Merge pull request #10 from laristra/headerfix

Wonton Installation

src/support/CMakeLists.txt

@@ -23,6 +23,7 @@ set(support_HEADERS
 
 # Add source files
 set(support_SOURCES
+    svd.cc
     PARENT_SCOPE
 )
 

src/support/lsfits.h

@@ -159,8 +159,8 @@ template<long D>
   }
 
   size_t ma = D*(D+3)/2;
-  std::vector<std::vector<double> > u(nvals-1, vector<double>(ma));
-  std::vector<std::vector<double> > v(ma, vector<double>(ma));
+  std::vector<std::vector<double> > u(nvals-1, std::vector<double>(ma));
+  std::vector<std::vector<double> > v(ma, std::vector<double>(ma));
   std::vector<double> w(ma);
   for (int i=0; i < nvals-1; i++) {
     for (int j=0; j < D*(D+3)/2; j++) {
@@ -194,7 +194,7 @@ template<long D>
   }
 
   // solve the problem for coefficients, in "result".
-  vector<double> result(ma);
+  std::vector<double> result(ma);
   svd_solve(u,w,v,F,result);
 
   return result;

src/support/svd.cc

@@ -0,0 +1,355 @@
+/*
+This file is part of the Ristra portage project.
+Please see the license file at the root of this repository, or at:
+    https://github.com/laristra/portage/blob/master/LICENSE
+*/
+
+/* 
+ * svd.cc - Double precision SVD decomposition routine. 
+ * Takes an mxn matrix a and decomposes it into udv, where u,v are
+ * left and right orthogonal transformation matrices, and d is a 
+ * diagonal matrix of singular values.
+ *
+ * This routine was adapted from Numerical Recipes SVD routines in C
+ * to be called with C++ std::vectors by Michael Rogers.
+ *
+ * Input to svd is as follows:
+ *   a = mxn matrix to be decomposed, gets overwritten with u
+ *   w = returns the vector of singular values of a
+ *   v = returns the right orthogonal transformation matrix
+*/
+
+#include "portage/support/svd.h"
+
+#include <stdio.h>
+#include <iostream>
+#include <vector>
+#include <stdlib.h>
+#include <math.h>
+#define MIN(x,y) ( (x) < (y) ? (x) : (y) )
+#define MAX(x,y) ((x)>(y)?(x):(y))
+#define SIGN(a, b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
+
+namespace Portage {
+
+
+static double PYTHAG(double a, double b)
+{
+    double at = fabs(a), bt = fabs(b), ct, result;
+
+    if (at > bt)       { ct = bt / at; result = at * sqrt(1.0 + ct * ct); }
+    else if (bt > 0.0) { ct = at / bt; result = bt * sqrt(1.0 + ct * ct); }
+    else result = 0.0;
+    return(result);
+}
+
+// Perform singular value decomposition
+
+int svd(std::vector<std::vector<double> > & a, std::vector<double> & w, std::vector<std::vector<double> > & v)
+{
+    int flag, i, its, j, jj, k, l, nm;
+    int m, n;        // dimensions of a (and u) 
+    double c, f, h, s, x, y, z;
+    double anorm = 0.0, g = 0.0, scale = 0.0;
+    double *rv1;
+
+    m = a.size();     // number of rows
+    n = a[0].size();  // number of columns
+
+    if (m < n) 
+    {
+        fprintf(stderr, "#rows must be >= #cols \n");
+        return(1);
+    }
+
+    rv1 = (double *)malloc((unsigned int) n*sizeof(double));
+
+/* Householder reduction to bidiagonal form */
+    for (i = 0; i < n; i++) 
+    {
+        /* left-hand reduction */
+        l = i + 1;
+        rv1[i] = scale * g;
+        g = s = scale = 0.0;
+        if (i < m) 
+        {
+            for (k = i; k < m; k++) 
+                scale += fabs((double)a[k][i]);
+            if (scale) 
+            {
+                for (k = i; k < m; k++) 
+                {		    
+                    a[k][i] = (double)((double)a[k][i]/scale);
+                    s += ((double)a[k][i] * (double)a[k][i]);
+                }
+                f = (double)a[i][i];
+                g = -SIGN(sqrt(s), f);
+                h = f * g - s;
+                a[i][i] = (double)(f - g);
+                if (i != n - 1) 
+                {
+                    for (j = l; j < n; j++) 
+                    {
+                        for (s = 0.0, k = i; k < m; k++) 
+                            s += ((double)a[k][i] * (double)a[k][j]);
+                        f = s / h;
+                        for (k = i; k < m; k++) 
+                            a[k][j] += (double)(f * (double)a[k][i]);
+                    }
+                }
+                for (k = i; k < m; k++) 
+                    a[k][i] = (double)((double)a[k][i]*scale);
+            }
+        }
+        w[i] = (double)(scale * g);
+
+        /* right-hand reduction */
+        g = s = scale = 0.0;
+        if (i < m && i != n - 1) 
+        {
+            for (k = l; k < n; k++) 
+                scale += fabs((double)a[i][k]);
+            if (scale) 
+            {
+                for (k = l; k < n; k++) 
+                {
+                    a[i][k] = (double)((double)a[i][k]/scale);
+                    s += ((double)a[i][k] * (double)a[i][k]);
+                }
+                f = (double)a[i][l];
+                g = -SIGN(sqrt(s), f);
+                h = f * g - s;
+                a[i][l] = (double)(f - g);
+                for (k = l; k < n; k++) 
+                    rv1[k] = (double)a[i][k] / h;
+                if (i != m - 1) 
+                {
+                    for (j = l; j < m; j++) 
+                    {
+                        for (s = 0.0, k = l; k < n; k++) 
+                            s += ((double)a[j][k] * (double)a[i][k]);
+                        for (k = l; k < n; k++) 
+                            a[j][k] += (double)(s * rv1[k]);
+                    }
+                }
+                for (k = l; k < n; k++) 
+                    a[i][k] = (double)((double)a[i][k]*scale);
+            }
+        }
+        anorm = MAX(anorm, (fabs((double)w[i]) + fabs(rv1[i])));
+    }
+
+    /* accumulate the right-hand transformation */
+    for (i = n - 1; i >= 0; i--) 
+    {
+        if (i < n - 1) 
+        {
+            if (g) 
+            {
+                for (j = l; j < n; j++)
+                    v[j][i] = (double)(((double)a[i][j] / (double)a[i][l]) / g);
+                    /* double division to avoid underflow */
+                for (j = l; j < n; j++) 
+                {
+                    for (s = 0.0, k = l; k < n; k++) 
+                        s += ((double)a[i][k] * (double)v[k][j]);
+                    for (k = l; k < n; k++) 
+                        v[k][j] += (double)(s * (double)v[k][i]);
+                }
+            }
+            for (j = l; j < n; j++) 
+                v[i][j] = v[j][i] = 0.0;
+        }
+        v[i][i] = 1.0;
+        g = rv1[i];
+        l = i;
+    }
+    /* accumulate the left-hand transformation */
+    for (i = n - 1; i >= 0; i--) 
+    {
+        l = i + 1;
+        g = (double)w[i];
+        if (i < n - 1) 
+            for (j = l; j < n; j++) 
+                a[i][j] = 0.0;
+        if (g) 
+        {
+            g = 1.0 / g;
+            if (i != n - 1) 
+            {
+                for (j = l; j < n; j++) 
+                {
+                    for (s = 0.0, k = l; k < m; k++) 
+                        s += ((double)a[k][i] * (double)a[k][j]);
+                    f = (s / (double)a[i][i]) * g;
+                    for (k = i; k < m; k++) 
+                        a[k][j] += (double)(f * (double)a[k][i]);
+                }
+            }
+            for (j = i; j < m; j++) 
+                a[j][i] = (double)((double)a[j][i]*g);
+        }
+        else 
+        {
+            for (j = i; j < m; j++) 
+                a[j][i] = 0.0;
+        }
+        ++a[i][i];
+    }
+
+    /* diagonalize the bidiagonal form */
+    for (k = n - 1; k >= 0; k--) 
+    {                             /* loop over singular values */
+        for (its = 0; its < 30; its++) 
+        {                         /* loop over allowed iterations */
+            flag = 1;
+            for (l = k; l >= 0; l--) 
+            {                     /* test for splitting */
+                nm = l - 1;
+                if (fabs(rv1[l]) + anorm == anorm) 
+                {
+                    flag = 0;
+                    break;
+                }
+                if (fabs((double)w[nm]) + anorm == anorm) 
+                    break;
+            }
+            if (flag) 
+            {
+                c = 0.0;
+                s = 1.0;
+                for (i = l; i <= k; i++) 
+                {
+                    f = s * rv1[i];
+                    if (fabs(f) + anorm != anorm) 
+                    {
+                        g = (double)w[i];
+                        h = PYTHAG(f, g);
+                        w[i] = (double)h; 
+                        h = 1.0 / h;
+                        c = g * h;
+                        s = (- f * h);
+                        for (j = 0; j < m; j++) 
+                        {
+                            y = (double)a[j][nm];
+                            z = (double)a[j][i];
+                            a[j][nm] = (double)(y * c + z * s);
+                            a[j][i] = (double)(z * c - y * s);
+                        }
+                    }
+                }
+            }
+            z = (double)w[k];
+            if (l == k) 
+            {                  /* convergence */
+                if (z < 0.0) 
+                {              /* make singular value nonnegative */
+                    w[k] = (double)(-z);
+                    for (j = 0; j < n; j++) 
+                        v[j][k] = (-v[j][k]);
+                }
+                break;
+            }
+            if (its >= 30) {
+                free((void*) rv1);
+                fprintf(stderr, "No convergence after 30,000! iterations \n");
+                return(1);
+            }
+
+            /* shift from bottom 2 x 2 minor */
+            x = (double)w[l];
+            nm = k - 1;
+            y = (double)w[nm];
+            g = rv1[nm];
+            h = rv1[k];
+            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;
+
+            /* next QR transformation */
+            c = s = 1.0;
+            for (j = l; j <= nm; j++) 
+            {
+                i = j + 1;
+                g = rv1[i];
+                y = (double)w[i];
+                h = s * g;
+                g = c * g;
+                z = PYTHAG(f, h);
+                rv1[j] = z;
+                c = f / z;
+                s = h / z;
+                f = x * c + g * s;
+                g = g * c - x * s;
+                h = y * s;
+                y = y * c;
+                for (jj = 0; jj < n; jj++) 
+                {
+                    x = (double)v[jj][j];
+                    z = (double)v[jj][i];
+                    v[jj][j] = (double)(x * c + z * s);
+                    v[jj][i] = (double)(z * c - x * s);
+                }
+                z = PYTHAG(f, h);
+                w[j] = (double)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 = 0; jj < m; jj++) 
+                {
+                    y = (double)a[jj][j];
+                    z = (double)a[jj][i];
+                    a[jj][j] = (double)(y * c + z * s);
+                    a[jj][i] = (double)(z * c - y * s);
+                }
+            }
+            rv1[l] = 0.0;
+            rv1[k] = f;
+            w[k] = (double)x;
+        }
+    }
+    free((void*) rv1);
+    return(0);
+}
+
+// Singular value backsubstitution.
+
+void svd_solve(const std::vector<std::vector<double> > & u, const std::vector<double> & w, \
+	       const std::vector<std::vector<double> > & v, \
+	       std::vector<double> & b, std::vector<double> & x)
+ // Solves A*x=b for vector x.  A is specified by the arrays
+ //   u[1...m][1...n], w[1...n],v[1...n[1...n], as returned by
+ //   svd.  m and n are the dimensions of a. b[1...m] is the rhs.
+ //   x[1...n] is the solution vector (output). Nothing is destroyed
+ //   so it can be called sequentially with different b vectors. 
+{
+  int jj, j, i;
+  int m, n;         // dimensions of the matrix u
+  double s;
+
+  m = u.size();     // number of rows
+  n = u[0].size();  // number of columns
+
+  std::vector<double> tmp(n,0.0);
+  for (j=0;j<=n-1;j++) {
+    s=0.0;
+    if (w[j]) {
+      for (i=0;i<=m-1;i++) s += u[i][j]*b[i];
+      s /= w[j];
+    }
+    tmp[j] = s;
+  }
+  for (j=0;j<=n-1;j++) {
+    s=0.0;
+    for (jj=0;jj<=n-1;jj++) s += v[j][jj]*tmp[jj];
+    x[j]=s;
+  }
+}
+
+}  // namespace Portage
+