///<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 FloatVector(mm); // singular values
#if MANAGED
// Derived from LINPACK code.
// Initialize.
u = new FloatMatrix(rows, rows); // left vectors
v = new FloatMatrix(cols, cols); // right vectors
FloatVector e = new FloatVector(cols);
FloatVector work = new FloatVector(rows);
int i, iter, j, k, kase, l, lp1, ls = 0, lu, m, nct, nctp1, ncu, nrt, nrtp1;
float b, c, cs = 0.0f, el, emm1, f, g, scale, shift, sl,
sm, sn = 0.0f, smm1, t1, test, ztest, xnorm, enorm;
float 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] != 0.0f)
{
if (matrix[l, l] != 0.0f)
{
s[l] = dsign(s[l], matrix[l, l]);
}
dscalColumn(matrix, l, l, 1.0f / s[l]);
matrix[l, l] = 1.0f + matrix[l, l];
}
s[l] = -s[l];
}
for (j = lp1; j < cols; j++)
{
if (l < nct)
{
if (s[l] != 0.0f)
{
// 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] != 0.0f)
{
if (e[lp1] != 0.0f)
{
e[l] = dsign(e[l], e[lp1]);
}
dscalVector(e, lp1, 1.0f / e[l]);
e[lp1] = 1.0f + e[lp1];
}
e[l] = -e[l];
if (lp1 < rows && e[l] != 0.0f)
{
// apply the transformation.
for (i = lp1; i < rows; i++)
{
work[i] = 0.0f;
}
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++)
{
float 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] = 0.0f;
}
if (nrtp1 < m)
{
e[nrtp1 - 1] = matrix[nrtp1 - 1, m - 1];
}
e[m - 1] = 0.0f;
// if required, generate u.
if (computeVectors)
{
for (j = nctp1 - 1; j < ncu; j++)
{
for (i = 0; i < rows; i++)
{
u[i, j] = 0.0f;
}
u[j, j] = 1.0f;
}
for (l = nct - 1; l >= 0; l--)
{
if (s[l] != 0.0f)
{
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, -1.0f);
u[l, l] = 1.0f + u[l, l];
for (i = 0; i < l; i++)
{
u[i, l] = 0.0f;
}
}
else
{
for (i = 0; i < rows; i++)
{
u[i, l] = 0.0f;
}
u[l, l] = 1.0f;
}
}
}
// if it is required, generate v.
if (computeVectors)
{
for (l = cols - 1; l >= 0; l--)
{
lp1 = l + 1;
if (l < nrt)
{
if (e[l] != 0.0f)
{
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] = 0.0f;
}
v[l, l] = 1.0f;
}
}
// transform s and e so that they are float .
for (i = 0; i < m; i++)
{
if (s[i] != 0.0f)
{
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] = 0.0f;
break;
}
}
if (l == m - 2)
{
kase = 4;
}
else
{
for (ls = m - 1; ls > l; ls--)
{
test = 0.0f;
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] = 0.0f;
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] = 0.0f;
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] = 0.0f;
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 = 0.0f;
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) / 2.0f;
c = (sm * emm1) * (sm * emm1);
shift = 0.0f;
if (b != 0.0f || c != 0.0f)
{
shift = (float)System.Math.Sqrt(b * b + c);
if (b < 0.0f)
{
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] < 0.0f)
{
s[l] = -s[l];
if (computeVectors)
{
dscalColumn(v, l, 0, -1.0f);
}
}
// 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 FloatMatrix(rows);
v = new FloatMatrix(cols);
float[] a = new float[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 FloatMatrix(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];
}
}
}
float eps = (float)System.Math.Pow(2.0, -52.0);
float tol = (float)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;
}
public void TransposeLong()
{
FloatMatrix a = new FloatMatrix(3, 2);
a[0, 0] = 1;
a[0, 1] = 2;
a[1, 0] = 3;
a[1, 1] = 4;
a[2, 0] = 5;
a[2, 1] = 6;
a.Transpose();
Assert.AreEqual(a[0, 0], 1);
Assert.AreEqual(a[0, 1], 3);
Assert.AreEqual(a[0, 2], 5);
Assert.AreEqual(a[1, 0], 2);
Assert.AreEqual(a[1, 1], 4);
Assert.AreEqual(a[1, 2], 6);
Assert.AreEqual(a.RowLength, 2);
Assert.AreEqual(a.ColumnLength, 3);
}
///<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 FloatVector(mm); // singular values
#if MANAGED
// Derived from LINPACK code.
// Initialize.
u = new FloatMatrix(rows, rows); // left vectors
v = new FloatMatrix(cols, cols); // right vectors
var e = new FloatVector(cols);
var work = new FloatVector(rows);
int i, iter, j, k, kase, l, lp1, ls = 0, lu, m, nct, nctp1, ncu, nrt, nrtp1;
float b, c, cs = 0.0f, el, emm1, f, g, scale, shift, sl,
sm, sn = 0.0f, smm1, t1, test, ztest, xnorm, enorm;
float 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] != 0.0f)
{
if (matrix[l, l] != 0.0f)
{
s[l] = dsign(s[l], matrix[l, l]);
}
dscalColumn(matrix, l, l, 1.0f / s[l]);
matrix[l, l] = 1.0f + matrix[l, l];
}
s[l] = -s[l];
}
for (j = lp1; j < cols; j++)
{
if (l < nct)
{
if (s[l] != 0.0f)
{
// 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] != 0.0f)
{
if (e[lp1] != 0.0f)
{
e[l] = dsign(e[l], e[lp1]);
}
dscalVector(e, lp1, 1.0f / e[l]);
e[lp1] = 1.0f + e[lp1];
}
e[l] = -e[l];
if (lp1 < rows && e[l] != 0.0f)
{
// apply the transformation.
for (i = lp1; i < rows; i++)
{
work[i] = 0.0f;
}
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++)
{
float 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] = 0.0f;
}
if (nrtp1 < m)
{
e[nrtp1 - 1] = matrix[nrtp1 - 1, m - 1];
}
e[m - 1] = 0.0f;
// if required, generate u.
if (computeVectors)
{
for (j = nctp1 - 1; j < ncu; j++)
{
for (i = 0; i < rows; i++)
{
u[i, j] = 0.0f;
}
u[j, j] = 1.0f;
}
for (l = nct - 1; l >= 0; l--)
{
if (s[l] != 0.0f)
{
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, -1.0f);
u[l, l] = 1.0f + u[l, l];
for (i = 0; i < l; i++)
{
u[i, l] = 0.0f;
}
}
else
{
for (i = 0; i < rows; i++)
{
u[i, l] = 0.0f;
}
u[l, l] = 1.0f;
}
}
}
// if it is required, generate v.
if (computeVectors)
{
for (l = cols - 1; l >= 0; l--)
{
lp1 = l + 1;
if (l < nrt)
{
if (e[l] != 0.0f)
{
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] = 0.0f;
}
v[l, l] = 1.0f;
}
}
// transform s and e so that they are float .
for (i = 0; i < m; i++)
{
if (s[i] != 0.0f)
{
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] = 0.0f;
break;
}
}
if (l == m - 2)
{
kase = 4;
}
else
{
for (ls = m - 1; ls > l; ls--)
{
test = 0.0f;
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] = 0.0f;
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] = 0.0f;
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] = 0.0f;
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 = 0.0f;
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) / 2.0f;
c = (sm * emm1) * (sm * emm1);
shift = 0.0f;
if (b != 0.0f || c != 0.0f)
{
shift = (float)System.Math.Sqrt(b * b + c);
if (b < 0.0f)
{
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] < 0.0f)
{
s[l] = -s[l];
if (computeVectors)
{
dscalColumn(v, l, 0, -1.0f);
}
}
// 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 FloatMatrix(rows);
v = new FloatMatrix(cols);
float[] a = new float[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 FloatMatrix(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];
}
}
}
float eps = (float)System.Math.Pow(2.0, -52.0);
float 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;
}
public void TransposeSquare()
{
FloatMatrix a = new FloatMatrix(2, 2);
a[0, 0] = 1;
a[0, 1] = 2;
a[1, 0] = 3;
a[1, 1] = 4;
a.Transpose();
Assert.AreEqual(a[0, 0], 1);
Assert.AreEqual(a[0, 1], 3);
Assert.AreEqual(a[1, 0], 2);
Assert.AreEqual(a[1, 1], 4);
}