added default bool option to svd to sort the singular values and V. the default is true so pass false to avoid sorting
Manohar Paluri
parent
f9c2000847
commit
693e13ef88
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@ -866,7 +866,7 @@ Matrix cholesky_inverse(const Matrix &A)
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/* ************************************************************************* */
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/* ************************************************************************* */
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// version with in place modification of A
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// version with in place modification of A
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void svd(Matrix& A, Vector& s, Matrix& V) {
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void svd(Matrix& A, Vector& s, Matrix& V, bool sort) {
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const size_t m=A.size1(), n=A.size2();
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const size_t m=A.size1(), n=A.size2();
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@ -878,7 +878,7 @@ void svd(Matrix& A, Vector& s, Matrix& V) {
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// perform SVD
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// perform SVD
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// need to pass pointer - 1 in NRC routines so u[1][1] is first element !
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// need to pass pointer - 1 in NRC routines so u[1][1] is first element !
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svdcmp(u-1,m,n,q-1,v-1);
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svdcmp(u-1,m,n,q-1,v-1, sort);
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// copy singular values back
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// copy singular values back
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s.resize(n);
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s.resize(n);
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@ -891,9 +891,9 @@ void svd(Matrix& A, Vector& s, Matrix& V) {
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}
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}
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/* ************************************************************************* */
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/* ************************************************************************* */
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void svd(const Matrix& A, Matrix& U, Vector& s, Matrix& V) {
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void svd(const Matrix& A, Matrix& U, Vector& s, Matrix& V, bool sort) {
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U = A; // copy
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U = A; // copy
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svd(U,s,V); // call in-place version
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svd(U,s,V,sort); // call in-place version
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}
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}
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#if 0
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#if 0
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@ -941,7 +941,7 @@ Matrix square_root_positive(const Matrix& A) {
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// Perform SVD, TODO: symmetric SVD?
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// Perform SVD, TODO: symmetric SVD?
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Matrix U,V;
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Matrix U,V;
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Vector S;
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Vector S;
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svd(A,U,S,V);
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svd(A,U,S,V,false);
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// invert and sqrt diagonal of S
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// invert and sqrt diagonal of S
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// We also arbitrarily choose sign to make result have positive signs
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// We also arbitrarily choose sign to make result have positive signs
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@ -308,11 +308,12 @@ inline Matrix skewSymmetric(const Vector& w) { return skewSymmetric(w(0),w(1),w(
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* @param U output argument: m*n matrix
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* @param U output argument: m*n matrix
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* @param S output argument: n-dim vector of singular values, *not* sorted !!!
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* @param S output argument: n-dim vector of singular values, *not* sorted !!!
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* @param V output argument: n*n matrix
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* @param V output argument: n*n matrix
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* @param sort boolean flag to sort singular values and V
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*/
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*/
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void svd(const Matrix& A, Matrix& U, Vector& S, Matrix& V);
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void svd(const Matrix& A, Matrix& U, Vector& S, Matrix& V, bool sort=true);
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// in-place version
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// in-place version
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void svd(Matrix& A, Vector& S, Matrix& V);
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void svd(Matrix& A, Vector& S, Matrix& V, bool sort=true);
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/** Use SVD to calculate inverse square root of a matrix */
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/** Use SVD to calculate inverse square root of a matrix */
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Matrix inverse_square_root(const Matrix& A);
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Matrix inverse_square_root(const Matrix& A);
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476
cpp/svdcmp.cpp
476
cpp/svdcmp.cpp
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@ -8,247 +8,299 @@
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#include <math.h> /* for 'fabs' */
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#include <math.h> /* for 'fabs' */
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#include <iostream>
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#include <iostream>
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#include <vector>
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#include <vector>
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#include "Matrix.h"
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using namespace std;
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using namespace std;
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#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
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#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
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static double sqrarg;
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static double sqrarg;
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#define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg)
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#define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg)
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static double maxarg1,maxarg2;
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static double maxarg1, maxarg2;
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#define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ?\
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#define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ?\
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(maxarg1) : (maxarg2))
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(maxarg1) : (maxarg2))
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static int iminarg1,iminarg2;
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static int iminarg1, iminarg2;
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#define IMIN(a,b) (iminarg1=(a),iminarg2=(b),(iminarg1) < (iminarg2) ?\
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#define IMIN(a,b) (iminarg1=(a),iminarg2=(b),(iminarg1) < (iminarg2) ?\
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(iminarg1) : (iminarg2))
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(iminarg1) : (iminarg2))
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/* ************************************************************************* */
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/* ************************************************************************* */
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/*
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/*
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double pythag(double a, double b)
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double pythag(double a, double b)
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{
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{
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double absa = 0.0, absb = 0.0;
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double absa = 0.0, absb = 0.0;
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absa=fabs(a);
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absa=fabs(a);
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absb=fabs(b);
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absb=fabs(b);
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if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa));
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if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa));
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else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+SQR(absa/absb)));
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else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+SQR(absa/absb)));
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}
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}
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*/
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*/
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/* ************************************************************************* */
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/* ************************************************************************* */
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double pythag(double a, double b)
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double pythag(double a, double b) {
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{
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double absa = 0.0, absb = 0.0;
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double absa = 0.0, absb = 0.0;
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absa = fabs(a);
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absa=fabs(a);
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absb = fabs(b);
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absb=fabs(b);
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if (absa > absb)
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if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa));
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return absa * sqrt(1.0 + SQR(absb/absa));
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else {
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else {
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if(absb == 0.0)
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if (absb == 0.0)
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return 0.0;
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return 0.0;
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else
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else
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return (absb * sqrt(1.0 + SQR(absa/absb)));
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return (absb * sqrt(1.0 + SQR(absa/absb)));
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}
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}
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}
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}
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/* ************************************************************************* */
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/* ************************************************************************* */
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void svdcmp(double **a, int m, int n, double w[], double **v)
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void svdcmp(double **a, int m, int n, double w[], double **v, bool sort) {
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{
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int flag, i, its, j, jj, k, l, nm;
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int flag,i,its,j,jj,k,l,nm;
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double anorm, c, f, g, h, s, scale, x, y, z;
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double anorm,c,f,g,h,s,scale,x,y,z;
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//vector sizes:
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//vector sizes:
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// w[n] - q-1 passed in
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// w[n] - q-1 passed in
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// a[m] - u-1 passed in
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// a[m] - u-1 passed in
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// v[n] - v-1 passed in
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// v[n] - v-1 passed in
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//Current progress on verifying array bounds:
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//Current progress on verifying array bounds:
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// rv1 references have been fixed
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// rv1 references have been fixed
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double *rv1 = new double[n];
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double *rv1 = new double[n];
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g= 0.0;
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g = 0.0;
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scale= 0.0;
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scale = 0.0;
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anorm= 0.0;
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anorm = 0.0;
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for (i=1;i<=n;i++) {
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for (i = 1; i <= n; i++) {
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l=i+1;
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l = i + 1;
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rv1[i-1]=scale*g;
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rv1[i - 1] = scale * g;
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g=s=scale=0.0;
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g = s = scale = 0.0;
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if (i <= m) {
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if (i <= m) {
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for (k=i;k<=m;k++) scale += fabs(a[k][i]);
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for (k = i; k <= m; k++)
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if (scale) {
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scale += fabs(a[k][i]);
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for (k=i;k<=m;k++) {
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if (scale) {
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a[k][i] /= scale;
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for (k = i; k <= m; k++) {
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s += a[k][i]*a[k][i];
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a[k][i] /= scale;
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}
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s += a[k][i] * a[k][i];
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f=a[i][i];
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}
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g = -SIGN(sqrt(s),f);
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f = a[i][i];
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h=f*g-s;
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g = -SIGN(sqrt(s),f);
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a[i][i]=f-g;
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h = f * g - s;
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for (j=l;j<=n;j++) {
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a[i][i] = f - g;
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for (s=0.0,k=i;k<=m;k++) s += a[k][i]*a[k][j];
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for (j = l; j <= n; j++) {
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f=s/h;
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for (s = 0.0, k = i; k <= m; k++)
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for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
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s += a[k][i] * a[k][j];
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}
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f = s / h;
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for (k=i;k<=m;k++) a[k][i] *= scale;
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for (k = i; k <= m; k++)
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}
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a[k][j] += f * a[k][i];
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}
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}
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w[i]=scale *g;
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for (k = i; k <= m; k++)
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g=s=scale=0.0;
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a[k][i] *= scale;
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if (i <= m && i != n) {
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}
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for (k=l;k<=n;k++) scale += fabs(a[i][k]);
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}
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if (scale) {
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w[i] = scale * g;
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for (k=l;k<=n;k++) {
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g = s = scale = 0.0;
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a[i][k] /= scale;
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if (i <= m && i != n) {
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s += a[i][k]*a[i][k];
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for (k = l; k <= n; k++)
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}
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scale += fabs(a[i][k]);
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f=a[i][l];
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if (scale) {
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g = -SIGN(sqrt(s),f);
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for (k = l; k <= n; k++) {
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h=f*g-s;
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a[i][k] /= scale;
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a[i][l]=f-g;
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s += a[i][k] * a[i][k];
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for (k=l;k<=n;k++)
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}
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{
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f = a[i][l];
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rv1[k-1]=a[i][k]/h;
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g = -SIGN(sqrt(s),f);
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}
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h = f * g - s;
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a[i][l] = f - g;
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for (k = l; k <= n; k++) {
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rv1[k - 1] = a[i][k] / h;
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}
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for (j=l;j<=m;j++) {
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for (j = l; j <= m; j++) {
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for (s=0.0,k=l;k<=n;k++)
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for (s = 0.0, k = l; k <= n; k++)
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s += a[j][k]*a[i][k];
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s += a[j][k] * a[i][k];
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for (k=l;k<=n;k++)
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for (k = l; k <= n; k++) {
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{
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a[j][k] += s * rv1[k - 1];
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a[j][k] += s*rv1[k-1];
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}
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}
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}
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}
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for (k = l; k <= n; k++)
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for (k=l;k<=n;k++) a[i][k] *= scale;
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a[i][k] *= scale;
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}
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}
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}
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}
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anorm=FMAX(anorm,(fabs(w[i])+fabs(rv1[i-1])));
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anorm = FMAX(anorm,(fabs(w[i])+fabs(rv1[i-1])));
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}
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for (i=n;i>=1;i--) {
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if (i < n) {
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if (g) {
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for (j=l;j<=n;j++)
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v[j][i]=(a[i][j]/a[i][l])/g;
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for (j=l;j<=n;j++) {
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for (s=0.0,k=l;k<=n;k++) s += a[i][k]*v[k][j];
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for (k=l;k<=n;k++) v[k][j] += s*v[k][i];
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}
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}
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}
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for (i = n; i >= 1; i--) {
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for (j=l;j<=n;j++) v[i][j]=v[j][i]=0.0;
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if (i < n) {
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}
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if (g) {
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v[i][i]=1.0;
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for (j = l; j <= n; j++)
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g=rv1[i-1];
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v[j][i] = (a[i][j] / a[i][l]) / g;
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l=i;
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for (j = l; j <= n; j++) {
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}
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for (s = 0.0, k = l; k <= n; k++)
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for (i=IMIN(m,n);i>=1;i--) {
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s += a[i][k] * v[k][j];
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l=i+1;
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for (k = l; k <= n; k++)
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g=w[i];
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v[k][j] += s * v[k][i];
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for (j=l;j<=n;j++) a[i][j]=0.0;
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}
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if (g) {
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}
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g=1.0/g;
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for (j = l; j <= n; j++)
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for (j=l;j<=n;j++) {
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v[i][j] = v[j][i] = 0.0;
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for (s=0.0,k=l;k<=m;k++) s += a[k][i]*a[k][j];
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}
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f=(s/a[i][i])*g;
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v[i][i] = 1.0;
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for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
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g = rv1[i - 1];
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}
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l = i;
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for (j=i;j<=m;j++) a[j][i] *= g;
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} else for (j=i;j<=m;j++) a[j][i]=0.0;
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++a[i][i];
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}
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for (k=n;k>=1;k--) {
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for (its=1;its<=30;its++) {
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flag=1;
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for (l=k;l>=1;l--) {
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nm=l-1;
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if ((double)(fabs(rv1[l-1])+anorm) == anorm) {
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flag=0;
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break;
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}
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}
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if ((double)(fabs(w[nm])+anorm) == anorm) break;
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for (i = IMIN(m,n); i >= 1; i--) {
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}
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l = i + 1;
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if (flag) {
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g = w[i];
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c=0.0;
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for (j = l; j <= n; j++)
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s=1.0;
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a[i][j] = 0.0;
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for (i=l;i<=k;i++) {
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if (g) {
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f=s*rv1[i-1];
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g = 1.0 / g;
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rv1[i-1]=c*rv1[i-1];
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for (j = l; j <= n; j++) {
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if ((double)(fabs(f)+anorm) == anorm) break;
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for (s = 0.0, k = l; k <= m; k++)
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g=w[i];
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s += a[k][i] * a[k][j];
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h=pythag(f,g);
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f = (s / a[i][i]) * g;
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w[i]=h;
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for (k = i; k <= m; k++)
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h=1.0/h;
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a[k][j] += f * a[k][i];
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c=g*h;
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}
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s = -f*h;
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for (j = i; j <= m; j++)
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for (j=1;j<=m;j++) {
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a[j][i] *= g;
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y=a[j][nm];
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} else
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z=a[j][i];
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for (j = i; j <= m; j++)
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a[j][nm]=y*c+z*s;
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a[j][i] = 0.0;
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a[j][i]=z*c-y*s;
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++a[i][i];
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}
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}
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}
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}
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for (k = n; k >= 1; k--) {
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z=w[k];
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for (its = 1; its <= 30; its++) {
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if (l == k) {
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flag = 1;
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if (z < 0.0) {
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for (l = k; l >= 1; l--) {
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w[k] = -z;
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nm = l - 1;
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for (j=1;j<=n;j++) v[j][k] = -v[j][k];
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if ((double) (fabs(rv1[l - 1]) + anorm) == anorm) {
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flag = 0;
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break;
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}
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if ((double) (fabs(w[nm]) + anorm) == anorm)
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break;
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}
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if (flag) {
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c = 0.0;
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s = 1.0;
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for (i = l; i <= k; i++) {
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f = s * rv1[i - 1];
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rv1[i - 1] = c * rv1[i - 1];
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if ((double) (fabs(f) + anorm) == anorm)
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break;
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g = w[i];
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h = pythag(f, g);
|
||||||
|
w[i] = h;
|
||||||
|
h = 1.0 / h;
|
||||||
|
c = g * h;
|
||||||
|
s = -f * h;
|
||||||
|
for (j = 1; j <= m; j++) {
|
||||||
|
y = a[j][nm];
|
||||||
|
z = a[j][i];
|
||||||
|
a[j][nm] = y * c + z * s;
|
||||||
|
a[j][i] = z * c - y * s;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
z = w[k];
|
||||||
|
if (l == k) {
|
||||||
|
if (z < 0.0) {
|
||||||
|
w[k] = -z;
|
||||||
|
for (j = 1; j <= n; j++)
|
||||||
|
v[j][k] = -v[j][k];
|
||||||
|
}
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
if (its == 30)
|
||||||
|
throw(std::domain_error(
|
||||||
|
"no convergence in 30 svdcmp iterations"));
|
||||||
|
x = w[l];
|
||||||
|
nm = k - 1;
|
||||||
|
y = w[nm];
|
||||||
|
g = rv1[nm - 1];
|
||||||
|
h = rv1[k - 1];
|
||||||
|
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
|
||||||
|
g = pythag(f, 1.0);
|
||||||
|
f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g,f))) - h)) / x;
|
||||||
|
c = s = 1.0;
|
||||||
|
for (j = l; j <= nm; j++) {
|
||||||
|
i = j + 1;
|
||||||
|
g = rv1[i - 1];
|
||||||
|
y = w[i];
|
||||||
|
h = s * g;
|
||||||
|
g = c * g;
|
||||||
|
z = pythag(f, h);
|
||||||
|
rv1[j - 1] = z;
|
||||||
|
c = f / z;
|
||||||
|
s = h / z;
|
||||||
|
f = x * c + g * s;
|
||||||
|
g = g * c - x * s;
|
||||||
|
h = y * s;
|
||||||
|
y *= c;
|
||||||
|
for (jj = 1; jj <= n; jj++) {
|
||||||
|
x = v[jj][j];
|
||||||
|
z = v[jj][i];
|
||||||
|
v[jj][j] = x * c + z * s;
|
||||||
|
v[jj][i] = z * c - x * s;
|
||||||
|
}
|
||||||
|
z = pythag(f, h);
|
||||||
|
w[j] = z;
|
||||||
|
if (z) {
|
||||||
|
z = 1.0 / z;
|
||||||
|
c = f * z;
|
||||||
|
s = h * z;
|
||||||
|
}
|
||||||
|
f = c * g + s * y;
|
||||||
|
x = c * y - s * g;
|
||||||
|
for (jj = 1; jj <= m; jj++) {
|
||||||
|
y = a[jj][j];
|
||||||
|
z = a[jj][i];
|
||||||
|
a[jj][j] = y * c + z * s;
|
||||||
|
a[jj][i] = z * c - y * s;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
rv1[l - 1] = 0.0;
|
||||||
|
rv1[k - 1] = f;
|
||||||
|
w[k] = x;
|
||||||
|
}
|
||||||
}
|
}
|
||||||
break;
|
|
||||||
}
|
|
||||||
if (its == 30) throw(std::domain_error("no convergence in 30 svdcmp iterations"));
|
|
||||||
x=w[l];
|
|
||||||
nm=k-1;
|
|
||||||
y=w[nm];
|
|
||||||
g=rv1[nm-1] ;
|
|
||||||
h=rv1[k-1];
|
|
||||||
f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
|
|
||||||
g=pythag(f,1.0);
|
|
||||||
f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
|
|
||||||
c=s=1.0;
|
|
||||||
for (j=l;j<=nm;j++) {
|
|
||||||
i=j+1;
|
|
||||||
g=rv1[i-1];
|
|
||||||
y=w[i];
|
|
||||||
h=s*g;
|
|
||||||
g=c*g;
|
|
||||||
z=pythag(f,h);
|
|
||||||
rv1[j-1]=z;
|
|
||||||
c=f/z;
|
|
||||||
s=h/z;
|
|
||||||
f=x*c+g*s;
|
|
||||||
g = g*c-x*s;
|
|
||||||
h=y*s;
|
|
||||||
y *= c;
|
|
||||||
for (jj=1;jj<=n;jj++) {
|
|
||||||
x=v[jj][j];
|
|
||||||
z=v[jj][i];
|
|
||||||
v[jj][j]=x*c+z*s;
|
|
||||||
v[jj][i]=z*c-x*s;
|
|
||||||
}
|
|
||||||
z=pythag(f,h);
|
|
||||||
w[j]=z;
|
|
||||||
if (z) {
|
|
||||||
z=1.0/z;
|
|
||||||
c=f*z;
|
|
||||||
s=h*z;
|
|
||||||
}
|
|
||||||
f=c*g+s*y;
|
|
||||||
x=c*y-s*g;
|
|
||||||
for (jj=1;jj<=m;jj++) {
|
|
||||||
y=a[jj][j];
|
|
||||||
z=a[jj][i];
|
|
||||||
a[jj][j]=y*c+z*s;
|
|
||||||
a[jj][i]=z*c-y*s;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
rv1[l-1]=0.0;
|
|
||||||
rv1[k-1]=f;
|
|
||||||
w[k]=x;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
delete[] rv1;
|
if (sort) {
|
||||||
|
int *indices1 = new int[n];
|
||||||
|
int *indices2 = new int[n];
|
||||||
|
for (int i1 = 1; i1 <= n; i1++) {
|
||||||
|
indices1[i1] = i1;
|
||||||
|
indices2[i1] = i1;
|
||||||
|
}
|
||||||
|
|
||||||
|
for (int i1 = 1; i1 <= n; i1++) {
|
||||||
|
for (int i2 = i1; i2 <= n; i2++) {
|
||||||
|
if (w[i1] < w[i2]) {
|
||||||
|
double temp = w[i1];
|
||||||
|
w[i1] = w[i2];
|
||||||
|
w[i2] = temp;
|
||||||
|
int ind = indices2[i1];
|
||||||
|
indices2[i1] = indices2[i2];
|
||||||
|
indices2[i2] = ind;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for (int i1 = 1; i1 <= n; i1++) {
|
||||||
|
if (indices1[i1] != indices2[i1]) {
|
||||||
|
int src = indices1[i1], dst = indices2[i1];
|
||||||
|
for (int j = 1; j <= n; j++) {
|
||||||
|
double temp = v[j][src];
|
||||||
|
v[j][src] = v[j][dst];
|
||||||
|
v[j][dst] = temp;
|
||||||
|
}
|
||||||
|
indices1[dst] = src;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
delete[] indices1;
|
||||||
|
delete[] indices2;
|
||||||
|
}
|
||||||
|
|
||||||
|
delete[] rv1;
|
||||||
|
|
||||||
}
|
}
|
||||||
|
|
||||||
/* ************************************************************************* */
|
/* ************************************************************************* */
|
||||||
|
|
|
||||||
|
|
@ -10,5 +10,5 @@
|
||||||
#pragma once
|
#pragma once
|
||||||
|
|
||||||
/** SVD decomposition */
|
/** SVD decomposition */
|
||||||
void svdcmp(double **a, int m, int n, double w[], double **v);
|
void svdcmp(double **a, int m, int n, double w[], double **v, bool sort = true);
|
||||||
|
|
||||||
|
|
|
||||||
File diff suppressed because it is too large
Load Diff
Loading…
Reference in New Issue