@@ -13,26 +13,26 @@ module la_lapack
1313 public
1414
1515 !> BBCSD: computes the CS decomposition of a unitary matrix in
16- !> bidiagonal-block form,
17- !> [ B11 | B12 0 0 ]
18- !> [ 0 | 0 -I 0 ]
19- !> X = [----------------]
20- !> [ B21 | B22 0 0 ]
21- !> [ 0 | 0 0 I ]
22- !> [ C | -S 0 0 ]
23- !> [ U1 | ] [ 0 | 0 -I 0 ] [ V1 | ]**H
24- !> = [---------] [---------------] [---------] .
25- !> [ | U2 ] [ S | C 0 0 ] [ | V2 ]
26- !> [ 0 | 0 0 I ]
27- !> X is M-by-M, its top-left block is P-by-Q, and Q must be no larger
28- !> than P, M-P, or M-Q. (If Q is not the smallest index, then X must be
29- !> transposed and/or permuted. This can be done in constant time using
30- !> the TRANS and SIGNS options. See CUNCSD for details.)
31- !> The bidiagonal matrices B11, B12, B21, and B22 are represented
32- !> implicitly by angles THETA(1:Q) and PHI(1:Q-1).
33- !> The unitary matrices U1, U2, V1T, and V2T are input/output.
34- !> The input matrices are pre- or post-multiplied by the appropriate
35- !> singular vector matrices.
16+ !! bidiagonal-block form,
17+ !! [ B11 | B12 0 0 ]
18+ !! [ 0 | 0 -I 0 ]
19+ !! X = [----------------]
20+ !! [ B21 | B22 0 0 ]
21+ !! [ 0 | 0 0 I ]
22+ !! [ C | -S 0 0 ]
23+ !! [ U1 | ] [ 0 | 0 -I 0 ] [ V1 | ]**H
24+ !! = [---------] [---------------] [---------] .
25+ !! [ | U2 ] [ S | C 0 0 ] [ | V2 ]
26+ !! [ 0 | 0 0 I ]
27+ !! X is M-by-M, its top-left block is P-by-Q, and Q must be no larger
28+ !! than P, M-P, or M-Q. (If Q is not the smallest index, then X must be
29+ !! transposed and/or permuted. This can be done in constant time using
30+ !! the TRANS and SIGNS options. See CUNCSD for details.)
31+ !! The bidiagonal matrices B11, B12, B21, and B22 are represented
32+ !! implicitly by angles THETA(1:Q) and PHI(1:Q-1).
33+ !! The unitary matrices U1, U2, V1T, and V2T are input/output.
34+ !! The input matrices are pre- or post-multiplied by the appropriate
35+ !! singular vector matrices.
3636 interface bbcsd
3737#ifdef LA_EXTERNAL_LAPACK
3838 pure subroutine cbbcsd(jobu1,jobu2,jobv1t,jobv2t,trans,m,p,q,theta,phi, &
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