public static void svdcmp( double[,] a, out double[] w, out double[,] v )
{
// number of rows in A
int m = a.GetLength( 0 );
// number of columns in A
int n = a.GetLength( 1 );
if ( m < n )
{
throw new ArgumentException( "Number of rows in A must be greater or equal to number of columns" );
}
w = new double[n];
v = new double[n, n];
int flag, i, its, j, jj, k, l = 0, nm = 0;
double anorm, c, f, g, h, s, scale, x, y, z;
double[] rv1 = new double[n];
// householder reduction to bidiagonal form
g = scale = anorm = 0.0;
for ( i = 0; i < n; i++ )
{
l = i + 1;
rv1[i] = scale * g;
g = s = scale = 0;
if ( i < m )
{
for ( k = i; k < m; k++ )
{
scale += System.Math.Abs( a[k, i] );
}
if ( scale != 0.0 )
{
for ( k = i; k < m; k++ )
{
a[k, i] /= scale;
s += a[k, i] * a[k, i];
}
f = a[i, i];
g = -Sign( System.Math.Sqrt( s ), f );
h = f * g - s;
a[i, i] = f - g;
if ( i != n - 1 )
{
for ( j = l; j < n; j++ )
{
for ( s = 0.0, k = i; k < m; k++ )
{
s += a[k, i] * a[k, j];
}
f = s / h;
for ( k = i; k < m; k++ )
{
a[k, j] += f * a[k, i];
}
}
}
for ( k = i; k < m; k++ )
{
a[k, i] *= scale;
}
}
}
w[i] = scale * g;
g = s = scale = 0.0;
if ( ( i < m ) && ( i != n - 1 ) )
{
for ( k = l; k < n; k++ )
{
scale += System.Math.Abs( a[i, k] );
}
if ( scale != 0.0 )
{
for ( k = l; k < n; k++ )
{
a[i, k] /= scale;
s += a[i, k] * a[i, k];
}
f = a[i, l];
g = -Sign( System.Math.Sqrt( s ), f );
h = f * g - s;
a[i, l] = f - g;
for ( k = l; k < n; k++ )
{
rv1[k] = a[i, k] / h;
}
if ( i != m - 1 )
{
for ( j = l; j < m; j++ )
{
for ( s = 0.0, k = l; k < n; k++ )
{
s += a[j, k] * a[i, k];
}
for ( k = l; k < n; k++ )
{
a[j, k] += s * rv1[k];
}
}
}
for ( k = l; k < n; k++ )
{
a[i, k] *= scale;
}
}
}
anorm = System.Math.Max( anorm, ( System.Math.Abs( w[i] ) + System.Math.Abs( rv1[i] ) ) );
}
// accumulation of right-hand transformations
for ( i = n - 1; i >= 0; i-- )
{
if ( i < n - 1 )
{
if ( g != 0.0 )
{
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, 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 ( j = l; j < n; j++ )
{
v[i, j] = v[j, i] = 0;
}
}
v[i, i] = 1;
g = rv1[i];
l = i;
}
// accumulation of left-hand transformations
for ( i = n - 1; i >= 0; i-- )
{
l = i + 1;
g = w[i];
if ( i < n - 1 )
{
for ( j = l; j < n; j++ )
{
a[i, j] = 0.0;
}
}
if ( g != 0 )
{
g = 1.0 / g;
if ( i != n - 1 )
{
for ( j = l; j < n; j++ )
{
for ( s = 0, k = l; k < m; k++ )
{
s += a[k, i] * a[k, j];
}
f = ( s / a[i, i] ) * g;
for ( k = i; k < m; k++ )
{
a[k, j] += f * a[k, i];
}
}
}
for ( j = i; j < m; j++ )
{
a[j, i] *= g;
}
}
else
{
for ( j = i; j < m; j++ )
{
a[j, i] = 0;
}
}
++a[i, i];
}
// diagonalization of the bidiagonal form: Loop over singular values
// and over allowed iterations
for ( k = n - 1; k >= 0; k-- )
{
for ( its = 1; its <= 30; its++ )
{
flag = 1;
for ( l = k; l >= 0; l-- )
{
// test for splitting
nm = l - 1;
if ( System.Math.Abs( rv1[l] ) + anorm == anorm )
{
flag = 0;
break;
}
if ( System.Math.Abs( w[nm] ) + anorm == anorm )
break;
}
if ( flag != 0 )
{
c = 0.0;
s = 1.0;
for ( i = l; i <= k; i++ )
{
f = s * rv1[i];
if ( System.Math.Abs( f ) + anorm != anorm )
{
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 )
{
// convergence
if ( z < 0.0 )
{
// singular value is made nonnegative
w[k] = -z;
for ( j = 0; j < n; j++ )
{
v[j, k] = -v[j, k];
}
}
break;
}
if ( its == 30 )
{
Throw();
}
// shift from bottom 2-by-2 minor
x = w[l];
nm = k - 1;
y = 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 = 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 *= c;
for ( jj = 0; 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 != 0 )
{
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 = a[jj, j];
z = a[jj, i];
a[jj, j] = y * c + z * s;
a[jj, i] = z * c - y * s;
}
}
rv1[l] = 0.0;
rv1[k] = f;
w[k] = x;
}
}
}
