @@ #include #include #include +#include namespace boost::math::ccmath { @@ -23,6 +24,13 @@ namespace detail { template inline constexpr T floor_pos_impl(T arg) noexcept { + constexpr auto max_comp_val = T(1) / std::numeric_limits::epsilon(); + + if (arg >= max_comp_val) + { + return arg; + } + T result = 1; if(result < arg) From 6aaba2e5a3084f29114183e26bc0b303c372ceae Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 16 Nov 2023 11:28:39 +0100 Subject: [PATCH 005/142] Add 1 / eps test case to be sure --- test/ccmath_ceil_test.cpp | 4 ++++ test/ccmath_floor_test.cpp | 4 ++++ 2 files changed, 8 insertions(+) diff --git a/test/ccmath_ceil_test.cpp b/test/ccmath_ceil_test.cpp index b374e1035e..b898477609 100644 --- a/test/ccmath_ceil_test.cpp +++ b/test/ccmath_ceil_test.cpp @@ -45,6 +45,10 @@ constexpr void test() constexpr T third_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits::max)() / 3)); static_assert(third_max_ceil == (std::numeric_limits::max)() / 3); assert(third_max_ceil == std::ceil((std::numeric_limits::max)() / 3)); + + constexpr T one_over_eps = boost::math::ccmath::ceil(1 / T(std::numeric_limits::epsilon())); + static_assert(one_over_eps == 1 / T(std::numeric_limits::epsilon())); + assert(one_over_eps != std::ceil(1 / T(std::numeric_limits::epsilon()))) } #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P) diff --git a/test/ccmath_floor_test.cpp b/test/ccmath_floor_test.cpp index 3662526d36..149513cd71 100644 --- a/test/ccmath_floor_test.cpp +++ b/test/ccmath_floor_test.cpp @@ -45,6 +45,10 @@ constexpr void test() constexpr T third_max_floor = boost::math::ccmath::floor(T((std::numeric_limits::max)() / 3)); static_assert(third_max_floor == (std::numeric_limits::max)() / 3); assert(third_max_floor == std::floor((std::numeric_limits::max)() / 3)); + + constexpr T one_over_eps = boost::math::ccmath::floor(1 / T(std::numeric_limits::epsilon())); + static_assert(one_over_eps == 1 / T(std::numeric_limits::epsilon())); + assert(one_over_eps == std::floor(1 / T(std::numeric_limits::epsilon()))); } #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P) From 2cb550d65ec2e5109507f23e06ce751dc5474f2d Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 16 Nov 2023 11:39:53 +0100 Subject: [PATCH 006/142] Replace C style asserts with BOOST_MATH_ASSERT --- test/ccmath_ceil_test.cpp | 6 +++--- test/ccmath_floor_test.cpp | 6 +++--- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/test/ccmath_ceil_test.cpp b/test/ccmath_ceil_test.cpp index b898477609..5a407473d9 100644 --- a/test/ccmath_ceil_test.cpp +++ b/test/ccmath_ceil_test.cpp @@ -40,15 +40,15 @@ constexpr void test() constexpr T half_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits::max)() / 2)); static_assert(half_max_ceil == (std::numeric_limits::max)() / 2); - assert(half_max_ceil == std::ceil((std::numeric_limits::max)() / 2)); + BOOST_MATH_ASSERT(half_max_ceil == std::ceil((std::numeric_limits::max)() / 2)); constexpr T third_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits::max)() / 3)); static_assert(third_max_ceil == (std::numeric_limits::max)() / 3); - assert(third_max_ceil == std::ceil((std::numeric_limits::max)() / 3)); + BOOST_MATH_ASSERT(third_max_ceil == std::ceil((std::numeric_limits::max)() / 3)); constexpr T one_over_eps = boost::math::ccmath::ceil(1 / T(std::numeric_limits::epsilon())); static_assert(one_over_eps == 1 / T(std::numeric_limits::epsilon())); - assert(one_over_eps != std::ceil(1 / T(std::numeric_limits::epsilon()))) + BOOST_MATH_ASSERT(one_over_eps == std::ceil(1 / T(std::numeric_limits::epsilon()))); } #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P) diff --git a/test/ccmath_floor_test.cpp b/test/ccmath_floor_test.cpp index 149513cd71..6a06787b00 100644 --- a/test/ccmath_floor_test.cpp +++ b/test/ccmath_floor_test.cpp @@ -40,15 +40,15 @@ constexpr void test() constexpr T half_max_floor = boost::math::ccmath::floor(T((std::numeric_limits::max)() / 2)); static_assert(half_max_floor == (std::numeric_limits::max)() / 2); - assert(half_max_floor == std::floor((std::numeric_limits::max)() / 2)); + BOOST_MATH_ASSERT(half_max_floor == std::floor((std::numeric_limits::max)() / 2)); constexpr T third_max_floor = boost::math::ccmath::floor(T((std::numeric_limits::max)() / 3)); static_assert(third_max_floor == (std::numeric_limits::max)() / 3); - assert(third_max_floor == std::floor((std::numeric_limits::max)() / 3)); + BOOST_MATH_ASSERT(third_max_floor == std::floor((std::numeric_limits::max)() / 3)); constexpr T one_over_eps = boost::math::ccmath::floor(1 / T(std::numeric_limits::epsilon())); static_assert(one_over_eps == 1 / T(std::numeric_limits::epsilon())); - assert(one_over_eps == std::floor(1 / T(std::numeric_limits::epsilon()))); + BOOST_MATH_ASSERT(one_over_eps == std::floor(1 / T(std::numeric_limits::epsilon()))); } #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P) From 6c5fd09a406784480401f89a5121824a2536451a Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Fri, 17 Nov 2023 08:20:05 +0100 Subject: [PATCH 007/142] Fix ADL failures for __float128 --- test/ccmath_ceil_test.cpp | 8 +++++--- test/ccmath_floor_test.cpp | 8 +++++--- 2 files changed, 10 insertions(+), 6 deletions(-) diff --git a/test/ccmath_ceil_test.cpp b/test/ccmath_ceil_test.cpp index 5a407473d9..79c92bffd8 100644 --- a/test/ccmath_ceil_test.cpp +++ b/test/ccmath_ceil_test.cpp @@ -38,17 +38,19 @@ constexpr void test() static_assert(boost::math::ccmath::ceil(T(-2.7)) == T(-2)); static_assert(boost::math::ccmath::ceil(T(-2)) == T(-2)); + using std::ceil; + constexpr T half_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits::max)() / 2)); static_assert(half_max_ceil == (std::numeric_limits::max)() / 2); - BOOST_MATH_ASSERT(half_max_ceil == std::ceil((std::numeric_limits::max)() / 2)); + BOOST_MATH_ASSERT(half_max_ceil == ceil((std::numeric_limits::max)() / 2)); constexpr T third_max_ceil = boost::math::ccmath::ceil(T((std::numeric_limits::max)() / 3)); static_assert(third_max_ceil == (std::numeric_limits::max)() / 3); - BOOST_MATH_ASSERT(third_max_ceil == std::ceil((std::numeric_limits::max)() / 3)); + BOOST_MATH_ASSERT(third_max_ceil == ceil((std::numeric_limits::max)() / 3)); constexpr T one_over_eps = boost::math::ccmath::ceil(1 / T(std::numeric_limits::epsilon())); static_assert(one_over_eps == 1 / T(std::numeric_limits::epsilon())); - BOOST_MATH_ASSERT(one_over_eps == std::ceil(1 / T(std::numeric_limits::epsilon()))); + BOOST_MATH_ASSERT(one_over_eps == ceil(1 / T(std::numeric_limits::epsilon()))); } #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P) diff --git a/test/ccmath_floor_test.cpp b/test/ccmath_floor_test.cpp index 6a06787b00..ddd0a53e9d 100644 --- a/test/ccmath_floor_test.cpp +++ b/test/ccmath_floor_test.cpp @@ -38,17 +38,19 @@ constexpr void test() static_assert(boost::math::ccmath::floor(T(-2.7)) == T(-3)); static_assert(boost::math::ccmath::floor(T(-2)) == T(-2)); + using std::floor; + constexpr T half_max_floor = boost::math::ccmath::floor(T((std::numeric_limits::max)() / 2)); static_assert(half_max_floor == (std::numeric_limits::max)() / 2); - BOOST_MATH_ASSERT(half_max_floor == std::floor((std::numeric_limits::max)() / 2)); + BOOST_MATH_ASSERT(half_max_floor == floor((std::numeric_limits::max)() / 2)); constexpr T third_max_floor = boost::math::ccmath::floor(T((std::numeric_limits::max)() / 3)); static_assert(third_max_floor == (std::numeric_limits::max)() / 3); - BOOST_MATH_ASSERT(third_max_floor == std::floor((std::numeric_limits::max)() / 3)); + BOOST_MATH_ASSERT(third_max_floor == floor((std::numeric_limits::max)() / 3)); constexpr T one_over_eps = boost::math::ccmath::floor(1 / T(std::numeric_limits::epsilon())); static_assert(one_over_eps == 1 / T(std::numeric_limits::epsilon())); - BOOST_MATH_ASSERT(one_over_eps == std::floor(1 / T(std::numeric_limits::epsilon()))); + BOOST_MATH_ASSERT(one_over_eps == floor(1 / T(std::numeric_limits::epsilon()))); } #if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P) From d938d3e8362cff07e3c88a08d40e5b398e84c26a Mon Sep 17 00:00:00 2001 From: jzmaddock Date: Fri, 17 Nov 2023 18:25:02 +0000 Subject: [PATCH 008/142] Update version history. 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doc/html/quaternions.html | 12 +- doc/html/root_finding.html | 12 +- doc/html/special.html | 12 +- doc/html/standalone_HTML.manifest | 1 + doc/html/statistics.html | 13 +- doc/html/status.html | 12 +- doc/html/using_udt.html | 12 +- doc/html/utils.html | 12 +- doc/html/vector_functionals.html | 18 +- doc/math.qbk | 2 +- doc/overview/roadmap.qbk | 16 ++ .../special_functions/detail/round_fwd.hpp | 32 ++-- .../boost/math/special_functions/round.hpp | 28 ++-- .../boost/math/special_functions/trunc.hpp | 38 ++--- 493 files changed, 2466 insertions(+), 3132 deletions(-) create mode 100644 doc/html/math_toolkit/chatterjee_correlation.html diff --git a/doc/html/backgrounders.html b/doc/html/backgrounders.html index b29bcfd47e..86ab4b66b3 100644 --- a/doc/html/backgrounders.html +++ b/doc/html/backgrounders.html @@ -4,10 +4,11 @@ Chapter 23. Backgrounders - - + + + @@ -50,9 +51,7 @@ -
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-Math Toolkit 4.1.0

+Math Toolkit 4.1.1

Nikhar Agrawal @@ -133,10 +134,7 @@

-
- - -

Last revised: February 23, 2023 at 18:11:17 GMT

+
Next
diff --git a/doc/html/indexes.html b/doc/html/indexes.html index f3d1541533..2b99eff987 100644 --- a/doc/html/indexes.html +++ b/doc/html/indexes.html @@ -4,10 +4,11 @@ Chapter 25. Indexes - - + + + @@ -36,9 +37,7 @@ -
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-Function Index

+Function Index

1 2 4 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _

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-Class Index

+Class Index

A B C D E F G H I K L M N O P Q R S T U V W

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-Typedef Index

+Typedef Index

A B C D E F G H I K L N P R S T U V W

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-Macro Index

+Macro Index

B F

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-Index

+Index

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PrevUpHome diff --git a/doc/html/internals.html b/doc/html/internals.html index daf0ab7b2c..56aa0eccc4 100644 --- a/doc/html/internals.html +++ b/doc/html/internals.html @@ -4,10 +4,11 @@ Chapter 19. Internal Details: Series, Rationals and Continued Fractions, Testing, and Development Tools - - + + + @@ -56,9 +57,7 @@ -
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PrevUpHomeNext diff --git a/doc/html/interpolation.html b/doc/html/interpolation.html index 2d54f46114..b603e18533 100644 --- a/doc/html/interpolation.html +++ b/doc/html/interpolation.html @@ -4,10 +4,11 @@ Chapter 12. Interpolation - - + + + @@ -50,9 +51,7 @@ -
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+

PrevUpHomeNext diff --git a/doc/html/inverse_complex.html b/doc/html/inverse_complex.html index 781eea65cd..ffffbc7595 100644 --- a/doc/html/inverse_complex.html +++ b/doc/html/inverse_complex.html @@ -4,10 +4,11 @@ Chapter 15. Complex Number Functions - - + + + @@ -46,9 +47,7 @@ Report on C++ Library Extensions.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/acknowledgement.html b/doc/html/math_toolkit/acknowledgement.html index 52eaee594f..32ec4dd3ee 100644 --- a/doc/html/math_toolkit/acknowledgement.html +++ b/doc/html/math_toolkit/acknowledgement.html @@ -4,10 +4,11 @@ Acknowledgements - + + @@ -33,9 +34,7 @@ section. Thank you to all who contributed to the discution about this library.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/acknowledgements.html b/doc/html/math_toolkit/acknowledgements.html index 0a0906b9d4..15d6762589 100644 --- a/doc/html/math_toolkit/acknowledgements.html +++ b/doc/html/math_toolkit/acknowledgements.html @@ -4,10 +4,11 @@ Acknowledgements - + + @@ -33,9 +34,7 @@ section. Thank you to all who contributed to the discussion about this library.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/acos.html b/doc/html/math_toolkit/acos.html index f813c0b1d2..dc9e90dc63 100644 --- a/doc/html/math_toolkit/acos.html +++ b/doc/html/math_toolkit/acos.html @@ -4,10 +4,11 @@ acos - + + @@ -47,9 +48,7 @@
Formula:

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Formula:

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy.html b/doc/html/math_toolkit/airy.html index 272a42631a..f278a7397e 100644 --- a/doc/html/math_toolkit/airy.html +++ b/doc/html/math_toolkit/airy.html @@ -4,10 +4,11 @@ Airy Functions - + + @@ -34,9 +35,7 @@
Finding Zeros of Airy Functions
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Alpha.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/anderson_darling.html b/doc/html/math_toolkit/anderson_darling.html index f9a66831ea..6ee8655a78 100644 --- a/doc/html/math_toolkit/anderson_darling.html +++ b/doc/html/math_toolkit/anderson_darling.html @@ -4,10 +4,11 @@ The Anderson-Darling Test - + + @@ -190,9 +191,7 @@

of the Anderson-Darling test statistic agrees with Mathematica.

-

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/archetypes.html b/doc/html/math_toolkit/archetypes.html index 6b8083aab2..01a0539917 100644 --- a/doc/html/math_toolkit/archetypes.html +++ b/doc/html/math_toolkit/archetypes.html @@ -4,10 +4,11 @@ Conceptual Archetypes for Reals and Distributions - + + @@ -177,9 +178,7 @@

implemented in there too.)

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/asin.html b/doc/html/math_toolkit/asin.html index f41968c9ff..d24d241600 100644 --- a/doc/html/math_toolkit/asin.html +++ b/doc/html/math_toolkit/asin.html @@ -4,10 +4,11 @@ asin - + + @@ -47,9 +48,7 @@
Formula:

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Formula:

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Formula:

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Formula:

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manual.

-

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+

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and for z0 > 0 the steps are actually divergent.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/barycentric.html b/doc/html/math_toolkit/barycentric.html index 659ded546f..5d443533af 100644 --- a/doc/html/math_toolkit/barycentric.html +++ b/doc/html/math_toolkit/barycentric.html @@ -4,10 +4,11 @@ Barycentric Rational Interpolation - + + @@ -268,9 +269,7 @@

Root was found in 10 iterations. -

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel.html b/doc/html/math_toolkit/bessel.html index bfcd26d3b7..ba429d56ec 100644 --- a/doc/html/math_toolkit/bessel.html +++ b/doc/html/math_toolkit/bessel.html @@ -4,10 +4,11 @@ Bessel Functions - + + @@ -40,9 +41,7 @@ the Bessel Functions -
- - -
+

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recurrence.

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and sph_neumann.

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Alpha.

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two values and fν, the Wronskian yields Iν(x) directly.

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main definition as x → 0.

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Bilinear<double>/8192 13.2 ns -

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the sources. Boost.Build will do this automatically when appropriate.

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ISO Standard

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Found in 3 iterations -

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+

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differentiable, but not three or four times differentiable.

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of data by spline functions. Diss. City, University of London, 1975.

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} // Namespaces -

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Boost C++ LibrariesHomeLibrariesPeopleFAQMore
+
+
+PrevUpHomeNext +
+
+ +

+ + Synopsis +

+
#include <boost/math/statistics/chatterjee_correlation.hpp>
+
+namespace boost::math::statistics {
+
+    C++17:
+    template <typename ExecutionPolicy, typename Container>
+    auto chatterjee_correlation(ExecutionPolicy&& exec, const Container& u, const Container& v);
+
+    C++11:
+    template <typename Container>
+    auto chatterjee_correlation(const Container& u, const Container& v);
+}
+
+

+ + Description +

+

+ The classical correlation coefficients like the Pearson's correlation are useful + primarily for distinguishing when one dataset depends linearly on another. + However, Pearson's correlation coefficient has a known weakness in that when + the dependent variable has an obvious functional relationship with the independent + variable, the value of the correlation coefficient can take on any value. As + Chatterjee says: +

+

+ > Ideally, one would like a coefficient that approaches its maximum value + if and only if one variable looks more and more like a noiseless function of + the other, just as Pearson correlation is close to its maximum value if and + only if one variable is close to being a noiseless linear function of the other. +

+

+ This is the problem Chatterjee's coefficient solves. Let X and Y be random + variables, where Y is not constant, and let (X_i, Y_i) be samples from this + distribution. Rearrange these samples so that X_(0) < X_{(1)} < ... X_{(n-1)} + and create (R(X_{(i)}), R(Y_{(i)})). The Chatterjee correlation is then given + by +

+

+ +

+

+ In the limit of an infinite amount of i.i.d data, the statistic lies in [0, + 1]. However, if the data is not infinite, the statistic may be negative. If + X and Y are independent, the value is zero, and if Y is a measurable function + of X, then the statistic is unity. The complexity is O(n log n). +

+

+ An example is given below: +

+
std::vector<double> X{1,2,3,4,5};
+std::vector<double> Y{1,2,3,4,5};
+using boost::math::statistics::chatterjee_correlation;
+double coeff = chatterjee_correlation(X, Y);
+
+

+ The implementation follows Chatterjee's + paper. +

+

+ Nota bene: If the input is an integer type the output + will be a double precision type. +

+

+ + Invariants +

+

+ The function expects at least two samples, a non-constant vector Y, and the + same number of X's as Y's. If Y is constant, the result is a quiet NaN. The + data set must be sorted by X values. If there are ties in the values of X, + then the statistic is random due to the random breaking of ties. Of course, + random numbers are not used internally, but the result is not guaranteed to + be identical on different systems. +

+

+ + References +

+
  • + Chatterjee, Sourav. "A new coefficient of correlation." Journal + of the American Statistical Association 116.536 (2021): 2009-2022. +
+
+ +
+
+PrevUpHomeNext +
+ + diff --git a/doc/html/math_toolkit/comp_compilers.html b/doc/html/math_toolkit/comp_compilers.html index e33a1aa759..703c20936a 100644 --- a/doc/html/math_toolkit/comp_compilers.html +++ b/doc/html/math_toolkit/comp_compilers.html @@ -4,10 +4,11 @@ Comparing Different Compilers - + + @@ -3192,9 +3193,7 @@
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- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/comparisons.html b/doc/html/math_toolkit/comparisons.html index 9f52bfddc4..403cf326e7 100644 --- a/doc/html/math_toolkit/comparisons.html +++ b/doc/html/math_toolkit/comparisons.html @@ -4,10 +4,11 @@ Comparisons to Other Open Source Libraries - + + @@ -4718,9 +4719,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/compilers_overview.html b/doc/html/math_toolkit/compilers_overview.html index 92984b75b1..72a0a507fa 100644 --- a/doc/html/math_toolkit/compilers_overview.html +++ b/doc/html/math_toolkit/compilers_overview.html @@ -4,10 +4,11 @@ Compilers - + + @@ -664,9 +665,7 @@ acceptable or not.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/complex_history.html b/doc/html/math_toolkit/complex_history.html index a8a2a30c82..c2518faa2a 100644 --- a/doc/html/math_toolkit/complex_history.html +++ b/doc/html/math_toolkit/complex_history.html @@ -4,10 +4,11 @@ History - + + @@ -35,9 +36,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/complex_implementation.html b/doc/html/math_toolkit/complex_implementation.html index 98ee347fff..b5573b7d17 100644 --- a/doc/html/math_toolkit/complex_implementation.html +++ b/doc/html/math_toolkit/complex_implementation.html @@ -4,10 +4,11 @@ Implementation and Accuracy - + + @@ -44,9 +45,7 @@ paper for more information on the implementation methodology.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cond.html b/doc/html/math_toolkit/cond.html index 8b3a9fd1a7..95329b7ff9 100644 --- a/doc/html/math_toolkit/cond.html +++ b/doc/html/math_toolkit/cond.html @@ -4,10 +4,11 @@ Condition Numbers - + + @@ -166,9 +167,7 @@

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/config_macros.html b/doc/html/math_toolkit/config_macros.html index 4a3bb6cd47..7681b650c5 100644 --- a/doc/html/math_toolkit/config_macros.html +++ b/doc/html/math_toolkit/config_macros.html @@ -4,10 +4,11 @@ Configuration Macros - + + @@ -364,9 +365,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/constants.html b/doc/html/math_toolkit/constants.html index be6e72dfa4..e3b72df283 100644 --- a/doc/html/math_toolkit/constants.html +++ b/doc/html/math_toolkit/constants.html @@ -4,10 +4,11 @@ The Mathematical Constants - + + @@ -1755,9 +1756,7 @@

- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/constants_faq.html b/doc/html/math_toolkit/constants_faq.html index ac9f30e609..2ef4467247 100644 --- a/doc/html/math_toolkit/constants_faq.html +++ b/doc/html/math_toolkit/constants_faq.html @@ -4,10 +4,11 @@ Math Constants FAQs - + + @@ -451,9 +452,7 @@
Some physical constants may be available in Boost.Units.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/constants_intro.html b/doc/html/math_toolkit/constants_intro.html index 8a41a50a55..ee4060f28d 100644 --- a/doc/html/math_toolkit/constants_intro.html +++ b/doc/html/math_toolkit/constants_intro.html @@ -4,10 +4,11 @@ Introduction - + + @@ -120,9 +121,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/contact.html b/doc/html/math_toolkit/contact.html index e5f03273a5..31abd5e876 100644 --- a/doc/html/math_toolkit/contact.html +++ b/doc/html/math_toolkit/contact.html @@ -4,10 +4,11 @@ Contact Info and Support - + + @@ -54,9 +55,7 @@ at - hetp.u-net.com.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/conventions.html b/doc/html/math_toolkit/conventions.html index 294692313e..fd89586f00 100644 --- a/doc/html/math_toolkit/conventions.html +++ b/doc/html/math_toolkit/conventions.html @@ -4,10 +4,11 @@ Document Conventions - + + @@ -27,7 +28,7 @@ Document Conventions

- +

This documentation aims to use of the following naming and formatting conventions. @@ -68,9 +69,7 @@ -

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/create.html b/doc/html/math_toolkit/create.html index 3090c4e169..6a951137fb 100644 --- a/doc/html/math_toolkit/create.html +++ b/doc/html/math_toolkit/create.html @@ -4,10 +4,11 @@ Quaternion Creation Functions - + + @@ -102,9 +103,7 @@ test file).

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/credits.html b/doc/html/math_toolkit/credits.html index f33f506436..7070d31aba 100644 --- a/doc/html/math_toolkit/credits.html +++ b/doc/html/math_toolkit/credits.html @@ -4,10 +4,11 @@ Credits and Acknowledgements - + + @@ -189,9 +190,7 @@ in Boost.Math.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cubic_hermite.html b/doc/html/math_toolkit/cubic_hermite.html index ff2bcfeab6..1e4da4d425 100644 --- a/doc/html/math_toolkit/cubic_hermite.html +++ b/doc/html/math_toolkit/cubic_hermite.html @@ -4,10 +4,11 @@ Cubic Hermite interpolation - + + @@ -244,9 +245,7 @@

the problem size gets larger.

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cubic_roots.html b/doc/html/math_toolkit/cubic_roots.html index 38e8ced847..8de9fddc7d 100644 --- a/doc/html/math_toolkit/cubic_roots.html +++ b/doc/html/math_toolkit/cubic_roots.html @@ -4,10 +4,11 @@ Roots of Cubic Polynomials - + + @@ -140,9 +141,7 @@

estimate.

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/daubechies.html b/doc/html/math_toolkit/daubechies.html index 79dae5c61c..d10e5be211 100644 --- a/doc/html/math_toolkit/daubechies.html +++ b/doc/html/math_toolkit/daubechies.html @@ -4,10 +4,11 @@ Daubechies Wavelets and Scaling Functions - + + @@ -183,6 +184,54 @@
The 8 vanishing moment scaling function.

+

+ Boost.Math also provides numerical evaluation of the Fourier transform of these + functions. This is useful in sparse recovery problems where the measurements + are taken in the Fourier basis. The usage is exhibited below: +

+
#include <boost/math/special_functions/fourier_transform_daubechies_scaling.hpp>
+using boost::math::fourier_transform_daubechies_scaling;
+// Evaluate the Fourier transform of the 4-vanishing moment Daubechies scaling function at ω=1.8:
+std::complex<float> hat_phi = fourier_transform_daubechies_scaling<float, 4>(1.8f);
+
+

+ The Fourier transform convention is unitary with the sign of the imaginary + unit being given in Daubechies Ten Lectures. In particular, this means that + fourier_transform_daubechies_scaling<float, + p>(0.0) returns + 1/sqrt(2π). +

+

+ The implementation computes an infinite product of trigonometric polynomials + as can be found from recursive application of the identity 𝓕[φ](ω) = m(ω/2)𝓕[φ](ω/2). + This is neither particularly fast nor accurate, but there appears to be no + literature on this extremely useful topic, and hence the naive method must + suffice. +

+

+ +

+

+ A benchmark can be found in reporting/performance/fourier_transform_daubechies_performance.cpp; the + results on a ~2021 M1 Macbook pro are presented below: +

+

+ Run on (10 X 24.1212 MHz CPU s) CPU Caches: L1 Data 64 KiB (x10) L1 Instruction + 128 KiB (x10) L2 Unified 4096 KiB (x5) Load Average: 1.33, 1.52, 1.62 ----------------------------------------------------------- + Benchmark Time ----------------------------------------------------------- + FourierTransformDaubechiesScaling<double, 1> 70.3 ns FourierTransformDaubechiesScaling<double, + 2> 330 ns FourierTransformDaubechiesScaling<double, 3> 335 ns FourierTransformDaubechiesScaling<double, + 4> 364 ns FourierTransformDaubechiesScaling<double, 5> 386 ns FourierTransformDaubechiesScaling<double, + 6> 436 ns FourierTransformDaubechiesScaling<double, 7> 447 ns FourierTransformDaubechiesScaling<double, + 8> 473 ns FourierTransformDaubechiesScaling<double, 9> 503 ns FourierTransformDaubechiesScaling<double, + 10> 554 ns +

+

+ Due to the low accuracy of this method, float + precision is arg-promoted to double, + and hence takes just as long as double + precision to execute. +

References @@ -202,9 +251,7 @@

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/daubechies_filters.html b/doc/html/math_toolkit/daubechies_filters.html index 5fe91b2916..9d9db53f09 100644 --- a/doc/html/math_toolkit/daubechies_filters.html +++ b/doc/html/math_toolkit/daubechies_filters.html @@ -4,10 +4,11 @@ Daubechies Filters - + + @@ -179,9 +180,7 @@

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/diff.html b/doc/html/math_toolkit/diff.html index 9114719d4c..4834ca13e6 100644 --- a/doc/html/math_toolkit/diff.html +++ b/doc/html/math_toolkit/diff.html @@ -4,10 +4,11 @@ Numerical Differentiation - + + @@ -346,9 +347,7 @@

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/diff0.html b/doc/html/math_toolkit/diff0.html index f02ab05b66..5981deadd9 100644 --- a/doc/html/math_toolkit/diff0.html +++ b/doc/html/math_toolkit/diff0.html @@ -4,10 +4,11 @@ Lanczos Smoothing Derivatives - + + @@ -230,9 +231,7 @@

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/directories.html b/doc/html/math_toolkit/directories.html index d4910cdcd0..856c9a4f9c 100644 --- a/doc/html/math_toolkit/directories.html +++ b/doc/html/math_toolkit/directories.html @@ -4,10 +4,11 @@ Directory and File Structure - + + @@ -109,9 +110,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_concept.html b/doc/html/math_toolkit/dist_concept.html index 082ba61f67..1afc3dba1d 100644 --- a/doc/html/math_toolkit/dist_concept.html +++ b/doc/html/math_toolkit/dist_concept.html @@ -4,10 +4,11 @@ Conceptual Requirements for Distribution Types - + + @@ -378,9 +379,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref.html b/doc/html/math_toolkit/dist_ref.html index 6cc2dfa208..361c091bdb 100644 --- a/doc/html/math_toolkit/dist_ref.html +++ b/doc/html/math_toolkit/dist_ref.html @@ -4,10 +4,11 @@ Statistical Distributions Reference - + + @@ -94,9 +95,7 @@
Distribution Algorithms
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dist_algorithms.html b/doc/html/math_toolkit/dist_ref/dist_algorithms.html index 70c9c54391..85ffa58e0c 100644 --- a/doc/html/math_toolkit/dist_ref/dist_algorithms.html +++ b/doc/html/math_toolkit/dist_ref/dist_algorithms.html @@ -4,10 +4,11 @@ Distribution Algorithms - + + @@ -117,9 +118,7 @@
of normally distributed weights to meet a specification.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists.html b/doc/html/math_toolkit/dist_ref/dists.html index 97f8c00382..19f1293c05 100644 --- a/doc/html/math_toolkit/dist_ref/dists.html +++ b/doc/html/math_toolkit/dist_ref/dists.html @@ -4,10 +4,11 @@ Distributions - + + @@ -89,9 +90,7 @@
Weibull Distribution
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html b/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html index 1b11642588..e9e5ac39ec 100644 --- a/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html @@ -4,10 +4,11 @@ Arcsine Distribution - + + @@ -628,9 +629,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html b/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html index 463924e7b9..bc96ba061f 100644 --- a/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html @@ -4,10 +4,11 @@ Bernoulli Distribution - + + @@ -348,9 +349,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/beta_dist.html b/doc/html/math_toolkit/dist_ref/dists/beta_dist.html index b1318a5c03..070ab2dfe3 100644 --- a/doc/html/math_toolkit/dist_ref/dists/beta_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/beta_dist.html @@ -4,10 +4,11 @@ Beta Distribution - + + @@ -601,9 +602,7 @@
MathWorld

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html b/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html index 7e4ee26871..ecb7a346bd 100644 --- a/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html @@ -4,10 +4,11 @@ Binomial Distribution - + + @@ -696,7 +697,7 @@

Using the relation:

-
p = I[sub 1-p](n - k, k + 1)
+
p = I[sub 1-p](n - k, k + 1)
   = 1 - I[sub p](k + 1, n - k)
   = ibetac(k + 1, n - k, p)

@@ -885,9 +886,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html b/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html index 0ca26933c4..a34aacd90b 100644 --- a/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html @@ -4,10 +4,11 @@ Cauchy-Lorentz Distribution - + + @@ -291,9 +292,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html b/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html index f7391bf489..1d15177982 100644 --- a/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/chi_squared_dist.html @@ -4,10 +4,11 @@ Chi Squared Distribution - + + @@ -394,9 +395,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/empirical_cdf.html b/doc/html/math_toolkit/dist_ref/dists/empirical_cdf.html index e8ff267e3d..1c13570e92 100644 --- a/doc/html/math_toolkit/dist_ref/dists/empirical_cdf.html +++ b/doc/html/math_toolkit/dist_ref/dists/empirical_cdf.html @@ -4,10 +4,11 @@ Empirical Cumulative Distribution Function - + + @@ -185,9 +186,7 @@
is itself a fairly expensive operation.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/exp_dist.html b/doc/html/math_toolkit/dist_ref/dists/exp_dist.html index bfaa7c65b7..c9b9801ba5 100644 --- a/doc/html/math_toolkit/dist_ref/dists/exp_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/exp_dist.html @@ -4,10 +4,11 @@ Exponential Distribution - + + @@ -305,15 +306,13 @@
Distributions.)

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html b/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html index 261413c36b..721c625aff 100644 --- a/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/extreme_dist.html @@ -4,10 +4,11 @@ Extreme Value Distribution - + + @@ -65,7 +66,7 @@

The relationship of the types of extreme value distributions, of which - this is but one, is discussed by Extreme + this is but one, is discussed by Extreme Value Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah.

@@ -314,9 +315,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/f_dist.html b/doc/html/math_toolkit/dist_ref/dists/f_dist.html index 483643351a..a873909927 100644 --- a/doc/html/math_toolkit/dist_ref/dists/f_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/f_dist.html @@ -4,10 +4,11 @@ F Distribution - + + @@ -418,9 +419,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html b/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html index 28809f24d5..803fc5d1c0 100644 --- a/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/gamma_dist.html @@ -4,10 +4,11 @@ Gamma (and Erlang) Distribution - + + @@ -349,9 +350,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html b/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html index 55d87e4b09..7326c05234 100644 --- a/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/geometric_dist.html @@ -4,10 +4,11 @@ Geometric Distribution - + + @@ -826,9 +827,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html b/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html index edf29cb621..687f2b52f0 100644 --- a/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/hyperexponential_dist.html @@ -4,10 +4,11 @@ Hyperexponential Distribution - + + @@ -1452,9 +1453,7 @@

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html b/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html index 096abe2e9a..778333ea5a 100644 --- a/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/hypergeometric_dist.html @@ -4,10 +4,11 @@ Hypergeometric Distribution - + + @@ -41,11 +42,11 @@ typedefRealTypevalue_type;typedefPolicypolicy_type;// Construct: - hypergeometric_distribution(unsignedr,unsignedn,unsignedN);// r=defective/failures/success, n=trials/draws, N=total population. + hypergeometric_distribution(uint64_tr,uint64_tn,uint64_tN);// r=defective/failures/success, n=trials/draws, N=total population.// Accessors: - unsignedtotal()const; - unsigneddefective()const; - unsignedsample_count()const; + uint64_ttotal()const; + uint64_tdefective()const; + uint64_tsample_count()const;};typedefhypergeometric_distribution<>hypergeometric; @@ -104,25 +105,25 @@
Member Functions
-
hypergeometric_distribution(unsigned r, unsigned n, unsigned N);
+
hypergeometric_distribution(uint64_t r, uint64_t n, uint64_t N);
 

Constructs a hypergeometric distribution with a population of N objects, of which r are defective, and from which n are sampled.

-
unsigned total()const;
+
uint64_t total()const;
 

Returns the total number of objects N.

-
unsigned defective()const;
+
uint64_t defective()const;
 

Returns the number of objects r in population N which are defective.

-
unsigned sample_count()const;
+
uint64_t sample_count()const;
 

Returns the number of objects n which are sampled @@ -158,8 +159,8 @@

range and support.

- The domain of the random variable is the unsigned integers in the range - [max(0, n + r - N), min(n, r)]. A domain_error + The domain of the random variable are the 64-bit unsigned integers in the + range [max(0, n + r - N), min(n, r)]. A domain_error is raised if the random variable is outside this range, or is not an integral value.

@@ -343,9 +344,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html b/doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html index 0faeea9f1b..c11f3ffef1 100644 --- a/doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html @@ -4,10 +4,11 @@ Inverse Chi Squared Distribution - + + @@ -456,9 +457,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html b/doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html index 027d8eb422..aaa37929a6 100644 --- a/doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/inverse_gamma_dist.html @@ -4,10 +4,11 @@ Inverse Gamma Distribution - + + @@ -350,9 +351,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html b/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html index 1d62ee2d9d..5437b52ebb 100644 --- a/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/inverse_gaussian_dist.html @@ -4,10 +4,11 @@ Inverse Gaussian (or Inverse Normal) Distribution - + + @@ -429,9 +430,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/kolmogorov_smirnov_dist.html b/doc/html/math_toolkit/dist_ref/dists/kolmogorov_smirnov_dist.html index e12cd3407d..e7763e2b31 100644 --- a/doc/html/math_toolkit/dist_ref/dists/kolmogorov_smirnov_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/kolmogorov_smirnov_dist.html @@ -4,10 +4,11 @@ Kolmogorov-Smirnov Distribution - + + @@ -333,9 +334,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/laplace_dist.html b/doc/html/math_toolkit/dist_ref/dists/laplace_dist.html index 81f576e639..8516ec0a8f 100644 --- a/doc/html/math_toolkit/dist_ref/dists/laplace_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/laplace_dist.html @@ -4,10 +4,11 @@ Laplace Distribution - + + @@ -343,9 +344,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/logistic_dist.html b/doc/html/math_toolkit/dist_ref/dists/logistic_dist.html index 3d4950e558..1588cd6d89 100644 --- a/doc/html/math_toolkit/dist_ref/dists/logistic_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/logistic_dist.html @@ -4,10 +4,11 @@ Logistic Distribution - + + @@ -280,9 +281,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html b/doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html index 965b79392a..acf05886d6 100644 --- a/doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/lognormal_dist.html @@ -4,10 +4,11 @@ Log Normal Distribution - + + @@ -314,9 +315,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html b/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html index 83b04ff565..4de21e8980 100644 --- a/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/nc_beta_dist.html @@ -4,10 +4,11 @@ Noncentral Beta Distribution - + + @@ -476,9 +477,7 @@
warranted).

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html b/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html index 234b860b4f..3ed83da0e5 100644 --- a/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/nc_chi_squared_dist.html @@ -4,10 +4,11 @@ Noncentral Chi-Squared Distribution - + + @@ -561,9 +562,7 @@
141 (2003) 3-12.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html b/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html index df8b452325..df0d0c664a 100644 --- a/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html @@ -4,10 +4,11 @@ Noncentral F Distribution - + + @@ -401,9 +402,7 @@
141 (2003) 3-12.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html b/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html index 1bff26bef1..44b4b862a0 100644 --- a/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html @@ -4,10 +4,11 @@ Noncentral T Distribution - + + @@ -557,9 +558,7 @@
141 (2003) 3-12.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html b/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html index ad48034c92..5f586c3623 100644 --- a/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/negative_binomial_dist.html @@ -4,10 +4,11 @@ Negative Binomial Distribution - + + @@ -867,9 +868,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/normal_dist.html b/doc/html/math_toolkit/dist_ref/dists/normal_dist.html index 55664eee25..6cb6a3c9ec 100644 --- a/doc/html/math_toolkit/dist_ref/dists/normal_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/normal_dist.html @@ -4,10 +4,11 @@ Normal (Gaussian) Distribution - + + @@ -310,9 +311,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/pareto.html b/doc/html/math_toolkit/dist_ref/dists/pareto.html index be5d2ca31d..943f0790ee 100644 --- a/doc/html/math_toolkit/dist_ref/dists/pareto.html +++ b/doc/html/math_toolkit/dist_ref/dists/pareto.html @@ -4,10 +4,11 @@ Pareto Distribution - + + @@ -333,9 +334,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/poisson_dist.html b/doc/html/math_toolkit/dist_ref/dists/poisson_dist.html index 93c91b1805..bbed802bdc 100644 --- a/doc/html/math_toolkit/dist_ref/dists/poisson_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/poisson_dist.html @@ -4,10 +4,11 @@ Poisson Distribution - + + @@ -313,9 +314,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/rayleigh.html b/doc/html/math_toolkit/dist_ref/dists/rayleigh.html index c216a24805..cbd8b887cf 100644 --- a/doc/html/math_toolkit/dist_ref/dists/rayleigh.html +++ b/doc/html/math_toolkit/dist_ref/dists/rayleigh.html @@ -4,10 +4,11 @@ Rayleigh Distribution - + + @@ -331,9 +332,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/skew_normal_dist.html b/doc/html/math_toolkit/dist_ref/dists/skew_normal_dist.html index 3f807e2400..dbdebadfde 100644 --- a/doc/html/math_toolkit/dist_ref/dists/skew_normal_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/skew_normal_dist.html @@ -4,10 +4,11 @@ Skew Normal Distribution - + + @@ -505,9 +506,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/students_t_dist.html b/doc/html/math_toolkit/dist_ref/dists/students_t_dist.html index af1b79b6a7..68024ac33d 100644 --- a/doc/html/math_toolkit/dist_ref/dists/students_t_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/students_t_dist.html @@ -4,10 +4,11 @@ Students t Distribution - + + @@ -425,9 +426,7 @@
also https://svn.boost.org/trac/boost/ticket/7177.)

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/triangular_dist.html b/doc/html/math_toolkit/dist_ref/dists/triangular_dist.html index 8c9da8079a..c0a44ae2e7 100644 --- a/doc/html/math_toolkit/dist_ref/dists/triangular_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/triangular_dist.html @@ -4,10 +4,11 @@ Triangular Distribution - + + @@ -64,9 +65,8 @@ vaguely known, but, like the uniform distribution, upper and limits are 'known', but a 'best guess', the mode or center point, is also added. It has been recommended as a - proxy - for the beta distribution. The distribution is used in business - decision making and project planning. + proxy for the beta distribution. + The distribution is used in business decision making and project planning.

The triangular @@ -426,9 +426,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/uniform_dist.html b/doc/html/math_toolkit/dist_ref/dists/uniform_dist.html index c53383617b..fc94bafa2a 100644 --- a/doc/html/math_toolkit/dist_ref/dists/uniform_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/uniform_dist.html @@ -4,10 +4,11 @@ Uniform Distribution - + + @@ -348,9 +349,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/dists/weibull_dist.html b/doc/html/math_toolkit/dist_ref/dists/weibull_dist.html index f94d0800bb..6852e6850d 100644 --- a/doc/html/math_toolkit/dist_ref/dists/weibull_dist.html +++ b/doc/html/math_toolkit/dist_ref/dists/weibull_dist.html @@ -4,10 +4,11 @@ Weibull Distribution - + + @@ -108,7 +109,7 @@
distribution. When α = 1, the Weibull distribution reduces to the exponential distribution. The relationship of the types of extreme value distributions, - of which the Weibull is but one, is discussed by Extreme + of which the Weibull is but one, is discussed by Extreme Value Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah.

@@ -355,9 +356,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/dist_ref/nmp.html b/doc/html/math_toolkit/dist_ref/nmp.html index 8917309640..b657f5fcf5 100644 --- a/doc/html/math_toolkit/dist_ref/nmp.html +++ b/doc/html/math_toolkit/dist_ref/nmp.html @@ -4,10 +4,11 @@ Non-Member Properties - + + @@ -714,9 +715,7 @@
the entropy of continuous probability distributions for more information.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential.html b/doc/html/math_toolkit/double_exponential.html index b3bb681eed..0267217e47 100644 --- a/doc/html/math_toolkit/double_exponential.html +++ b/doc/html/math_toolkit/double_exponential.html @@ -4,10 +4,11 @@ Double-exponential quadrature - + + @@ -42,9 +43,7 @@
References
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_caveats.html b/doc/html/math_toolkit/double_exponential/de_caveats.html index 7f60788900..3f94494092 100644 --- a/doc/html/math_toolkit/double_exponential/de_caveats.html +++ b/doc/html/math_toolkit/double_exponential/de_caveats.html @@ -4,10 +4,11 @@ Caveats - + + @@ -169,9 +170,7 @@ classes.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_exp_sinh.html b/doc/html/math_toolkit/double_exponential/de_exp_sinh.html index de457bb333..bb4e89c84e 100644 --- a/doc/html/math_toolkit/double_exponential/de_exp_sinh.html +++ b/doc/html/math_toolkit/double_exponential/de_exp_sinh.html @@ -4,10 +4,11 @@ exp_sinh - + + @@ -99,9 +100,7 @@ as the result (a NaN).

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_levels.html b/doc/html/math_toolkit/double_exponential/de_levels.html index 0c34b057f3..b7c7a75900 100644 --- a/doc/html/math_toolkit/double_exponential/de_levels.html +++ b/doc/html/math_toolkit/double_exponential/de_levels.html @@ -4,10 +4,11 @@ Setting the Maximum Interval Halvings and Memory Requirements - + + @@ -60,9 +61,7 @@ can quickly grow out of control.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_overview.html b/doc/html/math_toolkit/double_exponential/de_overview.html index 241ac8df55..deab5bc415 100644 --- a/doc/html/math_toolkit/double_exponential/de_overview.html +++ b/doc/html/math_toolkit/double_exponential/de_overview.html @@ -4,10 +4,11 @@ Overview - + + @@ -213,9 +214,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_refes.html b/doc/html/math_toolkit/double_exponential/de_refes.html index fc1b431147..154ea5068a 100644 --- a/doc/html/math_toolkit/double_exponential/de_refes.html +++ b/doc/html/math_toolkit/double_exponential/de_refes.html @@ -4,10 +4,11 @@ References - + + @@ -48,9 +49,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_sinh_sinh.html b/doc/html/math_toolkit/double_exponential/de_sinh_sinh.html index 932ec739d1..a8a417380a 100644 --- a/doc/html/math_toolkit/double_exponential/de_sinh_sinh.html +++ b/doc/html/math_toolkit/double_exponential/de_sinh_sinh.html @@ -4,10 +4,11 @@ sinh_sinh - + + @@ -77,9 +78,7 @@ } -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_tanh_sinh.html b/doc/html/math_toolkit/double_exponential/de_tanh_sinh.html index 6dfd850862..1a69e60fdf 100644 --- a/doc/html/math_toolkit/double_exponential/de_tanh_sinh.html +++ b/doc/html/math_toolkit/double_exponential/de_tanh_sinh.html @@ -4,10 +4,11 @@ tanh_sinh - + + @@ -522,9 +523,7 @@
} -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_tanh_sinh_2_arg.html b/doc/html/math_toolkit/double_exponential/de_tanh_sinh_2_arg.html index f5afef0cde..aaba47eca6 100644 --- a/doc/html/math_toolkit/double_exponential/de_tanh_sinh_2_arg.html +++ b/doc/html/math_toolkit/double_exponential/de_tanh_sinh_2_arg.html @@ -4,10 +4,11 @@ Handling functions with large features near an endpoint with tanh-sinh quadrature - + + @@ -84,9 +85,7 @@ to the result faster as well.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_thread.html b/doc/html/math_toolkit/double_exponential/de_thread.html index 772e20e929..1bc0a9a82b 100644 --- a/doc/html/math_toolkit/double_exponential/de_thread.html +++ b/doc/html/math_toolkit/double_exponential/de_thread.html @@ -4,10 +4,11 @@ Thread Safety - + + @@ -47,9 +48,7 @@ and means that integrators for these types are relatively cheap to construct.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/double_exponential/de_tol.html b/doc/html/math_toolkit/double_exponential/de_tol.html index 66d19b1b8c..63ba20b152 100644 --- a/doc/html/math_toolkit/double_exponential/de_tol.html +++ b/doc/html/math_toolkit/double_exponential/de_tol.html @@ -4,10 +4,11 @@ Setting the Termination Condition for Integration - + + @@ -57,9 +58,7 @@ scheme.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint.html b/doc/html/math_toolkit/ellint.html index 6a43e16b7a..a44239f1da 100644 --- a/doc/html/math_toolkit/ellint.html +++ b/doc/html/math_toolkit/ellint.html @@ -4,10 +4,11 @@ Elliptic Integrals - + + @@ -42,9 +43,7 @@
Heuman Lambda Function
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint/ellint_1.html b/doc/html/math_toolkit/ellint/ellint_1.html index 206b27b353..125f29580f 100644 --- a/doc/html/math_toolkit/ellint/ellint_1.html +++ b/doc/html/math_toolkit/ellint/ellint_1.html @@ -4,10 +4,11 @@ Elliptic Integrals of the First Kind - Legendre Form - + + @@ -275,9 +276,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint/ellint_2.html b/doc/html/math_toolkit/ellint/ellint_2.html index 21ee4204be..f405abf1f9 100644 --- a/doc/html/math_toolkit/ellint/ellint_2.html +++ b/doc/html/math_toolkit/ellint/ellint_2.html @@ -4,10 +4,11 @@ Elliptic Integrals of the Second Kind - Legendre Form - + + @@ -304,9 +305,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint/ellint_3.html b/doc/html/math_toolkit/ellint/ellint_3.html index 94d56593a5..0fbd278c50 100644 --- a/doc/html/math_toolkit/ellint/ellint_3.html +++ b/doc/html/math_toolkit/ellint/ellint_3.html @@ -4,10 +4,11 @@ Elliptic Integrals of the Third Kind - Legendre Form - + + @@ -343,9 +344,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint/ellint_carlson.html b/doc/html/math_toolkit/ellint/ellint_carlson.html index 6c7b421e1d..fd1027eb75 100644 --- a/doc/html/math_toolkit/ellint/ellint_carlson.html +++ b/doc/html/math_toolkit/ellint/ellint_carlson.html @@ -4,10 +4,11 @@ Elliptic Integrals - Carlson Form - + + @@ -981,9 +982,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint/ellint_d.html b/doc/html/math_toolkit/ellint/ellint_d.html index 1a9a36e6de..440e0620ec 100644 --- a/doc/html/math_toolkit/ellint/ellint_d.html +++ b/doc/html/math_toolkit/ellint/ellint_d.html @@ -4,10 +4,11 @@ Elliptic Integral D - Legendre Form - + + @@ -362,9 +363,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint/ellint_intro.html b/doc/html/math_toolkit/ellint/ellint_intro.html index 21ae73444e..bb51386e67 100644 --- a/doc/html/math_toolkit/ellint/ellint_intro.html +++ b/doc/html/math_toolkit/ellint/ellint_intro.html @@ -4,10 +4,11 @@ Elliptic Integral Overview - + + @@ -482,9 +483,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint/heuman_lambda.html b/doc/html/math_toolkit/ellint/heuman_lambda.html index 546419f33a..23bc06cb87 100644 --- a/doc/html/math_toolkit/ellint/heuman_lambda.html +++ b/doc/html/math_toolkit/ellint/heuman_lambda.html @@ -4,10 +4,11 @@ Heuman Lambda Function - + + @@ -205,9 +206,7 @@
definition in terms of the Jacobi Zeta is used.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ellint/jacobi_zeta.html b/doc/html/math_toolkit/ellint/jacobi_zeta.html index ec42bd9084..6fe850a2fc 100644 --- a/doc/html/math_toolkit/ellint/jacobi_zeta.html +++ b/doc/html/math_toolkit/ellint/jacobi_zeta.html @@ -4,10 +4,11 @@ Jacobi Zeta Function - + + @@ -260,9 +261,7 @@
is jacobi_zeta_example.cpp.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/error_handling.html b/doc/html/math_toolkit/error_handling.html index 8207071288..66bca356c9 100644 --- a/doc/html/math_toolkit/error_handling.html +++ b/doc/html/math_toolkit/error_handling.html @@ -4,10 +4,11 @@ Error Handling - + + @@ -1103,9 +1104,7 @@

or denormalisation.

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/estrin.html b/doc/html/math_toolkit/estrin.html index 2edc45645b..d3335ec707 100644 --- a/doc/html/math_toolkit/estrin.html +++ b/doc/html/math_toolkit/estrin.html @@ -4,10 +4,11 @@ Estrin's method for polynomial evaluation - + + @@ -84,9 +85,7 @@
(2nd ed.). Birkhäuser. p. 58. ISBN 0-8176-4372-9. -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/exact_typdefs.html b/doc/html/math_toolkit/exact_typdefs.html index 1ef25f2b17..afa1098558 100644 --- a/doc/html/math_toolkit/exact_typdefs.html +++ b/doc/html/math_toolkit/exact_typdefs.html @@ -4,10 +4,11 @@ Exact-Width Floating-Point typedefs - + + @@ -156,9 +157,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/examples.html b/doc/html/math_toolkit/examples.html index 71402a15de..9406fb7e6d 100644 --- a/doc/html/math_toolkit/examples.html +++ b/doc/html/math_toolkit/examples.html @@ -4,10 +4,11 @@ Examples - + + @@ -121,9 +122,7 @@

normal_table<boost::floatmax_t>(); -

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/exp.html b/doc/html/math_toolkit/exp.html index 2a50dbb740..56bd1b36ce 100644 --- a/doc/html/math_toolkit/exp.html +++ b/doc/html/math_toolkit/exp.html @@ -4,10 +4,11 @@ The Quaternionic Exponential - + + @@ -39,9 +40,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/expint.html b/doc/html/math_toolkit/expint.html index af6bb1d1e5..3929fd1e73 100644 --- a/doc/html/math_toolkit/expint.html +++ b/doc/html/math_toolkit/expint.html @@ -4,10 +4,11 @@ Exponential Integrals - + + @@ -31,9 +32,7 @@
Exponential Integral Ei
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/expint/expint_i.html b/doc/html/math_toolkit/expint/expint_i.html index afb5cf1198..3809ad459c 100644 --- a/doc/html/math_toolkit/expint/expint_i.html +++ b/doc/html/math_toolkit/expint/expint_i.html @@ -4,10 +4,11 @@ Exponential Integral Ei - + + @@ -319,9 +320,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/expint/expint_n.html b/doc/html/math_toolkit/expint/expint_n.html index 7d5bb79ae5..2eb75a665f 100644 --- a/doc/html/math_toolkit/expint/expint_n.html +++ b/doc/html/math_toolkit/expint/expint_n.html @@ -4,10 +4,11 @@ Exponential Integral En - + + @@ -271,9 +272,7 @@
is used.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/factorials.html b/doc/html/math_toolkit/factorials.html index ff91a8e370..cf21a2a14c 100644 --- a/doc/html/math_toolkit/factorials.html +++ b/doc/html/math_toolkit/factorials.html @@ -4,10 +4,11 @@ Factorials and Binomial Coefficients - + + @@ -35,9 +36,7 @@
Binomial Coefficients
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/factorials/sf_binomial.html b/doc/html/math_toolkit/factorials/sf_binomial.html index b6fd92486e..bd9520139d 100644 --- a/doc/html/math_toolkit/factorials/sf_binomial.html +++ b/doc/html/math_toolkit/factorials/sf_binomial.html @@ -4,10 +4,11 @@ Binomial Coefficients - + + @@ -127,9 +128,7 @@
n-k))

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/factorials/sf_double_factorial.html b/doc/html/math_toolkit/factorials/sf_double_factorial.html index 3657e24a3a..e5daf15eeb 100644 --- a/doc/html/math_toolkit/factorials/sf_double_factorial.html +++ b/doc/html/math_toolkit/factorials/sf_double_factorial.html @@ -4,10 +4,11 @@ Double Factorial - + + @@ -143,9 +144,7 @@
(2n-1)!! = Γ((2n+1)/2) * 2n / sqrt(pi)

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/factorials/sf_factorial.html b/doc/html/math_toolkit/factorials/sf_factorial.html index e557c627aa..3ad5a89523 100644 --- a/doc/html/math_toolkit/factorials/sf_factorial.html +++ b/doc/html/math_toolkit/factorials/sf_factorial.html @@ -4,10 +4,11 @@ Factorial - + + @@ -178,9 +179,7 @@
larger arguments.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/factorials/sf_falling_factorial.html b/doc/html/math_toolkit/factorials/sf_falling_factorial.html index c11ee4af87..530a204bf2 100644 --- a/doc/html/math_toolkit/factorials/sf_falling_factorial.html +++ b/doc/html/math_toolkit/factorials/sf_falling_factorial.html @@ -4,10 +4,11 @@ Falling Factorial - + + @@ -91,9 +92,7 @@
function.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/factorials/sf_rising_factorial.html b/doc/html/math_toolkit/factorials/sf_rising_factorial.html index 6eb050bc64..e96a7de159 100644 --- a/doc/html/math_toolkit/factorials/sf_rising_factorial.html +++ b/doc/html/math_toolkit/factorials/sf_rising_factorial.html @@ -4,10 +4,11 @@ Rising Factorial - + + @@ -96,9 +97,7 @@
function.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/fastest_typdefs.html b/doc/html/math_toolkit/fastest_typdefs.html index 2c9ef34cca..121262fbbd 100644 --- a/doc/html/math_toolkit/fastest_typdefs.html +++ b/doc/html/math_toolkit/fastest_typdefs.html @@ -4,10 +4,11 @@ Fastest floating-point typedefs - + + @@ -45,9 +46,7 @@ will also be supported, etc.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/float128.html b/doc/html/math_toolkit/float128.html index 9a02d4cfab..698ee654af 100644 --- a/doc/html/math_toolkit/float128.html +++ b/doc/html/math_toolkit/float128.html @@ -4,10 +4,11 @@ Implementation of Float128 type - + + @@ -153,9 +154,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/float128/exp_function.html b/doc/html/math_toolkit/float128/exp_function.html index 56969e456b..39f4afbf55 100644 --- a/doc/html/math_toolkit/float128/exp_function.html +++ b/doc/html/math_toolkit/float128/exp_function.html @@ -4,10 +4,11 @@ Exponential function - + + @@ -53,9 +54,7 @@ .

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/float128/overloading.html b/doc/html/math_toolkit/float128/overloading.html index 6adf16c0af..c538e0662a 100644 --- a/doc/html/math_toolkit/float128/overloading.html +++ b/doc/html/math_toolkit/float128/overloading.html @@ -4,10 +4,11 @@ Overloading template functions with float128_t - + + @@ -78,9 +79,7 @@ that we provide in #include <boost/cstdfloat.hpp>.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/float128/typeinfo.html b/doc/html/math_toolkit/float128/typeinfo.html index 22fbe5ef97..0df6270c50 100644 --- a/doc/html/math_toolkit/float128/typeinfo.html +++ b/doc/html/math_toolkit/float128/typeinfo.html @@ -4,10 +4,11 @@ typeinfo - + + @@ -59,9 +60,7 @@

- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/float128_hints.html b/doc/html/math_toolkit/float128_hints.html index 510574bfe8..07df24e3b6 100644 --- a/doc/html/math_toolkit/float128_hints.html +++ b/doc/html/math_toolkit/float128_hints.html @@ -4,10 +4,11 @@ Hints on using float128 (and __float128) - + + @@ -88,9 +89,7 @@
Some examples of what can go horribly and silently wrong are at float128_example.cpp.

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/float_comparison.html b/doc/html/math_toolkit/float_comparison.html index f4962ef9b4..732f596c4d 100644 --- a/doc/html/math_toolkit/float_comparison.html +++ b/doc/html/math_toolkit/float_comparison.html @@ -4,10 +4,11 @@ Floating-point Comparison - + + @@ -395,9 +396,7 @@
we may need a slightly higher value - some trial and error will be necessary).

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/fourier_integrals.html b/doc/html/math_toolkit/fourier_integrals.html index e5100402ef..d03f6a78bd 100644 --- a/doc/html/math_toolkit/fourier_integrals.html +++ b/doc/html/math_toolkit/fourier_integrals.html @@ -4,10 +4,11 @@ Fourier Integrals - + + @@ -297,9 +298,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/fp_facets.html b/doc/html/math_toolkit/fp_facets.html index 19521c6039..187e2f087b 100644 --- a/doc/html/math_toolkit/fp_facets.html +++ b/doc/html/math_toolkit/fp_facets.html @@ -4,10 +4,11 @@ Facets for Floating-Point Infinities and NaNs - + + @@ -73,9 +74,7 @@
#include <boost\math\special_functions\nonfinite_num_facets.hpp>
 
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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/fp_facets/examples.html b/doc/html/math_toolkit/fp_facets/examples.html index 023e42b9cf..03e6b28f27 100644 --- a/doc/html/math_toolkit/fp_facets/examples.html +++ b/doc/html/math_toolkit/fp_facets/examples.html @@ -4,10 +4,11 @@ Examples - + + @@ -239,9 +240,7 @@
A full demonstration of serialization by Francois Mauger is at ../../example/nonfinite_num_facet_serialization.cpp

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/fp_facets/facets_intro.html b/doc/html/math_toolkit/fp_facets/facets_intro.html index 014ce3b1c5..c7aefcbe85 100644 --- a/doc/html/math_toolkit/fp_facets/facets_intro.html +++ b/doc/html/math_toolkit/fp_facets/facets_intro.html @@ -4,10 +4,11 @@ Introduction - + + @@ -361,9 +362,7 @@

- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/fp_facets/portability.html b/doc/html/math_toolkit/fp_facets/portability.html index bd6ded4e5a..47f2e678cf 100644 --- a/doc/html/math_toolkit/fp_facets/portability.html +++ b/doc/html/math_toolkit/fp_facets/portability.html @@ -4,10 +4,11 @@ Portability - + + @@ -32,9 +33,7 @@ See the portability information for that library.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/fp_facets/rationale.html b/doc/html/math_toolkit/fp_facets/rationale.html index 30b487fea1..a3c6f03601 100644 --- a/doc/html/math_toolkit/fp_facets/rationale.html +++ b/doc/html/math_toolkit/fp_facets/rationale.html @@ -4,10 +4,11 @@ Design Rationale - + + @@ -49,9 +50,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/fp_facets/reference.html b/doc/html/math_toolkit/fp_facets/reference.html index aea7e18b66..0fdaed850b 100644 --- a/doc/html/math_toolkit/fp_facets/reference.html +++ b/doc/html/math_toolkit/fp_facets/reference.html @@ -4,10 +4,11 @@ Reference - + + @@ -472,9 +473,7 @@
positive and negative NaN are trapped instead.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/fpclass.html b/doc/html/math_toolkit/fpclass.html index 28968ac47d..6da5857bcd 100644 --- a/doc/html/math_toolkit/fpclass.html +++ b/doc/html/math_toolkit/fpclass.html @@ -4,10 +4,11 @@ Floating-Point Classification: Infinities and NaNs - + + @@ -233,9 +234,7 @@
infinity and NaNs.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/future.html b/doc/html/math_toolkit/future.html index 8068eb6e14..3167af062d 100644 --- a/doc/html/math_toolkit/future.html +++ b/doc/html/math_toolkit/future.html @@ -4,10 +4,11 @@ Extras/Future Directions - + + @@ -129,9 +130,7 @@
double p = probability(acc); -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/gauss.html b/doc/html/math_toolkit/gauss.html index 70c1442609..65e566141b 100644 --- a/doc/html/math_toolkit/gauss.html +++ b/doc/html/math_toolkit/gauss.html @@ -4,10 +4,11 @@ Gauss-Legendre quadrature - + + @@ -196,9 +197,7 @@

Which yields 0.2106572512258069881080923020669, which is accurate to 5e-28.

-

- - -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/gauss_kronrod.html b/doc/html/math_toolkit/gauss_kronrod.html index fabc54db4c..3b530a9b65 100644 --- a/doc/html/math_toolkit/gauss_kronrod.html +++ b/doc/html/math_toolkit/gauss_kronrod.html @@ -4,10 +4,11 @@ Gauss-Kronrod Quadrature - + + @@ -268,9 +269,7 @@

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/getting_best.html b/doc/html/math_toolkit/getting_best.html index 7af5f354d2..0137a49805 100644 --- a/doc/html/math_toolkit/getting_best.html +++ b/doc/html/math_toolkit/getting_best.html @@ -4,10 +4,11 @@ Getting the Best Performance from this Library: Compiler and Compiler Options - + + @@ -137,9 +138,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/greatest_typdefs.html b/doc/html/math_toolkit/greatest_typdefs.html index 558c6485ce..94416cc450 100644 --- a/doc/html/math_toolkit/greatest_typdefs.html +++ b/doc/html/math_toolkit/greatest_typdefs.html @@ -4,10 +4,11 @@ Greatest-width floating-point typedef - + + @@ -77,9 +78,7 @@ BOOST_FLOAT128_C(123.4567890123456789012345678901234567890)=123.456789012345678901234567890123453 -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hankel.html b/doc/html/math_toolkit/hankel.html index d5eede2313..aa3671e35c 100644 --- a/doc/html/math_toolkit/hankel.html +++ b/doc/html/math_toolkit/hankel.html @@ -4,10 +4,11 @@ Hankel Functions - + + @@ -31,9 +32,7 @@
Spherical Hankel Functions
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hankel/cyl_hankel.html b/doc/html/math_toolkit/hankel/cyl_hankel.html index 9412a8c3f9..515ceab48f 100644 --- a/doc/html/math_toolkit/hankel/cyl_hankel.html +++ b/doc/html/math_toolkit/hankel/cyl_hankel.html @@ -4,10 +4,11 @@ Cyclic Hankel Functions - + + @@ -157,9 +158,7 @@
for integer order are used.

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hankel/sph_hankel.html b/doc/html/math_toolkit/hankel/sph_hankel.html index 4a2a424be4..bac2f410b5 100644 --- a/doc/html/math_toolkit/hankel/sph_hankel.html +++ b/doc/html/math_toolkit/hankel/sph_hankel.html @@ -4,10 +4,11 @@ Spherical Hankel Functions - + + @@ -107,9 +108,7 @@
and cyl_hankel_2.

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/high_precision.html b/doc/html/math_toolkit/high_precision.html index 0a9e1e5e2d..6aabb560eb 100644 --- a/doc/html/math_toolkit/high_precision.html +++ b/doc/html/math_toolkit/high_precision.html @@ -4,10 +4,11 @@ Using Boost.Math with High-Precision Floating-Point Libraries - + + @@ -96,9 +97,7 @@ have been demonstrated.

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/high_precision/e_float.html b/doc/html/math_toolkit/high_precision/e_float.html index e6ddc8d2c4..8859a945c0 100644 --- a/doc/html/math_toolkit/high_precision/e_float.html +++ b/doc/html/math_toolkit/high_precision/e_float.html @@ -4,10 +4,11 @@ Using e_float Library - + + @@ -42,9 +43,7 @@ or cpp_dec_float instead.

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- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/high_precision/float128.html b/doc/html/math_toolkit/high_precision/float128.html index 90db09b199..64c47267aa 100644 --- a/doc/html/math_toolkit/high_precision/float128.html +++ b/doc/html/math_toolkit/high_precision/float128.html @@ -4,10 +4,11 @@ Using with GCC's __float128 datatype - + + @@ -47,9 +48,7 @@ Ultimately these facilities should be provided by GCC and libstdc++.

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/high_precision/use_mpfr.html b/doc/html/math_toolkit/high_precision/use_mpfr.html index 08dc27d9e5..eaf04c05c8 100644 --- a/doc/html/math_toolkit/high_precision/use_mpfr.html +++ b/doc/html/math_toolkit/high_precision/use_mpfr.html @@ -4,10 +4,11 @@ Using With MPFR or GMP - High-Precision Floating-Point Library - + + @@ -90,9 +91,7 @@ and here.

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/high_precision/use_multiprecision.html b/doc/html/math_toolkit/high_precision/use_multiprecision.html index 579a14c081..b12ab97a67 100644 --- a/doc/html/math_toolkit/high_precision/use_multiprecision.html +++ b/doc/html/math_toolkit/high_precision/use_multiprecision.html @@ -4,10 +4,11 @@ Using Boost.Multiprecision - + + @@ -280,9 +281,7 @@
The full source of this example is at fft_sines_table.cpp

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/high_precision/use_ntl.html b/doc/html/math_toolkit/high_precision/use_ntl.html index 205ab33b0c..debdd1694e 100644 --- a/doc/html/math_toolkit/high_precision/use_ntl.html +++ b/doc/html/math_toolkit/high_precision/use_ntl.html @@ -4,10 +4,11 @@ Using NTL Library - + + @@ -55,9 +56,7 @@ There is a concept checking test program for NTL support here.

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/high_precision/using_test.html b/doc/html/math_toolkit/high_precision/using_test.html index 61fa29620c..a0c23bc854 100644 --- a/doc/html/math_toolkit/high_precision/using_test.html +++ b/doc/html/math_toolkit/high_precision/using_test.html @@ -4,10 +4,11 @@ Using without expression templates for Boost.Test and others - + + @@ -125,9 +126,7 @@ A full example code is at test_cpp_float_close_fraction.cpp

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/high_precision/why_high_precision.html b/doc/html/math_toolkit/high_precision/why_high_precision.html index 4d73a8faec..6aea5032ff 100644 --- a/doc/html/math_toolkit/high_precision/why_high_precision.html +++ b/doc/html/math_toolkit/high_precision/why_high_precision.html @@ -4,10 +4,11 @@ Why use a high-precision library rather than built-in floating-point types? - + + @@ -121,9 +122,7 @@ (almost always) correctly rounded values.

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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hints.html b/doc/html/math_toolkit/hints.html index defc878cd1..933b3e209e 100644 --- a/doc/html/math_toolkit/hints.html +++ b/doc/html/math_toolkit/hints.html @@ -4,10 +4,11 @@ Other Hints and tips - + + @@ -116,9 +117,7 @@

- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/history1.html b/doc/html/math_toolkit/history1.html index 98fb5757d4..4dfdd6e260 100644 --- a/doc/html/math_toolkit/history1.html +++ b/doc/html/math_toolkit/history1.html @@ -4,10 +4,11 @@ History and What's New - + + @@ -38,6 +39,53 @@

+ Math-4.1.1 + (Boost-1.84) +
+
    +
  • + Improve ccmath error detection. +
  • +
  • + Remove use of deprecated std::numeric_limits<>::has_denorm, see + 1028. +
  • +
  • + Correct non-convergence bug in non-central-t distribution, see 1035. +
  • +
  • + Adjust Bessel function approximation to 1F1 to avoid taking tgamma at a + negative integer, see 1034. +
  • +
  • + Avoid spurious overflow and divide by zero in ibeta, see 1006. +
  • +
  • + Improve accuracy when using Sterling's approximation to tgamma, completes + work started in 1007. +
  • +
  • + Fix inverse_discrete_quantile for large initial guesses, see 1007. +
  • +
  • + Improve Newton root finding, see 1000. +
  • +
  • + Fix median_absolute_deviation for non-zero centre, see 997. +
  • +
  • + Fix up cstdfloat.hpp for gcc-14. +
  • +
  • + Update to work for the new types declared in <stdfloat>. +
  • +
  • + Change hypergeometric_distribution to use 64 rather than 32 bit integers + to avoid unnecessary overflow and restrictions on use. +
  • +
+
+ Math-4.1.0 (Boost-1.82)
@@ -115,7 +163,7 @@
- + Math-4.0.0 (Boost-1.81)
@@ -179,7 +227,7 @@
- + Math-3.4.0 (Boost-1.80)
@@ -207,7 +255,7 @@
- + Math-3.3.0 (Boost-1.79)
@@ -249,7 +297,7 @@
- + Math-3.2.0 (Boost-1.78)
@@ -286,7 +334,7 @@
- + Math-3.1.0 (Boost-1.77)
@@ -322,7 +370,7 @@
- + Math-3.0.0 (Boost-1.76)
@@ -373,7 +421,7 @@
- + Math-2.13.0 (Boost-1.75)
@@ -424,7 +472,7 @@
- + Math-2.12.0 (Boost-1.73)
@@ -466,7 +514,7 @@
- + Math-2.11.0 (Boost-1.72)
@@ -528,7 +576,7 @@
- + Math-2.10.0 (Boost-1.71)
@@ -562,7 +610,7 @@
- + Math-2.9.0 (Boost-1.70)
@@ -616,7 +664,7 @@
- + Math-2.8.0 (Boost-1.69)
@@ -673,7 +721,7 @@
- + Math-2.7.1 (Boost-1.68)
@@ -687,7 +735,7 @@
- + Math-2.7.0 (Boost-1.66)
@@ -704,7 +752,7 @@
- + Math-2.6.0 (Boost-1.65)
@@ -741,7 +789,7 @@
- + Math-2.5.2 (Boost-1.64)
@@ -758,7 +806,7 @@
- + Math-2.5.1 (Boost-1.63)
@@ -774,7 +822,7 @@
- + Math-2.5.0 (Boost-1.62)
@@ -799,7 +847,7 @@
- + Math-2.4.0 (Boost-1.61)
@@ -810,7 +858,7 @@
Polynomial arithmetic added to tools.
- + Math-2.3.0 (Boost-1.60)
@@ -889,7 +937,7 @@
- + Math-2.2.1

@@ -908,7 +956,7 @@

- + Math-2.2.0 (boost-1.58.0)
@@ -952,7 +1000,7 @@
- + Math-2.1.0 (boost-1.57.0)
@@ -978,7 +1026,7 @@
- + Math-2.0.0 (Boost-1.56.0)
@@ -1029,7 +1077,7 @@
- + Math-1.9.1
    @@ -1044,7 +1092,7 @@
- + Math-1.9.0
    @@ -1111,7 +1159,7 @@
- + Boost-1.55
    @@ -1170,7 +1218,7 @@
    and Accurate Parallel Inversion of the Gamma Distribution, Thomas Luu

    - + Boost-1.54
    @@ -1224,7 +1272,7 @@
- + Boost-1.53
    @@ -1259,7 +1307,7 @@
- + Boost-1.52
    @@ -1306,14 +1354,14 @@
- + Boost-1.51

See Boost-1.52 - some items were added but not listed in time for the release.

- + Boost-1.50
    @@ -1350,7 +1398,7 @@
- + Boost-1.49
    @@ -1394,7 +1442,7 @@
- + Boost-1.48
    @@ -1445,7 +1493,7 @@
- + Boost-1.47
    @@ -1462,7 +1510,7 @@
- + Boost-1.46.1
  • @@ -1470,7 +1518,7 @@
    #5113.
- + Boost-1.46.0
    @@ -1485,7 +1533,7 @@
- + Boost-1.45.0
    @@ -1502,7 +1550,7 @@
- + Boost-1.44.0
    @@ -1516,7 +1564,7 @@
- + Boost-1.41.0
  • @@ -1524,7 +1572,7 @@
    its inverse.
- + Boost-1.40.0
    @@ -1560,7 +1608,7 @@
- + Boost-1.38.0
    @@ -1572,14 +1620,14 @@
- + Boost-1.37.0
  • Improved accuracy and testing of the inverse hypergeometric functions.
- + Boost-1.36.0
    @@ -1612,7 +1660,7 @@
- + Boost-1.35.0: Post Review First Official Release
@@ -1644,7 +1692,7 @@
- + Milestone 4: Second Review Candidate (1st March 2007)
@@ -1658,7 +1706,7 @@
- + Milestone 3: First Review Candidate (31st Dec 2006)
@@ -1686,7 +1734,7 @@
- + Milestone 2: Released September 10th 2006
@@ -1722,7 +1770,7 @@
- + Milestone 1: Released March 31st 2006
@@ -1754,9 +1802,7 @@
Sandbox and trunk last synchonised at revision: .

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/history2.html b/doc/html/math_toolkit/history2.html index 290b0a4fee..de14e35d09 100644 --- a/doc/html/math_toolkit/history2.html +++ b/doc/html/math_toolkit/history2.html @@ -4,10 +4,11 @@ History and What's New - + + @@ -38,6 +39,53 @@

+ Math-4.1.1 + (Boost-1.84) +
+
    +
  • + Improve ccmath error detection. +
  • +
  • + Remove use of deprecated std::numeric_limits<>::has_denorm, see + 1028. +
  • +
  • + Correct non-convergence bug in non-central-t distribution, see 1035. +
  • +
  • + Adjust Bessel function approximation to 1F1 to avoid taking tgamma at a + negative integer, see 1034. +
  • +
  • + Avoid spurious overflow and divide by zero in ibeta, see 1006. +
  • +
  • + Improve accuracy when using Sterling's approximation to tgamma, completes + work started in 1007. +
  • +
  • + Fix inverse_discrete_quantile for large initial guesses, see 1007. +
  • +
  • + Improve Newton root finding, see 1000. +
  • +
  • + Fix median_absolute_deviation for non-zero centre, see 997. +
  • +
  • + Fix up cstdfloat.hpp for gcc-14. +
  • +
  • + Update to work for the new types declared in <stdfloat>. +
  • +
  • + Change hypergeometric_distribution to use 64 rather than 32 bit integers + to avoid unnecessary overflow and restrictions on use. +
  • +
+
+ Math-4.1.0 (Boost-1.82)
@@ -115,7 +163,7 @@
- + Math-4.0.0 (Boost-1.81)
@@ -179,7 +227,7 @@
- + Math-3.4.0 (Boost-1.80)
@@ -207,7 +255,7 @@
- + Math-3.3.0 (Boost-1.79)
@@ -249,7 +297,7 @@
- + Math-3.2.0 (Boost-1.78)
@@ -286,7 +334,7 @@
- + Math-3.1.0 (Boost-1.77)
@@ -322,7 +370,7 @@
- + Math-3.0.0 (Boost-1.76)
@@ -373,7 +421,7 @@
- + Math-2.13.0 (Boost-1.75)
@@ -424,7 +472,7 @@
- + Math-2.12.0 (Boost-1.73)
@@ -466,7 +514,7 @@
- + Math-2.11.0 (Boost-1.72)
@@ -528,7 +576,7 @@
- + Math-2.10.0 (Boost-1.71)
@@ -562,7 +610,7 @@
- + Math-2.9.0 (Boost-1.70)
@@ -616,7 +664,7 @@
- + Math-2.8.0 (Boost-1.69)
@@ -673,7 +721,7 @@
- + Math-2.7.1 (Boost-1.68)
@@ -687,7 +735,7 @@
- + Math-2.7.0 (Boost-1.66)
@@ -704,7 +752,7 @@
- + Math-2.6.0 (Boost-1.65)
@@ -741,7 +789,7 @@
- + Math-2.5.2 (Boost-1.64)
@@ -758,7 +806,7 @@
- + Math-2.5.1 (Boost-1.63)
@@ -774,7 +822,7 @@
- + Math-2.5.0 (Boost-1.62)
@@ -799,7 +847,7 @@
- + Math-2.4.0 (Boost-1.61)
@@ -810,7 +858,7 @@
Polynomial arithmetic added to tools.
- + Math-2.3.0 (Boost-1.60)
@@ -889,7 +937,7 @@
- + Math-2.2.1

@@ -908,7 +956,7 @@

- + Math-2.2.0 (boost-1.58.0)
@@ -952,7 +1000,7 @@
- + Math-2.1.0 (boost-1.57.0)
@@ -978,7 +1026,7 @@
- + Math-2.0.0 (Boost-1.56.0)
@@ -1029,7 +1077,7 @@
- + Math-1.9.1
    @@ -1044,7 +1092,7 @@
- + Math-1.9.0
    @@ -1111,7 +1159,7 @@
- + Boost-1.55
    @@ -1170,7 +1218,7 @@
    and Accurate Parallel Inversion of the Gamma Distribution, Thomas Luu

    - + Boost-1.54
    @@ -1224,7 +1272,7 @@
- + Boost-1.53
    @@ -1259,7 +1307,7 @@
- + Boost-1.52
    @@ -1306,14 +1354,14 @@
- + Boost-1.51

See Boost-1.52 - some items were added but not listed in time for the release.

- + Boost-1.50
    @@ -1350,7 +1398,7 @@
- + Boost-1.49
    @@ -1394,7 +1442,7 @@
- + Boost-1.48
    @@ -1445,7 +1493,7 @@
- + Boost-1.47
    @@ -1462,7 +1510,7 @@
- + Boost-1.46.1
  • @@ -1470,7 +1518,7 @@
    #5113.
- + Boost-1.46.0
    @@ -1485,7 +1533,7 @@
- + Boost-1.45.0
    @@ -1502,7 +1550,7 @@
- + Boost-1.44.0
    @@ -1516,7 +1564,7 @@
- + Boost-1.41.0
  • @@ -1524,7 +1572,7 @@
    its inverse.
- + Boost-1.40.0
    @@ -1560,7 +1608,7 @@
- + Boost-1.38.0
    @@ -1572,14 +1620,14 @@
- + Boost-1.37.0
  • Improved accuracy and testing of the inverse hypergeometric functions.
- + Boost-1.36.0
    @@ -1612,7 +1660,7 @@
- + Boost-1.35.0: Post Review First Official Release
@@ -1644,7 +1692,7 @@
- + Milestone 4: Second Review Candidate (1st March 2007)
@@ -1658,7 +1706,7 @@
- + Milestone 3: First Review Candidate (31st Dec 2006)
@@ -1686,7 +1734,7 @@
- + Milestone 2: Released September 10th 2006
@@ -1722,7 +1770,7 @@
- + Milestone 1: Released March 31st 2006
@@ -1754,9 +1802,7 @@
Sandbox and trunk last synchonised at revision: .

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hypergeometric.html b/doc/html/math_toolkit/hypergeometric.html index a00a07a330..f2b82cef28 100644 --- a/doc/html/math_toolkit/hypergeometric.html +++ b/doc/html/math_toolkit/hypergeometric.html @@ -4,10 +4,11 @@ Hypergeometric Functions - + + @@ -41,9 +42,7 @@ References -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hypergeometric/hypergeometric_0f1.html b/doc/html/math_toolkit/hypergeometric/hypergeometric_0f1.html index 896e86e06b..cfbb85f1e3 100644 --- a/doc/html/math_toolkit/hypergeometric/hypergeometric_0f1.html +++ b/doc/html/math_toolkit/hypergeometric/hypergeometric_0f1.html @@ -4,10 +4,11 @@ Hypergeometric 0F1 - + + @@ -93,9 +94,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hypergeometric/hypergeometric_1f0.html b/doc/html/math_toolkit/hypergeometric/hypergeometric_1f0.html index d3359ab2b4..8ce4389812 100644 --- a/doc/html/math_toolkit/hypergeometric/hypergeometric_1f0.html +++ b/doc/html/math_toolkit/hypergeometric/hypergeometric_1f0.html @@ -4,10 +4,11 @@ Hypergeometric 1F0 - + + @@ -81,9 +82,7 @@
1F0(a, z) = (1-z)-a

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hypergeometric/hypergeometric_1f1.html b/doc/html/math_toolkit/hypergeometric/hypergeometric_1f1.html index d4c3df9b9a..dfd2a36608 100644 --- a/doc/html/math_toolkit/hypergeometric/hypergeometric_1f1.html +++ b/doc/html/math_toolkit/hypergeometric/hypergeometric_1f1.html @@ -4,10 +4,11 @@ Hypergeometric 1F1 - + + @@ -772,9 +773,7 @@
if more than half the digits are destroyed by cancellation.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hypergeometric/hypergeometric_2f0.html b/doc/html/math_toolkit/hypergeometric/hypergeometric_2f0.html index a9001e984c..31b2540b3f 100644 --- a/doc/html/math_toolkit/hypergeometric/hypergeometric_2f0.html +++ b/doc/html/math_toolkit/hypergeometric/hypergeometric_2f0.html @@ -4,10 +4,11 @@ Hypergeometric 2F0 - + + @@ -102,9 +103,7 @@
Otherwise we use the defining series.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hypergeometric/hypergeometric_pfq.html b/doc/html/math_toolkit/hypergeometric/hypergeometric_pfq.html index 3181281415..fbb7193728 100644 --- a/doc/html/math_toolkit/hypergeometric/hypergeometric_pfq.html +++ b/doc/html/math_toolkit/hypergeometric/hypergeometric_pfq.html @@ -4,10 +4,11 @@ Hypergeometric pFq - + + @@ -139,9 +140,7 @@
via logarithms.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/hypergeometric/hypergeometric_refs.html b/doc/html/math_toolkit/hypergeometric/hypergeometric_refs.html index 6b4b09598e..51d697e7e6 100644 --- a/doc/html/math_toolkit/hypergeometric/hypergeometric_refs.html +++ b/doc/html/math_toolkit/hypergeometric/hypergeometric_refs.html @@ -4,10 +4,11 @@ Hypergeometric References - + + @@ -91,9 +92,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals.html b/doc/html/math_toolkit/internals.html index 07b265fc23..4e2a0856af 100644 --- a/doc/html/math_toolkit/internals.html +++ b/doc/html/math_toolkit/internals.html @@ -4,10 +4,11 @@ Internal tools - + + @@ -49,9 +50,7 @@
Color Maps
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/agm.html b/doc/html/math_toolkit/internals/agm.html index b9c89bd6d7..9637275360 100644 --- a/doc/html/math_toolkit/internals/agm.html +++ b/doc/html/math_toolkit/internals/agm.html @@ -4,10 +4,11 @@ Arithmetic-Geometric Mean - + + @@ -116,9 +117,7 @@
2003. -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/centered_continued_fraction.html b/doc/html/math_toolkit/internals/centered_continued_fraction.html index 0706f5e6e7..02dbdcbf6b 100644 --- a/doc/html/math_toolkit/internals/centered_continued_fraction.html +++ b/doc/html/math_toolkit/internals/centered_continued_fraction.html @@ -4,10 +4,11 @@ Centered Continued Fractions - + + @@ -87,9 +88,7 @@ respect to its characterization as a centered continued fraction.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/cf.html b/doc/html/math_toolkit/internals/cf.html index 7ef644f0a7..d0c89c2e82 100644 --- a/doc/html/math_toolkit/internals/cf.html +++ b/doc/html/math_toolkit/internals/cf.html @@ -4,10 +4,11 @@ Continued Fraction Evaluation - + + @@ -367,9 +368,7 @@
} -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/cohen_acceleration.html b/doc/html/math_toolkit/internals/cohen_acceleration.html index 5b88a9b053..e504fbc63d 100644 --- a/doc/html/math_toolkit/internals/cohen_acceleration.html +++ b/doc/html/math_toolkit/internals/cohen_acceleration.html @@ -4,10 +4,11 @@ Cohen Acceleration - + + @@ -151,9 +152,7 @@
9.1 (2000): 3-12. -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/color_maps.html b/doc/html/math_toolkit/internals/color_maps.html index be499c5b24..b234275133 100644 --- a/doc/html/math_toolkit/internals/color_maps.html +++ b/doc/html/math_toolkit/internals/color_maps.html @@ -4,10 +4,11 @@ Color Maps - + + @@ -156,9 +157,7 @@
About it . -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/engel_expansion.html b/doc/html/math_toolkit/internals/engel_expansion.html index 738844dd8c..f57df92bfc 100644 --- a/doc/html/math_toolkit/internals/engel_expansion.html +++ b/doc/html/math_toolkit/internals/engel_expansion.html @@ -4,10 +4,11 @@ Engel Expansion - + + @@ -65,9 +66,7 @@ autoengel=engel_expansion<__float128,checked_int1024_t>(pi<__float128>()); -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/error_test.html b/doc/html/math_toolkit/internals/error_test.html index 8ab8f65984..90ff11fcd2 100644 --- a/doc/html/math_toolkit/internals/error_test.html +++ b/doc/html/math_toolkit/internals/error_test.html @@ -4,10 +4,11 @@ Relative Error and Testing - + + @@ -220,9 +221,7 @@
// -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/luroth_expansion.html b/doc/html/math_toolkit/internals/luroth_expansion.html index 8ccaf8cdea..dc92fae641 100644 --- a/doc/html/math_toolkit/internals/luroth_expansion.html +++ b/doc/html/math_toolkit/internals/luroth_expansion.html @@ -4,10 +4,11 @@ Luroth Expansions - + + @@ -97,9 +98,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/minimax.html b/doc/html/math_toolkit/internals/minimax.html index 40b1d9dc35..2b7004ce1c 100644 --- a/doc/html/math_toolkit/internals/minimax.html +++ b/doc/html/math_toolkit/internals/minimax.html @@ -4,10 +4,11 @@ Minimax Approximations and the Remez Algorithm - + + @@ -265,9 +266,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/recurrence.html b/doc/html/math_toolkit/internals/recurrence.html index 9a2160e039..dcd27f0261 100644 --- a/doc/html/math_toolkit/internals/recurrence.html +++ b/doc/html/math_toolkit/internals/recurrence.html @@ -4,10 +4,11 @@ Tools For 3-Term Recurrence Relations - + + @@ -283,9 +284,7 @@
returned successively to Fn-1, Fn-2 etc.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/series_evaluation.html b/doc/html/math_toolkit/internals/series_evaluation.html index 5d345dfdab..9fe60a3542 100644 --- a/doc/html/math_toolkit/internals/series_evaluation.html +++ b/doc/html/math_toolkit/internals/series_evaluation.html @@ -4,10 +4,11 @@ Series Evaluation - + + @@ -234,9 +235,7 @@
examples.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/simple_continued_fraction.html b/doc/html/math_toolkit/internals/simple_continued_fraction.html index 213e766c38..3ce36560d7 100644 --- a/doc/html/math_toolkit/internals/simple_continued_fraction.html +++ b/doc/html/math_toolkit/internals/simple_continued_fraction.html @@ -4,10 +4,11 @@ Simple Continued Fractions - + + @@ -102,9 +103,7 @@ geometric mean is precisely 2.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/test_data.html b/doc/html/math_toolkit/internals/test_data.html index ce368af8fa..2e9229699d 100644 --- a/doc/html/math_toolkit/internals/test_data.html +++ b/doc/html/math_toolkit/internals/test_data.html @@ -4,10 +4,11 @@ Graphing, Profiling, and Generating Test Data for Special Functions - + + @@ -545,9 +546,7 @@
need for the original pseudo-parameter to be included in program output.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals/tuples.html b/doc/html/math_toolkit/internals/tuples.html index 611d066749..712f114782 100644 --- a/doc/html/math_toolkit/internals/tuples.html +++ b/doc/html/math_toolkit/internals/tuples.html @@ -4,10 +4,11 @@ Tuples - + + @@ -66,9 +67,7 @@
portability.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/internals_overview.html b/doc/html/math_toolkit/internals_overview.html index 4be3427097..7e15f059a7 100644 --- a/doc/html/math_toolkit/internals_overview.html +++ b/doc/html/math_toolkit/internals_overview.html @@ -4,10 +4,11 @@ Overview - + + @@ -42,9 +43,7 @@ submissions to this library.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/interp.html b/doc/html/math_toolkit/interp.html index b025267027..fa33d5019c 100644 --- a/doc/html/math_toolkit/interp.html +++ b/doc/html/math_toolkit/interp.html @@ -4,10 +4,11 @@ Interpreting these Results - + + @@ -55,9 +56,7 @@

- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/intro_pol_overview.html b/doc/html/math_toolkit/intro_pol_overview.html index 172d994ff3..bdb428749f 100644 --- a/doc/html/math_toolkit/intro_pol_overview.html +++ b/doc/html/math_toolkit/intro_pol_overview.html @@ -4,10 +4,11 @@ Policies - + + @@ -99,9 +100,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/inv_hyper.html b/doc/html/math_toolkit/inv_hyper.html index 548d02ad61..32b68b3b47 100644 --- a/doc/html/math_toolkit/inv_hyper.html +++ b/doc/html/math_toolkit/inv_hyper.html @@ -4,10 +4,11 @@ Inverse Hyperbolic Functions - + + @@ -34,9 +35,7 @@
atanh
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/inv_hyper/acosh.html b/doc/html/math_toolkit/inv_hyper/acosh.html index 1daa9605f9..da1af1d83a 100644 --- a/doc/html/math_toolkit/inv_hyper/acosh.html +++ b/doc/html/math_toolkit/inv_hyper/acosh.html @@ -4,10 +4,11 @@ acosh - + + @@ -117,9 +118,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/inv_hyper/asinh.html b/doc/html/math_toolkit/inv_hyper/asinh.html index 0cf7d5d5e9..bfc1b4071e 100644 --- a/doc/html/math_toolkit/inv_hyper/asinh.html +++ b/doc/html/math_toolkit/inv_hyper/asinh.html @@ -4,10 +4,11 @@ asinh - + + @@ -112,9 +113,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/inv_hyper/atanh.html b/doc/html/math_toolkit/inv_hyper/atanh.html index 6173d76876..be189fb04e 100644 --- a/doc/html/math_toolkit/inv_hyper/atanh.html +++ b/doc/html/math_toolkit/inv_hyper/atanh.html @@ -4,10 +4,11 @@ atanh - + + @@ -121,9 +122,7 @@
is used.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/inv_hyper/inv_hyper_over.html b/doc/html/math_toolkit/inv_hyper/inv_hyper_over.html index 50848f8d38..e1cc07b261 100644 --- a/doc/html/math_toolkit/inv_hyper/inv_hyper_over.html +++ b/doc/html/math_toolkit/inv_hyper/inv_hyper_over.html @@ -4,10 +4,11 @@ Inverse Hyperbolic Functions Overview - + + @@ -132,9 +133,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/issues.html b/doc/html/math_toolkit/issues.html index bbd93c6c83..3622a3478a 100644 --- a/doc/html/math_toolkit/issues.html +++ b/doc/html/math_toolkit/issues.html @@ -4,10 +4,11 @@ Known Issues, and TODO List - + + @@ -1188,9 +1189,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi.html b/doc/html/math_toolkit/jacobi.html index 7e889fd1bf..896244ca97 100644 --- a/doc/html/math_toolkit/jacobi.html +++ b/doc/html/math_toolkit/jacobi.html @@ -4,10 +4,11 @@ Jacobi Elliptic Functions - + + @@ -57,9 +58,7 @@ sn -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jac_over.html b/doc/html/math_toolkit/jacobi/jac_over.html index 5ad7acc799..d50bb11696 100644 --- a/doc/html/math_toolkit/jacobi/jac_over.html +++ b/doc/html/math_toolkit/jacobi/jac_over.html @@ -4,10 +4,11 @@ Overview of the Jacobi Elliptic Functions - + + @@ -119,9 +120,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_cd.html b/doc/html/math_toolkit/jacobi/jacobi_cd.html index 6e1bb01356..caedb1328a 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_cd.html +++ b/doc/html/math_toolkit/jacobi/jacobi_cd.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function cd - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_cn.html b/doc/html/math_toolkit/jacobi/jacobi_cn.html index ec535074df..2c8b29f4a4 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_cn.html +++ b/doc/html/math_toolkit/jacobi/jacobi_cn.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function cn - + + @@ -64,9 +65,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_cs.html b/doc/html/math_toolkit/jacobi/jacobi_cs.html index c8fcba93e9..5f48391c94 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_cs.html +++ b/doc/html/math_toolkit/jacobi/jacobi_cs.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function cs - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_dc.html b/doc/html/math_toolkit/jacobi/jacobi_dc.html index b1bd60360d..e9d4c07af5 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_dc.html +++ b/doc/html/math_toolkit/jacobi/jacobi_dc.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function dc - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_dn.html b/doc/html/math_toolkit/jacobi/jacobi_dn.html index 5444c77670..c76b16b7bf 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_dn.html +++ b/doc/html/math_toolkit/jacobi/jacobi_dn.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function dn - + + @@ -64,9 +65,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_ds.html b/doc/html/math_toolkit/jacobi/jacobi_ds.html index ef749c44b0..4aa916b2e7 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_ds.html +++ b/doc/html/math_toolkit/jacobi/jacobi_ds.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function ds - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_elliptic.html b/doc/html/math_toolkit/jacobi/jacobi_elliptic.html index 2ecae058fe..4447204dc6 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_elliptic.html +++ b/doc/html/math_toolkit/jacobi/jacobi_elliptic.html @@ -4,10 +4,11 @@ Jacobi Elliptic SN, CN and DN - + + @@ -754,9 +755,7 @@
geometric means.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_nc.html b/doc/html/math_toolkit/jacobi/jacobi_nc.html index 33e52e2c39..778027e45e 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_nc.html +++ b/doc/html/math_toolkit/jacobi/jacobi_nc.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function nc - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_nd.html b/doc/html/math_toolkit/jacobi/jacobi_nd.html index b45b3a96e8..d810fdcfb7 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_nd.html +++ b/doc/html/math_toolkit/jacobi/jacobi_nd.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function nd - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_ns.html b/doc/html/math_toolkit/jacobi/jacobi_ns.html index 4a4b98868f..9a9ad99a98 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_ns.html +++ b/doc/html/math_toolkit/jacobi/jacobi_ns.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function ns - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_sc.html b/doc/html/math_toolkit/jacobi/jacobi_sc.html index b1c8a62f58..4ed248f20d 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_sc.html +++ b/doc/html/math_toolkit/jacobi/jacobi_sc.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function sc - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_sd.html b/doc/html/math_toolkit/jacobi/jacobi_sd.html index 9d415832a0..a715ada557 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_sd.html +++ b/doc/html/math_toolkit/jacobi/jacobi_sd.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function sd - + + @@ -68,9 +69,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi/jacobi_sn.html b/doc/html/math_toolkit/jacobi/jacobi_sn.html index 348626cf69..b7f7e74246 100644 --- a/doc/html/math_toolkit/jacobi/jacobi_sn.html +++ b/doc/html/math_toolkit/jacobi/jacobi_sn.html @@ -4,10 +4,11 @@ Jacobi Elliptic Function sn - + + @@ -64,9 +65,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi_theta.html b/doc/html/math_toolkit/jacobi_theta.html index d9087cbc25..58cf0232e6 100644 --- a/doc/html/math_toolkit/jacobi_theta.html +++ b/doc/html/math_toolkit/jacobi_theta.html @@ -4,10 +4,11 @@ Jacobi Theta Functions - + + @@ -39,9 +40,7 @@ Function θ4 -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi_theta/jacobi_theta1.html b/doc/html/math_toolkit/jacobi_theta/jacobi_theta1.html index 8ca3f0a715..f061b15f2d 100644 --- a/doc/html/math_toolkit/jacobi_theta/jacobi_theta1.html +++ b/doc/html/math_toolkit/jacobi_theta/jacobi_theta1.html @@ -4,10 +4,11 @@ Jacobi Theta Function θ1 - + + @@ -133,9 +134,7 @@
in a small number of iterations.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi_theta/jacobi_theta2.html b/doc/html/math_toolkit/jacobi_theta/jacobi_theta2.html index d59dd9791d..6833348451 100644 --- a/doc/html/math_toolkit/jacobi_theta/jacobi_theta2.html +++ b/doc/html/math_toolkit/jacobi_theta/jacobi_theta2.html @@ -4,10 +4,11 @@ Jacobi Theta Function θ2 - + + @@ -133,9 +134,7 @@
in a small number of iterations.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi_theta/jacobi_theta3.html b/doc/html/math_toolkit/jacobi_theta/jacobi_theta3.html index deea68a796..e2520c8b09 100644 --- a/doc/html/math_toolkit/jacobi_theta/jacobi_theta3.html +++ b/doc/html/math_toolkit/jacobi_theta/jacobi_theta3.html @@ -4,10 +4,11 @@ Jacobi Theta Function θ3 - + + @@ -150,9 +151,7 @@
in a small number of iterations.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi_theta/jacobi_theta4.html b/doc/html/math_toolkit/jacobi_theta/jacobi_theta4.html index ae5006a166..cc37e870e3 100644 --- a/doc/html/math_toolkit/jacobi_theta/jacobi_theta4.html +++ b/doc/html/math_toolkit/jacobi_theta/jacobi_theta4.html @@ -4,10 +4,11 @@ Jacobi Theta Function θ4 - + + @@ -150,9 +151,7 @@
in a small number of iterations.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/jacobi_theta/jacobi_theta_overview.html b/doc/html/math_toolkit/jacobi_theta/jacobi_theta_overview.html index 9eab9402ae..896167e4c2 100644 --- a/doc/html/math_toolkit/jacobi_theta/jacobi_theta_overview.html +++ b/doc/html/math_toolkit/jacobi_theta/jacobi_theta_overview.html @@ -4,10 +4,11 @@ Overview of the Jacobi Theta Functions - + + @@ -156,9 +157,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/lambert_w.html b/doc/html/math_toolkit/lambert_w.html index 8fac2c1a7b..fa00f1a330 100644 --- a/doc/html/math_toolkit/lambert_w.html +++ b/doc/html/math_toolkit/lambert_w.html @@ -4,10 +4,11 @@ Lambert W function - + + @@ -705,8 +706,9 @@

z < -std::numeric_limits<T>::min(), means that z is zero or denormalized - (if std::numeric_limits<T>::has_denorm_min == - true), for example: r = lambert_wm1(-std::numeric_limits<double>::denorm_min()); + (if boost::math::detail::has_denorm_now<T>() == true), + for example: r = + lambert_wm1(-std::numeric_limits<double>::denorm_min()); and an overflow_error exception is thrown, and will give a message like:

@@ -1907,9 +1909,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/lanczos.html b/doc/html/math_toolkit/lanczos.html index cd9323de67..80b54f502c 100644 --- a/doc/html/math_toolkit/lanczos.html +++ b/doc/html/math_toolkit/lanczos.html @@ -4,10 +4,11 @@ The Lanczos Approximation - + + @@ -568,9 +569,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/linear_regression.html b/doc/html/math_toolkit/linear_regression.html index 71a06032c7..060bf019e9 100644 --- a/doc/html/math_toolkit/linear_regression.html +++ b/doc/html/math_toolkit/linear_regression.html @@ -4,10 +4,11 @@ Linear Regression - + - + + @@ -20,7 +21,7 @@

-PrevUpHomeNext +PrevUpHomeNext

@@ -211,9 +212,7 @@

BMSimpleOrdinaryLeastSquaresWRSquared<double>_RMS 1 %

- - - -
+

-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/html/math_toolkit/ljung_box.html b/doc/html/math_toolkit/ljung_box.html index 53b0261142..edba513b69 100644 --- a/doc/html/math_toolkit/ljung_box.html +++ b/doc/html/math_toolkit/ljung_box.html @@ -4,10 +4,11 @@ The Ljung-Box Test - + + @@ -114,9 +115,7 @@

p + q.

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/logs_and_tables.html b/doc/html/math_toolkit/logs_and_tables.html index d3d2a639d1..5dba04f38f 100644 --- a/doc/html/math_toolkit/logs_and_tables.html +++ b/doc/html/math_toolkit/logs_and_tables.html @@ -4,10 +4,11 @@ Error logs and tables - + + @@ -33,9 +34,7 @@ Rate Tables -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/logs_and_tables/all_table.html b/doc/html/math_toolkit/logs_and_tables/all_table.html index a02eac14c7..0f3c9cffe9 100644 --- a/doc/html/math_toolkit/logs_and_tables/all_table.html +++ b/doc/html/math_toolkit/logs_and_tables/all_table.html @@ -4,10 +4,11 @@ Tables of Error Rates for all Functions - + + @@ -12046,9 +12047,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/logs_and_tables/logs.html b/doc/html/math_toolkit/logs_and_tables/logs.html index eeb0b33b89..74ae8541fc 100644 --- a/doc/html/math_toolkit/logs_and_tables/logs.html +++ b/doc/html/math_toolkit/logs_and_tables/logs.html @@ -4,10 +4,11 @@ Error Logs For Error Rate Tables - + + @@ -3139,9 +3140,7 @@
30, 6.33825e+29, -0
underflow
30, 1.26765e+30, -0

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/macros.html b/doc/html/math_toolkit/macros.html index 942619c495..d1194f3cf4 100644 --- a/doc/html/math_toolkit/macros.html +++ b/doc/html/math_toolkit/macros.html @@ -4,10 +4,11 @@ Floating-Point Constant Macros - + + @@ -69,9 +70,7 @@ See the complete list of constants.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/main_faq.html b/doc/html/math_toolkit/main_faq.html index 8c380f5912..c56890de5e 100644 --- a/doc/html/math_toolkit/main_faq.html +++ b/doc/html/math_toolkit/main_faq.html @@ -4,10 +4,11 @@ Boost.Math Frequently Asked Questions (FAQs) - + + @@ -368,9 +369,7 @@ needed for your application.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/main_intro.html b/doc/html/math_toolkit/main_intro.html index b37d4ddc24..6b033b2c98 100644 --- a/doc/html/math_toolkit/main_intro.html +++ b/doc/html/math_toolkit/main_intro.html @@ -4,10 +4,11 @@ About the Math Toolkit - + + @@ -178,9 +179,7 @@
(forward mode) of mathematical functions of single and multiple variables.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/main_tr1.html b/doc/html/math_toolkit/main_tr1.html index 8d1b2bc829..d8c4d8c58b 100644 --- a/doc/html/math_toolkit/main_tr1.html +++ b/doc/html/math_toolkit/main_tr1.html @@ -4,10 +4,11 @@ C99 and TR1 C Functions Overview - + + @@ -598,9 +599,7 @@
long double x); -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/makima.html b/doc/html/math_toolkit/makima.html index 9169fcfa08..c308ecae44 100644 --- a/doc/html/math_toolkit/makima.html +++ b/doc/html/math_toolkit/makima.html @@ -4,10 +4,11 @@ Modified Akima interpolation - + + @@ -126,9 +127,7 @@

since this object simply constructs derivatives and forwards the data to cubic_hermite.hpp.

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/mem_typedef.html b/doc/html/math_toolkit/mem_typedef.html index 047e633e2d..ca2370fff3 100644 --- a/doc/html/math_toolkit/mem_typedef.html +++ b/doc/html/math_toolkit/mem_typedef.html @@ -4,10 +4,11 @@ Quaternion Member Typedefs - + + @@ -53,9 +54,7 @@ These provide easy access to the type the template is built upon.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/minimum_typdefs.html b/doc/html/math_toolkit/minimum_typdefs.html index 24f32457e1..75aa1b02f3 100644 --- a/doc/html/math_toolkit/minimum_typdefs.html +++ b/doc/html/math_toolkit/minimum_typdefs.html @@ -4,10 +4,11 @@ Minimum-width floating-point typedefs - + + @@ -43,9 +44,7 @@ will also be supported, etc.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/multiprecision.html b/doc/html/math_toolkit/multiprecision.html index 981a5c3e16..7680172984 100644 --- a/doc/html/math_toolkit/multiprecision.html +++ b/doc/html/math_toolkit/multiprecision.html @@ -4,10 +4,11 @@ Cost of High-Precision Non-built-in Floating-point - + + @@ -107,9 +108,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/naive_monte_carlo.html b/doc/html/math_toolkit/naive_monte_carlo.html index 8231578d04..50431971a6 100644 --- a/doc/html/math_toolkit/naive_monte_carlo.html +++ b/doc/html/math_toolkit/naive_monte_carlo.html @@ -4,10 +4,11 @@ Naive Monte Carlo Integration - + + @@ -218,9 +219,7 @@

naive_monte_carlo<Real, decltype(g), std::mt19937> mc(g, bounds, (Real) 0.001);
 
-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/namespaces.html b/doc/html/math_toolkit/namespaces.html index 91675be026..9055183fe4 100644 --- a/doc/html/math_toolkit/namespaces.html +++ b/doc/html/math_toolkit/namespaces.html @@ -4,10 +4,11 @@ Namespaces - + + @@ -86,9 +87,7 @@

- - - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/navigation.html b/doc/html/math_toolkit/navigation.html index f96ffccc10..d04cd30c12 100644 --- a/doc/html/math_toolkit/navigation.html +++ b/doc/html/math_toolkit/navigation.html @@ -4,10 +4,11 @@ Navigation - + + @@ -27,7 +28,7 @@ Navigation

- +

Boost.Math documentation is provided in both HTML and PDF formats. @@ -85,9 +86,7 @@

- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/new_const.html b/doc/html/math_toolkit/new_const.html index 66ee6754b4..ee168e19f3 100644 --- a/doc/html/math_toolkit/new_const.html +++ b/doc/html/math_toolkit/new_const.html @@ -4,10 +4,11 @@ Defining New Constants - + + @@ -244,9 +245,7 @@ }// namespace boost -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/next_float.html b/doc/html/math_toolkit/next_float.html index 99b353d1f7..19aa6a13e5 100644 --- a/doc/html/math_toolkit/next_float.html +++ b/doc/html/math_toolkit/next_float.html @@ -4,10 +4,11 @@ Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values - + + @@ -97,9 +98,7 @@ plots reveal math-function accuracy.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/next_float/float_advance.html b/doc/html/math_toolkit/next_float/float_advance.html index 1d4d28bdd3..20193660d3 100644 --- a/doc/html/math_toolkit/next_float/float_advance.html +++ b/doc/html/math_toolkit/next_float/float_advance.html @@ -4,10 +4,11 @@ Advancing a floating-point Value by a Specific Representation Distance (ULP) float_advance - + + @@ -53,9 +54,7 @@
Returns a floating-point number r such that float_distance(val, r) == distance.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/next_float/float_distance.html b/doc/html/math_toolkit/next_float/float_distance.html index c3d449584e..1c8956b4a9 100644 --- a/doc/html/math_toolkit/next_float/float_distance.html +++ b/doc/html/math_toolkit/next_float/float_distance.html @@ -4,10 +4,11 @@ Calculating the Representation Distance Between Two floating-point Values (ULP) float_distance - + + @@ -87,9 +88,7 @@
an exact integer by type FPT, but in practice this is unlikely to be a issue.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/next_float/float_next.html b/doc/html/math_toolkit/next_float/float_next.html index c556bfa826..65cd2cec44 100644 --- a/doc/html/math_toolkit/next_float/float_next.html +++ b/doc/html/math_toolkit/next_float/float_next.html @@ -4,10 +4,11 @@ Finding the Next Greater Representable Value (float_next) - + + @@ -57,9 +58,7 @@
nextafter(val, (std::numeric_limits<FPT>::max)());
 
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/next_float/float_prior.html b/doc/html/math_toolkit/next_float/float_prior.html index 9cb59d9963..de078e9c5b 100644 --- a/doc/html/math_toolkit/next_float/float_prior.html +++ b/doc/html/math_toolkit/next_float/float_prior.html @@ -4,10 +4,11 @@ Finding the Next Smaller Representable Value (float_prior) - + + @@ -57,9 +58,7 @@
nextafter(val, -(std::numeric_limits<FPT>::max)());  // Note most negative value -max.
 
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/next_float/nextafter.html b/doc/html/math_toolkit/next_float/nextafter.html index 0e6b80d267..9b4b9342ce 100644 --- a/doc/html/math_toolkit/next_float/nextafter.html +++ b/doc/html/math_toolkit/next_float/nextafter.html @@ -4,10 +4,11 @@ Finding the Next Representable Value in a Specific Direction (nextafter) - + + @@ -111,9 +112,7 @@
nextafter(0.1F, 10) is 0.099999994 -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/next_float/ulp.html b/doc/html/math_toolkit/next_float/ulp.html index 487326bb12..86959c37ac 100644 --- a/doc/html/math_toolkit/next_float/ulp.html +++ b/doc/html/math_toolkit/next_float/ulp.html @@ -4,10 +4,11 @@ Obtaining the Size of a Unit In the Last Place - ULP - + + @@ -109,11 +110,10 @@
When the argument becomes very small, it may be that there is no floating-point value that represents one ULP. Whether this is the case or not depends not only on whether the hardware may sometimes support - denormals (as signalled by std::numeric_limits<FPT>::has_denorm), - but also whether these are currently enabled at runtime (for example - on SSE hardware, the DAZ or FTZ flags will disable denormal support). - In this situation, the ulp - function may return a value that is many orders of magnitude too large. + denormals (as signalled by boost::math::detail::has_denorm_now<FPT>()), but also whether these are currently + enabled at runtime (for example on SSE hardware, the DAZ or FTZ flags + will disable denormal support). In this situation, the ulp function may return a value that + is many orders of magnitude too large.

@@ -145,9 +145,7 @@

xc) / ulp(xt).

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/norms.html b/doc/html/math_toolkit/norms.html index 8a656bf443..8da588c41e 100644 --- a/doc/html/math_toolkit/norms.html +++ b/doc/html/math_toolkit/norms.html @@ -4,10 +4,11 @@ Norms - + + @@ -360,9 +361,7 @@

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/number_series.html b/doc/html/math_toolkit/number_series.html index 8ecbc138d4..0f85421c9e 100644 --- a/doc/html/math_toolkit/number_series.html +++ b/doc/html/math_toolkit/number_series.html @@ -4,10 +4,11 @@ Number Series - + + @@ -35,9 +36,7 @@ Numbers -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/number_series/bernoulli_numbers.html b/doc/html/math_toolkit/number_series/bernoulli_numbers.html index ec16aa3bfe..0ecd875026 100644 --- a/doc/html/math_toolkit/number_series/bernoulli_numbers.html +++ b/doc/html/math_toolkit/number_series/bernoulli_numbers.html @@ -4,10 +4,11 @@ Bernoulli Numbers - + + @@ -365,9 +366,7 @@

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/number_series/fibonacci_numbers.html b/doc/html/math_toolkit/number_series/fibonacci_numbers.html index d76286d0fb..b543d86b6d 100644 --- a/doc/html/math_toolkit/number_series/fibonacci_numbers.html +++ b/doc/html/math_toolkit/number_series/fibonacci_numbers.html @@ -4,10 +4,11 @@ Fibonacci Numbers - + + @@ -178,9 +179,7 @@
version.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/number_series/primes.html b/doc/html/math_toolkit/number_series/primes.html index bcad5eaec9..10e8499bc7 100644 --- a/doc/html/math_toolkit/number_series/primes.html +++ b/doc/html/math_toolkit/number_series/primes.html @@ -4,10 +4,11 @@ Prime Numbers - + + @@ -69,9 +70,7 @@
if the compiler supports C++14 constexpr functions.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/number_series/tangent_numbers.html b/doc/html/math_toolkit/number_series/tangent_numbers.html index be8a1f3cfc..885a4494ae 100644 --- a/doc/html/math_toolkit/number_series/tangent_numbers.html +++ b/doc/html/math_toolkit/number_series/tangent_numbers.html @@ -4,10 +4,11 @@ Tangent Numbers - + + @@ -121,9 +122,7 @@
numbers documentation for details.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_create.html b/doc/html/math_toolkit/oct_create.html index e76ecdb9ca..418c7a51d0 100644 --- a/doc/html/math_toolkit/oct_create.html +++ b/doc/html/math_toolkit/oct_create.html @@ -4,10 +4,11 @@ Octonion Creation Functions - + + @@ -65,9 +66,7 @@ the complex value operation arg as the situation is somewhat more complicated.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_header.html b/doc/html/math_toolkit/oct_header.html index 5679493fa9..203014293f 100644 --- a/doc/html/math_toolkit/oct_header.html +++ b/doc/html/math_toolkit/oct_header.html @@ -4,10 +4,11 @@ Header File - + + @@ -30,9 +31,7 @@ The interface and implementation are both supplied by the header file octonion.hpp.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_history.html b/doc/html/math_toolkit/oct_history.html index b8036cd066..1afae0c892 100644 --- a/doc/html/math_toolkit/oct_history.html +++ b/doc/html/math_toolkit/oct_history.html @@ -4,10 +4,11 @@ History - + + @@ -92,9 +93,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_mem_fun.html b/doc/html/math_toolkit/oct_mem_fun.html index 35b6cbdf1d..5cc4caa125 100644 --- a/doc/html/math_toolkit/oct_mem_fun.html +++ b/doc/html/math_toolkit/oct_mem_fun.html @@ -4,10 +4,11 @@ Octonion Member Functions - + + @@ -240,9 +241,7 @@
for the multiplication, remember to group any two factors using parenthesis.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_non_mem.html b/doc/html/math_toolkit/oct_non_mem.html index 388f9949b8..9ecc4cbbad 100644 --- a/doc/html/math_toolkit/oct_non_mem.html +++ b/doc/html/math_toolkit/oct_non_mem.html @@ -4,10 +4,11 @@ Octonion Non-Member Operators - + + @@ -204,9 +205,7 @@
} -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_overview.html b/doc/html/math_toolkit/oct_overview.html index b7060d92aa..4ac38cc492 100644 --- a/doc/html/math_toolkit/oct_overview.html +++ b/doc/html/math_toolkit/oct_overview.html @@ -4,10 +4,11 @@ Overview - + + @@ -67,9 +68,7 @@ known since quite a long time ago).

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_specialization.html b/doc/html/math_toolkit/oct_specialization.html index caedb45d16..b3e5e42561 100644 --- a/doc/html/math_toolkit/oct_specialization.html +++ b/doc/html/math_toolkit/oct_specialization.html @@ -4,10 +4,11 @@ Octonion Specializations - + + @@ -223,9 +224,7 @@ }}// namespaces -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_synopsis.html b/doc/html/math_toolkit/oct_synopsis.html index d3bdc3ae6b..a2d51a9b24 100644 --- a/doc/html/math_toolkit/oct_synopsis.html +++ b/doc/html/math_toolkit/oct_synopsis.html @@ -4,10 +4,11 @@ Synopsis - + + @@ -122,9 +123,7 @@ }}// namespaces -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_tests.html b/doc/html/math_toolkit/oct_tests.html index 86b2d67e3a..df3b07f34c 100644 --- a/doc/html/math_toolkit/oct_tests.html +++ b/doc/html/math_toolkit/oct_tests.html @@ -4,10 +4,11 @@ Test Program - + + @@ -41,9 +42,7 @@ standard input (instead of hard-coding it in the test).

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_todo.html b/doc/html/math_toolkit/oct_todo.html index f78835fcc5..eeec84a3b0 100644 --- a/doc/html/math_toolkit/oct_todo.html +++ b/doc/html/math_toolkit/oct_todo.html @@ -4,10 +4,11 @@ To Do - + + @@ -38,9 +39,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_trans.html b/doc/html/math_toolkit/oct_trans.html index df543a689f..859d0ba71e 100644 --- a/doc/html/math_toolkit/oct_trans.html +++ b/doc/html/math_toolkit/oct_trans.html @@ -4,10 +4,11 @@ Octonions Transcendentals - + + @@ -129,9 +130,7 @@
Computes the n-th power of the octonion q.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_typedefs.html b/doc/html/math_toolkit/oct_typedefs.html index 79953ca994..7c59f5eb94 100644 --- a/doc/html/math_toolkit/oct_typedefs.html +++ b/doc/html/math_toolkit/oct_typedefs.html @@ -4,10 +4,11 @@ Octonion Member Typedefs - + + @@ -53,9 +54,7 @@ These provide easy access to the type the template is built upon.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/oct_value_ops.html b/doc/html/math_toolkit/oct_value_ops.html index fbbc70268c..b3892eb43b 100644 --- a/doc/html/math_toolkit/oct_value_ops.html +++ b/doc/html/math_toolkit/oct_value_ops.html @@ -4,10 +4,11 @@ Octonion Value Operations - + + @@ -89,9 +90,7 @@
norm.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/octonion.html b/doc/html/math_toolkit/octonion.html index 97b2098867..69d64e26c7 100644 --- a/doc/html/math_toolkit/octonion.html +++ b/doc/html/math_toolkit/octonion.html @@ -4,10 +4,11 @@ Template Class octonion - + + @@ -95,9 +96,7 @@ }}// namespaces -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/overview_tr1.html b/doc/html/math_toolkit/overview_tr1.html index 08d0076b7e..9fa7548f7a 100644 --- a/doc/html/math_toolkit/overview_tr1.html +++ b/doc/html/math_toolkit/overview_tr1.html @@ -4,10 +4,11 @@ C99 and C++ TR1 C-style Functions - + + @@ -598,9 +599,7 @@
long double x); -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/owens_t.html b/doc/html/math_toolkit/owens_t.html index 2ea13feaf0..82fa969af4 100644 --- a/doc/html/math_toolkit/owens_t.html +++ b/doc/html/math_toolkit/owens_t.html @@ -4,10 +4,11 @@ Owen's T function - + + @@ -304,9 +305,7 @@
is close to 1, and greater than 95 decimal places elsewhere.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pchip.html b/doc/html/math_toolkit/pchip.html index d430591ff4..95031b7068 100644 --- a/doc/html/math_toolkit/pchip.html +++ b/doc/html/math_toolkit/pchip.html @@ -4,10 +4,11 @@ PCHIP interpolation - + + @@ -119,9 +120,7 @@

interpolator, so the performance is stated in the documentation for cubic_hermite.hpp.

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/perf_over1.html b/doc/html/math_toolkit/perf_over1.html index 115daa7755..ee179e0503 100644 --- a/doc/html/math_toolkit/perf_over1.html +++ b/doc/html/math_toolkit/perf_over1.html @@ -4,10 +4,11 @@ Performance - + + @@ -69,9 +70,7 @@ this library compares to some other open source alternatives.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/perf_over2.html b/doc/html/math_toolkit/perf_over2.html index 91b4b5d77e..7dd368ddbf 100644 --- a/doc/html/math_toolkit/perf_over2.html +++ b/doc/html/math_toolkit/perf_over2.html @@ -4,10 +4,11 @@ Performance Overview - + + @@ -69,9 +70,7 @@ this library compares to some other open source alternatives.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/perf_test_app.html b/doc/html/math_toolkit/perf_test_app.html index 612edcc08b..d76bd1f94e 100644 --- a/doc/html/math_toolkit/perf_test_app.html +++ b/doc/html/math_toolkit/perf_test_app.html @@ -4,10 +4,11 @@ The Performance Test Applications - + + @@ -99,9 +100,7 @@ the compiler.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_overview.html b/doc/html/math_toolkit/pol_overview.html index 910e229f5d..3854748b8d 100644 --- a/doc/html/math_toolkit/pol_overview.html +++ b/doc/html/math_toolkit/pol_overview.html @@ -4,10 +4,11 @@ Policy Overview - + + @@ -99,9 +100,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref.html b/doc/html/math_toolkit/pol_ref.html index d7ec9d1a57..22f32ccd2f 100644 --- a/doc/html/math_toolkit/pol_ref.html +++ b/doc/html/math_toolkit/pol_ref.html @@ -4,10 +4,11 @@ Policy Reference - + + @@ -45,9 +46,7 @@
Policy Class Reference
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/assert_undefined.html b/doc/html/math_toolkit/pol_ref/assert_undefined.html index 38965e75e0..4bb5ec1715 100644 --- a/doc/html/math_toolkit/pol_ref/assert_undefined.html +++ b/doc/html/math_toolkit/pol_ref/assert_undefined.html @@ -4,10 +4,11 @@ Mathematically Undefined Function Policies - + + @@ -83,9 +84,7 @@ Macros to Change the Policy Defaults.

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- - -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/discrete_quant_ref.html b/doc/html/math_toolkit/pol_ref/discrete_quant_ref.html index 14663c0019..1b187cc223 100644 --- a/doc/html/math_toolkit/pol_ref/discrete_quant_ref.html +++ b/doc/html/math_toolkit/pol_ref/discrete_quant_ref.html @@ -4,10 +4,11 @@ Discrete Quantile Policies - + + @@ -233,9 +234,7 @@
(rounded from 68.1584).

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/error_handling_policies.html b/doc/html/math_toolkit/pol_ref/error_handling_policies.html index 61acead8d7..c175fd00fd 100644 --- a/doc/html/math_toolkit/pol_ref/error_handling_policies.html +++ b/doc/html/math_toolkit/pol_ref/error_handling_policies.html @@ -4,10 +4,11 @@ Error Handling Policies - + + @@ -754,9 +755,7 @@
double q = quantile(my_norm(), 0.05); // = -1.64485 -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/internal_promotion.html b/doc/html/math_toolkit/pol_ref/internal_promotion.html index d5fc111353..5db79d6771 100644 --- a/doc/html/math_toolkit/pol_ref/internal_promotion.html +++ b/doc/html/math_toolkit/pol_ref/internal_promotion.html @@ -4,10 +4,11 @@ Internal Floating-point Promotion Policies - + + @@ -131,9 +132,7 @@
float q = quantile(my_norm(), 0.05f); -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/iteration_pol.html b/doc/html/math_toolkit/pol_ref/iteration_pol.html index d861c9bce6..ea0bd5f7e8 100644 --- a/doc/html/math_toolkit/pol_ref/iteration_pol.html +++ b/doc/html/math_toolkit/pol_ref/iteration_pol.html @@ -4,10 +4,11 @@ Iteration Limits Policies - + + @@ -48,9 +49,7 @@ before the special function gives up and returns the result of evaluation_error.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/namespace_pol.html b/doc/html/math_toolkit/pol_ref/namespace_pol.html index bb03649c66..ecb578fe31 100644 --- a/doc/html/math_toolkit/pol_ref/namespace_pol.html +++ b/doc/html/math_toolkit/pol_ref/namespace_pol.html @@ -4,10 +4,11 @@ Setting Polices at Namespace Scope - + + @@ -139,9 +140,7 @@ with the "_distribution" suffix removed.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/pol_ref_ref.html b/doc/html/math_toolkit/pol_ref/pol_ref_ref.html index 1db3e8e84f..c38c641cca 100644 --- a/doc/html/math_toolkit/pol_ref/pol_ref_ref.html +++ b/doc/html/math_toolkit/pol_ref/pol_ref_ref.html @@ -4,10 +4,11 @@ Policy Class Reference - + + @@ -242,9 +243,7 @@ only on the policy types that they actually use.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/policy_defaults.html b/doc/html/math_toolkit/pol_ref/policy_defaults.html index f483931a4b..73ee7e0043 100644 --- a/doc/html/math_toolkit/pol_ref/policy_defaults.html +++ b/doc/html/math_toolkit/pol_ref/policy_defaults.html @@ -4,10 +4,11 @@ Using Macros to Change the Policy Defaults - + + @@ -239,9 +240,7 @@
in a source .cpp file.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_ref/precision_pol.html b/doc/html/math_toolkit/pol_ref/precision_pol.html index a89560f2cc..705295fc8b 100644 --- a/doc/html/math_toolkit/pol_ref/precision_pol.html +++ b/doc/html/math_toolkit/pol_ref/precision_pol.html @@ -4,10 +4,11 @@ Precision Policies - + + @@ -91,9 +92,7 @@ 0.05);// 5% quantile. -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial.html b/doc/html/math_toolkit/pol_tutorial.html index d8a16b8213..4a95b37954 100644 --- a/doc/html/math_toolkit/pol_tutorial.html +++ b/doc/html/math_toolkit/pol_tutorial.html @@ -4,10 +4,11 @@ Policy Tutorial - + + @@ -47,9 +48,7 @@ Quantiles of Discrete Distributions -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html b/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html index b884c06ce1..1c6c45d575 100644 --- a/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html +++ b/doc/html/math_toolkit/pol_tutorial/ad_hoc_dist_policies.html @@ -4,10 +4,11 @@ Setting Policies for Distributions on an Ad Hoc Basis - + + @@ -86,9 +87,7 @@

quantile is: 40
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html b/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html index 20856ed96e..59919961cc 100644 --- a/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html +++ b/doc/html/math_toolkit/pol_tutorial/ad_hoc_sf_policies.html @@ -4,10 +4,11 @@ Changing the Policy on an Ad Hoc Basis for the Special Functions - + + @@ -155,9 +156,7 @@ } -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html b/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html index 6a589ce926..7b9fa8fa0d 100644 --- a/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html +++ b/doc/html/math_toolkit/pol_tutorial/changing_policy_defaults.html @@ -4,10 +4,11 @@ Changing the Policy Defaults - + + @@ -239,9 +240,7 @@ errno is set to: 33 -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/namespace_policies.html b/doc/html/math_toolkit/pol_tutorial/namespace_policies.html index b2af59f47b..0be96325bd 100644 --- a/doc/html/math_toolkit/pol_tutorial/namespace_policies.html +++ b/doc/html/math_toolkit/pol_tutorial/namespace_policies.html @@ -4,10 +4,11 @@ Setting Policies at Namespace or Translation Unit Scope - + + @@ -347,9 +348,7 @@ } -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html b/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html index 920998f4bb..cb920fd2d9 100644 --- a/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html +++ b/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html @@ -4,10 +4,11 @@ Policies Have Sensible Defaults - + + @@ -139,9 +140,7 @@ typedefnormalise<my_policy,digits2<9>>::typemy_policy_9;// errno on error, and limited precision. -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/policy_usage.html b/doc/html/math_toolkit/pol_tutorial/policy_usage.html index 8bb0dd9161..ab16e0189d 100644 --- a/doc/html/math_toolkit/pol_tutorial/policy_usage.html +++ b/doc/html/math_toolkit/pol_tutorial/policy_usage.html @@ -4,10 +4,11 @@ So How are Policies Used Anyway? - + + @@ -54,9 +55,7 @@ The following sections introduce these methods in more detail.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html b/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html index 4a299c32a8..3fd89e1e6a 100644 --- a/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html +++ b/doc/html/math_toolkit/pol_tutorial/understand_dis_quant.html @@ -4,10 +4,11 @@ Understanding Quantiles of Discrete Distributions - + + @@ -398,9 +399,7 @@
real 18.701 30.299 -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html b/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html index 2bc55d8d80..4de77094f7 100644 --- a/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html +++ b/doc/html/math_toolkit/pol_tutorial/user_def_err_pol.html @@ -4,10 +4,11 @@ Calling User Defined Error Handlers - + + @@ -435,9 +436,7 @@ then notices that it is dividing by infinity and so underflows.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html b/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html index 2af940ea34..5332a0439c 100644 --- a/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html +++ b/doc/html/math_toolkit/pol_tutorial/what_is_a_policy.html @@ -4,10 +4,11 @@ So Just What is a Policy Anyway? - + + @@ -82,9 +83,7 @@ >my_policy; -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/polynomials.html b/doc/html/math_toolkit/polynomials.html index bc0e52fd81..ff88e552af 100644 --- a/doc/html/math_toolkit/polynomials.html +++ b/doc/html/math_toolkit/polynomials.html @@ -4,10 +4,11 @@ Polynomials - + + @@ -317,9 +318,7 @@
The source code is at polynomial_arithmetic.cpp

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers.html b/doc/html/math_toolkit/powers.html index 4942bad9f7..7d3baaf178 100644 --- a/doc/html/math_toolkit/powers.html +++ b/doc/html/math_toolkit/powers.html @@ -4,10 +4,11 @@ Basic Functions - + + @@ -41,9 +42,7 @@
logaddexp and logsumexp
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/cbrt.html b/doc/html/math_toolkit/powers/cbrt.html index 186a9dc901..8dd57b0390 100644 --- a/doc/html/math_toolkit/powers/cbrt.html +++ b/doc/html/math_toolkit/powers/cbrt.html @@ -4,10 +4,11 @@ cbrt - + + @@ -146,9 +147,7 @@
calculated using NTL::RR at 1000-bit precision.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/cos_pi.html b/doc/html/math_toolkit/powers/cos_pi.html index c11c0bf596..3c3325952f 100644 --- a/doc/html/math_toolkit/powers/cos_pi.html +++ b/doc/html/math_toolkit/powers/cos_pi.html @@ -4,10 +4,11 @@ cos_pi - + + @@ -150,9 +151,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/ct_pow.html b/doc/html/math_toolkit/powers/ct_pow.html index aa4b96218f..0fbd674b89 100644 --- a/doc/html/math_toolkit/powers/ct_pow.html +++ b/doc/html/math_toolkit/powers/ct_pow.html @@ -4,10 +4,11 @@ Compile Time Power of a Runtime Base - + + @@ -255,9 +256,7 @@
Algorithms, 2nd ed., Addison-Wesley, Reading, MA, 1981

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- - -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/expm1.html b/doc/html/math_toolkit/powers/expm1.html index 6907d193e0..be5faa03e0 100644 --- a/doc/html/math_toolkit/powers/expm1.html +++ b/doc/html/math_toolkit/powers/expm1.html @@ -4,10 +4,11 @@ expm1 - + + @@ -156,9 +157,7 @@
calculated using NTL::RR at 1000-bit precision.

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- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/hypot.html b/doc/html/math_toolkit/powers/hypot.html index 1f23074c74..028f1dbdc7 100644 --- a/doc/html/math_toolkit/powers/hypot.html +++ b/doc/html/math_toolkit/powers/hypot.html @@ -4,10 +4,11 @@ hypot - + + @@ -84,9 +85,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/log1p.html b/doc/html/math_toolkit/powers/log1p.html index 655b3f71c5..d9db795364 100644 --- a/doc/html/math_toolkit/powers/log1p.html +++ b/doc/html/math_toolkit/powers/log1p.html @@ -4,10 +4,11 @@ log1p - + + @@ -171,9 +172,7 @@
calculated using NTL::RR at 1000-bit precision.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/logaddexp.html b/doc/html/math_toolkit/powers/logaddexp.html index 66fe9738cc..65569874be 100644 --- a/doc/html/math_toolkit/powers/logaddexp.html +++ b/doc/html/math_toolkit/powers/logaddexp.html @@ -4,10 +4,11 @@ logaddexp and logsumexp - + + @@ -146,9 +147,7 @@
is the Log-Sum-Exp Function? -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/powm1.html b/doc/html/math_toolkit/powers/powm1.html index d13d0987be..179a25e5ed 100644 --- a/doc/html/math_toolkit/powers/powm1.html +++ b/doc/html/math_toolkit/powers/powm1.html @@ -4,10 +4,11 @@ powm1 - + + @@ -150,9 +151,7 @@
at 1000-bit precision.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/rsqrt.html b/doc/html/math_toolkit/powers/rsqrt.html index 411cd5d616..11b5d56a1d 100644 --- a/doc/html/math_toolkit/powers/rsqrt.html +++ b/doc/html/math_toolkit/powers/rsqrt.html @@ -4,10 +4,11 @@ Reciprocal square root - + + @@ -96,9 +97,7 @@
Rsqrt<cpp_bin_float_100> 9393 ns 9393 ns 72967 -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/sin_pi.html b/doc/html/math_toolkit/powers/sin_pi.html index 50b839712c..6122beefa9 100644 --- a/doc/html/math_toolkit/powers/sin_pi.html +++ b/doc/html/math_toolkit/powers/sin_pi.html @@ -4,10 +4,11 @@ sin_pi - + + @@ -150,9 +151,7 @@
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/powers/sqrt1pm1.html b/doc/html/math_toolkit/powers/sqrt1pm1.html index 9c6717de4f..8be59d586f 100644 --- a/doc/html/math_toolkit/powers/sqrt1pm1.html +++ b/doc/html/math_toolkit/powers/sqrt1pm1.html @@ -4,10 +4,11 @@ sqrt1pm1 - + + @@ -148,9 +149,7 @@
at 1000-bit precision.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quartic_roots.html b/doc/html/math_toolkit/quartic_roots.html index f03dd34e67..acebfb7979 100644 --- a/doc/html/math_toolkit/quartic_roots.html +++ b/doc/html/math_toolkit/quartic_roots.html @@ -4,10 +4,11 @@ Roots of Quartic Polynomials - + + @@ -68,9 +69,7 @@

your system.

-

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat.html b/doc/html/math_toolkit/quat.html index 0d51daf609..9534563cc2 100644 --- a/doc/html/math_toolkit/quat.html +++ b/doc/html/math_toolkit/quat.html @@ -4,10 +4,11 @@ Template Class quaternion - + + @@ -80,9 +81,7 @@ }// namespace boost -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat_header.html b/doc/html/math_toolkit/quat_header.html index ac90fcf967..ed33dd0404 100644 --- a/doc/html/math_toolkit/quat_header.html +++ b/doc/html/math_toolkit/quat_header.html @@ -4,10 +4,11 @@ Header File - + + @@ -30,9 +31,7 @@ The interface and implementation are both supplied by the header file quaternion.hpp.

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- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat_history.html b/doc/html/math_toolkit/quat_history.html index c0bb97d44f..ce37895fb0 100644 --- a/doc/html/math_toolkit/quat_history.html +++ b/doc/html/math_toolkit/quat_history.html @@ -4,10 +4,11 @@ History - + + @@ -94,9 +95,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat_mem_fun.html b/doc/html/math_toolkit/quat_mem_fun.html index 6a69c8f6ab..5a2ab3b7ec 100644 --- a/doc/html/math_toolkit/quat_mem_fun.html +++ b/doc/html/math_toolkit/quat_mem_fun.html @@ -4,10 +4,11 @@ Quaternion Member Functions - + + @@ -217,9 +218,7 @@
unspecialized form, the base type's assignment operators must not throw.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat_non_mem.html b/doc/html/math_toolkit/quat_non_mem.html index 6e1f2e85e8..844bbbf5ae 100644 --- a/doc/html/math_toolkit/quat_non_mem.html +++ b/doc/html/math_toolkit/quat_non_mem.html @@ -4,10 +4,11 @@ Quaternion Non-Member Operators - + + @@ -205,9 +206,7 @@
} -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat_overview.html b/doc/html/math_toolkit/quat_overview.html index 036f35987c..d7dbd746f5 100644 --- a/doc/html/math_toolkit/quat_overview.html +++ b/doc/html/math_toolkit/quat_overview.html @@ -4,10 +4,11 @@ Overview - + + @@ -77,9 +78,7 @@ root, do not.

-
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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat_synopsis.html b/doc/html/math_toolkit/quat_synopsis.html index d5c5de839e..11a71292f3 100644 --- a/doc/html/math_toolkit/quat_synopsis.html +++ b/doc/html/math_toolkit/quat_synopsis.html @@ -4,10 +4,11 @@ Synopsis - + + @@ -109,9 +110,7 @@ }// namespace boost -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat_tests.html b/doc/html/math_toolkit/quat_tests.html index 5a4d0b54a3..2a311a00ee 100644 --- a/doc/html/math_toolkit/quat_tests.html +++ b/doc/html/math_toolkit/quat_tests.html @@ -4,10 +4,11 @@ Test Program - + + @@ -42,9 +43,7 @@ standard input (instead of hard-coding it in the test).

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- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quat_todo.html b/doc/html/math_toolkit/quat_todo.html index 5bf303d087..91a8c2e1c8 100644 --- a/doc/html/math_toolkit/quat_todo.html +++ b/doc/html/math_toolkit/quat_todo.html @@ -4,10 +4,11 @@ To Do - + + @@ -42,9 +43,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/quintic_hermite.html b/doc/html/math_toolkit/quintic_hermite.html index b28715839a..b2909a87ca 100644 --- a/doc/html/math_toolkit/quintic_hermite.html +++ b/doc/html/math_toolkit/quintic_hermite.html @@ -4,10 +4,11 @@ Quintic Hermite interpolation - + + @@ -222,9 +223,7 @@

CardinalQuinticHermiteAOS<double>_BigO 5.64 (1) -

- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/rational.html b/doc/html/math_toolkit/rational.html index d6ad6f9c31..52a7646790 100644 --- a/doc/html/math_toolkit/rational.html +++ b/doc/html/math_toolkit/rational.html @@ -4,10 +4,11 @@ Polynomial and Rational Function Evaluation - + + @@ -212,9 +213,7 @@
changing the default settings.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/rationale.html b/doc/html/math_toolkit/rationale.html index f896eed07f..c498c2499d 100644 --- a/doc/html/math_toolkit/rationale.html +++ b/doc/html/math_toolkit/rationale.html @@ -4,10 +4,11 @@ Rationale - + + @@ -136,9 +137,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/real_concepts.html b/doc/html/math_toolkit/real_concepts.html index 6e79184503..af2cf6e404 100644 --- a/doc/html/math_toolkit/real_concepts.html +++ b/doc/html/math_toolkit/real_concepts.html @@ -4,10 +4,11 @@ Conceptual Requirements for Real Number Types - + + @@ -1357,9 +1358,7 @@
in any function that makes use of the gamma/beta/erf family of functions.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/refs.html b/doc/html/math_toolkit/refs.html index 4dd108f64f..36f0990264 100644 --- a/doc/html/math_toolkit/refs.html +++ b/doc/html/math_toolkit/refs.html @@ -4,10 +4,11 @@ References - + + @@ -78,10 +79,10 @@
by N.A.J. Hastings, Brian Peacock, Merran Evans, ISBN: 0471371246, Wiley 2000.

- Extreme Value - Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah, - ISBN 978-1-86094-224-2 & 1-86094-224-5 Oct 2000, Chapter 1.2 discusses - the various extreme value distributions. + Extreme + Value Distributions, Theory and Applications Samuel Kotz & Saralees + Nadarajah, ISBN 978-1-86094-224-2 & 1-86094-224-5 Oct 2000, Chapter 1.2 + discusses the various extreme value distributions.

pugh.pdf @@ -196,9 +197,7 @@

in finance.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/relative_error.html b/doc/html/math_toolkit/relative_error.html index 5aab6c6207..575ea9077a 100644 --- a/doc/html/math_toolkit/relative_error.html +++ b/doc/html/math_toolkit/relative_error.html @@ -4,10 +4,11 @@ Relative Error - + + @@ -106,9 +107,7 @@
for more information.

-
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/remez.html b/doc/html/math_toolkit/remez.html index 03a1ad2246..343bd3ab51 100644 --- a/doc/html/math_toolkit/remez.html +++ b/doc/html/math_toolkit/remez.html @@ -4,10 +4,11 @@ The Remez Method - + + @@ -536,9 +537,7 @@
Physics, vol.1, No. 3, 1994.

-
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/result_type.html b/doc/html/math_toolkit/result_type.html index d147b54fb7..ea53ca2191 100644 --- a/doc/html/math_toolkit/result_type.html +++ b/doc/html/math_toolkit/result_type.html @@ -4,10 +4,11 @@ Calculation of the Type of the Result - + + @@ -165,9 +166,7 @@ 5.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_comparison.html b/doc/html/math_toolkit/root_comparison.html index c886cc232d..c545227eba 100644 --- a/doc/html/math_toolkit/root_comparison.html +++ b/doc/html/math_toolkit/root_comparison.html @@ -4,10 +4,11 @@ Comparison of Root Finding Algorithms - + + @@ -36,9 +37,7 @@ of Elliptic Integral Root Finding Algorithms -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_comparison/cbrt_comparison.html b/doc/html/math_toolkit/root_comparison/cbrt_comparison.html index f8a544863e..a0158901ab 100644 --- a/doc/html/math_toolkit/root_comparison/cbrt_comparison.html +++ b/doc/html/math_toolkit/root_comparison/cbrt_comparison.html @@ -4,10 +4,11 @@ Comparison of Cube Root Finding Algorithms - + + @@ -1569,9 +1570,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_comparison/elliptic_comparison.html b/doc/html/math_toolkit/root_comparison/elliptic_comparison.html index 1373fb8be2..9cc8024f57 100644 --- a/doc/html/math_toolkit/root_comparison/elliptic_comparison.html +++ b/doc/html/math_toolkit/root_comparison/elliptic_comparison.html @@ -4,10 +4,11 @@ Comparison of Elliptic Integral Root Finding Algorithms - + + @@ -1850,9 +1851,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_comparison/root_n_comparison.html b/doc/html/math_toolkit/root_comparison/root_n_comparison.html index 51bf8503fe..67f92e92f7 100644 --- a/doc/html/math_toolkit/root_comparison/root_n_comparison.html +++ b/doc/html/math_toolkit/root_comparison/root_n_comparison.html @@ -4,10 +4,11 @@ Comparison of Nth-root Finding Algorithms - + + @@ -5267,9 +5268,7 @@

And of course, compiler optimisation is crucial for speed.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_finding_examples.html b/doc/html/math_toolkit/root_finding_examples.html index b76a0e12d3..4f279cd351 100644 --- a/doc/html/math_toolkit/root_finding_examples.html +++ b/doc/html/math_toolkit/root_finding_examples.html @@ -4,10 +4,11 @@ Examples of Root-Finding (with and without derivatives) - + + @@ -70,9 +71,7 @@ easily.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_finding_examples/5th_root_eg.html b/doc/html/math_toolkit/root_finding_examples/5th_root_eg.html index 447490f5a1..f67517a6a7 100644 --- a/doc/html/math_toolkit/root_finding_examples/5th_root_eg.html +++ b/doc/html/math_toolkit/root_finding_examples/5th_root_eg.html @@ -4,10 +4,11 @@ Computing the Fifth Root - + + @@ -147,9 +148,7 @@ and root_finding_n_example.cpp.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_finding_examples/cbrt_eg.html b/doc/html/math_toolkit/root_finding_examples/cbrt_eg.html index 520f8e8280..2bc257481b 100644 --- a/doc/html/math_toolkit/root_finding_examples/cbrt_eg.html +++ b/doc/html/math_toolkit/root_finding_examples/cbrt_eg.html @@ -4,10 +4,11 @@ Finding the Cubed Root With and Without Derivatives - + + @@ -465,9 +466,7 @@

Full code of this example is at root_finding_example.cpp,

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_finding_examples/elliptic_eg.html b/doc/html/math_toolkit/root_finding_examples/elliptic_eg.html index 8382257dc3..32c1ce278b 100644 --- a/doc/html/math_toolkit/root_finding_examples/elliptic_eg.html +++ b/doc/html/math_toolkit/root_finding_examples/elliptic_eg.html @@ -4,10 +4,11 @@ A More complex example - Inverting the Elliptic Integrals - + + @@ -253,9 +254,7 @@ Full code of this example is at root_elliptic_finding.cpp.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_finding_examples/lambda.html b/doc/html/math_toolkit/root_finding_examples/lambda.html index 291d1923ff..598d98f590 100644 --- a/doc/html/math_toolkit/root_finding_examples/lambda.html +++ b/doc/html/math_toolkit/root_finding_examples/lambda.html @@ -4,10 +4,11 @@ Using C++11 Lambda's - + + @@ -59,9 +60,7 @@ Full code of this example is at root_finding_example.cpp,

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_finding_examples/multiprecision_root.html b/doc/html/math_toolkit/root_finding_examples/multiprecision_root.html index 71a55f3184..11ce9ccc4b 100644 --- a/doc/html/math_toolkit/root_finding_examples/multiprecision_root.html +++ b/doc/html/math_toolkit/root_finding_examples/multiprecision_root.html @@ -4,10 +4,11 @@ Root-finding using Boost.Multiprecision - + + @@ -271,9 +272,7 @@ Full code of this example is at root_finding_multiprecision_example.cpp.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/root_finding_examples/nth_root.html b/doc/html/math_toolkit/root_finding_examples/nth_root.html index 534d27ba2b..1e76bdd158 100644 --- a/doc/html/math_toolkit/root_finding_examples/nth_root.html +++ b/doc/html/math_toolkit/root_finding_examples/nth_root.html @@ -4,10 +4,11 @@ Generalizing to Compute the nth root - + + @@ -168,9 +169,7 @@ Full code of this example is at root_finding_n_example.cpp.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/roots_deriv.html b/doc/html/math_toolkit/roots_deriv.html index 47737b68f4..7ace9a4368 100644 --- a/doc/html/math_toolkit/roots_deriv.html +++ b/doc/html/math_toolkit/roots_deriv.html @@ -4,10 +4,11 @@ Root Finding With Derivatives: Newton-Raphson, Halley & Schröder - + + @@ -359,9 +360,7 @@
See root-finding examples.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/roots_noderiv.html b/doc/html/math_toolkit/roots_noderiv.html index f1a80f892a..8073172f1e 100644 --- a/doc/html/math_toolkit/roots_noderiv.html +++ b/doc/html/math_toolkit/roots_noderiv.html @@ -4,10 +4,11 @@ Root Finding Without Derivatives - + + @@ -200,9 +201,7 @@
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/roots_noderiv/TOMS748.html b/doc/html/math_toolkit/roots_noderiv/TOMS748.html index e9fd0a8e30..130d98223a 100644 --- a/doc/html/math_toolkit/roots_noderiv/TOMS748.html +++ b/doc/html/math_toolkit/roots_noderiv/TOMS748.html @@ -4,10 +4,11 @@ Algorithm TOMS 748: Alefeld, Potra and Shi: Enclosing zeros of continuous functions - + + @@ -178,9 +179,7 @@ termination condition tol was satisfied.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/roots_noderiv/bisect.html b/doc/html/math_toolkit/roots_noderiv/bisect.html index 3373d3f885..6fa318bb50 100644 --- a/doc/html/math_toolkit/roots_noderiv/bisect.html +++ b/doc/html/math_toolkit/roots_noderiv/bisect.html @@ -4,10 +4,11 @@ Bisection - + + @@ -135,9 +136,7 @@ tol was satisfied.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/roots_noderiv/bracket_solve.html b/doc/html/math_toolkit/roots_noderiv/bracket_solve.html index 2801de0638..a386408ac7 100644 --- a/doc/html/math_toolkit/roots_noderiv/bracket_solve.html +++ b/doc/html/math_toolkit/roots_noderiv/bracket_solve.html @@ -4,10 +4,11 @@ Bracket and Solve Root - + + @@ -167,9 +168,7 @@ was satisfied.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/roots_noderiv/brent.html b/doc/html/math_toolkit/roots_noderiv/brent.html index e1f0e04d95..cae96c99ee 100644 --- a/doc/html/math_toolkit/roots_noderiv/brent.html +++ b/doc/html/math_toolkit/roots_noderiv/brent.html @@ -4,10 +4,11 @@ Brent-Decker Algorithm - + + @@ -34,9 +35,7 @@ and solve are superior and provide equivalent functionality.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/roots_noderiv/implementation.html b/doc/html/math_toolkit/roots_noderiv/implementation.html index 04a308642a..fc9b6ac03e 100644 --- a/doc/html/math_toolkit/roots_noderiv/implementation.html +++ b/doc/html/math_toolkit/roots_noderiv/implementation.html @@ -4,10 +4,11 @@ Implementation - + + @@ -44,9 +45,7 @@ The implementation here is a faithful translation of this paper into C++.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/roots_noderiv/root_termination.html b/doc/html/math_toolkit/roots_noderiv/root_termination.html index 65435c89ee..7aced32cbc 100644 --- a/doc/html/math_toolkit/roots_noderiv/root_termination.html +++ b/doc/html/math_toolkit/roots_noderiv/root_termination.html @@ -4,10 +4,11 @@ Termination Condition Functors - + + @@ -83,9 +84,7 @@ as soon as both ends of the interval round to the same nearest integer.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/rounding.html b/doc/html/math_toolkit/rounding.html index 1f32944042..f9c1c4d6b1 100644 --- a/doc/html/math_toolkit/rounding.html +++ b/doc/html/math_toolkit/rounding.html @@ -4,10 +4,11 @@ Rounding Truncation and Integer Conversion - + + @@ -34,9 +35,7 @@ Splitting (modf) -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/rounding/modf.html b/doc/html/math_toolkit/rounding/modf.html index 294c5a175a..005f52a25b 100644 --- a/doc/html/math_toolkit/rounding/modf.html +++ b/doc/html/math_toolkit/rounding/modf.html @@ -4,10 +4,11 @@ Integer and Fractional Part Splitting (modf) - + + @@ -64,9 +65,7 @@ by default this throws an instance of boost::math::rounding_error.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/rounding/round.html b/doc/html/math_toolkit/rounding/round.html index 0bb17969c5..607dfaa9c0 100644 --- a/doc/html/math_toolkit/rounding/round.html +++ b/doc/html/math_toolkit/rounding/round.html @@ -4,10 +4,11 @@ Rounding Functions - + + @@ -64,9 +65,7 @@ by default this throws an instance of boost::math::rounding_error.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/rounding/trunc.html b/doc/html/math_toolkit/rounding/trunc.html index 4287e8d475..ca124c9eb8 100644 --- a/doc/html/math_toolkit/rounding/trunc.html +++ b/doc/html/math_toolkit/rounding/trunc.html @@ -4,10 +4,11 @@ Truncation Functions - + + @@ -66,9 +67,7 @@ by default this throws an instance of boost::math::rounding_error.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/runs_test.html b/doc/html/math_toolkit/runs_test.html index 6c759cc02d..63c82ca118 100644 --- a/doc/html/math_toolkit/runs_test.html +++ b/doc/html/math_toolkit/runs_test.html @@ -4,10 +4,11 @@ Runs tests - + + @@ -212,9 +213,7 @@

BMRunsAboveAndBelowThreshold<double>_BigO 5.59 N 5.59 N -

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_beta.html b/doc/html/math_toolkit/sf_beta.html index f43596808a..25d9d56c6a 100644 --- a/doc/html/math_toolkit/sf_beta.html +++ b/doc/html/math_toolkit/sf_beta.html @@ -4,10 +4,11 @@ Beta Functions - + + @@ -36,9 +37,7 @@ Incomplete Beta Function -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_beta/beta_derivative.html b/doc/html/math_toolkit/sf_beta/beta_derivative.html index 5ffe5563fa..ebde100610 100644 --- a/doc/html/math_toolkit/sf_beta/beta_derivative.html +++ b/doc/html/math_toolkit/sf_beta/beta_derivative.html @@ -4,10 +4,11 @@ Derivative of the Incomplete Beta Function - + + @@ -84,9 +85,7 @@
the documentation for that function for more information.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_beta/beta_function.html b/doc/html/math_toolkit/sf_beta/beta_function.html index 14e9e92453..2795fbd415 100644 --- a/doc/html/math_toolkit/sf_beta/beta_function.html +++ b/doc/html/math_toolkit/sf_beta/beta_function.html @@ -4,10 +4,11 @@ Beta - + + @@ -286,9 +287,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_beta/ibeta_function.html b/doc/html/math_toolkit/sf_beta/ibeta_function.html index 2ff888003c..9605cf3cd1 100644 --- a/doc/html/math_toolkit/sf_beta/ibeta_function.html +++ b/doc/html/math_toolkit/sf_beta/ibeta_function.html @@ -4,10 +4,11 @@ Incomplete Beta Functions - + + @@ -882,9 +883,7 @@
and Morris TOMS 708 paper.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_beta/ibeta_inv_function.html b/doc/html/math_toolkit/sf_beta/ibeta_inv_function.html index a506ec68ea..61648a5634 100644 --- a/doc/html/math_toolkit/sf_beta/ibeta_inv_function.html +++ b/doc/html/math_toolkit/sf_beta/ibeta_inv_function.html @@ -4,10 +4,11 @@ The Incomplete Beta Function Inverses - + + @@ -904,9 +905,7 @@
are required to find the root.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_erf.html b/doc/html/math_toolkit/sf_erf.html index e3daeff4af..06ffa7d065 100644 --- a/doc/html/math_toolkit/sf_erf.html +++ b/doc/html/math_toolkit/sf_erf.html @@ -4,10 +4,11 @@ Error Functions - + + @@ -32,9 +33,7 @@
Error Function Inverses
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_erf/error_function.html b/doc/html/math_toolkit/sf_erf/error_function.html index 1a743cdc63..90d310bfc5 100644 --- a/doc/html/math_toolkit/sf_erf/error_function.html +++ b/doc/html/math_toolkit/sf_erf/error_function.html @@ -4,10 +4,11 @@ Error Function erf and complement erfc - + + @@ -523,9 +524,7 @@
z)) / z;

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_erf/error_inv.html b/doc/html/math_toolkit/sf_erf/error_inv.html index 5418bfddd0..5847f551de 100644 --- a/doc/html/math_toolkit/sf_erf/error_inv.html +++ b/doc/html/math_toolkit/sf_erf/error_inv.html @@ -4,10 +4,11 @@ Error Function Inverses - + + @@ -358,9 +359,7 @@
that the tail goes on for a very long way indeed).

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma.html b/doc/html/math_toolkit/sf_gamma.html index c637e057d5..72a67095d0 100644 --- a/doc/html/math_toolkit/sf_gamma.html +++ b/doc/html/math_toolkit/sf_gamma.html @@ -4,10 +4,11 @@ Gamma Functions - + + @@ -40,9 +41,7 @@ the Incomplete Gamma Function -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/digamma.html b/doc/html/math_toolkit/sf_gamma/digamma.html index 7cdbdd62de..33b09393ce 100644 --- a/doc/html/math_toolkit/sf_gamma/digamma.html +++ b/doc/html/math_toolkit/sf_gamma/digamma.html @@ -4,10 +4,11 @@ Digamma - + + @@ -465,9 +466,7 @@
will not be zero.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/gamma_derivatives.html b/doc/html/math_toolkit/sf_gamma/gamma_derivatives.html index 0ba6ace86c..d4d84aaf7f 100644 --- a/doc/html/math_toolkit/sf_gamma/gamma_derivatives.html +++ b/doc/html/math_toolkit/sf_gamma/gamma_derivatives.html @@ -4,10 +4,11 @@ Derivative of the Incomplete Gamma Function - + + @@ -89,9 +90,7 @@
documentation for that function for more information.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/gamma_ratios.html b/doc/html/math_toolkit/sf_gamma/gamma_ratios.html index e981c9157f..5dd4ff67c8 100644 --- a/doc/html/math_toolkit/sf_gamma/gamma_ratios.html +++ b/doc/html/math_toolkit/sf_gamma/gamma_ratios.html @@ -4,10 +4,11 @@ Ratios of Gamma Functions - + + @@ -402,9 +403,7 @@
which case table lookup of factorials can be used to calculate the ratio.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/igamma.html b/doc/html/math_toolkit/sf_gamma/igamma.html index 86ab20d95c..9ab91403ed 100644 --- a/doc/html/math_toolkit/sf_gamma/igamma.html +++ b/doc/html/math_toolkit/sf_gamma/igamma.html @@ -4,10 +4,11 @@ Incomplete Gamma Functions - + + @@ -997,9 +998,7 @@
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/igamma_inv.html b/doc/html/math_toolkit/sf_gamma/igamma_inv.html index 98b281a94f..b438558e9a 100644 --- a/doc/html/math_toolkit/sf_gamma/igamma_inv.html +++ b/doc/html/math_toolkit/sf_gamma/igamma_inv.html @@ -4,10 +4,11 @@ Incomplete Gamma Function Inverses - + + @@ -607,9 +608,7 @@
so, the root is usually found in fewer than 10 iterations.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/lgamma.html b/doc/html/math_toolkit/sf_gamma/lgamma.html index 1e2f2977f3..dad6cac67a 100644 --- a/doc/html/math_toolkit/sf_gamma/lgamma.html +++ b/doc/html/math_toolkit/sf_gamma/lgamma.html @@ -4,10 +4,11 @@ Log Gamma - + + @@ -476,9 +477,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/polygamma.html b/doc/html/math_toolkit/sf_gamma/polygamma.html index f9ef2e7538..6c43abb36b 100644 --- a/doc/html/math_toolkit/sf_gamma/polygamma.html +++ b/doc/html/math_toolkit/sf_gamma/polygamma.html @@ -4,10 +4,11 @@ Polygamma - + + @@ -401,9 +402,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/tgamma.html b/doc/html/math_toolkit/sf_gamma/tgamma.html index cff1526f04..32a381573f 100644 --- a/doc/html/math_toolkit/sf_gamma/tgamma.html +++ b/doc/html/math_toolkit/sf_gamma/tgamma.html @@ -4,10 +4,11 @@ Gamma - + + @@ -518,9 +519,7 @@
can be used directly.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_gamma/trigamma.html b/doc/html/math_toolkit/sf_gamma/trigamma.html index 0f97aaa978..ec708a0421 100644 --- a/doc/html/math_toolkit/sf_gamma/trigamma.html +++ b/doc/html/math_toolkit/sf_gamma/trigamma.html @@ -4,10 +4,11 @@ Trigamma - + + @@ -210,9 +211,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_implementation.html b/doc/html/math_toolkit/sf_implementation.html index 6d5b9d5787..f73be55a4a 100644 --- a/doc/html/math_toolkit/sf_implementation.html +++ b/doc/html/math_toolkit/sf_implementation.html @@ -4,10 +4,11 @@ Additional Implementation Notes - + + @@ -843,9 +844,7 @@
enhanced and now reasonably mature and usable, by Paul A. Bristow, is at .\boost-sandbox\SOC\2007\visualization).

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly.html b/doc/html/math_toolkit/sf_poly.html index 6cd11175b3..09e69033a4 100644 --- a/doc/html/math_toolkit/sf_poly.html +++ b/doc/html/math_toolkit/sf_poly.html @@ -4,10 +4,11 @@ Polynomials - + + @@ -41,9 +42,7 @@
Jacobi Polynomials
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/cardinal_b_splines.html b/doc/html/math_toolkit/sf_poly/cardinal_b_splines.html index 06124f7ee5..a052b63979 100644 --- a/doc/html/math_toolkit/sf_poly/cardinal_b_splines.html +++ b/doc/html/math_toolkit/sf_poly/cardinal_b_splines.html @@ -4,10 +4,11 @@ Cardinal B-splines - + + @@ -205,9 +206,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/chebyshev.html b/doc/html/math_toolkit/sf_poly/chebyshev.html index 089a304cfa..bfeb0ceff5 100644 --- a/doc/html/math_toolkit/sf_poly/chebyshev.html +++ b/doc/html/math_toolkit/sf_poly/chebyshev.html @@ -4,10 +4,11 @@ Chebyshev Polynomials - + + @@ -243,9 +244,7 @@
in the constructor.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/gegenbauer.html b/doc/html/math_toolkit/sf_poly/gegenbauer.html index 0375bd042c..4833c89128 100644 --- a/doc/html/math_toolkit/sf_poly/gegenbauer.html +++ b/doc/html/math_toolkit/sf_poly/gegenbauer.html @@ -4,10 +4,11 @@ Gegenbauer Polynomials - + + @@ -149,9 +150,7 @@

In this case, only the zeroth Gegenbauer polynomial is nonzero.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/hermite.html b/doc/html/math_toolkit/sf_poly/hermite.html index 932ebe83b1..fcc095a1a4 100644 --- a/doc/html/math_toolkit/sf_poly/hermite.html +++ b/doc/html/math_toolkit/sf_poly/hermite.html @@ -4,10 +4,11 @@ Hermite Polynomials - + + @@ -227,9 +228,7 @@
error near one of the roots of the polynomials.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/jacobi.html b/doc/html/math_toolkit/sf_poly/jacobi.html index 5abeaccf35..bf83420bf1 100644 --- a/doc/html/math_toolkit/sf_poly/jacobi.html +++ b/doc/html/math_toolkit/sf_poly/jacobi.html @@ -4,10 +4,11 @@ Jacobi Polynomials - + + @@ -91,9 +92,7 @@

rising.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/laguerre.html b/doc/html/math_toolkit/sf_poly/laguerre.html index 8297c80994..fc1b4f855f 100644 --- a/doc/html/math_toolkit/sf_poly/laguerre.html +++ b/doc/html/math_toolkit/sf_poly/laguerre.html @@ -4,10 +4,11 @@ Laguerre (and Associated) Polynomials - + + @@ -370,9 +371,7 @@
error near one of the roots of the polynomials.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/legendre.html b/doc/html/math_toolkit/sf_poly/legendre.html index aeb73ceb8e..c1a3ed639f 100644 --- a/doc/html/math_toolkit/sf_poly/legendre.html +++ b/doc/html/math_toolkit/sf_poly/legendre.html @@ -4,10 +4,11 @@ Legendre (and Associated) Polynomials - + + @@ -637,9 +638,7 @@
error near one of the roots of the polynomials.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html b/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html index fbe5f02e60..fc96a1e7c8 100644 --- a/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html +++ b/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html @@ -4,10 +4,11 @@ Legendre-Stieltjes Polynomials - + + @@ -124,9 +125,7 @@
double norm = std::sqrt(E.norm_sq()); -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sf_poly/sph_harm.html b/doc/html/math_toolkit/sf_poly/sph_harm.html index 5621e622e5..f859df9721 100644 --- a/doc/html/math_toolkit/sf_poly/sph_harm.html +++ b/doc/html/math_toolkit/sf_poly/sph_harm.html @@ -4,10 +4,11 @@ Spherical Harmonics - + + @@ -318,9 +319,7 @@
calculate values near the roots of the associated Legendre functions.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sign_functions.html b/doc/html/math_toolkit/sign_functions.html index 178c7130c6..75aea53071 100644 --- a/doc/html/math_toolkit/sign_functions.html +++ b/doc/html/math_toolkit/sign_functions.html @@ -4,10 +4,11 @@ Sign Manipulation Functions - + + @@ -232,9 +233,7 @@
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/signal_statistics.html b/doc/html/math_toolkit/signal_statistics.html index 5a2a56f930..f598764af1 100644 --- a/doc/html/math_toolkit/signal_statistics.html +++ b/doc/html/math_toolkit/signal_statistics.html @@ -4,10 +4,11 @@ Signal Statistics - + + @@ -316,9 +317,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sinc.html b/doc/html/math_toolkit/sinc.html index c442a3b370..73313eb81a 100644 --- a/doc/html/math_toolkit/sinc.html +++ b/doc/html/math_toolkit/sinc.html @@ -4,10 +4,11 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions - + + @@ -34,9 +35,7 @@
sinhc_pi
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sinc/sinc_overview.html b/doc/html/math_toolkit/sinc/sinc_overview.html index 56953b2aab..54054a77bf 100644 --- a/doc/html/math_toolkit/sinc/sinc_overview.html +++ b/doc/html/math_toolkit/sinc/sinc_overview.html @@ -4,10 +4,11 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview - + + @@ -66,9 +67,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sinc/sinc_pi.html b/doc/html/math_toolkit/sinc/sinc_pi.html index a2c082f21e..1d00a12206 100644 --- a/doc/html/math_toolkit/sinc/sinc_pi.html +++ b/doc/html/math_toolkit/sinc/sinc_pi.html @@ -4,10 +4,11 @@ sinc_pi - + + @@ -62,9 +63,7 @@ documentation for more details.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/sinc/sinhc_pi.html b/doc/html/math_toolkit/sinc/sinhc_pi.html index 774c157869..5aa54574ee 100644 --- a/doc/html/math_toolkit/sinc/sinhc_pi.html +++ b/doc/html/math_toolkit/sinc/sinhc_pi.html @@ -4,10 +4,11 @@ sinhc_pi - + + @@ -67,9 +68,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/spec.html b/doc/html/math_toolkit/spec.html index 7543862c01..9fd7b1b0d5 100644 --- a/doc/html/math_toolkit/spec.html +++ b/doc/html/math_toolkit/spec.html @@ -4,10 +4,11 @@ Quaternion Specializations - + + @@ -173,9 +174,7 @@ }// namespace boost -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/special_tut.html b/doc/html/math_toolkit/special_tut.html index 36ca6fee27..732220d713 100644 --- a/doc/html/math_toolkit/special_tut.html +++ b/doc/html/math_toolkit/special_tut.html @@ -4,10 +4,11 @@ Tutorial: How to Write a New Special Function - + + @@ -32,9 +33,7 @@
Testing
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/special_tut/special_tut_impl.html b/doc/html/math_toolkit/special_tut/special_tut_impl.html index c85aa5a77e..9abe4d116a 100644 --- a/doc/html/math_toolkit/special_tut/special_tut_impl.html +++ b/doc/html/math_toolkit/special_tut/special_tut_impl.html @@ -4,10 +4,11 @@ Implementation - + + @@ -371,9 +372,7 @@
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/special_tut/special_tut_test.html b/doc/html/math_toolkit/special_tut/special_tut_test.html index 06bbed71e3..22f8c4de99 100644 --- a/doc/html/math_toolkit/special_tut/special_tut_test.html +++ b/doc/html/math_toolkit/special_tut/special_tut_test.html @@ -4,10 +4,11 @@ Testing - + + @@ -506,9 +507,7 @@
and follow their examples.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/specified_typedefs.html b/doc/html/math_toolkit/specified_typedefs.html index f71cab8f0a..18f6e0fdda 100644 --- a/doc/html/math_toolkit/specified_typedefs.html +++ b/doc/html/math_toolkit/specified_typedefs.html @@ -4,10 +4,11 @@ Overview - + + @@ -89,9 +90,7 @@ distribution as an example of a statistical distribution from Boost.Math.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/standalone.html b/doc/html/math_toolkit/standalone.html index 92689749f4..fbe0b47332 100644 --- a/doc/html/math_toolkit/standalone.html +++ b/doc/html/math_toolkit/standalone.html @@ -4,10 +4,11 @@ Standalone Usage - + + @@ -67,9 +68,7 @@ bleeding edge code (develop branch).

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut.html b/doc/html/math_toolkit/stat_tut.html index 5727011c1d..e35cfb5ce9 100644 --- a/doc/html/math_toolkit/stat_tut.html +++ b/doc/html/math_toolkit/stat_tut.html @@ -4,10 +4,11 @@ Statistical Distributions Tutorial - + + @@ -137,9 +138,7 @@ few worked examples of applying the library to statistical tests.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/dist_params.html b/doc/html/math_toolkit/stat_tut/dist_params.html index 378c2c0e1f..16eb43bc9e 100644 --- a/doc/html/math_toolkit/stat_tut/dist_params.html +++ b/doc/html/math_toolkit/stat_tut/dist_params.html @@ -4,10 +4,11 @@ Discrete Probability Distributions - + + @@ -81,9 +82,7 @@
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/overview.html b/doc/html/math_toolkit/stat_tut/overview.html index 958650e21d..afc8c2a66c 100644 --- a/doc/html/math_toolkit/stat_tut/overview.html +++ b/doc/html/math_toolkit/stat_tut/overview.html @@ -4,10 +4,11 @@ Overview of Statistical Distributions - + + @@ -41,9 +42,7 @@
Summary
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/overview/complements.html b/doc/html/math_toolkit/stat_tut/overview/complements.html index 698fef80cd..f4bb058c79 100644 --- a/doc/html/math_toolkit/stat_tut/overview/complements.html +++ b/doc/html/math_toolkit/stat_tut/overview/complements.html @@ -4,10 +4,11 @@ Complements are supported too - and when to use them - + + @@ -181,9 +182,7 @@
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/overview/generic.html b/doc/html/math_toolkit/stat_tut/overview/generic.html index e3f040c678..0f84ebd4ec 100644 --- a/doc/html/math_toolkit/stat_tut/overview/generic.html +++ b/doc/html/math_toolkit/stat_tut/overview/generic.html @@ -4,10 +4,11 @@ Generic operations common to all distributions are non-member functions - + + @@ -238,9 +239,7 @@
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/overview/headers.html b/doc/html/math_toolkit/stat_tut/overview/headers.html index a1a78fa5db..28de31003e 100644 --- a/doc/html/math_toolkit/stat_tut/overview/headers.html +++ b/doc/html/math_toolkit/stat_tut/overview/headers.html @@ -4,10 +4,11 @@ Headers and Namespaces - + + @@ -60,9 +61,7 @@

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/overview/objects.html b/doc/html/math_toolkit/stat_tut/overview/objects.html index 6df3984533..1d04da942a 100644 --- a/doc/html/math_toolkit/stat_tut/overview/objects.html +++ b/doc/html/math_toolkit/stat_tut/overview/objects.html @@ -4,10 +4,11 @@ Distributions are Objects - + + @@ -116,9 +117,7 @@ and quantiles etc for these distributions.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/overview/parameters.html b/doc/html/math_toolkit/stat_tut/overview/parameters.html index 4f1280ee28..3c363c1a5f 100644 --- a/doc/html/math_toolkit/stat_tut/overview/parameters.html +++ b/doc/html/math_toolkit/stat_tut/overview/parameters.html @@ -4,10 +4,11 @@ Parameters can be calculated - + + @@ -54,9 +55,7 @@ sample size.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/overview/summary.html b/doc/html/math_toolkit/stat_tut/overview/summary.html index 2771da5ab3..cd04f51e69 100644 --- a/doc/html/math_toolkit/stat_tut/overview/summary.html +++ b/doc/html/math_toolkit/stat_tut/overview/summary.html @@ -4,10 +4,11 @@ Summary - + + @@ -56,9 +57,7 @@ Now that you have the basics, the next section looks at some worked examples.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/variates.html b/doc/html/math_toolkit/stat_tut/variates.html index 851e1afcab..9f782b593b 100644 --- a/doc/html/math_toolkit/stat_tut/variates.html +++ b/doc/html/math_toolkit/stat_tut/variates.html @@ -4,10 +4,11 @@ Random Variates and Distribution Parameters - + + @@ -57,9 +58,7 @@
pdf(binomial_distribution<RealType>(n, p), k);
 
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg.html b/doc/html/math_toolkit/stat_tut/weg.html index 404cd9be66..d73cbd2cf3 100644 --- a/doc/html/math_toolkit/stat_tut/weg.html +++ b/doc/html/math_toolkit/stat_tut/weg.html @@ -4,10 +4,11 @@ Worked Examples - + + @@ -110,9 +111,7 @@ from Within C# -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/binom_eg.html b/doc/html/math_toolkit/stat_tut/weg/binom_eg.html index ff0fee7f83..4ce94ce3ba 100644 --- a/doc/html/math_toolkit/stat_tut/weg/binom_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/binom_eg.html @@ -4,10 +4,11 @@ Binomial Distribution Examples - + + @@ -42,9 +43,7 @@ Distribution.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html b/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html index 535ab436a1..64a8def685 100644 --- a/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html +++ b/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_conf.html @@ -4,10 +4,11 @@ Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution - + + @@ -222,9 +223,7 @@ small.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html b/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html index 07d7eda55a..fd49d7d12f 100644 --- a/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/binom_eg/binom_size_eg.html @@ -4,10 +4,11 @@ Estimating Sample Sizes for a Binomial Distribution. - + + @@ -141,9 +142,7 @@ chance of no failure).

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html b/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html index 6765aad9ad..5d3089be1b 100644 --- a/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html +++ b/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html @@ -4,10 +4,11 @@ Binomial Coin-Flipping Example - + + @@ -261,9 +262,7 @@ 10 1 or 1 in 1, or 100% -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html b/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html index a526b64fa9..ba0ddd8743 100644 --- a/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html +++ b/doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_quiz_example.html @@ -4,10 +4,11 @@ Binomial Quiz Example - + + @@ -439,9 +440,7 @@
for full source code and output.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/c_sharp.html b/doc/html/math_toolkit/stat_tut/weg/c_sharp.html index ac17f35f51..5254fa9385 100644 --- a/doc/html/math_toolkit/stat_tut/weg/c_sharp.html +++ b/doc/html/math_toolkit/stat_tut/weg/c_sharp.html @@ -4,10 +4,11 @@ Using the Distributions from Within C# - + + @@ -39,9 +40,7 @@ properties.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/cs_eg.html b/doc/html/math_toolkit/stat_tut/weg/cs_eg.html index d4ca42e550..02fe704344 100644 --- a/doc/html/math_toolkit/stat_tut/weg/cs_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/cs_eg.html @@ -4,10 +4,11 @@ Chi Squared Distribution Examples - + + @@ -36,9 +37,7 @@ the Required Sample Sizes for a Chi-Square Test for the Standard Deviation -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html b/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html index f764ce6d50..29afb16509 100644 --- a/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html +++ b/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_intervals.html @@ -4,10 +4,11 @@ Confidence Intervals on the Standard Deviation - + + @@ -231,9 +232,7 @@
convincing + or -1% confidence.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html b/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html index fd09f65bef..2058f4332e 100644 --- a/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html +++ b/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_size.html @@ -4,10 +4,11 @@ Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation - + + @@ -163,9 +164,7 @@ that we would need a sample size of 51.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html b/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html index bd410f10e3..49879499b2 100644 --- a/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html +++ b/doc/html/math_toolkit/stat_tut/weg/cs_eg/chi_sq_test.html @@ -4,10 +4,11 @@ Chi-Square Test for the Standard Deviation - + + @@ -278,9 +279,7 @@ and so we reject the manufacturers claim.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html b/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html index 3755da6ed6..2e84f78511 100644 --- a/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/dist_construct_eg.html @@ -4,10 +4,11 @@ Distribution Construction Examples - + + @@ -329,9 +330,7 @@
for full source code.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/error_eg.html b/doc/html/math_toolkit/stat_tut/weg/error_eg.html index 7bb87bba7f..c66c630dab 100644 --- a/doc/html/math_toolkit/stat_tut/weg/error_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/error_eg.html @@ -4,10 +4,11 @@ Error Handling Example - + + @@ -187,9 +188,7 @@
- - - -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/f_eg.html b/doc/html/math_toolkit/stat_tut/weg/f_eg.html index ba5b54baee..ed93aa1361 100644 --- a/doc/html/math_toolkit/stat_tut/weg/f_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/f_eg.html @@ -4,10 +4,11 @@ F Distribution Examples - + + @@ -310,9 +311,7 @@ conclude that there is a change for the better in our standard deviation.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/find_eg.html b/doc/html/math_toolkit/stat_tut/weg/find_eg.html index 92a4691072..48f453a52d 100644 --- a/doc/html/math_toolkit/stat_tut/weg/find_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/find_eg.html @@ -4,10 +4,11 @@ Find Location and Scale Examples - + + @@ -36,9 +37,7 @@ mean and standard deviation example -
- - -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html b/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html index 76a23c672f..f1bc26bdc4 100644 --- a/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/find_eg/find_location_eg.html @@ -4,10 +4,11 @@ Find Location (Mean) Example - + + @@ -171,9 +172,7 @@
Normal distribution with mean = 0.355146 has fraction > 2 = 0.05 -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html b/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html index ec32943ca1..d359bc900e 100644 --- a/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/find_eg/find_mean_and_sd_eg.html @@ -4,10 +4,11 @@ Find mean and standard deviation example - + + @@ -436,9 +437,7 @@
for full source code & appended program output.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html b/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html index 4a60a24b43..d7d8768f7f 100644 --- a/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/find_eg/find_scale_eg.html @@ -4,10 +4,11 @@ Find Scale (Standard Deviation) Example - + + @@ -190,9 +191,7 @@
Normal distribution with mean = 0.946339 has fraction > -2 = 0.999 -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/geometric_eg.html b/doc/html/math_toolkit/stat_tut/weg/geometric_eg.html index dbbe89e65b..72d5ba46e0 100644 --- a/doc/html/math_toolkit/stat_tut/weg/geometric_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/geometric_eg.html @@ -4,10 +4,11 @@ Geometric Distribution Examples - + + @@ -403,9 +404,7 @@
negative_binomial confidence interval example.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html b/doc/html/math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html index 1d651f7520..01a346f6ad 100644 --- a/doc/html/math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html @@ -4,10 +4,11 @@ Inverse Chi-Squared Distribution Bayes Example - + + @@ -342,9 +343,7 @@
See the full source C++ of this example at ../../example/inverse_chi_squared_bayes_eg.cpp

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/nag_library.html b/doc/html/math_toolkit/stat_tut/weg/nag_library.html index d98301e8da..f07286527c 100644 --- a/doc/html/math_toolkit/stat_tut/weg/nag_library.html +++ b/doc/html/math_toolkit/stat_tut/weg/nag_library.html @@ -4,10 +4,11 @@ Comparison with C, R, FORTRAN-style Free Functions - + + @@ -97,9 +98,7 @@ for details.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/nccs_eg.html b/doc/html/math_toolkit/stat_tut/weg/nccs_eg.html index 668f53b4ab..0da80791a7 100644 --- a/doc/html/math_toolkit/stat_tut/weg/nccs_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/nccs_eg.html @@ -4,10 +4,11 @@ Non Central Chi Squared Example - + + @@ -34,9 +35,7 @@ Chi Squared Distribution.)

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html b/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html index c5c20d8b4e..c89bfd89ff 100644 --- a/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/nccs_eg/nccs_power_eg.html @@ -4,10 +4,11 @@ Tables of the power function of the chi2 test. - + + @@ -1268,9 +1269,7 @@ for the full C++ source code.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg.html b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg.html index f663fd70c3..c02fe49027 100644 --- a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg.html @@ -4,10 +4,11 @@ Negative Binomial Distribution Examples - + + @@ -43,9 +44,7 @@ Binomial Distribution.)

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html index b8799de463..ee043e0303 100644 --- a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html +++ b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_conf.html @@ -4,10 +4,11 @@ Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution - + + @@ -202,9 +203,7 @@ value of 0.1.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html index 6bf357dc4d..5833bcb19a 100644 --- a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html @@ -4,10 +4,11 @@ Estimating Sample Sizes for the Negative Binomial. - + + @@ -188,9 +189,7 @@ certainty.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html index 4792c2c0aa..5e84a99817 100644 --- a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html +++ b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html @@ -4,10 +4,11 @@ Negative Binomial Sales Quota Example. - + + @@ -476,9 +477,7 @@ Number of failures argument is -1, but must be >= 0 ! -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html index eef70c6723..47a93aa3d0 100644 --- a/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html +++ b/doc/html/math_toolkit/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html @@ -4,10 +4,11 @@ Negative Binomial Table Printing Example. - + + @@ -117,9 +118,7 @@ 63,0.000246103187649585660.99882473495070978 -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/normal_example.html b/doc/html/math_toolkit/stat_tut/weg/normal_example.html index 22f05bab2b..e5ef09bca0 100644 --- a/doc/html/math_toolkit/stat_tut/weg/normal_example.html +++ b/doc/html/math_toolkit/stat_tut/weg/normal_example.html @@ -4,10 +4,11 @@ Normal Distribution Examples - + + @@ -34,9 +35,7 @@ Distribution.)

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/normal_example/normal_misc.html b/doc/html/math_toolkit/stat_tut/weg/normal_example/normal_misc.html index 018b093c51..a67cb48947 100644 --- a/doc/html/math_toolkit/stat_tut/weg/normal_example/normal_misc.html +++ b/doc/html/math_toolkit/stat_tut/weg/normal_example/normal_misc.html @@ -4,10 +4,11 @@ Some Miscellaneous Examples of the Normal (Gaussian) Distribution - + + @@ -499,9 +500,7 @@
cout << "95% of bolts are shorter than " << quantile(bolts, 0.95) << endl; -
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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/st_eg.html b/doc/html/math_toolkit/stat_tut/weg/st_eg.html index a20ce7313e..453a6e0905 100644 --- a/doc/html/math_toolkit/stat_tut/weg/st_eg.html +++ b/doc/html/math_toolkit/stat_tut/weg/st_eg.html @@ -4,10 +4,11 @@ Student's t Distribution Examples - + + @@ -41,9 +42,7 @@ two paired samples with the Student's t distribution -
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+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html b/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html index 32d902243a..4a84eb3773 100644 --- a/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html +++ b/doc/html/math_toolkit/stat_tut/weg/st_eg/paired_st.html @@ -4,10 +4,11 @@ Comparing two paired samples with the Student's t distribution - + + @@ -62,9 +63,7 @@ -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html b/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html index e992c0276c..30456616a1 100644 --- a/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html +++ b/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_intervals.html @@ -4,10 +4,11 @@ Calculating confidence intervals on the mean with the Students-t distribution - + + @@ -249,9 +250,7 @@ confident in the location of the mean.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html b/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html index 5ad2834d0c..9b15a9f9e5 100644 --- a/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html +++ b/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_size.html @@ -4,10 +4,11 @@ Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test - + + @@ -160,9 +161,7 @@ example at the 95% level, 14 measurements in total for a two-sided test.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html b/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html index 59e12d32c5..dea5a807e7 100644 --- a/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html +++ b/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html @@ -4,10 +4,11 @@ Testing a sample mean for difference from a "true" mean - + + @@ -315,9 +316,7 @@ more accurate data), is needed for a more convincing conclusion.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html b/doc/html/math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html index 1dc8c61660..fee1de4b2c 100644 --- a/doc/html/math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html +++ b/doc/html/math_toolkit/stat_tut/weg/st_eg/two_sample_students_t.html @@ -4,10 +4,11 @@ Comparing the means of two samples with the Students-t test - + + @@ -343,9 +344,7 @@ than Japanese models.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/t_test.html b/doc/html/math_toolkit/t_test.html index 5cef11e3e3..47d5e49d20 100644 --- a/doc/html/math_toolkit/t_test.html +++ b/doc/html/math_toolkit/t_test.html @@ -4,10 +4,11 @@ t-tests - + + @@ -254,9 +255,7 @@

OneSampleTTestKnownMeanAndVariance<double> 207 ns -

- - -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/threads.html b/doc/html/math_toolkit/threads.html index 38e4a88ce3..76ae2574cd 100644 --- a/doc/html/math_toolkit/threads.html +++ b/doc/html/math_toolkit/threads.html @@ -4,10 +4,11 @@ Thread Safety - + + @@ -33,9 +34,7 @@ removed.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/tr1_ref.html b/doc/html/math_toolkit/tr1_ref.html index af9772bac2..4253638b20 100644 --- a/doc/html/math_toolkit/tr1_ref.html +++ b/doc/html/math_toolkit/tr1_ref.html @@ -4,10 +4,11 @@ TR1 C Functions Quick Reference - + + @@ -540,9 +541,7 @@

- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/tradoffs.html b/doc/html/math_toolkit/tradoffs.html index dd301a9f8b..f5608e2350 100644 --- a/doc/html/math_toolkit/tradoffs.html +++ b/doc/html/math_toolkit/tradoffs.html @@ -4,10 +4,11 @@ Trading Accuracy for Performance - + + @@ -2549,9 +2550,7 @@
-
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/trans.html b/doc/html/math_toolkit/trans.html index 8aa5404b19..6ada811a97 100644 --- a/doc/html/math_toolkit/trans.html +++ b/doc/html/math_toolkit/trans.html @@ -4,10 +4,11 @@ Quaternion Transcendentals - + + @@ -125,9 +126,7 @@
Computes the n-th power of the quaternion q.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/trapezoidal.html b/doc/html/math_toolkit/trapezoidal.html index ea30cf4474..4659213fb9 100644 --- a/doc/html/math_toolkit/trapezoidal.html +++ b/doc/html/math_toolkit/trapezoidal.html @@ -4,10 +4,11 @@ Trapezoidal Quadrature - + + @@ -226,9 +227,7 @@

(2003): 265-275.

-

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/tuning.html b/doc/html/math_toolkit/tuning.html index 2698db5c57..e37daaa188 100644 --- a/doc/html/math_toolkit/tuning.html +++ b/doc/html/math_toolkit/tuning.html @@ -4,10 +4,11 @@ Performance Tuning Macros - + + @@ -7909,9 +7910,7 @@
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/tutorial.html b/doc/html/math_toolkit/tutorial.html index 9f9d224d98..9ef4441291 100644 --- a/doc/html/math_toolkit/tutorial.html +++ b/doc/html/math_toolkit/tutorial.html @@ -4,10 +4,11 @@ Tutorial - + + @@ -34,9 +35,7 @@ Types -
- - -
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/tutorial/non_templ.html b/doc/html/math_toolkit/tutorial/non_templ.html index b4ffe3c884..6a798c93e7 100644 --- a/doc/html/math_toolkit/tutorial/non_templ.html +++ b/doc/html/math_toolkit/tutorial/non_templ.html @@ -4,10 +4,11 @@ Use in non-template code - + + @@ -67,9 +68,7 @@ Some examples of using constants are at constants_eg1.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/tutorial/templ.html b/doc/html/math_toolkit/tutorial/templ.html index 77efab4359..5c3c37052d 100644 --- a/doc/html/math_toolkit/tutorial/templ.html +++ b/doc/html/math_toolkit/tutorial/templ.html @@ -4,10 +4,11 @@ Use in template code - + + @@ -138,9 +139,7 @@
- - - -
+
PrevUpHomeNext diff --git a/doc/html/math_toolkit/tutorial/user_def.html b/doc/html/math_toolkit/tutorial/user_def.html index fb8e3facf9..ce6f9150a2 100644 --- a/doc/html/math_toolkit/tutorial/user_def.html +++ b/doc/html/math_toolkit/tutorial/user_def.html @@ -4,10 +4,11 @@ Use With User-Defined Types - + + @@ -317,9 +318,7 @@
the constant will be constructed from a string on each call. -
- - -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/ulps_plots.html b/doc/html/math_toolkit/ulps_plots.html index 4b468d6dc2..b006e367b3 100644 --- a/doc/html/math_toolkit/ulps_plots.html +++ b/doc/html/math_toolkit/ulps_plots.html @@ -4,10 +4,11 @@ ULPs Plots - + + @@ -208,9 +209,7 @@

https://blogs.mathworks.com/cleve/2017/01/23/ulps-plots-reveal-math-function-accurary/ -

- - -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/univariate_statistics.html b/doc/html/math_toolkit/univariate_statistics.html index 0ce43dadc1..04b92ecc48 100644 --- a/doc/html/math_toolkit/univariate_statistics.html +++ b/doc/html/math_toolkit/univariate_statistics.html @@ -4,10 +4,11 @@ Univariate Statistics - + + @@ -523,9 +524,7 @@

-

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/value_op.html b/doc/html/math_toolkit/value_op.html index 8485c8e066..c5b7042d2e 100644 --- a/doc/html/math_toolkit/value_op.html +++ b/doc/html/math_toolkit/value_op.html @@ -4,10 +4,11 @@ Quaternion Value Operations - + + @@ -90,9 +91,7 @@
root of the Cayley norm.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/vector_barycentric.html b/doc/html/math_toolkit/vector_barycentric.html index 21a157c33b..7c8241dfb4 100644 --- a/doc/html/math_toolkit/vector_barycentric.html +++ b/doc/html/math_toolkit/vector_barycentric.html @@ -4,10 +4,11 @@ Vector-valued Barycentric Rational Interpolation - + + @@ -109,9 +110,7 @@

both values at once.

-

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/wavelet_transforms.html b/doc/html/math_toolkit/wavelet_transforms.html index 64a5d58a92..3536353616 100644 --- a/doc/html/math_toolkit/wavelet_transforms.html +++ b/doc/html/math_toolkit/wavelet_transforms.html @@ -4,10 +4,11 @@ Wavelet Transforms - + + @@ -90,9 +91,7 @@

-

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/whittaker_shannon.html b/doc/html/math_toolkit/whittaker_shannon.html index ae4ab001ce..ffdea709f1 100644 --- a/doc/html/math_toolkit/whittaker_shannon.html +++ b/doc/html/math_toolkit/whittaker_shannon.html @@ -4,10 +4,11 @@ Whittaker-Shannon interpolation - + + @@ -99,9 +100,7 @@

n is the number of points to interpolate.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/z_test.html b/doc/html/math_toolkit/z_test.html index 43adb19d10..139c76651e 100644 --- a/doc/html/math_toolkit/z_test.html +++ b/doc/html/math_toolkit/z_test.html @@ -4,10 +4,11 @@ z-tests - + + @@ -155,9 +156,7 @@

not need to be equal.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/zetas.html b/doc/html/math_toolkit/zetas.html index ccb10f0ed3..6985a23f75 100644 --- a/doc/html/math_toolkit/zetas.html +++ b/doc/html/math_toolkit/zetas.html @@ -4,10 +4,11 @@ Zeta Functions - + + @@ -28,9 +29,7 @@ -
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/zetas/zeta.html b/doc/html/math_toolkit/zetas/zeta.html index 8c18c4a011..16e1b91b32 100644 --- a/doc/html/math_toolkit/zetas/zeta.html +++ b/doc/html/math_toolkit/zetas/zeta.html @@ -4,10 +4,11 @@ Riemann Zeta Function - + + @@ -387,9 +388,7 @@
are of great benefit to some infinite series calculations.

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PrevUpHomeNext diff --git a/doc/html/octonions.html b/doc/html/octonions.html index 63b22d4403..e33d95f510 100644 --- a/doc/html/octonions.html +++ b/doc/html/octonions.html @@ -4,10 +4,11 @@ Chapter 17. Octonions - - + + + @@ -46,9 +47,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/overview.html b/doc/html/overview.html index 0a2f0fe4eb..dfcf52c9b0 100644 --- a/doc/html/overview.html +++ b/doc/html/overview.html @@ -4,10 +4,11 @@ Chapter 1. Overview - - - + + + + @@ -53,9 +54,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/perf.html b/doc/html/perf.html index 1383fdd8b4..5729145601 100644 --- a/doc/html/perf.html +++ b/doc/html/perf.html @@ -4,10 +4,11 @@ Chapter 22. Performance - - + + + @@ -43,9 +44,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/policy.html b/doc/html/policy.html index d1b2f9d5d2..6217f4049f 100644 --- a/doc/html/policy.html +++ b/doc/html/policy.html @@ -4,10 +4,11 @@ Chapter 21. Policies: Controlling Precision, Error Handling etc - - + + + @@ -72,9 +73,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/poly.html b/doc/html/poly.html index bbf641faa0..95269f5adb 100644 --- a/doc/html/poly.html +++ b/doc/html/poly.html @@ -4,10 +4,11 @@ Chapter 11. Polynomials and Rational Functions - - + + + @@ -35,9 +36,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/quadrature.html b/doc/html/quadrature.html index a8f9899184..20ee60ca6e 100644 --- a/doc/html/quadrature.html +++ b/doc/html/quadrature.html @@ -4,10 +4,11 @@ Chapter 13. Quadrature and Differentiation - - + + + @@ -56,9 +57,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/quaternions.html b/doc/html/quaternions.html index 51d01f1bb2..3ecfef471a 100644 --- a/doc/html/quaternions.html +++ b/doc/html/quaternions.html @@ -4,10 +4,11 @@ Chapter 16. Quaternions - - + + + @@ -47,9 +48,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/root_finding.html b/doc/html/root_finding.html index 3e83b07fc4..e7d5cb320e 100644 --- a/doc/html/root_finding.html +++ b/doc/html/root_finding.html @@ -4,10 +4,11 @@ Chapter 10. Root Finding & Minimization Algorithms - - + + + @@ -116,9 +117,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/special.html b/doc/html/special.html index bd3c56e4cd..37a7a6d2db 100644 --- a/doc/html/special.html +++ b/doc/html/special.html @@ -4,10 +4,11 @@ Chapter 8. Special Functions - - + + + @@ -240,9 +241,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/standalone_HTML.manifest b/doc/html/standalone_HTML.manifest index 719bb49ba1..e08f316425 100644 --- a/doc/html/standalone_HTML.manifest +++ b/doc/html/standalone_HTML.manifest @@ -162,6 +162,7 @@ math_toolkit/z_test.html math_toolkit/runs_test.html math_toolkit/ljung_box.html math_toolkit/linear_regression.html +math_toolkit/chatterjee_correlation.html vector_functionals.html math_toolkit/norms.html special.html diff --git a/doc/html/statistics.html b/doc/html/statistics.html index f84711f383..38ea19d8a1 100644 --- a/doc/html/statistics.html +++ b/doc/html/statistics.html @@ -4,10 +4,11 @@ Chapter 6. Statistics - - + + + @@ -37,12 +38,11 @@
Runs tests
The Ljung-Box Test
Linear Regression
+
Chatterjee Correlation
-
- - -
+

PrevUpHomeNext diff --git a/doc/html/status.html b/doc/html/status.html index 5f6c96026c..9bdf1a7e61 100644 --- a/doc/html/status.html +++ b/doc/html/status.html @@ -4,10 +4,11 @@ Chapter 24. Library Status - - + + + @@ -34,9 +35,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/using_udt.html b/doc/html/using_udt.html index 3d361c18cc..53c48b57c2 100644 --- a/doc/html/using_udt.html +++ b/doc/html/using_udt.html @@ -4,10 +4,11 @@ Chapter 20. Use with User-Defined Floating-Point Types - Boost.Multiprecision and others - - + + + @@ -54,9 +55,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/utils.html b/doc/html/utils.html index 200bc8f054..473f43eb09 100644 --- a/doc/html/utils.html +++ b/doc/html/utils.html @@ -4,10 +4,11 @@ Chapter 2. Floating Point Utilities - - + + + @@ -70,9 +71,7 @@ -
- - -
+

PrevUpHomeNext diff --git a/doc/html/vector_functionals.html b/doc/html/vector_functionals.html index c413640a82..67a8f380d1 100644 --- a/doc/html/vector_functionals.html +++ b/doc/html/vector_functionals.html @@ -4,10 +4,11 @@ Chapter 7. Vector Functionals - Norms - - - + + + + @@ -20,7 +21,7 @@

-PrevUpHomeNext +PrevUpHomeNext

@@ -30,9 +31,7 @@
Norms

- - - -
+

-PrevUpHomeNext +PrevUpHomeNext
diff --git a/doc/math.qbk b/doc/math.qbk index f3374a73d6..f4e80a39a7 100644 --- a/doc/math.qbk +++ b/doc/math.qbk @@ -9,7 +9,7 @@ ] [authors [Agrawal, Nikhar], [Bikineev, Anton], [Borland, Matthew], [Bristow, Paul A.], [Holin, Hubert], [Guazzone, Marco], [Kormanyos, Christopher], [Lalande, Bruno], [Maddock, John], [Miller, Evan], [Murphy, Jeremy W.], [Pulver, Matthew], [Råde, Johan], [Sobotta, Benjamin], [Sewani, Gautam], [Thompson, Nicholas], [van den Berg, Thijs], [Walker, Daryle], [Zhang, Xiaogang]] [/last-revision $Date$] - [version 4.1.0] + [version 4.1.1] ] [template mathpart[id title] diff --git a/doc/overview/roadmap.qbk b/doc/overview/roadmap.qbk index 10196bcfd1..b1c8b694da 100644 --- a/doc/overview/roadmap.qbk +++ b/doc/overview/roadmap.qbk @@ -8,6 +8,22 @@ All old bug reports including closed ones can be viewed on Trac Recent issues on GitHub [@https://github.com/boostorg/math/issues?utf8=%E2%9C%93&q=is%3Aissue here]. +[h4 Math-4.1.1 (Boost-1.84)] + +* Improve ccmath error detection. +* Remove use of deprecated std::numeric_limits<>::has_denorm, see [@https://github.com/boostorg/math/issues/1028 1028]. +* Correct non-convergence bug in non-central-t distribution, see [@https://github.com/boostorg/math/issues/1035 1035]. +* Adjust Bessel function approximation to [sub 1]F[sub 1] to avoid taking tgamma at a negative integer, see [@https://github.com/boostorg/math/issues/1034 1034]. +* Avoid spurious overflow and divide by zero in ibeta, see [@https://github.com/boostorg/math/issues/1006 1006]. +* Improve accuracy when using Sterling's approximation to tgamma, completes work started in [@https://github.com/boostorg/math/pull/1007 1007]. +* Fix inverse_discrete_quantile for large initial guesses, see [@https://github.com/boostorg/math/pull/1007 1007]. +* Improve Newton root finding, see [@https://github.com/boostorg/math/pull/1000 1000]. +* Fix median_absolute_deviation for non-zero centre, see [@https://github.com/boostorg/math/pull/997 997]. +* Fix up cstdfloat.hpp for gcc-14. +* Update to work for the new types declared in . +* Change hypergeometric_distribution to use 64 rather than 32 bit integers to avoid unnecessary overflow and restrictions on use. + + [h4 Math-4.1.0 (Boost-1.82)] * Added Estrin's method for polynomial evaluation. diff --git a/include/boost/math/special_functions/detail/round_fwd.hpp b/include/boost/math/special_functions/detail/round_fwd.hpp index c58459e36d..5d2e2688c3 100644 --- a/include/boost/math/special_functions/detail/round_fwd.hpp +++ b/include/boost/math/special_functions/detail/round_fwd.hpp @@ -21,37 +21,37 @@ namespace boost { template - typename tools::promote_args::type trunc(const T& v, const Policy& pol); + constexpr typename tools::promote_args::type trunc(const T& v, const Policy& pol); template - typename tools::promote_args::type trunc(const T& v); + constexpr typename tools::promote_args::type trunc(const T& v); template - int itrunc(const T& v, const Policy& pol); + constexpr int itrunc(const T& v, const Policy& pol); template - int itrunc(const T& v); + constexpr int itrunc(const T& v); template - long ltrunc(const T& v, const Policy& pol); + constexpr long ltrunc(const T& v, const Policy& pol); template - long ltrunc(const T& v); + constexpr long ltrunc(const T& v); template - long long lltrunc(const T& v, const Policy& pol); + constexpr long long lltrunc(const T& v, const Policy& pol); template - long long lltrunc(const T& v); + constexpr long long lltrunc(const T& v); template - typename tools::promote_args::type round(const T& v, const Policy& pol); + constexpr typename tools::promote_args::type round(const T& v, const Policy& pol); template - typename tools::promote_args::type round(const T& v); + constexpr typename tools::promote_args::type round(const T& v); template - int iround(const T& v, const Policy& pol); + constexpr int iround(const T& v, const Policy& pol); template - int iround(const T& v); + constexpr int iround(const T& v); template - long lround(const T& v, const Policy& pol); + constexpr long lround(const T& v, const Policy& pol); template - long lround(const T& v); + constexpr long lround(const T& v); template - long long llround(const T& v, const Policy& pol); + constexpr long long llround(const T& v, const Policy& pol); template - long long llround(const T& v); + constexpr long long llround(const T& v); template T modf(const T& v, T* ipart, const Policy& pol); template diff --git a/include/boost/math/special_functions/round.hpp b/include/boost/math/special_functions/round.hpp index e74acba85b..a482aa2e91 100644 --- a/include/boost/math/special_functions/round.hpp +++ b/include/boost/math/special_functions/round.hpp @@ -12,7 +12,7 @@ #endif #include -#include +#include #include #include #include @@ -30,12 +30,12 @@ namespace boost{ namespace math{ namespace detail{ template -inline tools::promote_args_t round(const T& v, const Policy& pol, const std::false_type&) +constexpr inline tools::promote_args_t round(const T& v, const Policy& pol, const std::false_type&) { BOOST_MATH_STD_USING using result_type = tools::promote_args_t; - if(!(boost::math::isfinite)(v)) + if(!BOOST_MATH_CONSTEXPR_ISFINITE(v)) { return policies::raise_rounding_error("boost::math::round<%1%>(%1%)", nullptr, static_cast(v), static_cast(v), pol); } @@ -54,18 +54,18 @@ inline tools::promote_args_t round(const T& v, const Policy& pol, const std:: { // subtract v from ceil(v) first in order to avoid rounding // errors on largest representable integer numbers - result_type c(ceil(v)); + result_type c(BOOST_MATH_CONSTEXPR_CEIL(v)); return T(0.5) < c - v ? c - 1 : c; } else { // see former branch - result_type f(floor(v)); + result_type f(BOOST_MATH_CONSTEXPR_FLOOR(v)); return T(0.5) < v - f ? f + 1 : f; } } template -inline tools::promote_args_t round(const T& v, const Policy&, const std::true_type&) +constexpr inline tools::promote_args_t round(const T& v, const Policy&, const std::true_type&) { return v; } @@ -73,12 +73,12 @@ inline tools::promote_args_t round(const T& v, const Policy&, const std::true } // namespace detail template -inline tools::promote_args_t round(const T& v, const Policy& pol) +constexpr inline tools::promote_args_t round(const T& v, const Policy& pol) { return detail::round(v, pol, std::integral_constant::value>()); } template -inline tools::promote_args_t round(const T& v) +constexpr inline tools::promote_args_t round(const T& v) { return round(v, policies::policy<>()); } @@ -96,7 +96,7 @@ inline tools::promote_args_t round(const T& v) // https://stackoverflow.com/questions/27442885/syntax-error-with-stdnumeric-limitsmax // template -inline int iround(const T& v, const Policy& pol) +constexpr inline int iround(const T& v, const Policy& pol) { BOOST_MATH_STD_USING using result_type = tools::promote_args_t; @@ -138,13 +138,13 @@ inline int iround(const T& v, const Policy& pol) return static_cast(r); } template -inline int iround(const T& v) +constexpr inline int iround(const T& v) { return iround(v, policies::policy<>()); } template -inline long lround(const T& v, const Policy& pol) +constexpr inline long lround(const T& v, const Policy& pol) { BOOST_MATH_STD_USING using result_type = tools::promote_args_t; @@ -186,13 +186,13 @@ inline long lround(const T& v, const Policy& pol) return static_cast(r); } template -inline long lround(const T& v) +constexpr inline long lround(const T& v) { return lround(v, policies::policy<>()); } template -inline long long llround(const T& v, const Policy& pol) +constexpr inline long long llround(const T& v, const Policy& pol) { BOOST_MATH_STD_USING using result_type = boost::math::tools::promote_args_t; @@ -234,7 +234,7 @@ inline long long llround(const T& v, const Policy& pol) return static_cast(r); } template -inline long long llround(const T& v) +constexpr inline long long llround(const T& v) { return llround(v, policies::policy<>()); } diff --git a/include/boost/math/special_functions/trunc.hpp b/include/boost/math/special_functions/trunc.hpp index a084de560b..e7515fa7df 100644 --- a/include/boost/math/special_functions/trunc.hpp +++ b/include/boost/math/special_functions/trunc.hpp @@ -14,7 +14,7 @@ #include #include #include -#include +#include #include #include #include @@ -27,19 +27,19 @@ namespace boost{ namespace math{ namespace detail{ template -inline tools::promote_args_t trunc(const T& v, const Policy& pol, const std::false_type&) +constexpr inline tools::promote_args_t trunc(const T& v, const Policy& pol, const std::false_type&) { BOOST_MATH_STD_USING using result_type = tools::promote_args_t; - if(!(boost::math::isfinite)(v)) + if(!BOOST_MATH_CONSTEXPR_ISFINITE(v)) { return policies::raise_rounding_error("boost::math::trunc<%1%>(%1%)", nullptr, static_cast(v), static_cast(v), pol); } - return (v >= 0) ? static_cast(floor(v)) : static_cast(ceil(v)); + return (v >= 0) ? static_cast(BOOST_MATH_CONSTEXPR_FLOOR(v)) : static_cast(BOOST_MATH_CONSTEXPR_CEIL(v)); } template -inline tools::promote_args_t trunc(const T& v, const Policy&, const std::true_type&) +constexpr inline tools::promote_args_t trunc(const T& v, const Policy&, const std::true_type&) { return v; } @@ -47,12 +47,12 @@ inline tools::promote_args_t trunc(const T& v, const Policy&, const std::true } template -inline tools::promote_args_t trunc(const T& v, const Policy& pol) +constexpr inline tools::promote_args_t trunc(const T& v, const Policy& pol) { return detail::trunc(v, pol, std::integral_constant::value>()); } template -inline tools::promote_args_t trunc(const T& v) +constexpr inline tools::promote_args_t trunc(const T& v) { return trunc(v, policies::policy<>()); } @@ -70,7 +70,7 @@ inline tools::promote_args_t trunc(const T& v) // https://stackoverflow.com/questions/27442885/syntax-error-with-stdnumeric-limitsmax // template -inline int itrunc(const T& v, const Policy& pol) +constexpr inline int itrunc(const T& v, const Policy& pol) { BOOST_MATH_STD_USING using result_type = tools::promote_args_t; @@ -111,13 +111,13 @@ inline int itrunc(const T& v, const Policy& pol) return static_cast(r); } template -inline int itrunc(const T& v) +constexpr inline int itrunc(const T& v) { return itrunc(v, policies::policy<>()); } template -inline long ltrunc(const T& v, const Policy& pol) +constexpr inline long ltrunc(const T& v, const Policy& pol) { BOOST_MATH_STD_USING using result_type = tools::promote_args_t; @@ -158,13 +158,13 @@ inline long ltrunc(const T& v, const Policy& pol) return static_cast(r); } template -inline long ltrunc(const T& v) +constexpr inline long ltrunc(const T& v) { return ltrunc(v, policies::policy<>()); } template -inline long long lltrunc(const T& v, const Policy& pol) +constexpr inline long long lltrunc(const T& v, const Policy& pol) { BOOST_MATH_STD_USING using result_type = tools::promote_args_t; @@ -205,20 +205,20 @@ inline long long lltrunc(const T& v, const Policy& pol) return static_cast(r); } template -inline long long lltrunc(const T& v) +constexpr inline long long lltrunc(const T& v) { return lltrunc(v, policies::policy<>()); } template -inline typename std::enable_if::value, int>::type +constexpr inline typename std::enable_if::value, int>::type iconvert(const T& v, const Policy&) { return static_cast(v); } template -inline typename std::enable_if::value, int>::type +constexpr inline typename std::enable_if::value, int>::type iconvert(const T& v, const Policy& pol) { using boost::math::itrunc; @@ -226,14 +226,14 @@ inline typename std::enable_if::value, int>::type } template -inline typename std::enable_if::value, long>::type +constexpr inline typename std::enable_if::value, long>::type lconvert(const T& v, const Policy&) { return static_cast(v); } template -inline typename std::enable_if::value, long>::type +constexpr inline typename std::enable_if::value, long>::type lconvert(const T& v, const Policy& pol) { using boost::math::ltrunc; @@ -241,14 +241,14 @@ inline typename std::enable_if::value, long>::ty } template -inline typename std::enable_if::value, long long>::type +constexpr inline typename std::enable_if::value, long long>::type llconvertert(const T& v, const Policy&) { return static_cast(v); } template -inline typename std::enable_if::value, long long>::type +constexpr inline typename std::enable_if::value, long long>::type llconvertert(const T& v, const Policy& pol) { using boost::math::lltrunc; From 2dd018b8c7e9e9bf9c9acba1c0c9893441b27f5f Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Sat, 18 Nov 2023 08:30:17 +0100 Subject: [PATCH 009/142] Revert "Update version history." 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doc/html/quaternions.html | 12 +- doc/html/root_finding.html | 12 +- doc/html/special.html | 12 +- doc/html/standalone_HTML.manifest | 1 - doc/html/statistics.html | 13 +- doc/html/status.html | 12 +- doc/html/using_udt.html | 12 +- doc/html/utils.html | 12 +- doc/html/vector_functionals.html | 18 +- doc/math.qbk | 2 +- doc/overview/roadmap.qbk | 16 -- .../special_functions/detail/round_fwd.hpp | 32 ++-- .../boost/math/special_functions/round.hpp | 28 ++-- .../boost/math/special_functions/trunc.hpp | 38 ++--- 493 files changed, 3132 insertions(+), 2466 deletions(-) delete mode 100644 doc/html/math_toolkit/chatterjee_correlation.html diff --git a/doc/html/backgrounders.html b/doc/html/backgrounders.html index 86ab4b66b3..b29bcfd47e 100644 --- a/doc/html/backgrounders.html +++ b/doc/html/backgrounders.html @@ -4,11 +4,10 @@ Chapter 23. Backgrounders - - + + - @@ -51,7 +50,9 @@ -
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Daubechies Filters
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-Math Toolkit 4.1.1

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Nikhar Agrawal @@ -134,7 +133,10 @@

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Last revised: February 23, 2023 at 18:11:17 GMT


Next
diff --git a/doc/html/indexes.html b/doc/html/indexes.html index 2b99eff987..f3d1541533 100644 --- a/doc/html/indexes.html +++ b/doc/html/indexes.html @@ -4,11 +4,10 @@ Chapter 25. Indexes - - + + - @@ -37,7 +36,9 @@ -
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+ + +
+

PrevUpHome diff --git a/doc/html/internals.html b/doc/html/internals.html index 56aa0eccc4..daf0ab7b2c 100644 --- a/doc/html/internals.html +++ b/doc/html/internals.html @@ -4,11 +4,10 @@ Chapter 19. Internal Details: Series, Rationals and Continued Fractions, Testing, and Development Tools - - + + - @@ -57,7 +56,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/interpolation.html b/doc/html/interpolation.html index b603e18533..2d54f46114 100644 --- a/doc/html/interpolation.html +++ b/doc/html/interpolation.html @@ -4,11 +4,10 @@ Chapter 12. Interpolation - - + + - @@ -51,7 +50,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/inverse_complex.html b/doc/html/inverse_complex.html index ffffbc7595..781eea65cd 100644 --- a/doc/html/inverse_complex.html +++ b/doc/html/inverse_complex.html @@ -4,11 +4,10 @@ Chapter 15. Complex Number Functions - - + + - @@ -47,7 +46,9 @@ Report on C++ Library Extensions.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/acknowledgement.html b/doc/html/math_toolkit/acknowledgement.html index 32ec4dd3ee..52eaee594f 100644 --- a/doc/html/math_toolkit/acknowledgement.html +++ b/doc/html/math_toolkit/acknowledgement.html @@ -4,11 +4,10 @@ Acknowledgements - + - @@ -34,7 +33,9 @@ section. Thank you to all who contributed to the discution about this library.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/acknowledgements.html b/doc/html/math_toolkit/acknowledgements.html index 15d6762589..0a0906b9d4 100644 --- a/doc/html/math_toolkit/acknowledgements.html +++ b/doc/html/math_toolkit/acknowledgements.html @@ -4,11 +4,10 @@ Acknowledgements - + - @@ -34,7 +33,9 @@ section. Thank you to all who contributed to the discussion about this library.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/acos.html b/doc/html/math_toolkit/acos.html index dc9e90dc63..f813c0b1d2 100644 --- a/doc/html/math_toolkit/acos.html +++ b/doc/html/math_toolkit/acos.html @@ -4,11 +4,10 @@ acos - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/acosh.html b/doc/html/math_toolkit/acosh.html index f137666eae..a0130c330f 100644 --- a/doc/html/math_toolkit/acosh.html +++ b/doc/html/math_toolkit/acosh.html @@ -4,11 +4,10 @@ acosh - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy.html b/doc/html/math_toolkit/airy.html index f278a7397e..272a42631a 100644 --- a/doc/html/math_toolkit/airy.html +++ b/doc/html/math_toolkit/airy.html @@ -4,11 +4,10 @@ Airy Functions - + - @@ -35,7 +34,9 @@
Finding Zeros of Airy Functions
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/ai.html b/doc/html/math_toolkit/airy/ai.html index 2aa4357847..bc4cde1534 100644 --- a/doc/html/math_toolkit/airy/ai.html +++ b/doc/html/math_toolkit/airy/ai.html @@ -4,11 +4,10 @@ Airy Ai Function - + - @@ -116,7 +115,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/aip.html b/doc/html/math_toolkit/airy/aip.html index 13621f8ca0..a16bc4113c 100644 --- a/doc/html/math_toolkit/airy/aip.html +++ b/doc/html/math_toolkit/airy/aip.html @@ -4,11 +4,10 @@ Airy Ai' Function - + - @@ -108,7 +107,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/airy_root.html b/doc/html/math_toolkit/airy/airy_root.html index 43bfee0eef..4f5dcfdbc8 100644 --- a/doc/html/math_toolkit/airy/airy_root.html +++ b/doc/html/math_toolkit/airy/airy_root.html @@ -4,11 +4,10 @@ Finding Zeros of Airy Functions - + - @@ -461,7 +460,9 @@

Alpha.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/bi.html b/doc/html/math_toolkit/airy/bi.html index 78e19f5846..14b6541e97 100644 --- a/doc/html/math_toolkit/airy/bi.html +++ b/doc/html/math_toolkit/airy/bi.html @@ -4,11 +4,10 @@ Airy Bi Function - + - @@ -107,7 +106,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/bip.html b/doc/html/math_toolkit/airy/bip.html index 411b622fba..77ac68c130 100644 --- a/doc/html/math_toolkit/airy/bip.html +++ b/doc/html/math_toolkit/airy/bip.html @@ -4,11 +4,10 @@ Airy Bi' Function - + - @@ -108,7 +107,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/anderson_darling.html b/doc/html/math_toolkit/anderson_darling.html index 6ee8655a78..f9a66831ea 100644 --- a/doc/html/math_toolkit/anderson_darling.html +++ b/doc/html/math_toolkit/anderson_darling.html @@ -4,11 +4,10 @@ The Anderson-Darling Test - + - @@ -191,7 +190,9 @@

of the Anderson-Darling test statistic agrees with Mathematica.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/archetypes.html b/doc/html/math_toolkit/archetypes.html index 01a0539917..6b8083aab2 100644 --- a/doc/html/math_toolkit/archetypes.html +++ b/doc/html/math_toolkit/archetypes.html @@ -4,11 +4,10 @@ Conceptual Archetypes for Reals and Distributions - + - @@ -178,7 +177,9 @@

implemented in there too.)

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/asin.html b/doc/html/math_toolkit/asin.html index d24d241600..f41968c9ff 100644 --- a/doc/html/math_toolkit/asin.html +++ b/doc/html/math_toolkit/asin.html @@ -4,11 +4,10 @@ asin - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/asinh.html b/doc/html/math_toolkit/asinh.html index 42166c69b9..f495ad9a46 100644 --- a/doc/html/math_toolkit/asinh.html +++ b/doc/html/math_toolkit/asinh.html @@ -4,11 +4,10 @@ asinh - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/atan.html b/doc/html/math_toolkit/atan.html index 6ebf1f0a3f..6189591fee 100644 --- a/doc/html/math_toolkit/atan.html +++ b/doc/html/math_toolkit/atan.html @@ -4,11 +4,10 @@ atan - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/atanh.html b/doc/html/math_toolkit/atanh.html index 4e63a8612b..16e89c8fb4 100644 --- a/doc/html/math_toolkit/atanh.html +++ b/doc/html/math_toolkit/atanh.html @@ -4,11 +4,10 @@ atanh - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/autodiff.html b/doc/html/math_toolkit/autodiff.html index fd4fdc5876..6e4b20a98b 100644 --- a/doc/html/math_toolkit/autodiff.html +++ b/doc/html/math_toolkit/autodiff.html @@ -4,11 +4,10 @@ Automatic Differentiation - + - @@ -400,7 +399,9 @@

manual.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bad_guess.html b/doc/html/math_toolkit/bad_guess.html index d873721a2f..756d317647 100644 --- a/doc/html/math_toolkit/bad_guess.html +++ b/doc/html/math_toolkit/bad_guess.html @@ -4,11 +4,10 @@ The Effect of a Poor Initial Guess - + - @@ -758,7 +757,9 @@ when using derivatives.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bad_roots.html b/doc/html/math_toolkit/bad_roots.html index df4e4eccc9..f26e434e0d 100644 --- a/doc/html/math_toolkit/bad_roots.html +++ b/doc/html/math_toolkit/bad_roots.html @@ -4,11 +4,10 @@ Examples Where Root Finding Goes Wrong - + - @@ -109,7 +108,9 @@

and for z0 > 0 the steps are actually divergent.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/barycentric.html b/doc/html/math_toolkit/barycentric.html index 5d443533af..659ded546f 100644 --- a/doc/html/math_toolkit/barycentric.html +++ b/doc/html/math_toolkit/barycentric.html @@ -4,11 +4,10 @@ Barycentric Rational Interpolation - + - @@ -269,7 +268,9 @@

Root was found in 10 iterations. -

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel.html b/doc/html/math_toolkit/bessel.html index ba429d56ec..bfcd26d3b7 100644 --- a/doc/html/math_toolkit/bessel.html +++ b/doc/html/math_toolkit/bessel.html @@ -4,11 +4,10 @@ Bessel Functions - + - @@ -41,7 +40,9 @@ the Bessel Functions -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/bessel_derivatives.html b/doc/html/math_toolkit/bessel/bessel_derivatives.html index 9c3b68f06c..129a03766d 100644 --- a/doc/html/math_toolkit/bessel/bessel_derivatives.html +++ b/doc/html/math_toolkit/bessel/bessel_derivatives.html @@ -4,11 +4,10 @@ Derivatives of the Bessel Functions - + - @@ -1437,7 +1436,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/bessel_first.html b/doc/html/math_toolkit/bessel/bessel_first.html index 46e55e05d8..e5942506b6 100644 --- a/doc/html/math_toolkit/bessel/bessel_first.html +++ b/doc/html/math_toolkit/bessel/bessel_first.html @@ -4,11 +4,10 @@ Bessel Functions of the First and Second Kinds - + - @@ -1368,7 +1367,9 @@
recurrence.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/bessel_over.html b/doc/html/math_toolkit/bessel/bessel_over.html index 1960c93cec..c2a200ddf3 100644 --- a/doc/html/math_toolkit/bessel/bessel_over.html +++ b/doc/html/math_toolkit/bessel/bessel_over.html @@ -4,11 +4,10 @@ Bessel Function Overview - + - @@ -216,7 +215,9 @@
and sph_neumann.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/bessel_root.html b/doc/html/math_toolkit/bessel/bessel_root.html index 92971a0641..f2d03c3a7a 100644 --- a/doc/html/math_toolkit/bessel/bessel_root.html +++ b/doc/html/math_toolkit/bessel/bessel_root.html @@ -4,11 +4,10 @@ Finding Zeros of Bessel Functions of the First and Second Kinds - + - @@ -756,7 +755,9 @@

Alpha.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/mbessel.html b/doc/html/math_toolkit/bessel/mbessel.html index bfd73b84d5..1d5880d21b 100644 --- a/doc/html/math_toolkit/bessel/mbessel.html +++ b/doc/html/math_toolkit/bessel/mbessel.html @@ -4,11 +4,10 @@ Modified Bessel Functions of the First and Second Kinds - + - @@ -1181,7 +1180,9 @@
two values and fν, the Wronskian yields Iν(x) directly.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/sph_bessel.html b/doc/html/math_toolkit/bessel/sph_bessel.html index d42a7bbfe7..025b803cc7 100644 --- a/doc/html/math_toolkit/bessel/sph_bessel.html +++ b/doc/html/math_toolkit/bessel/sph_bessel.html @@ -4,11 +4,10 @@ Spherical Bessel Functions of the First and Second Kinds - + - @@ -273,7 +272,9 @@
main definition as x → 0.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bezier_polynomial.html b/doc/html/math_toolkit/bezier_polynomial.html index 6dd232725e..5ec26eeeb6 100644 --- a/doc/html/math_toolkit/bezier_polynomial.html +++ b/doc/html/math_toolkit/bezier_polynomial.html @@ -4,11 +4,10 @@ Bezier Polynomials - + - @@ -234,7 +233,9 @@

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bilinear_uniform.html b/doc/html/math_toolkit/bilinear_uniform.html index e5b9a43fd4..26cca6dff2 100644 --- a/doc/html/math_toolkit/bilinear_uniform.html +++ b/doc/html/math_toolkit/bilinear_uniform.html @@ -4,11 +4,10 @@ Bilinear Uniform Interpolation - + - @@ -125,7 +124,9 @@

Bilinear<double>/8192 13.2 ns -

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bivariate_statistics.html b/doc/html/math_toolkit/bivariate_statistics.html index 5b39e5da55..1435f61652 100644 --- a/doc/html/math_toolkit/bivariate_statistics.html +++ b/doc/html/math_toolkit/bivariate_statistics.html @@ -4,11 +4,10 @@ Bivariate Statistics - + - @@ -138,7 +137,9 @@

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/brent_minima.html b/doc/html/math_toolkit/brent_minima.html index 4315a77e37..de2304809a 100644 --- a/doc/html/math_toolkit/brent_minima.html +++ b/doc/html/math_toolkit/brent_minima.html @@ -4,11 +4,10 @@ Locating Function Minima using Brent's algorithm - + - @@ -650,7 +649,9 @@
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/building.html b/doc/html/math_toolkit/building.html index f49a9f9e34..c270a5a7d0 100644 --- a/doc/html/math_toolkit/building.html +++ b/doc/html/math_toolkit/building.html @@ -4,11 +4,10 @@ If and How to Build a Boost.Math Library, and its Examples and Tests - + - @@ -146,7 +145,9 @@
the sources. Boost.Build will do this automatically when appropriate.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/c99.html b/doc/html/math_toolkit/c99.html index 3867e13765..5881569324 100644 --- a/doc/html/math_toolkit/c99.html +++ b/doc/html/math_toolkit/c99.html @@ -4,11 +4,10 @@ C99 C Functions - + - @@ -462,7 +461,9 @@
ISO Standard

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cardinal_cubic_b.html b/doc/html/math_toolkit/cardinal_cubic_b.html index faf45cf96b..62dca00371 100644 --- a/doc/html/math_toolkit/cardinal_cubic_b.html +++ b/doc/html/math_toolkit/cardinal_cubic_b.html @@ -4,11 +4,10 @@ Cardinal Cubic B-spline interpolation - + - @@ -312,7 +311,9 @@

Found in 3 iterations -

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cardinal_quadratic_b.html b/doc/html/math_toolkit/cardinal_quadratic_b.html index fed84661ef..adf1717940 100644 --- a/doc/html/math_toolkit/cardinal_quadratic_b.html +++ b/doc/html/math_toolkit/cardinal_quadratic_b.html @@ -4,11 +4,10 @@ Cardinal Quadratic B-spline interpolation - + - @@ -84,7 +83,9 @@

differentiable, but not three or four times differentiable.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cardinal_quintic_b.html b/doc/html/math_toolkit/cardinal_quintic_b.html index 7961239352..30d27e0177 100644 --- a/doc/html/math_toolkit/cardinal_quintic_b.html +++ b/doc/html/math_toolkit/cardinal_quintic_b.html @@ -4,11 +4,10 @@ Cardinal Quintic B-spline interpolation - + - @@ -121,7 +120,9 @@

of data by spline functions. Diss. City, University of London, 1975.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cardinal_trigonometric.html b/doc/html/math_toolkit/cardinal_trigonometric.html index 4c9049f63a..230f548a45 100644 --- a/doc/html/math_toolkit/cardinal_trigonometric.html +++ b/doc/html/math_toolkit/cardinal_trigonometric.html @@ -4,11 +4,10 @@ Cardinal Trigonometric interpolation - + - @@ -149,7 +148,9 @@

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/catmull_rom.html b/doc/html/math_toolkit/catmull_rom.html index 7867e8ff35..dfe10da166 100644 --- a/doc/html/math_toolkit/catmull_rom.html +++ b/doc/html/math_toolkit/catmull_rom.html @@ -4,11 +4,10 @@ Catmull-Rom Splines - + - @@ -352,7 +351,9 @@

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/ccmath.html b/doc/html/math_toolkit/ccmath.html index 670550ee7c..ad68936f98 100644 --- a/doc/html/math_toolkit/ccmath.html +++ b/doc/html/math_toolkit/ccmath.html @@ -4,11 +4,10 @@ Constexpr CMath - + - @@ -233,7 +232,9 @@

} // Namespaces -

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/chatterjee_correlation.html b/doc/html/math_toolkit/chatterjee_correlation.html deleted file mode 100644 index b00f732609..0000000000 --- a/doc/html/math_toolkit/chatterjee_correlation.html +++ /dev/null @@ -1,132 +0,0 @@ - - - -Chatterjee Correlation - - - - - - - - - - - - - - - - -
Boost C++ LibrariesHomeLibrariesPeopleFAQMore
-
-
-PrevUpHomeNext -
-
- -

- - Synopsis -

-
#include <boost/math/statistics/chatterjee_correlation.hpp>
-
-namespace boost::math::statistics {
-
-    C++17:
-    template <typename ExecutionPolicy, typename Container>
-    auto chatterjee_correlation(ExecutionPolicy&& exec, const Container& u, const Container& v);
-
-    C++11:
-    template <typename Container>
-    auto chatterjee_correlation(const Container& u, const Container& v);
-}
-
-

- - Description -

-

- The classical correlation coefficients like the Pearson's correlation are useful - primarily for distinguishing when one dataset depends linearly on another. - However, Pearson's correlation coefficient has a known weakness in that when - the dependent variable has an obvious functional relationship with the independent - variable, the value of the correlation coefficient can take on any value. As - Chatterjee says: -

-

- > Ideally, one would like a coefficient that approaches its maximum value - if and only if one variable looks more and more like a noiseless function of - the other, just as Pearson correlation is close to its maximum value if and - only if one variable is close to being a noiseless linear function of the other. -

-

- This is the problem Chatterjee's coefficient solves. Let X and Y be random - variables, where Y is not constant, and let (X_i, Y_i) be samples from this - distribution. Rearrange these samples so that X_(0) < X_{(1)} < ... X_{(n-1)} - and create (R(X_{(i)}), R(Y_{(i)})). The Chatterjee correlation is then given - by -

-

- -

-

- In the limit of an infinite amount of i.i.d data, the statistic lies in [0, - 1]. However, if the data is not infinite, the statistic may be negative. If - X and Y are independent, the value is zero, and if Y is a measurable function - of X, then the statistic is unity. The complexity is O(n log n). -

-

- An example is given below: -

-
std::vector<double> X{1,2,3,4,5};
-std::vector<double> Y{1,2,3,4,5};
-using boost::math::statistics::chatterjee_correlation;
-double coeff = chatterjee_correlation(X, Y);
-
-

- The implementation follows Chatterjee's - paper. -

-

- Nota bene: If the input is an integer type the output - will be a double precision type. -

-

- - Invariants -

-

- The function expects at least two samples, a non-constant vector Y, and the - same number of X's as Y's. If Y is constant, the result is a quiet NaN. The - data set must be sorted by X values. If there are ties in the values of X, - then the statistic is random due to the random breaking of ties. Of course, - random numbers are not used internally, but the result is not guaranteed to - be identical on different systems. -

-

- - References -

-
  • - Chatterjee, Sourav. "A new coefficient of correlation." Journal - of the American Statistical Association 116.536 (2021): 2009-2022. -
-
- -
-
-PrevUpHomeNext -
- - diff --git a/doc/html/math_toolkit/comp_compilers.html b/doc/html/math_toolkit/comp_compilers.html index 703c20936a..e33a1aa759 100644 --- a/doc/html/math_toolkit/comp_compilers.html +++ b/doc/html/math_toolkit/comp_compilers.html @@ -4,11 +4,10 @@ Comparing Different Compilers - + - @@ -3193,7 +3192,9 @@
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/comparisons.html b/doc/html/math_toolkit/comparisons.html index 403cf326e7..9f52bfddc4 100644 --- a/doc/html/math_toolkit/comparisons.html +++ b/doc/html/math_toolkit/comparisons.html @@ -4,11 +4,10 @@ Comparisons to Other Open Source Libraries - + - @@ -4719,7 +4718,9 @@
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/compilers_overview.html b/doc/html/math_toolkit/compilers_overview.html index 72a0a507fa..92984b75b1 100644 --- a/doc/html/math_toolkit/compilers_overview.html +++ b/doc/html/math_toolkit/compilers_overview.html @@ -4,11 +4,10 @@ Compilers - + - @@ -665,7 +664,9 @@ acceptable or not.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/complex_history.html b/doc/html/math_toolkit/complex_history.html index c2518faa2a..a8a2a30c82 100644 --- a/doc/html/math_toolkit/complex_history.html +++ b/doc/html/math_toolkit/complex_history.html @@ -4,11 +4,10 @@ History - + - @@ -36,7 +35,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/complex_implementation.html b/doc/html/math_toolkit/complex_implementation.html index b5573b7d17..98ee347fff 100644 --- a/doc/html/math_toolkit/complex_implementation.html +++ b/doc/html/math_toolkit/complex_implementation.html @@ -4,11 +4,10 @@ Implementation and Accuracy - + - @@ -45,7 +44,9 @@ paper for more information on the implementation methodology.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cond.html b/doc/html/math_toolkit/cond.html index 95329b7ff9..8b3a9fd1a7 100644 --- a/doc/html/math_toolkit/cond.html +++ b/doc/html/math_toolkit/cond.html @@ -4,11 +4,10 @@ Condition Numbers - + - @@ -167,7 +166,9 @@

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/config_macros.html b/doc/html/math_toolkit/config_macros.html index 7681b650c5..4a3bb6cd47 100644 --- a/doc/html/math_toolkit/config_macros.html +++ b/doc/html/math_toolkit/config_macros.html @@ -4,11 +4,10 @@ Configuration Macros - + - @@ -365,7 +364,9 @@
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/constants.html b/doc/html/math_toolkit/constants.html index e3b72df283..be6e72dfa4 100644 --- a/doc/html/math_toolkit/constants.html +++ b/doc/html/math_toolkit/constants.html @@ -4,11 +4,10 @@ The Mathematical Constants - + - @@ -1756,7 +1755,9 @@

-