diff options
Diffstat (limited to '2.3-1/src/c/matrixOperations/logm')
12 files changed, 1814 insertions, 0 deletions
diff --git a/2.3-1/src/c/matrixOperations/logm/Makefile.am b/2.3-1/src/c/matrixOperations/logm/Makefile.am new file mode 100644 index 00000000..f21ded7d --- /dev/null +++ b/2.3-1/src/c/matrixOperations/logm/Makefile.am @@ -0,0 +1,81 @@ +## +## Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +## Copyright (C) 2008 - INRIA - Arnaud TORSET +## +## This file must be used under the terms of the CeCILL. +## This source file is licensed as described in the file COPYING, which +## you should have received as part of this distribution. The terms +## are also available at +## http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt +## +## + + + + +libLogm_la_CFLAGS = -I ./includes \ + -I $(top_builddir)/src/c/type \ + -I $(top_builddir)/src/c/elementaryFunctions/includes \ + -I $(top_builddir)/src/c/operations/includes \ + -I $(top_builddir)/src/c/auxiliaryFunctions/includes \ + -I $(top_builddir)/src/c/matrixOperations/includes + + +instdir = $(top_builddir)/lib + + +pkglib_LTLIBRARIES = libLogm.la + +HEAD = ../includes/logm.h + + +libLogm_la_SOURCES = $(HEAD) \ + zlogma.c \ + clogma.c \ + slogma.c \ + dlogma.c + +############# +## CHECK ## +############# + +check_PROGRAMS = testDoubleLogm testFloatLogm + +check_LDADD = $(top_builddir)/src/c/type/libDoubleComplex.la \ + $(top_builddir)/src/c/type/libFloatComplex.la \ + $(top_builddir)/src/fortran/lapack/libscilapack.la \ + $(top_builddir)/src/fortran/blas/libsciblas.la \ + $(top_builddir)/src/c/elementaryFunctions/log/libLog.la \ + $(top_builddir)/src/c/elementaryFunctions/sqrt/libSqrt.la \ + $(top_builddir)/src/c/elementaryFunctions/log1p/libLog1p.la \ + $(top_builddir)/src/c/elementaryFunctions/lnp1m1/libLnp1m1.la \ + $(top_builddir)/src/c/auxiliaryFunctions/abs/libAbs.la \ + $(top_builddir)/src/c/auxiliaryFunctions/conj/libConj.la \ + $(top_builddir)/src/c/auxiliaryFunctions/pythag/libPythag.la \ + $(top_builddir)/src/c/auxiliaryFunctions/sign/libSign.la \ + $(top_builddir)/src/c/operations/multiplication/libMultiplication.la \ + $(top_builddir)/src/c/operations/addition/libAddition.la \ + $(top_builddir)/src/c/matrixOperations/multiplication/libMatrixMultiplication.la \ + $(top_builddir)/src/c/matrixOperations/transpose/libMatrixTranspose.la \ + $(top_builddir)/src/c/matrixOperations/inversion/libMatrixInversion.la \ + $(top_builddir)/src/c/matrixOperations/spec2/libSpec2.la \ + $(top_builddir)/src/c/matrixOperations/zeros/libMatrixZeros.la \ + $(top_builddir)/src/c/matrixOperations/logm/libLogm.la + + +check_INCLUDES = -I ./includes \ + -I $(top_builddir)/src/c/type \ + -I $(top_builddir)/src/c/elementaryFunctions/includes \ + -I $(top_builddir)/src/c/operations/includes \ + -I $(top_builddir)/src/c/auxiliaryFunctions/includes \ + -I $(top_builddir)/src/c/matrixOperations/includes + +testDoubleLogm_SOURCES = testDoubleLogm.c +testDoubleLogm_LDADD = $(check_LDADD) +testDoubleLogm_CFLAGS = $(check_INCLUDES) + +testFloatLogm_SOURCES = testFloatLogm.c +testFloatLogm_LDADD = $(check_LDADD) +testFloatLogm_CFLAGS = $(check_INCLUDES) + +TESTS = testDoubleLogm testFloatLogm diff --git a/2.3-1/src/c/matrixOperations/logm/Makefile.in b/2.3-1/src/c/matrixOperations/logm/Makefile.in new file mode 100644 index 00000000..d4923eb3 --- /dev/null +++ b/2.3-1/src/c/matrixOperations/logm/Makefile.in @@ -0,0 +1,763 @@ +# Makefile.in generated by automake 1.11.1 from Makefile.am. +# @configure_input@ + +# Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, +# 2003, 2004, 2005, 2006, 2007, 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part of Scilab + * Copyright (C) 2008 - INRIA - Arnaud TORSET + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt + * + */ + +#include <stdlib.h> +#include "logm.h" + +void clogma (floatComplex* in, int rows, floatComplex* out){ + doubleComplex *inCopy, *outCopy; + int i=0; + + inCopy = (doubleComplex *)malloc((unsigned int)(rows*rows)*sizeof(doubleComplex)); + outCopy = (doubleComplex *)malloc((unsigned int)(rows*rows)*sizeof(doubleComplex)); + + for(i=0;i<rows*rows;i++) + inCopy[i]=DoubleComplex ((double)creals(in[i]), (double)cimags(in[i])); + + + zlogma(inCopy,rows,outCopy); + + for(i=0;i<rows*rows;i++) + out[i]=FloatComplex( (float)zreals(outCopy[i]),(float)zimags(outCopy[i])); + + + free(inCopy); + free(outCopy); + + +} diff --git a/2.3-1/src/c/matrixOperations/logm/dlogma.c b/2.3-1/src/c/matrixOperations/logm/dlogma.c new file mode 100644 index 00000000..2184c377 --- /dev/null +++ b/2.3-1/src/c/matrixOperations/logm/dlogma.c @@ -0,0 +1,31 @@ +/* + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA - Arnaud TORSET + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt + * + */ + +#include <stdlib.h> +#include "logm.h" + +void dlogma (double* in, int rows, double* out){ + doubleComplex *inCpx,*outCpx; + int i; + + inCpx=(doubleComplex *)malloc((unsigned int)(rows*rows)*sizeof(doubleComplex)); + outCpx=(doubleComplex *)malloc((unsigned int)(rows*rows)*sizeof(doubleComplex)); + + for (i=0;i<rows*rows;i++) inCpx[i] = DoubleComplex(in[i],0); + + zlogma(inCpx, rows, outCpx); + + for (i=0;i<rows*rows;i++) out[i]=zreals(outCpx[i]); + + free(inCpx); + free(outCpx); +} diff --git a/2.3-1/src/c/matrixOperations/logm/slogma.c b/2.3-1/src/c/matrixOperations/logm/slogma.c new file mode 100644 index 00000000..8b3120df --- /dev/null +++ b/2.3-1/src/c/matrixOperations/logm/slogma.c @@ -0,0 +1,32 @@ +/* + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA - Arnaud TORSET + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt + * + */ + +#include <stdlib.h> +#include "logm.h" + +void slogma (float* in, int rows, float* out){ + doubleComplex *inCpx, *outCopy; + int i; + + inCpx=(doubleComplex *)malloc((unsigned int)(rows*rows)*sizeof(doubleComplex)); + outCopy=(doubleComplex *)malloc((unsigned int)(rows*rows)*sizeof(doubleComplex)); + + for (i=0;i<rows*rows;i++) inCpx[i] = DoubleComplex(in[i],0); + + zlogma(inCpx, rows, outCopy); + + for(i=0;i<rows*rows;i++) + out[i]=(float)zreals(outCopy[i]); + + free(inCpx); + free(outCopy); +} diff --git a/2.3-1/src/c/matrixOperations/logm/testDoubleLogm.c b/2.3-1/src/c/matrixOperations/logm/testDoubleLogm.c new file mode 100644 index 00000000..039c6e81 --- /dev/null +++ b/2.3-1/src/c/matrixOperations/logm/testDoubleLogm.c @@ -0,0 +1,185 @@ +/* + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA - Arnaud TORSET + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt + * + */ + +#include <stdlib.h> +#include <assert.h> +#include <math.h> +#include <stdio.h> +#include "logm.h" + + +/* FIXME : Untested*/ + +static void dlogmaTest(void){ + int i=0; + + double in4[4] = {0.0683740368112921714783,0.5608486062847077846527, + 0.6623569373041391372681,0.7263506767340004444122 }; + double in9[9] = {0.1985143842175602912903,0.5442573162727057933807,0.2320747897028923034668, + 0.2312237196601927280426,0.2164632631465792655945,0.8833887814544141292572, + 0.6525134947150945663452,0.3076090742833912372589,0.9329616213217377662659}; + double in16[16] = {2.1460078610107302665710,3.126419968903064727783,3.6163610080257058143616,2.922266637906432151794, + 5.664248815737664699554,4.8264719732105731964111,3.3217189135029911994934,5.9350947011262178421021, + 5.0153415976092219352722,4.3685875833034515380859,2.6931248093023896217346,6.3257448654621839523315, + 4.051954015158116817474,9.1847078315913677215576,0.4373343335464596748352,4.818508932366967201233}; + double inHer[16] = {2,3,4,5,3,1,7,9,4,7,2,4,5,9,4,7}; + + double result4R[4]={- 0.8770746698483730119378,0.5288031941140065583795, + 0.6245116064569415925689,- 0.2566930821175439358939}; + + double result9R[9]={- 0.8537183024765053751537,1.9622873186332121520081,- 0.8931518563294031931577, + - 0.6983367178614473536,- 1.1199049557115796638129,1.539392415892589571769, + 1.0815849580686147657,- 0.4078285487954845245362,0.1789837218054647349774,}; + + double result16R[16]={1.4069394184534917968676,- 1.7915236034592834091228,2.3099248310776610004780,0.5320777350783232328979, + 0.6986579270151970222358,0.9874373592109859654187,0.8902400742596190408307,0.6067035092100719895214, + 0.0466142343271527676007,0.3821963653954382200695,1.129789301050062144682,1.2310339071369393870725, + 0.424502387440284123521,3.4580528009566289249221,- 2.1337657344549150195689,1.0826836628584670663145}; + + double resultHerR[16]={- 0.0707459665791660696765,0.9744491331561414559914,0.0316695005563280007621,0.9186825501429138896015, + 0.9744491331561416780360,1.9318283614573175110962,- 0.0664515082056250649956,0.3546926741474874522631, + 0.0316695005563280562733,- 0.0664515082056250649956,0.3206743709780528472919,1.82590946141052867802, + 0.9186825501429141116461,0.3546926741474875632854,1.82590946141052867802,0.9537374500729456361370}; + + + double out4[4],out9[9],out16[16],outHer[16]; + + + dlogma(in4,2,out4); + dlogma(in9,3,out9); + dlogma(in16,4,out16); + dlogma(inHer,4,outHer); + + for(i=0;i<4;i++) { + assert( (fabs(out4[i]-result4R[i]) / fabs(out4[i])) <3e-15); + } + + for(i=0;i<9;i++) { + assert( (fabs(out9[i]-result9R[i]) / fabs(out9[i])) <3e-14); + } + + for(i=0;i<16;i++) { + + assert( (fabs(out16[i]-result16R[i]) / fabs(out16[i])) <3e-14); + } + + for(i=0;i<16;i++) { + assert( (fabs(outHer[i]-resultHerR[i]) / fabs(outHer[i])) <3e-13); + } +} + + +static void zlogmaTest(void){ + int i; + + + double in4D[4] = {0.0683740368112921714783,0.5608486062847077846527, + 0.6623569373041391372681,0.7263506767340004444122 }; + double in9D[9] = {0.1985143842175602912903,0.5442573162727057933807,0.2320747897028923034668, + 0.2312237196601927280426,0.2164632631465792655945,0.8833887814544141292572, + 0.6525134947150945663452,0.3076090742833912372589,0.9329616213217377662659}; + double in16D[16] = {2.1460078610107302665710,3.126419968903064727783,3.6163610080257058143616,2.922266637906432151794, + 5.664248815737664699554,4.8264719732105731964111,3.3217189135029911994934,5.9350947011262178421021, + 5.0153415976092219352722,4.3685875833034515380859,2.6931248093023896217346,6.3257448654621839523315, + 4.051954015158116817474,9.1847078315913677215576,0.4373343335464596748352,4.818508932366967201233}; + double inHerD[16] = {2,3,4,5,3,1,7,9,4,7,2,4,5,9,4,7}; + + + double result4R[4]={- 0.8770746698483730119378,0.5288031941140065583795, + 0.6245116064569415925689,- 0.2566930821175439358939}; + double result4I[4]={2.3169161534469857599561,- 1.2719608554746495432397, + - 1.5021738258100643115256,0.8246765001428078001311}; + double result9R[9]={- 0.8537183024765053751537,1.9622873186332121520081,- 0.8931518563294031931577, + - 0.6983367178614473536,- 1.1199049557115796638129,1.539392415892589571769, + 1.0815849580686147657,- 0.4078285487954845245362,0.1789837218054647349774,}; + double result9I[9]={+ 0.0000000000000006661338,-0.0000000000000005551115,+0.0000000000000001110223, + -0.0000000000000002844947,+0.0000000000000004163336,+ 0.0000000000000008743006, + -0.0000000000000001665335,+ 0.0000000000000004996004,-0.0000000000000003330669}; + double result16R[16]={1.4069394184534917968676,- 1.7915236034592834091228,2.3099248310776610004780,0.5320777350783232328979, + 0.6986579270151970222358,0.9874373592109859654187,0.8902400742596190408307,0.6067035092100719895214, + 0.0466142343271527676007,0.3821963653954382200695,1.129789301050062144682,1.2310339071369393870725, + 0.424502387440284123521,3.4580528009566289249221,- 2.1337657344549150195689,1.0826836628584670663145}; + double result16I[16]={-1.4875734535892033427729,+ 1.8146634352088595321106,-0.0551064758054355952055,-0.8617364610492967980093, + + 1.0892397305420760122985,-1.3287434690517783142383,+ 0.0403503858667347281575,+ 0.6309857092212021179023, + + 1.3838992102024216813,-1.6881931367553519862668,+ 0.0512659110447117594145,+ 0.8016790061501579689463, + -0.6500053973791579675634,+ 0.7929296025459252605927,-0.0240791515993044047406,-0.3765416419935233571792}; + + + doubleComplex out4[4],out9[9],out16[16],outHer[16]; + doubleComplex in4[4],in9[9],in16[16],inHer[16]; + + + for(i=0;i<4;i++) in4[i]=DoubleComplex(in4D[i],0); + for(i=0;i<9;i++) in9[i]=DoubleComplex(in9D[i],0); + for(i=0;i<16;i++) in16[i]=DoubleComplex(in16D[i],0); + for(i=0;i<16;i++) inHer[i]=DoubleComplex(inHerD[i],0); + + + zlogma(in4,2,out4); + zlogma(in9,3,out9); + zlogma(in16,4,out16); + zlogma(inHer,4,outHer); + + + + + for(i=0;i<4;i++) { + assert( fabs(zreals(out4[i])-result4R[i]) / fabs(zreals(out4[i])) <3e-15); + assert( fabs(zimags(out4[i])-result4I[i]) / fabs(zimags(out4[i])) <3e-15); + } + + for(i=0;i<9;i++) { + assert( fabs(zreals(out9[i])-result9R[i]) / fabs(zreals(out9[i])) <3e-14); + if (zimags(out9[i])>3e-16) assert( fabs(zimags(out9[i])-result9I[i]) / fabs(zimags(out9[i])) <1e-16); + else assert(1); + } + + /* FIXME : sign pb with the imaginary part below : it's due to the reals eigenvalues which are + stored like that : eigenvalues + (-0)*i instead of eigenvalues + 0 *i + When we do operations with eigenvalues the sign isn't good + */ + + for(i=0;i<16;i++) { + printf("out[%d] = %f + %f *i ---result = %f + %f *i --- assert : %f + %f*i\n", + i, + zreals(out16[i]), + zimags(out16[i]), + result16R[i], + result16I[i], + fabs(zreals(out16[i])-result16R[i]) / fabs(zreals(out16[i])), + fabs(zimags(out16[i])-result16I[i]) / fabs(zimags(out16[i]))); + + assert( fabs(zreals(out16[i])-result16R[i]) / fabs(zreals(out16[i])) <3e-13); + assert( fabs(zimags(out16[i])-result16I[i]) / fabs(zimags(out16[i])) <3e-13); + } + + +} + +static int logmTest(void){ + dlogmaTest(); + zlogmaTest(); + return 0; +} + +int main (void){ + assert(logmTest()==0); + return 0; +} + + + + + + + + diff --git a/2.3-1/src/c/matrixOperations/logm/testFloatLogm.c b/2.3-1/src/c/matrixOperations/logm/testFloatLogm.c new file mode 100644 index 00000000..3ddd4b06 --- /dev/null +++ b/2.3-1/src/c/matrixOperations/logm/testFloatLogm.c @@ -0,0 +1,185 @@ +/* + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008 - INRIA - Arnaud TORSET + * + * This file must be used under the terms of the CeCILL. + * This source file is licensed as described in the file COPYING, which + * you should have received as part of this distribution. The terms + * are also available at + * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt + * + */ + +#include <assert.h> +#include <math.h> +#include <stdio.h> +#include "logm.h" + + +static void slogmaTest(void){ + int i=0; + + float in4[4] = {0.0683740368112921714783f,0.5608486062847077846527f, + 0.6623569373041391372681f,0.7263506767340004444122f }; + float in9[9] = {0.1985143842175602912903f,0.5442573162727057933807f,0.2320747897028923034668f, + 0.2312237196601927280426f,0.2164632631465792655945f,0.8833887814544141292572f, + 0.6525134947150945663452f,0.3076090742833912372589f,0.9329616213217377662659f}; + float in16[16] = {2.1460078610107302665710f,3.126419968903064727783f,3.6163610080257058143616f,2.922266637906432151794f, + 5.664248815737664699554f,4.8264719732105731964111f,3.3217189135029911994934f,5.9350947011262178421021f, + 5.0153415976092219352722f,4.3685875833034515380859f,2.6931248093023896217346f,6.3257448654621839523315f, + 4.051954015158116817474f,9.1847078315913677215576f,0.4373343335464596748352f,4.818508932366967201233f}; + float inHer[16] = {2.0f,3.0f,4.0f,5.0f,3.0f,1.0f,7.0f,9.0f,4.0f,7.0f,2.0f,4.0f,5.0f,9.0f,4.0f,7.0f}; + + float result4R[4]={- 0.8770746698483730119378f,0.5288031941140065583795f, + 0.6245116064569415925689f,- 0.2566930821175439358939f}; + + float result9R[9]={- 0.8537183024765053751537f,1.9622873186332121520081f,- 0.8931518563294031931577f, + - 0.6983367178614473536f,- 1.1199049557115796638129f,1.539392415892589571769f, + 1.0815849580686147657f,- 0.4078285487954845245362f,0.1789837218054647349774f}; + + float result16R[16]={1.4069394184534917968676f,- 1.7915236034592834091228f,2.3099248310776610004780f,0.5320777350783232328979f, + 0.6986579270151970222358f,0.9874373592109859654187f,0.8902400742596190408307f,0.6067035092100719895214f, + 0.0466142343271527676007f,0.3821963653954382200695f,1.129789301050062144682f,1.2310339071369393870725f, + 0.424502387440284123521f,3.4580528009566289249221f,- 2.1337657344549150195689f,1.0826836628584670663145f}; + + float resultHerR[16]={- 0.0707459665791660696765f,0.9744491331561414559914f,0.0316695005563280007621f,0.9186825501429138896015f, + 0.9744491331561416780360f,1.9318283614573175110962f,- 0.0664515082056250649956f,0.3546926741474874522631f, + 0.0316695005563280562733f,- 0.0664515082056250649956f,0.3206743709780528472919f,1.82590946141052867802f, + 0.9186825501429141116461f,0.3546926741474875632854f,1.82590946141052867802f,0.9537374500729456361370f}; + + + float out4[4],out9[9],out16[16],outHer[16]; + + + slogma(in4,2,out4); + slogma(in9,3,out9); + slogma(in16,4,out16); + slogma(inHer,4,outHer); + + for(i=0;i<4;i++) { + assert( (fabs(out4[i]-result4R[i]) / fabs(out4[i])) <1e-6); + } + + for(i=0;i<9;i++) { + assert( (fabs(out9[i]-result9R[i]) / fabs(out9[i])) <1e-6); + } + + for(i=0;i<16;i++) { + assert( (fabs(out16[i]-result16R[i]) / fabs(out16[i])) <1e-6); + } + + for(i=0;i<16;i++) { + assert( (fabs(outHer[i]-resultHerR[i]) / fabs(outHer[i])) <1e-7); + } +} + + +static void clogmaTest(void){ + int i; + + float in4D[4] = {0.0683740368112921714783f,0.5608486062847077846527f, + 0.6623569373041391372681f,0.7263506767340004444122f }; + float in9D[9] = {0.1985143842175602912903f,0.5442573162727057933807f,0.2320747897028923034668f, + 0.2312237196601927280426f,0.2164632631465792655945f,0.8833887814544141292572f, + 0.6525134947150945663452f,0.3076090742833912372589f,0.9329616213217377662659f}; + float in16D[16] = {2.1460078610107302665710f,3.126419968903064727783f,3.6163610080257058143616f,2.922266637906432151794f, + 5.664248815737664699554f,4.8264719732105731964111f,3.3217189135029911994934f,5.9350947011262178421021f, + 5.0153415976092219352722f,4.3685875833034515380859f,2.6931248093023896217346f,6.3257448654621839523315f, + 4.051954015158116817474f,9.1847078315913677215576f,0.4373343335464596748352f,4.818508932366967201233f}; + float inHerD[16] = {2.0f,3.0f,4.0f,5.0f,3.0f,1.0f,7.0f,9.0f,4.0f,7.0f,2.0f,4.0f,5.0f,9.0f,4.0f,7.0f}; + + + float result4R[4]={- 0.8770746698483730119378f,0.5288031941140065583795f, + 0.6245116064569415925689f,- 0.2566930821175439358939f}; + float result4I[4]={2.3169161534469857599561f,- 1.2719608554746495432397f, + - 1.5021738258100643115256f,0.8246765001428078001311f}; + float result9R[9]={- 0.8537183024765053751537f,1.9622873186332121520081f,- 0.8931518563294031931577f, + - 0.6983367178614473536f,- 1.1199049557115796638129f,1.539392415892589571769f, + 1.0815849580686147657f,- 0.4078285487954845245362f,0.1789837218054647349774f}; + float result9I[9]={- 0.0000000000000006661338f,0.0000000000000005551115f,0.0000000000000001110223f, + 0.0000000000000002844947f,0.0000000000000004163336f,- 0.0000000000000008743006f, + 0.0000000000000001665335f,- 0.0000000000000004996004f,0.0000000000000003330669f}; + float result16R[16]={1.4069394184534917968676f,- 1.7915236034592834091228f,2.3099248310776610004780f,0.5320777350783232328979f, + 0.6986579270151970222358f,0.9874373592109859654187f,0.8902400742596190408307f,0.6067035092100719895214f, + 0.0466142343271527676007f,0.3821963653954382200695f,1.129789301050062144682f,1.2310339071369393870725f, + 0.424502387440284123521f,3.4580528009566289249221f,- 2.1337657344549150195689f,1.0826836628584670663145f}; + float result16I[16]={-1.4875734535892033427729f,+ 1.8146634352088595321106f,-0.0551064758054355952055f,-0.8617364610492967980093f, + + 1.0892397305420760122985f,-1.3287434690517783142383f,+ 0.0403503858667347281575f,+ 0.6309857092212021179023f, + + 1.3838992102024216813f,-1.6881931367553519862668f,+ 0.0512659110447117594145f,+ 0.8016790061501579689463f, + -0.6500053973791579675634f,+ 0.7929296025459252605927f,-0.0240791515993044047406f,-0.3765416419935233571792f}; + float resultHerR[16]={- 0.0707459665791660696765f,0.9744491331561414559914f,0.0316695005563280007621f,0.9186825501429138896015f, + 0.9744491331561416780360f,1.9318283614573175110962f,- 0.0664515082056250649956f,0.3546926741474874522631f, + 0.0316695005563280562733f,- 0.0664515082056250649956f,0.3206743709780528472919f,1.82590946141052867802f, + 0.9186825501429141116461f,0.3546926741474875632854f,1.82590946141052867802f,0.9537374500729456361370f}; + float resultHerI[16]={2.1383917599789858954296f,- 0.5351429414718615884539f,- 1.3567950682942089279948f,0.1340361867044403687554f, + - 0.5351429414718615884539f,2.2766753224580762449136f,- 0.6151069729626167381653f,- 1.1421039303668867326280f, + - 1.3567950682942089279948f,- 0.6151069729626165161207f,1.2861990290089324595613f,0.4088471998565592624431f, + 0.1340361867044403965110f,- 1.1421039303668867326280f,0.4088471998565592624431f,0.5819191957335942966267f}; 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