计算特殊矩阵的逆的程序

/******************************************************************** AP Library version 1.2 Copyright (c) 2003-2007, Sergey Bochkanov (ALGLIB project). See www.alglib.net or alglib.sources.ru for details. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: - Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. - Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer listed in this license in the documentation and/or other materials provided with the distribution. - Neither the name of the copyright holders nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ********************************************************************/ #include "stdafx.h" #include "ap.h" /******************************************************************** Optimized ABLAS interface ********************************************************************/ #ifdef AP_WIN32 #include <windows.h> extern "C" { typedef double (*_ddot1)(const double*, const double*, long); typedef void (*_dmove1)(const double*, const double*, long); typedef void (*_dmoves1)(const double*, const double*, long, double); typedef void (*_dmoveneg1)(const double*, const double*, long); typedef void (*_dadd1)(const double*, const double*, long); typedef void (*_dadds1)(const double*, const double*, long, double); typedef void (*_dsub1)(const double*, const double*, long); typedef void (*_dmuls1)(const double*, long, double); } HINSTANCE ABLAS = LoadLibrary("ablas.dll"); static _ddot1 ddot1 = ABLAS==NULL ? NULL : (_ddot1) GetProcAddress(ABLAS, "ASMDotProduct1"); static _dmove1 dmove1 = ABLAS==NULL ? NULL : (_dmove1) GetProcAddress(ABLAS, "ASMMove1"); static _dmoves1 dmoves1 = ABLAS==NULL ? NULL : (_dmoves1) GetProcAddress(ABLAS, "ASMMoveS1"); static _dmoveneg1 dmoveneg1 = ABLAS==NULL ? NULL : (_dmoveneg1) GetProcAddress(ABLAS, "ASMMoveNeg1"); static _dadd1 dadd1 = ABLAS==NULL ? NULL : (_dadd1) GetProcAddress(ABLAS, "ASMAdd1"); static _dadds1 dadds1 = ABLAS==NULL ? NULL : (_dadds1) GetProcAddress(ABLAS, "ASMAddS1"); static _dsub1 dsub1 = ABLAS==NULL ? NULL : (_dsub1) GetProcAddress(ABLAS, "ASMSub1"); static _dmuls1 dmuls1 = ABLAS==NULL ? NULL : (_dmuls1) GetProcAddress(ABLAS, "ASMMulS1"); #endif const double ap::machineepsilon = 5E-16; const double ap::maxrealnumber = 1E300; const double ap::minrealnumber = 1E-300; /******************************************************************** ap::complex operations ********************************************************************/ const bool ap::operator==(const ap::complex& lhs, const ap::complex& rhs) { return lhs.x==rhs.x && lhs.y==rhs.y; } const bool ap::operator!=(const ap::complex& lhs, const ap::complex& rhs) { return lhs.x!=rhs.x || lhs.y!=rhs.y; } const ap::complex ap::operator+(const ap::complex& lhs) { return lhs; } const ap::complex ap::operator-(const ap::complex& lhs) { return ap::complex(-lhs.x, -lhs.y); } const ap::complex ap::operator+(const ap::complex& lhs, const ap::complex& rhs) { ap::complex r = lhs; r += rhs; return r; } const ap::complex ap::operator+(const ap::complex& lhs, const double& rhs) { ap::complex r = lhs; r += rhs; return r; } const ap::complex ap::operator+(const double& lhs, const ap::complex& rhs) { ap::complex r = rhs; r += lhs; return r; } const ap::complex ap::operator-(const ap::complex& lhs, const ap::complex& rhs) { ap::complex r = lhs; r -= rhs; return r; } const ap::complex ap::operator-(const ap::complex& lhs, const double& rhs) { ap::complex r = lhs; r -= rhs; return r; } const ap::complex ap::operator-(const double& lhs, const ap::complex& rhs) { ap::complex r = lhs; r -= rhs; return r; } const ap::complex ap::operator*(const ap::complex& lhs, const ap::complex& rhs) { return ap::complex(lhs.x*rhs.x - lhs.y*rhs.y, lhs.x*rhs.y + lhs.y*rhs.x); } const ap::complex ap::operator*(const ap::complex& lhs, const double& rhs) { return ap::complex(lhs.x*rhs, lhs.y*rhs); } const ap::complex ap::operator*(const double& lhs, const ap::complex& rhs) { return ap::complex(lhs*rhs.x, lhs*rhs.y); } const ap::complex ap::operator/(const ap::complex& lhs, const ap::complex& rhs) { ap::complex result; double e; double f; if( fabs(rhs.y)<fabs(rhs.x) ) { e = rhs.y/rhs.x; f = rhs.x+rhs.y*e; result.x = (lhs.x+lhs.y*e)/f; result.y = (lhs.y-lhs.x*e)/f; } else { e = rhs.x/rhs.y; f = rhs.y+rhs.x*e; result.x = (lhs.y+lhs.x*e)/f; result.y = (-lhs.x+lhs.y*e)/f; } return result; } const ap::complex ap::operator/(const double& lhs, const ap::complex& rhs) { ap::complex result; double e; double f; if( fabs(rhs.y)<fabs(rhs.x) ) { e = rhs.y/rhs.x; f = rhs.x+rhs.y*e; result.x = lhs/f; result.y = -lhs*e/f; } else { e = rhs.x/rhs.y; f = rhs.y+rhs.x*e; result.x = lhs*e/f; result.y = -lhs/f; } return result; } const ap::complex ap::operator/(const ap::complex& lhs, const double& rhs) { return ap::complex(lhs.x/rhs, lhs.y/rhs); } const double ap::abscomplex(const ap::complex &z) { double w; double xabs; double yabs; double v; xabs = fabs(z.x); yabs = fabs(z.y); w = xabs>yabs ? xabs : yabs; v = xabs<yabs ? xabs : yabs; if( v==0 ) return w; else { double t = v/w; return w*sqrt(1+t*t); } } const ap::complex ap::conj(const ap::complex &z) { return ap::complex(z.x, -z.y); } const ap::complex ap::csqr(const ap::complex &z) { return ap::complex(z.x*z.x-z.y*z.y, 2*z.x*z.y); } /******************************************************************** BLAS functions ********************************************************************/ double ap::vdotproduct(const double *v1, const double *v2, int N) { #ifdef AP_WIN32 if( ddot1!=NULL ) return ddot1(v1, v2, N); #endif return ap::_vdotproduct<double>(v1, v2, N); } ap::complex ap::vdotproduct(const ap::complex *v1, const ap::complex *v2, int N) { return ap::_vdotproduct<ap::complex>(v1, v2, N); } void ap::vmove(double *vdst, const double* vsrc, int N) { #ifdef AP_WIN32 if( dmove1!=NULL ) { dmove1(vdst, vsrc, N); return; } #endif ap::_vmove<double>(vdst, vsrc, N); } void ap::vmove(ap::complex *vdst, const ap::complex* vsrc, int N) { ap::_vmove<ap::complex>(vdst, vsrc, N); } void ap::vmoveneg(double *vdst, const double *vsrc, int N) { #ifdef AP_WIN32 if( dmoveneg1!=NULL ) { dmoveneg1(vdst, vsrc, N); return; } #endif ap::_vmoveneg<doubl