public static double Compute(Complex a, Complex b)
{
Complex temp = a * ComplexMath.Conjugate(a);
temp += (b * ComplexMath.Conjugate(b));
double ret = ComplexMath.Absolute(temp);
return(System.Math.Sqrt(ret));
}
public static float Compute(ComplexFloat a, ComplexFloat b)
{
ComplexFloat temp = a * ComplexMath.Conjugate(a);
temp += (b * ComplexMath.Conjugate(b));
float ret = ComplexMath.Absolute(temp);
return((float)System.Math.Sqrt(ret));
}
public void SquareDecomp()
{
ComplexFloatMatrix a = new ComplexFloatMatrix(3);
a[0, 0] = new ComplexFloat(1.1f, 1.1f);
a[0, 1] = new ComplexFloat(2.2f, -2.2f);
a[0, 2] = new ComplexFloat(3.3f, 3.3f);
a[1, 0] = new ComplexFloat(4.4f, -4.4f);
a[1, 1] = new ComplexFloat(5.5f, 5.5f);
a[1, 2] = new ComplexFloat(6.6f, -6.6f);
a[2, 0] = new ComplexFloat(7.7f, 7.7f);
a[2, 1] = new ComplexFloat(8.8f, -8.8f);
a[2, 2] = new ComplexFloat(9.9f, 9.9f);
ComplexFloatQRDecomp qrd = new ComplexFloatQRDecomp(a);
ComplexFloatMatrix qq = qrd.Q.GetConjugateTranspose() * qrd.Q;
ComplexFloatMatrix qr = qrd.Q * qrd.R;
ComplexFloatMatrix I = ComplexFloatMatrix.CreateIdentity(3);
// determine the maximum relative error
double MaxError = 0.0;
for (int i = 0; i < 3; i++)
{
for (int j = 0; i < 3; i++)
{
double E = ComplexMath.Absolute((qq[i, j] - I[i, j]));
if (E > MaxError)
{
MaxError = E;
}
}
}
Assert.IsTrue(MaxError < 1.0E-6);
MaxError = 0.0;
for (int i = 0; i < 3; i++)
{
for (int j = 0; i < 3; i++)
{
double E = ComplexMath.Absolute((qr[i, j] - a[i, j]) / a[i, j]);
if (E > MaxError)
{
MaxError = E;
}
}
}
Assert.IsTrue(MaxError < 2.4E-6);
}
public static ComplexDoubleVector GenerateRow(IComplexDoubleMatrix A, int r, int c1, int c2)
{
int cu = c2 - c1 + 1;
ComplexDoubleVector u = new ComplexDoubleVector(cu);
for (int j = c1; j <= c2; j++)
{
u[j - c1] = A[r, j];
A[r, j] = Complex.Zero;
}
double norm = u.GetNorm();
if (c1 == c2 || norm == 0)
{
A[r, c1] = new Complex(-u[0].Real, -u[0].Imag);
u[0] = System.Math.Sqrt(2);
return(u);
}
Complex scale = new Complex(1 / norm);
Complex t = Complex.Zero;
Complex t1 = Complex.Zero;
if (u[0].Real != 0 || u[0].Imag != 0)
{
t = u[0];
t1 = ComplexMath.Conjugate(u[0]);
t = ComplexMath.Absolute(t);
t = t1 / t;
scale = scale * t;
}
A[r, c1] = -Complex.One / scale;
for (int j = 0; j < cu; j++)
{
u[j] *= scale;
}
u[0] = new Complex(u[0].Real + 1);
double s = System.Math.Sqrt(1 / u[0].Real);
for (int j = 0; j < cu; j++)
{
u[j] = new Complex(s * u[j].Real, -s * u[j].Imag);
}
return(u);
}
///<summary>Compute the Infinity Norm of this <c>ComplexFloatVector</c></summary>
///<returns><c>float</c> results from norm.</returns>
public float GetInfinityNorm()
{
float ret = 0;
for (int i = 0; i < data.Length; i++)
{
float tmp = ComplexMath.Absolute(data[i]);
if (tmp > ret)
{
ret = tmp;
}
}
return(ret);
}
public static ComplexFloatVector GenerateColumn(IComplexFloatMatrix A, int r1, int r2, int c)
{
int ru = r2 - r1 + 1;
ComplexFloatVector u = new ComplexFloatVector(r2 - r1 + 1);
for (int i = r1; i <= r2; i++)
{
u[i - r1] = A[i, c];
A[i, c] = ComplexFloat.Zero;
}
float norm = u.GetNorm();
if (r1 == r2 || norm == 0)
{
A[r1, c] = new ComplexFloat(-u[0]);
u[0] = (float)System.Math.Sqrt(2);
return(u);
}
ComplexFloat scale = new ComplexFloat(1 / norm, 0);
ComplexFloat t = ComplexFloat.Zero;
ComplexFloat t1 = ComplexFloat.Zero;
if (u[0].Real != 0 || u[0].Imag != 0)
{
t = u[0];
t1 = ComplexMath.Conjugate(u[0]);
t = ComplexMath.Absolute(t);
t = t1 / t;
scale = scale * t;
}
A[r1, c] = -ComplexFloat.One / scale;
for (int i = 0; i < ru; i++)
{
u[i] = u[i] * scale;
}
u[0] = new ComplexFloat(u[0].Real + 1, 0);
float s = (float)System.Math.Sqrt(1 / u[0].Real);
for (int i = 0; i < ru; i++)
{
u[i] = new ComplexFloat(s * u[i].Real, s * u[i].Imag);
}
return(u);
}
public void SquareDecomp()
{
ComplexDoubleMatrix a = new ComplexDoubleMatrix(3);
a[0, 0] = new Complex(1.1, 1.1);
a[0, 1] = new Complex(2.2, -2.2);
a[0, 2] = new Complex(3.3, 3.3);
a[1, 0] = new Complex(4.4, -4.4);
a[1, 1] = new Complex(5.5, 5.5);
a[1, 2] = new Complex(6.6, -6.6);
a[2, 0] = new Complex(7.7, 7.7);
a[2, 1] = new Complex(8.8, -8.8);
a[2, 2] = new Complex(9.9, 9.9);
ComplexDoubleQRDecomp qrd = new ComplexDoubleQRDecomp(a);
ComplexDoubleMatrix qq = qrd.Q.GetConjugateTranspose() * qrd.Q;
ComplexDoubleMatrix qr = qrd.Q * qrd.R;
ComplexDoubleMatrix I = ComplexDoubleMatrix.CreateIdentity(3);
// determine the maximum relative error
double MaxError = 0.0;
for (int i = 0; i < 3; i++)
{
for (int j = 0; i < 3; i++)
{
double E = ComplexMath.Absolute((qq[i, j] - I[i, j]));
if (E > MaxError)
{
MaxError = E;
}
}
}
Assert.IsTrue(MaxError < 1.0E-14);
MaxError = 0.0;
for (int i = 0; i < 3; i++)
{
for (int j = 0; i < 3; i++)
{
double E = ComplexMath.Absolute((qr[i, j] - a[i, j]) / a[i, j]);
if (E > MaxError)
{
MaxError = E;
}
}
}
Assert.IsTrue(MaxError < 1.0E-14);
}
///<summary>Compute the P Norm of this <c>ComplexFloatVector</c></summary>
///<returns><c>float</c> results from norm.</returns>
///<remarks>p > 0, if p < 0, ABS(p) is used. If p = 0, the infinity norm is returned.</remarks>
public float GetNorm(double p)
{
if (p == 0)
{
return(GetInfinityNorm());
}
if (p < 0)
{
p = -p;
}
double ret = 0;
for (int i = 0; i < data.Length; i++)
{
ret += System.Math.Pow(ComplexMath.Absolute(data[i]), p);
}
return((float)System.Math.Pow(ret, 1 / p));
}
public void Test()
{
DoubleMatrix test = svd.U * svd.W * svd.V.GetTranspose();
double e;
double me = 0;
for (int i = 0; i < test.RowLength; i++)
{
for (int j = 0; j < test.ColumnLength; j++)
{
e = ComplexMath.Absolute((a[i, j] - test[i, j]) / a[i, j]);
if (e > me)
{
me = e;
}
}
}
Assert.IsTrue(me < TOLERENCE, "Maximum Error = " + me.ToString());
}
public void WTest()
{
FloatMatrix test = wsvd.U * wsvd.W * wsvd.V.GetTranspose();
float e;
float me = 0;
for (int i = 0; i < test.RowLength; i++)
{
for (int j = 0; j < test.ColumnLength; j++)
{
e = ComplexMath.Absolute((wa[i, j] - test[i, j]) / wa[i, j]);
if (e > me)
{
me = e;
}
}
}
Assert.IsTrue(me < TOLERENCE, "Maximum Error = " + me.ToString());
}
internal static double Compute(int n, Complex[] X, int incx)
{
ArgumentCheck(n, X, X.Length, ref incx);
double ret = 0;
#if MANAGED
var temp = new Complex(0);
int ix = 0;
for (int i = 0; i < n; ++i)
{
temp += (X[ix] * ComplexMath.Conjugate(X[ix]));
ix += incx;
}
ret = System.Math.Sqrt(ComplexMath.Absolute(temp));
#else
ret = dna_blas_dznrm2(n, X, incx);
#endif
return(ret);
}
internal static float Compute(int n, ComplexFloat[] X, int incx)
{
ArgumentCheck(n, X, X.Length, ref incx);
float ret = 0;
#if MANAGED
ComplexFloat temp = new ComplexFloat(0);
int ix = 0;
for (int i = 0; i < n; ++i)
{
temp += (X[ix] * ComplexMath.Conjugate(X[ix]));
ix += incx;
}
ret = (float)System.Math.Sqrt(ComplexMath.Absolute(temp));
#else
ret = dna_blas_scnrm2(n, X, incx);
#endif
return(ret);
}
public void Absolute()
{
Complex cd1 = new Complex(1.1, -2.2);
Complex cd2 = new Complex(0, -2.2);
Complex cd3 = new Complex(1.1, 0);
Complex cd4 = new Complex(-1.1, 2.2);
ComplexFloat cf1 = new ComplexFloat(1.1f, -2.2f);
ComplexFloat cf2 = new ComplexFloat(0, -2.2f);
ComplexFloat cf3 = new ComplexFloat(1.1f, 0);
ComplexFloat cf4 = new ComplexFloat(-1.1f, 2.2f);
Assert.AreEqual(ComplexMath.Absolute(cd1), 2.460, TOLERENCE);
Assert.AreEqual(ComplexMath.Absolute(cd2), 2.2, TOLERENCE);
Assert.AreEqual(ComplexMath.Absolute(cd3), 1.1, TOLERENCE);
Assert.AreEqual(ComplexMath.Absolute(cd4), 2.460, TOLERENCE);
Assert.AreEqual(ComplexMath.Absolute(cf1), 2.460, TOLERENCE);
Assert.AreEqual(ComplexMath.Absolute(cf2), 2.2, TOLERENCE);
Assert.AreEqual(ComplexMath.Absolute(cf3), 1.1, TOLERENCE);
Assert.AreEqual(ComplexMath.Absolute(cf4), 2.460, TOLERENCE);
}
private static ComplexFloat csign(ComplexFloat z1, ComplexFloat z2)
{
ComplexFloat ret = ComplexMath.Absolute(z1) * (z2 / ComplexMath.Absolute(z2));
return(ret);
}
/// <summary>Performs the LU factorization.</summary>
protected override void InternalCompute()
{
#if MANAGED
factor = new ComplexDoubleMatrix(matrix).data;
int m = matrix.RowLength;
int n = matrix.ColumnLength;
pivots = new int[m];
for (int i = 0; i < m; i++)
{
pivots[i] = i;
}
sign = 1;
Complex[] LUrowi;
Complex[] LUcolj = new Complex[m];
// Outer loop.
for (int j = 0; j < n; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < m; i++)
{
LUcolj[i] = factor[i][j];
}
// Apply previous transformations.
for (int i = 0; i < m; i++)
{
LUrowi = factor[i];
// Most of the time is spent in the following dot product.
int kmax = System.Math.Min(i, j);
Complex s = Complex.Zero;
for (int k = 0; k < kmax; k++)
{
s += LUrowi[k] * LUcolj[k];
}
LUrowi[j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < m; i++)
{
if (ComplexMath.Absolute(LUcolj[i]) > ComplexMath.Absolute(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < n; k++)
{
Complex t = factor[p][k];
factor[p][k] = factor[j][k];
factor[j][k] = t;
}
int r = pivots[p];
pivots[p] = pivots[j];
pivots[j] = r;
sign = -sign;
}
// Compute multipliers.
if (j < m & factor[j][j] != Complex.Zero)
{
for (int i = j + 1; i < m; i++)
{
factor[i][j] /= factor[j][j];
}
}
}
#else
factor = new Complex[matrix.data.Length];
Array.Copy(matrix.data, factor, matrix.data.Length);
Lapack.Getrf.Compute(order, order, factor, order, out pivots);
GetSign();
#endif
SetLU();
this.singular = false;
for (int j = 0; j < u.RowLength; j++)
{
if (u[j, j] == 0)
{
this.singular = true;
break;
}
}
}
///<summary>Computes the algorithm.</summary>
protected override void InternalCompute()
{
rows = matrix.RowLength;
cols = matrix.ColumnLength;
int mm = System.Math.Min(rows + 1, cols);
s = new DoubleVector(mm); // singular values
#if MANAGED
// Derived from LINPACK code.
// Initialize.
u = new DoubleMatrix(rows, rows); // left vectors
v = new DoubleMatrix(cols, cols); // right vectors
DoubleVector e = new DoubleVector(cols);
DoubleVector work = new DoubleVector(rows);
int i, iter, j, k, kase, l, lp1, ls = 0, lu, m, nct, nctp1, ncu, nrt, nrtp1;
double b, c, cs = 0.0, el, emm1, f, g, scale, shift, sl,
sm, sn = 0.0, smm1, t1, test, ztest, xnorm, enorm;
double t, r;
ncu = rows;
// reduce matrix to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
int info = 0;
nct = System.Math.Min(rows - 1, cols);
nrt = System.Math.Max(0, System.Math.Min(cols - 2, rows));
lu = System.Math.Max(nct, nrt);
for (l = 0; l < lu; l++)
{
lp1 = l + 1;
if (l < nct)
{
// compute the transformation for the l-th column and
// place the l-th diagonal in s[l].
xnorm = dnrm2Column(matrix, l, l);
s[l] = xnorm;
if (s[l] != 0.0)
{
if (matrix[l, l] != 0.0)
{
s[l] = dsign(s[l], matrix[l, l]);
}
dscalColumn(matrix, l, l, 1.0 / s[l]);
matrix[l, l] = 1.0 + matrix[l, l];
}
s[l] = -s[l];
}
for (j = lp1; j < cols; j++)
{
if (l < nct)
{
if (s[l] != 0.0)
{
// apply the transformation.
t = -ddot(matrix, l, j, l) / matrix[l, l];
for (int ii = l; ii < matrix.RowLength; ii++)
{
matrix[ii, j] += t * matrix[ii, l];
}
}
}
//place the l-th row of matrix into e for the
//subsequent calculation of the row transformation.
e[j] = matrix[l, j];
}
if (computeVectors && l < nct)
{
// place the transformation in u for subsequent back multiplication.
for (i = l; i < rows; i++)
{
u[i, l] = matrix[i, l];
}
}
if (l < nrt)
{
// compute the l-th row transformation and place the l-th super-diagonal in e(l).
enorm = dnrm2Vector(e, lp1);
e[l] = enorm;
if (e[l] != 0.0)
{
if (e[lp1] != 0.0)
{
e[l] = dsign(e[l], e[lp1]);
}
dscalVector(e, lp1, 1.0 / e[l]);
e[lp1] = 1.0 + e[lp1];
}
e[l] = -e[l];
if (lp1 < rows && e[l] != 0.0)
{
// apply the transformation.
for (i = lp1; i < rows; i++)
{
work[i] = 0.0;
}
for (j = lp1; j < cols; j++)
{
for (int ii = lp1; ii < matrix.RowLength; ii++)
{
work[ii] += e[j] * matrix[ii, j];
}
}
for (j = lp1; j < cols; j++)
{
double ww = -e[j] / e[lp1];
for (int ii = lp1; ii < matrix.RowLength; ii++)
{
matrix[ii, j] += ww * work[ii];
}
}
}
if (computeVectors)
{
// place the transformation in v for subsequent back multiplication.
for (i = lp1; i < cols; i++)
{
v[i, l] = e[i];
}
}
}
}
// set up the final bidiagonal matrix or order m.
m = System.Math.Min(cols, rows + 1);
nctp1 = nct + 1;
nrtp1 = nrt + 1;
if (nct < cols)
{
s[nctp1 - 1] = matrix[nctp1 - 1, nctp1 - 1];
}
if (rows < m)
{
s[m - 1] = 0.0;
}
if (nrtp1 < m)
{
e[nrtp1 - 1] = matrix[nrtp1 - 1, m - 1];
}
e[m - 1] = 0.0;
// if required, generate u.
if (computeVectors)
{
for (j = nctp1 - 1; j < ncu; j++)
{
for (i = 0; i < rows; i++)
{
u[i, j] = 0.0;
}
u[j, j] = 1.0;
}
for (l = nct - 1; l >= 0; l--)
{
if (s[l] != 0.0)
{
for (j = l + 1; j < ncu; j++)
{
t = -ddot(u, l, j, l) / u[l, l];
for (int ii = l; ii < u.RowLength; ii++)
{
u[ii, j] += t * u[ii, l];
}
}
dscalColumn(u, l, l, -1.0);
u[l, l] = 1.0 + u[l, l];
for (i = 0; i < l; i++)
{
u[i, l] = 0.0;
}
}
else
{
for (i = 0; i < rows; i++)
{
u[i, l] = 0.0;
}
u[l, l] = 1.0;
}
}
}
// if it is required, generate v.
if (computeVectors)
{
for (l = cols - 1; l >= 0; l--)
{
lp1 = l + 1;
if (l < nrt)
{
if (e[l] != 0.0)
{
for (j = lp1; j < cols; j++)
{
t = -ddot(v, l, j, lp1) / v[lp1, l];
for (int ii = l; ii < v.RowLength; ii++)
{
v[ii, j] += t * v[ii, l];
}
}
}
}
for (i = 0; i < cols; i++)
{
v[i, l] = 0.0;
}
v[l, l] = 1.0;
}
}
// transform s and e so that they are double .
for (i = 0; i < m; i++)
{
if (s[i] != 0.0)
{
t = s[i];
r = s[i] / t;
s[i] = t;
if (i < m - 1)
{
e[i] = e[i] / r;
}
if (computeVectors)
{
dscalColumn(u, i, 0, r);
}
}
// ...exit
if (i == m - 1)
{
break;
}
if (e[i] != 0.0)
{
t = e[i];
r = t / e[i];
e[i] = t;
s[i + 1] = s[i + 1] * r;
if (computeVectors)
{
dscalColumn(v, i + 1, 0, r);
}
}
}
// main iteration loop for the singular values.
mm = m;
iter = 0;
while (m > 0)
{ // quit if all the singular values have been found.
// if too many iterations have been performed, set
// flag and return.
if (iter >= MAXITER)
{
info = m;
// ......exit
break;
}
// this section of the program inspects for
// negligible elements in the s and e arrays. on
// completion the variables kase and l are set as follows.
// kase = 1 if s[m] and e[l-1] are negligible and l < m
// kase = 2 if s[l] is negligible and l < m
// kase = 3 if e[l-1] is negligible, l < m, and
// s[l, ..., s[m] are not negligible (qr step).
// kase = 4 if e[m-1] is negligible (convergence).
for (l = m - 2; l >= 0; l--)
{
test = ComplexMath.Absolute(s[l]) + ComplexMath.Absolute(s[l + 1]);
ztest = test + ComplexMath.Absolute(e[l]);
if (ztest == test)
{
e[l] = 0.0;
break;
}
}
if (l == m - 2)
{
kase = 4;
}
else
{
for (ls = m - 1; ls > l; ls--)
{
test = 0.0;
if (ls != m - 1)
{
test = test + ComplexMath.Absolute(e[ls]);
}
if (ls != l + 1)
{
test = test + ComplexMath.Absolute(e[ls - 1]);
}
ztest = test + ComplexMath.Absolute(s[ls]);
if (ztest == test)
{
s[ls] = 0.0;
break;
}
}
if (ls == l)
{
kase = 3;
}
else if (ls == m - 1)
{
kase = 1;
}
else
{
kase = 2;
l = ls;
}
}
l = l + 1;
// perform the task indicated by kase.
switch (kase)
{
// deflate negligible s[m].
case 1:
f = e[m - 2];
e[m - 2] = 0.0;
for (k = m - 2; k >= 0; k--)
{
t1 = s[k];
drotg(ref t1, ref f, ref cs, ref sn);
s[k] = t1;
if (k != l)
{
f = -sn * e[k - 1];
e[k - 1] = cs * e[k - 1];
}
if (computeVectors)
{
drot(v, k, m - 1, cs, sn);
}
}
break;
// split at negligible s[l].
case 2:
f = e[l - 1];
e[l - 1] = 0.0;
for (k = l; k < m; k++)
{
t1 = s[k];
drotg(ref t1, ref f, ref cs, ref sn);
s[k] = t1;
f = -sn * e[k];
e[k] = cs * e[k];
if (computeVectors)
{
drot(u, k, l - 1, cs, sn);
}
}
break;
// perform one qr step.
case 3:
// calculate the shift.
scale = 0.0;
scale = System.Math.Max(scale, ComplexMath.Absolute(s[m - 1]));
scale = System.Math.Max(scale, ComplexMath.Absolute(s[m - 2]));
scale = System.Math.Max(scale, ComplexMath.Absolute(e[m - 2]));
scale = System.Math.Max(scale, ComplexMath.Absolute(s[l]));
scale = System.Math.Max(scale, ComplexMath.Absolute(e[l]));
sm = s[m - 1] / scale;
smm1 = s[m - 2] / scale;
emm1 = e[m - 2] / scale;
sl = s[l] / scale;
el = e[l] / scale;
b = ((smm1 + sm) * (smm1 - sm) + emm1 * emm1) / 2.0;
c = (sm * emm1) * (sm * emm1);
shift = 0.0;
if (b != 0.0 || c != 0.0)
{
shift = System.Math.Sqrt(b * b + c);
if (b < 0.0)
{
shift = -shift;
}
shift = c / (b + shift);
}
f = (sl + sm) * (sl - sm) + shift;
g = sl * el;
// chase zeros.
for (k = l; k < m - 1; k++)
{
drotg(ref f, ref g, ref cs, ref sn);
if (k != l)
{
e[k - 1] = f;
}
f = cs * s[k] + sn * e[k];
e[k] = cs * e[k] - sn * s[k];
g = sn * s[k + 1];
s[k + 1] = cs * s[k + 1];
if (computeVectors)
{
drot(v, k, k + 1, cs, sn);
}
drotg(ref f, ref g, ref cs, ref sn);
s[k] = f;
f = cs * e[k] + sn * s[k + 1];
s[k + 1] = -sn * e[k] + cs * s[k + 1];
g = sn * e[k + 1];
e[k + 1] = cs * e[k + 1];
if (computeVectors && k < rows)
{
drot(u, k, k + 1, cs, sn);
}
}
e[m - 2] = f;
iter = iter + 1;
break;
// convergence.
case 4:
// make the singular value positive
if (s[l] < 0.0)
{
s[l] = -s[l];
if (computeVectors)
{
dscalColumn(v, l, 0, -1.0);
}
}
// order the singular value.
while (l != mm - 1)
{
if (s[l] >= s[l + 1])
{
break;
}
t = s[l];
s[l] = s[l + 1];
s[l + 1] = t;
if (computeVectors && l < cols)
{
dswap(v, l, l + 1);
}
if (computeVectors && l < rows)
{
dswap(u, l, l + 1);
}
l = l + 1;
}
iter = 0;
m = m - 1;
break;
}
}
// make matrix w from vector s
// there is no constructor, creating diagonal matrix from vector
// doing it ourselves
mm = System.Math.Min(matrix.RowLength, matrix.ColumnLength);
#else
u = new DoubleMatrix(rows);
v = new DoubleMatrix(cols);
double[] a = new double[matrix.data.Length];
Array.Copy(matrix.data, a, matrix.data.Length);
Lapack.Gesvd.Compute(rows, cols, a, s.data, u.data, v.data);
v.Transpose();
#endif
w = new DoubleMatrix(matrix.RowLength, matrix.ColumnLength);
for (int ii = 0; ii < matrix.RowLength; ii++)
{
for (int jj = 0; jj < matrix.ColumnLength; jj++)
{
if (ii == jj)
{
w[ii, ii] = s[ii];
}
}
}
double eps = System.Math.Pow(2.0, -52.0);
double tol = System.Math.Max(matrix.RowLength, matrix.ColumnLength) * s[0] * eps;
rank = 0;
for (int h = 0; h < mm; h++)
{
if (s[h] > tol)
{
rank++;
}
}
if (!computeVectors)
{
u = null;
v = null;
}
matrix = null;
}
private static Complex csign(Complex z1, Complex z2)
{
Complex ret = ComplexMath.Absolute(z1) * (z2 / ComplexMath.Absolute(z2));
return(ret);
}