288 lines
6.2 KiB
C++
288 lines
6.2 KiB
C++
/**
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* @file svdcmp.cpp
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* @brief SVD decomposition adapted from NRC
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* @author Alireza Fathi
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* @author Frank Dellaert
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*/
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#include <stdexcept>
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#include <math.h> /* for 'fabs' */
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#include <iostream>
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#include <vector>
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#include "Matrix.h"
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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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static double 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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#define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ?\
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(maxarg1) : (maxarg2))
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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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(iminarg1) : (iminarg2))
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/* ************************************************************************* */
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/*
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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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absa=fabs(a);
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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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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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double pythag(double a, double b) {
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double absa = 0.0, absb = 0.0;
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absa = fabs(a);
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absb = fabs(b);
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if (absa > absb)
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return absa * sqrt(1.0 + SQR(absb/absa));
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else {
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if (absb == 0.0)
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return 0.0;
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else
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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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void svdcmp(double **a, int m, int n, double w[], double **v, bool sort) {
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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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//vector sizes:
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// w[n] - q-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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//Current progress on verifying array bounds:
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// rv1 references have been fixed
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double *rv1 = new double[n];
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g = 0.0;
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scale = 0.0;
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anorm = 0.0;
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for (i = 1; i <= n; i++) {
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l = i + 1;
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rv1[i - 1] = scale * g;
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g = s = scale = 0.0;
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if (i <= m) {
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for (k = i; k <= m; k++)
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scale += fabs(a[k][i]);
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if (scale) {
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for (k = i; k <= m; k++) {
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a[k][i] /= scale;
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s += a[k][i] * a[k][i];
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}
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f = a[i][i];
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g = -SIGN(sqrt(s),f);
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h = f * g - s;
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a[i][i] = f - g;
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for (j = l; j <= n; j++) {
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for (s = 0.0, k = i; k <= m; k++)
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s += a[k][i] * a[k][j];
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f = s / h;
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for (k = i; k <= m; k++)
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a[k][j] += f * a[k][i];
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}
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for (k = i; k <= m; k++)
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a[k][i] *= scale;
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}
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}
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w[i] = scale * g;
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g = s = scale = 0.0;
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if (i <= m && i != n) {
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for (k = l; k <= n; k++)
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scale += fabs(a[i][k]);
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if (scale) {
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for (k = l; k <= n; k++) {
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a[i][k] /= scale;
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s += a[i][k] * a[i][k];
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}
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f = a[i][l];
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g = -SIGN(sqrt(s),f);
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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 (s = 0.0, k = l; k <= n; 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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a[j][k] += s * rv1[k - 1];
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}
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}
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for (k = l; k <= n; k++)
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a[i][k] *= scale;
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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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}
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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++)
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s += a[i][k] * v[k][j];
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for (k = l; k <= n; k++)
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v[k][j] += s * v[k][i];
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}
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}
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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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}
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v[i][i] = 1.0;
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g = rv1[i - 1];
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l = i;
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}
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for (i = IMIN(m,n); i >= 1; i--) {
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l = i + 1;
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g = w[i];
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for (j = l; j <= n; j++)
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a[i][j] = 0.0;
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if (g) {
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g = 1.0 / g;
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for (j = l; j <= n; j++) {
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for (s = 0.0, k = l; k <= m; k++)
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s += a[k][i] * a[k][j];
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f = (s / a[i][i]) * g;
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for (k = i; k <= m; k++)
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a[k][j] += f * a[k][i];
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}
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for (j = i; j <= m; j++)
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a[j][i] *= g;
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} else
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for (j = i; j <= m; j++)
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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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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);
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w[i] = h;
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h = 1.0 / h;
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c = g * h;
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s = -f * h;
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for (j = 1; j <= m; j++) {
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y = a[j][nm];
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z = a[j][i];
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a[j][nm] = y * c + z * s;
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a[j][i] = z * c - y * s;
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}
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}
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}
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z = w[k];
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if (l == k) {
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if (z < 0.0) {
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w[k] = -z;
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for (j = 1; j <= n; j++)
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v[j][k] = -v[j][k];
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}
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break;
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}
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if (its == 30)
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throw(std::domain_error(
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"no convergence in 30 svdcmp iterations"));
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x = w[l];
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nm = k - 1;
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y = w[nm];
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g = rv1[nm - 1];
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h = rv1[k - 1];
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f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
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g = pythag(f, 1.0);
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f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g,f))) - h)) / x;
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c = s = 1.0;
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for (j = l; j <= nm; j++) {
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i = j + 1;
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g = rv1[i - 1];
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y = w[i];
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h = s * g;
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g = c * g;
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z = pythag(f, h);
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rv1[j - 1] = z;
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c = f / z;
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s = h / z;
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f = x * c + g * s;
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g = g * c - x * s;
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h = y * s;
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y *= c;
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for (jj = 1; jj <= n; jj++) {
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x = v[jj][j];
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z = v[jj][i];
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v[jj][j] = x * c + z * s;
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v[jj][i] = z * c - x * s;
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}
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z = pythag(f, h);
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w[j] = z;
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if (z) {
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z = 1.0 / z;
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c = f * z;
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s = h * z;
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}
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f = c * g + s * y;
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x = c * y - s * g;
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for (jj = 1; jj <= m; jj++) {
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y = a[jj][j];
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z = a[jj][i];
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a[jj][j] = y * c + z * s;
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a[jj][i] = z * c - y * s;
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}
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}
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rv1[l - 1] = 0.0;
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rv1[k - 1] = f;
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w[k] = x;
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}
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}
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if (sort) {
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for (int i1 = 1; i1 <= n; i1++) {
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for (int i2 = i1+1; i2 <= n; i2++) {
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if (w[i1] < w[i2]) {
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double temp = w[i1];
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w[i1] = w[i2];
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w[i2] = temp;
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for (int j = 1; j <= n; j++) {
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double temp1 = v[j][i1];
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v[j][i1] = v[j][i2];
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v[j][i2] = temp1;
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}
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}
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}
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}
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}
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delete[] rv1;
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}
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/* ************************************************************************* */
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