added default bool option to svd to sort the singular values and V. the default is true so pass false to avoid sorting

release/4.3a0
Manohar Paluri 2010-02-14 04:54:39 +00:00
parent f9c2000847
commit 693e13ef88
5 changed files with 741 additions and 664 deletions

View File

@ -866,7 +866,7 @@ Matrix cholesky_inverse(const Matrix &A)
/* ************************************************************************* */ /* ************************************************************************* */
// version with in place modification of A // version with in place modification of A
void svd(Matrix& A, Vector& s, Matrix& V) { void svd(Matrix& A, Vector& s, Matrix& V, bool sort) {
const size_t m=A.size1(), n=A.size2(); const size_t m=A.size1(), n=A.size2();
@ -878,7 +878,7 @@ void svd(Matrix& A, Vector& s, Matrix& V) {
// perform SVD // perform SVD
// need to pass pointer - 1 in NRC routines so u[1][1] is first element ! // need to pass pointer - 1 in NRC routines so u[1][1] is first element !
svdcmp(u-1,m,n,q-1,v-1); svdcmp(u-1,m,n,q-1,v-1, sort);
// copy singular values back // copy singular values back
s.resize(n); s.resize(n);
@ -891,9 +891,9 @@ void svd(Matrix& A, Vector& s, Matrix& V) {
} }
/* ************************************************************************* */ /* ************************************************************************* */
void svd(const Matrix& A, Matrix& U, Vector& s, Matrix& V) { void svd(const Matrix& A, Matrix& U, Vector& s, Matrix& V, bool sort) {
U = A; // copy U = A; // copy
svd(U,s,V); // call in-place version svd(U,s,V,sort); // call in-place version
} }
#if 0 #if 0
@ -941,7 +941,7 @@ Matrix square_root_positive(const Matrix& A) {
// Perform SVD, TODO: symmetric SVD? // Perform SVD, TODO: symmetric SVD?
Matrix U,V; Matrix U,V;
Vector S; Vector S;
svd(A,U,S,V); svd(A,U,S,V,false);
// invert and sqrt diagonal of S // invert and sqrt diagonal of S
// We also arbitrarily choose sign to make result have positive signs // We also arbitrarily choose sign to make result have positive signs

View File

@ -308,11 +308,12 @@ inline Matrix skewSymmetric(const Vector& w) { return skewSymmetric(w(0),w(1),w(
* @param U output argument: m*n matrix * @param U output argument: m*n matrix
* @param S output argument: n-dim vector of singular values, *not* sorted !!! * @param S output argument: n-dim vector of singular values, *not* sorted !!!
* @param V output argument: n*n matrix * @param V output argument: n*n matrix
* @param sort boolean flag to sort singular values and V
*/ */
void svd(const Matrix& A, Matrix& U, Vector& S, Matrix& V); void svd(const Matrix& A, Matrix& U, Vector& S, Matrix& V, bool sort=true);
// in-place version // in-place version
void svd(Matrix& A, Vector& S, Matrix& V); void svd(Matrix& A, Vector& S, Matrix& V, bool sort=true);
/** Use SVD to calculate inverse square root of a matrix */ /** Use SVD to calculate inverse square root of a matrix */
Matrix inverse_square_root(const Matrix& A); Matrix inverse_square_root(const Matrix& A);

View File

@ -8,247 +8,299 @@
#include <math.h> /* for 'fabs' */ #include <math.h> /* for 'fabs' */
#include <iostream> #include <iostream>
#include <vector> #include <vector>
#include "Matrix.h"
using namespace std; using namespace std;
#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a)) #define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
static double sqrarg; static double sqrarg;
#define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg) #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 : sqrarg*sqrarg)
static double maxarg1,maxarg2; static double maxarg1, maxarg2;
#define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ?\ #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ?\
(maxarg1) : (maxarg2)) (maxarg1) : (maxarg2))
static int iminarg1,iminarg2; static int iminarg1, iminarg2;
#define IMIN(a,b) (iminarg1=(a),iminarg2=(b),(iminarg1) < (iminarg2) ?\ #define IMIN(a,b) (iminarg1=(a),iminarg2=(b),(iminarg1) < (iminarg2) ?\
(iminarg1) : (iminarg2)) (iminarg1) : (iminarg2))
/* ************************************************************************* */ /* ************************************************************************* */
/* /*
double pythag(double a, double b) double pythag(double a, double b)
{ {
double absa = 0.0, absb = 0.0; double absa = 0.0, absb = 0.0;
absa=fabs(a); absa=fabs(a);
absb=fabs(b); absb=fabs(b);
if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa)); if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa));
else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+SQR(absa/absb))); else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+SQR(absa/absb)));
} }
*/ */
/* ************************************************************************* */ /* ************************************************************************* */
double pythag(double a, double b) double pythag(double a, double b) {
{ double absa = 0.0, absb = 0.0;
double absa = 0.0, absb = 0.0; absa = fabs(a);
absa=fabs(a); absb = fabs(b);
absb=fabs(b); if (absa > absb)
if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa)); return absa * sqrt(1.0 + SQR(absb/absa));
else { else {
if(absb == 0.0) if (absb == 0.0)
return 0.0; return 0.0;
else else
return (absb * sqrt(1.0 + SQR(absa/absb))); return (absb * sqrt(1.0 + SQR(absa/absb)));
} }
} }
/* ************************************************************************* */ /* ************************************************************************* */
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) {
{ int flag, i, its, j, jj, k, l, nm;
int flag,i,its,j,jj,k,l,nm; double anorm, c, f, g, h, s, scale, x, y, z;
double anorm,c,f,g,h,s,scale,x,y,z;
//vector sizes: //vector sizes:
// w[n] - q-1 passed in // w[n] - q-1 passed in
// a[m] - u-1 passed in // a[m] - u-1 passed in
// v[n] - v-1 passed in // v[n] - v-1 passed in
//Current progress on verifying array bounds: //Current progress on verifying array bounds:
// rv1 references have been fixed // rv1 references have been fixed
double *rv1 = new double[n]; double *rv1 = new double[n];
g= 0.0; g = 0.0;
scale= 0.0; scale = 0.0;
anorm= 0.0; anorm = 0.0;
for (i=1;i<=n;i++) { for (i = 1; i <= n; i++) {
l=i+1; l = i + 1;
rv1[i-1]=scale*g; rv1[i - 1] = scale * g;
g=s=scale=0.0; g = s = scale = 0.0;
if (i <= m) { if (i <= m) {
for (k=i;k<=m;k++) scale += fabs(a[k][i]); for (k = i; k <= m; k++)
if (scale) { scale += fabs(a[k][i]);
for (k=i;k<=m;k++) { if (scale) {
a[k][i] /= scale; for (k = i; k <= m; k++) {
s += a[k][i]*a[k][i]; a[k][i] /= scale;
} s += a[k][i] * a[k][i];
f=a[i][i]; }
g = -SIGN(sqrt(s),f); f = a[i][i];
h=f*g-s; g = -SIGN(sqrt(s),f);
a[i][i]=f-g; h = f * g - s;
for (j=l;j<=n;j++) { a[i][i] = f - g;
for (s=0.0,k=i;k<=m;k++) s += a[k][i]*a[k][j]; for (j = l; j <= n; j++) {
f=s/h; for (s = 0.0, k = i; k <= m; k++)
for (k=i;k<=m;k++) a[k][j] += f*a[k][i]; s += a[k][i] * a[k][j];
} f = s / h;
for (k=i;k<=m;k++) a[k][i] *= scale; for (k = i; k <= m; k++)
} a[k][j] += f * a[k][i];
} }
w[i]=scale *g; for (k = i; k <= m; k++)
g=s=scale=0.0; a[k][i] *= scale;
if (i <= m && i != n) { }
for (k=l;k<=n;k++) scale += fabs(a[i][k]); }
if (scale) { w[i] = scale * g;
for (k=l;k<=n;k++) { g = s = scale = 0.0;
a[i][k] /= scale; if (i <= m && i != n) {
s += a[i][k]*a[i][k]; for (k = l; k <= n; k++)
} scale += fabs(a[i][k]);
f=a[i][l]; if (scale) {
g = -SIGN(sqrt(s),f); for (k = l; k <= n; k++) {
h=f*g-s; a[i][k] /= scale;
a[i][l]=f-g; s += a[i][k] * a[i][k];
for (k=l;k<=n;k++) }
{ f = a[i][l];
rv1[k-1]=a[i][k]/h; g = -SIGN(sqrt(s),f);
} h = f * g - s;
a[i][l] = f - g;
for (k = l; k <= n; k++) {
rv1[k - 1] = a[i][k] / h;
}
for (j=l;j<=m;j++) { for (j = l; j <= m; j++) {
for (s=0.0,k=l;k<=n;k++) for (s = 0.0, k = l; k <= n; k++)
s += a[j][k]*a[i][k]; s += a[j][k] * a[i][k];
for (k=l;k<=n;k++) for (k = l; k <= n; k++) {
{ a[j][k] += s * rv1[k - 1];
a[j][k] += s*rv1[k-1]; }
} }
} for (k = l; k <= n; k++)
for (k=l;k<=n;k++) a[i][k] *= scale; a[i][k] *= scale;
} }
} }
anorm=FMAX(anorm,(fabs(w[i])+fabs(rv1[i-1]))); anorm = FMAX(anorm,(fabs(w[i])+fabs(rv1[i-1])));
}
for (i=n;i>=1;i--) {
if (i < n) {
if (g) {
for (j=l;j<=n;j++)
v[j][i]=(a[i][j]/a[i][l])/g;
for (j=l;j<=n;j++) {
for (s=0.0,k=l;k<=n;k++) s += a[i][k]*v[k][j];
for (k=l;k<=n;k++) v[k][j] += s*v[k][i];
} }
} for (i = n; i >= 1; i--) {
for (j=l;j<=n;j++) v[i][j]=v[j][i]=0.0; if (i < n) {
} if (g) {
v[i][i]=1.0; for (j = l; j <= n; j++)
g=rv1[i-1]; v[j][i] = (a[i][j] / a[i][l]) / g;
l=i; for (j = l; j <= n; j++) {
} for (s = 0.0, k = l; k <= n; k++)
for (i=IMIN(m,n);i>=1;i--) { s += a[i][k] * v[k][j];
l=i+1; for (k = l; k <= n; k++)
g=w[i]; v[k][j] += s * v[k][i];
for (j=l;j<=n;j++) a[i][j]=0.0; }
if (g) { }
g=1.0/g; for (j = l; j <= n; j++)
for (j=l;j<=n;j++) { v[i][j] = v[j][i] = 0.0;
for (s=0.0,k=l;k<=m;k++) s += a[k][i]*a[k][j]; }
f=(s/a[i][i])*g; v[i][i] = 1.0;
for (k=i;k<=m;k++) a[k][j] += f*a[k][i]; g = rv1[i - 1];
} l = i;
for (j=i;j<=m;j++) a[j][i] *= g;
} else for (j=i;j<=m;j++) a[j][i]=0.0;
++a[i][i];
}
for (k=n;k>=1;k--) {
for (its=1;its<=30;its++) {
flag=1;
for (l=k;l>=1;l--) {
nm=l-1;
if ((double)(fabs(rv1[l-1])+anorm) == anorm) {
flag=0;
break;
} }
if ((double)(fabs(w[nm])+anorm) == anorm) break; for (i = IMIN(m,n); i >= 1; i--) {
} l = i + 1;
if (flag) { g = w[i];
c=0.0; for (j = l; j <= n; j++)
s=1.0; a[i][j] = 0.0;
for (i=l;i<=k;i++) { if (g) {
f=s*rv1[i-1]; g = 1.0 / g;
rv1[i-1]=c*rv1[i-1]; for (j = l; j <= n; j++) {
if ((double)(fabs(f)+anorm) == anorm) break; for (s = 0.0, k = l; k <= m; k++)
g=w[i]; s += a[k][i] * a[k][j];
h=pythag(f,g); f = (s / a[i][i]) * g;
w[i]=h; for (k = i; k <= m; k++)
h=1.0/h; a[k][j] += f * a[k][i];
c=g*h; }
s = -f*h; for (j = i; j <= m; j++)
for (j=1;j<=m;j++) { a[j][i] *= g;
y=a[j][nm]; } else
z=a[j][i]; for (j = i; j <= m; j++)
a[j][nm]=y*c+z*s; a[j][i] = 0.0;
a[j][i]=z*c-y*s; ++a[i][i];
}
} }
} for (k = n; k >= 1; k--) {
z=w[k]; for (its = 1; its <= 30; its++) {
if (l == k) { flag = 1;
if (z < 0.0) { for (l = k; l >= 1; l--) {
w[k] = -z; nm = l - 1;
for (j=1;j<=n;j++) v[j][k] = -v[j][k]; if ((double) (fabs(rv1[l - 1]) + anorm) == anorm) {
flag = 0;
break;
}
if ((double) (fabs(w[nm]) + anorm) == anorm)
break;
}
if (flag) {
c = 0.0;
s = 1.0;
for (i = l; i <= k; i++) {
f = s * rv1[i - 1];
rv1[i - 1] = c * rv1[i - 1];
if ((double) (fabs(f) + anorm) == anorm)
break;
g = w[i];
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;
} }
/* ************************************************************************* */ /* ************************************************************************* */

View File

@ -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