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/*
* NumJS -- a JavaScript library for numerical computing
*
* Copyright (C) 2011 Clifford Wolf <clifford@clifford.at>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
"use strict";
NumJS.Cmplx = function(re, im) {
this.re = re;
this.im = im;
};
NumJS.C = function(re, im) {
return new NumJS.Cmplx(re, im);
};
NumJS.P = function(abs, arg) {
var re = abs * Math.cos(arg);
var im = abs * Math.sin(arg);
return new NumJS.Cmplx(re, im);
};
NumJS.Cmplx.prototype =
{
op_add: function(a, b) {
if ((a instanceof NumJS.Cmplx) && (b instanceof NumJS.Cmplx))
return NumJS.C(a.re + b.re, a.im + b.im);
if ((a instanceof NumJS.Cmplx) && (typeof(b) == "number"))
return NumJS.C(a.re + b, a.im);
if ((typeof(a) == "number") && (b instanceof NumJS.Cmplx))
return NumJS.C(a + b.re, b.im);
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_add) == "function"))
return b.op_add(a, b);
throw "NumJS.Cmplx type error";
},
op_sub: function(a, b) {
if ((a instanceof NumJS.Cmplx) && (b instanceof NumJS.Cmplx))
return NumJS.C(a.re - b.re, a.im - b.im);
if ((a instanceof NumJS.Cmplx) && (typeof(b) == "number"))
return NumJS.C(a.re - b, a.im);
if ((typeof(a) == "number") && (b instanceof NumJS.Cmplx))
return NumJS.C(a - b.re, -b.im);
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_sub) == "function"))
return b.op_sub(a, b);
throw "NumJS.Cmplx type error";
},
op_mul: function(a, b) {
if ((a instanceof NumJS.Cmplx) && (b instanceof NumJS.Cmplx))
return NumJS.C(a.re*b.re - a.im*b.im, a.re*b.im + a.im*b.re);
if ((a instanceof NumJS.Cmplx) && (typeof(b) == "number"))
return NumJS.C(a.re * b, a.im * b);
if ((typeof(a) == "number") && (b instanceof NumJS.Cmplx))
return NumJS.C(a * b.re, a * b.im);
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_mul) == "function"))
return b.op_mul(a, b);
throw "NumJS.Cmplx type error";
},
op_dot: function(a, b) {
if ((a instanceof NumJS.Cmplx) && (b instanceof NumJS.Cmplx))
return NumJS.C(a.re*b.re - a.im*b.im, a.re*b.im + a.im*b.re);
if ((a instanceof NumJS.Cmplx) && (typeof(b) == "number"))
return NumJS.C(a.re * b, a.im * b);
if ((typeof(a) == "number") && (b instanceof NumJS.Cmplx))
return NumJS.C(a * b.re, a * b.im);
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_dot) == "function"))
return b.op_dot(a, b);
throw "NumJS.Cmplx type error";
},
op_div: function(a, b) {
if ((a instanceof NumJS.Cmplx) && (b instanceof NumJS.Cmplx))
return NumJS.C((a.re*b.re + a.im*b.im) / (b.re*b.re + b.im*b.im),
(a.im*b.re - a.re*b.im) / (b.re*b.re + b.im*b.im));
if ((a instanceof NumJS.Cmplx) && (typeof(b) == "number"))
return NumJS.C(a.re / b, a.im / b);
if ((typeof(a) == "number") && (b instanceof NumJS.Cmplx))
return NumJS.C((a*b.re) / (b.re*b.re + b.im*b.im), (-a*b.im) / (b.re*b.re + b.im*b.im));
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_div) == "function"))
return b.op_div(a, b);
throw "NumJS.Cmplx type error";
},
op_solve: function(a, b) {
var aIsScalar = typeof(a) == "number" || a instanceof NumJS.Cmplx;
var bIsScalar = typeof(b) == "number" || b instanceof NumJS.Cmplx;
if (aIsScalar && bIsScalar)
return this.op_div(b, a);
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_solve) == "function"))
return b.op_solve(a, b);
throw "NumJS.Cmplx type error";
},
op_pow: function(a, b) {
var aIsScalar = typeof(a) == "number" || a instanceof NumJS.Cmplx;
var bIsScalar = typeof(b) == "number" || b instanceof NumJS.Cmplx;
if (aIsScalar && bIsScalar) {
var aIsReal = NumJS.IM(a) == 0;
var bIsReal = NumJS.IM(b) == 0;
if (aIsReal && bIsReal)
return Math.pow(NumJS.RE(a), NumJS.RE(b));
if (aIsReal)
return NumJS.EXP(NumJS.MUL(b, NumJS.LOG(a)));
if (bIsReal)
return NumJS.P(Math.pow(NumJS.ABS(a), NumJS.RE(b)), NumJS.ARG(a) * NumJS.RE(b));
}
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_pow) == "function"))
return b.op_pow(a, b);
throw "NumJS.Cmplx type error";
},
op_inv: function(a) {
return NumJS.C(1 / (a.re*a.re + a.im*a.im), -a.im / (a.re*a.re + a.im*a.im));
},
op_neg: function(a) {
return NumJS.C(-a.re, -a.im);
},
op_abs: function(a) {
return Math.sqrt(a.re*a.re + a.im*a.im);
},
op_norm: function(a) {
return Math.sqrt(a.re*a.re + a.im*a.im);
},
op_arg: function(a) {
return Math.atan2(a.im, a.re);
},
op_conj: function(a) {
return NumJS.C(a.re, -a.im);
},
op_transp: function(a) {
return a;
},
op_exp: function(a) {
var len = Math.exp(a.re);
if (a.im == 0)
return len;
return NumJS.C(len * Math.cos(a.im), len * Math.sin(a.im));
},
op_log: function(a) {
if (a.im == 0)
return Math.log(a.re);
throw "NumJS.Cmplx type error";
},
op_det: function(a) {
return a;
},
op_re: function(a) {
return a.re;
},
op_im: function(a) {
return a.im;
},
op_round: function(a, n) {
return NumJS.C(NumJS.ROUND(a.re, n), NumJS.ROUND(a.im, n));
},
op_eq: function(a, b) {
if ((a instanceof NumJS.Cmplx) && (b instanceof NumJS.Cmplx))
return a.re == b.re && a.im == b.im;
if ((a instanceof NumJS.Cmplx) && (typeof(b) == "number"))
return a.re == b && a.im == 0;
if ((typeof(a) == "number") && (b instanceof NumJS.Cmplx))
return a == b.re && 0 == b.im;
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_eq) == "function"))
return b.op_eq(a, b);
throw "NumJS.Cmplx type error";
},
op_eq_abs: function(a, b, d) {
var aIsScalar = typeof(a) == "number" || a instanceof NumJS.Cmplx;
var bIsScalar = typeof(b) == "number" || b instanceof NumJS.Cmplx;
if (aIsScalar && bIsScalar)
return NumJS.ABS(NumJS.SUB(a, b)) <= d;
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_eq_abs) == "function"))
return b.op_eq_abs(a, b);
throw "NumJS.Cmplx type error";
},
op_eq_rel: function(a, b, d) {
var aIsScalar = typeof(a) == "number" || a instanceof NumJS.Cmplx;
var bIsScalar = typeof(b) == "number" || b instanceof NumJS.Cmplx;
if (aIsScalar && bIsScalar)
return NumJS.ABS(NumJS.SUB(a, b)) <= d * (NumJS.ABS(a) + NumJS.ABS(b)) * 0.5;
if (!(b instanceof NumJS.Cmplx) && (typeof(b.op_eq_rel) == "function"))
return b.op_eq_rel(a, b);
throw "NumJS.Cmplx type error";
},
toString: function(n) {
return "(" + this.re.toString(n) + (this.im >= 0 ? "+" : "") +
this.im.toString(n) + "i)";
},
toFixed: function(n) {
return "(" + this.re.toFixed(n) + (this.im >= 0 ? "+" : "") +
this.im.toFixed(n) + "i)";
},
toPrecision: function(n) {
return "(" + this.re.toPrecision(n) + (this.im >= 0 ? "+" : "") +
this.im.toPrecision(n) + "i)";
}
};