/// <summary>
/// Returns the bi-diagonal matrix B of the transform.
/// </summary>
/// <returns>the B matrix</returns>
public RealMatrix getB()
{
if (cachedB == null)
{
int m = householderVectors.Length;
int n = householderVectors[0].Length;
double[][] ba = new double[m][];
for (int i = 0; i < main.Length; ++i)
{
ba[i][i] = main[i];
if (m < n)
{
if (i > 0)
{
ba[i][i - 1] = secondary[i - 1];
}
}
else
{
if (i < main.Length - 1)
{
ba[i][i + 1] = secondary[i];
}
}
}
cachedB = MatrixUtils.createRealMatrix(ba);
}
// return the cached matrix
return(cachedB);
}
/// <inheritdoc/>
public new RealMatrix outerProduct(RealVector v)
{
if (v is ArrayRealVector)
{
double[] vData = ((ArrayRealVector)v).data;
int m = data.Length;
int n = vData.Length;
RealMatrix outp = MatrixUtils.createRealMatrix(m, n);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
outp.setEntry(i, j, data[i] * vData[j]);
}
}
return(outp);
}
else
{
int m = data.Length;
int n = v.getDimension();
RealMatrix outp = MatrixUtils.createRealMatrix(m, n);
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
outp.setEntry(i, j, data[i] * v.getEntry(j));
}
}
return(outp);
}
}
/// <summary>
/// Returns the Hessenberg matrix H of the transform.
/// </summary>
/// <returns>the H matrix</returns>
public RealMatrix getH()
{
if (cachedH == null)
{
int m = householderVectors.Length;
double[][] h = new double[m][];
for (int i = 0; i < m; ++i)
{
if (i > 0)
{
// copy the entry of the lower sub-diagonal
h[i][i - 1] = householderVectors[i][i - 1];
}
// copy upper triangular part of the matrix
for (int j = i; j < m; ++j)
{
h[i][j] = householderVectors[i][j];
}
}
cachedH = MatrixUtils.createRealMatrix(h);
}
// return the cached matrix
return(cachedH);
}
/// <summary>
/// Get the inverse of the decomposed matrix.
/// </summary>
/// <returns>the inverse matrix.</returns>
/// <exception cref="SingularMatrixException"> if the decomposed matrix is singular.
/// </exception>
public RealMatrix getInverse()
{
if (!isNonSingular())
{
throw new SingularMatrixException();
}
int m = realEigenvalues.Length;
double[][] invData = new double[m][];
for (int i = 0; i < m; ++i)
{
double[] invI = invData[i];
for (int j = 0; j < m; ++j)
{
double invIJ = 0;
for (int k = 0; k < m; ++k)
{
double[] vK = eigenvectors[k].getDataRef();
invIJ += vK[i] * vK[j] / realEigenvalues[k];
}
invI[j] = invIJ;
}
}
return(MatrixUtils.createRealMatrix(invData));
}
/// <summary>
/// Returns the matrix P of the transform.
/// <para>P is an orthogonal matrix, i.e. its inverse is also its transpose.</para>
/// </summary>
/// <returns>the P matrix</returns>
public RealMatrix getP()
{
if (cachedP == null)
{
cachedP = MatrixUtils.createRealMatrix(matrixP);
}
return(cachedP);
}
/// <summary>
/// Returns the transpose of the matrix L of the decomposition.
/// <para>L^T is an upper-triangular matrix</para>
/// </summary>
/// <returns>the transpose of the matrix L of the decomposition</returns>
public RealMatrix getLT()
{
if (cachedLT == null)
{
cachedLT = MatrixUtils.createRealMatrix(lTData);
}
// return the cached matrix
return(cachedLT);
}
/// <summary>
/// Returns the quasi-triangular Schur matrix T of the transform.
/// </summary>
/// <returns>the T matrix</returns>
public RealMatrix getT()
{
if (cachedT == null)
{
cachedT = MatrixUtils.createRealMatrix(matrixT);
}
// return the cached matrix
return(cachedT);
}
/// <summary>
/// Gets the matrix V of the decomposition.
/// V is an orthogonal matrix, i.e. its transpose is also its inverse.
/// The columns of V are the eigenvectors of the original matrix.
/// No assumption is made about the orientation of the system axes formed
/// by the columns of V (e.g. in a 3-dimension space, V can form a left-
/// or right-handed system).
/// </summary>
/// <returns>the V matrix.</returns>
public RealMatrix getV()
{
if (cachedV == null)
{
int m = eigenvectors.Length;
cachedV = MatrixUtils.createRealMatrix(m, m);
for (int k = 0; k < m; ++k)
{
cachedV.setColumnVector(k, eigenvectors[k]);
}
}
// return the cached matrix
return(cachedV);
}
/// <summary>
/// Returns the matrix U of the transform.
/// <para>U is an orthogonal matrix, i.e. its transpose is also its inverse.</para>
/// </summary>
/// <returns>the U matrix</returns>
public RealMatrix getU()
{
if (cachedU == null)
{
int m = householderVectors.Length;
int n = householderVectors[0].Length;
int p = main.Length;
int diagOffset = (m >= n) ? 0 : 1;
double[] diagonal = (m >= n) ? main : secondary;
double[][] ua = new double[m][];
// fill up the part of the matrix not affected by Householder transforms
for (int k = m - 1; k >= p; --k)
{
ua[k][k] = 1;
}
// build up first part of the matrix by applying Householder transforms
for (int k = p - 1; k >= diagOffset; --k)
{
double[] hK = householderVectors[k];
ua[k][k] = 1;
if (hK[k - diagOffset] != 0.0)
{
for (int j = k; j < m; ++j)
{
double alpha = 0;
for (int i = k; i < m; ++i)
{
alpha -= ua[i][j] * householderVectors[i][k - diagOffset];
}
alpha /= diagonal[k - diagOffset] * hK[k - diagOffset];
for (int i = k; i < m; ++i)
{
ua[i][j] += -alpha * householderVectors[i][k - diagOffset];
}
}
}
}
if (diagOffset > 0)
{
ua[0][0] = 1;
}
cachedU = MatrixUtils.createRealMatrix(ua);
}
// return the cached matrix
return(cachedU);
}
/// <summary>
/// Returns the matrix V of the transform.
/// <para>V is an orthogonal matrix, i.e. its transpose is also its inverse.</para>
/// </summary>
/// <returns>the V matrix</returns>
public RealMatrix getV()
{
if (cachedV == null)
{
int m = householderVectors.Length;
int n = householderVectors[0].Length;
int p = main.Length;
int diagOffset = (m >= n) ? 1 : 0;
double[] diagonal = (m >= n) ? secondary : main;
double[][] va = new double[n][];
// fill up the part of the matrix not affected by Householder transforms
for (int k = n - 1; k >= p; --k)
{
va[k][k] = 1;
}
// build up first part of the matrix by applying Householder transforms
for (int k = p - 1; k >= diagOffset; --k)
{
double[] hK = householderVectors[k - diagOffset];
va[k][k] = 1;
if (hK[k] != 0.0)
{
for (int j = k; j < n; ++j)
{
double beta = 0;
for (int i = k; i < n; ++i)
{
beta -= va[i][j] * hK[i];
}
beta /= diagonal[k - diagOffset] * hK[k];
for (int i = k; i < n; ++i)
{
va[i][j] += -beta * hK[i];
}
}
}
}
if (diagOffset > 0)
{
va[0][0] = 1;
}
cachedV = MatrixUtils.createRealMatrix(va);
}
// return the cached matrix
return(cachedV);
}
/// <summary>
/// Returns the matrix P of the transform.
/// <para>P is an orthogonal matrix, i.e. its inverse is also its transpose.</para>
/// </summary>
/// <returns>the P matrix</returns>
public RealMatrix getP()
{
if (cachedP == null)
{
int n = householderVectors.Length;
int high = n - 1;
double[][] pa = new double[n][];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
pa[i][j] = (i == j) ? 1 : 0;
}
}
for (int m = high - 1; m >= 1; m--)
{
if (householderVectors[m][m - 1] != 0.0)
{
for (int i = m + 1; i <= high; i++)
{
ort[i] = householderVectors[i][m - 1];
}
for (int j = m; j <= high; j++)
{
double g = 0.0;
for (int i = m; i <= high; i++)
{
g += ort[i] * pa[i][j];
}
// Double division avoids possible underflow
g = (g / ort[m]) / householderVectors[m][m - 1];
for (int i = m; i <= high; i++)
{
pa[i][j] += g * ort[i];
}
}
}
}
cachedP = MatrixUtils.createRealMatrix(pa);
}
return(cachedP);
}
/// <summary>
/// Returns the transpose of the matrix Q of the decomposition.
/// <para>Q is an orthogonal matrix</para>
/// </summary>
/// <returns>the transpose of the Q matrix, Q^T</returns>
public RealMatrix getQT()
{
if (cachedQT == null)
{
// QT is supposed to be m x m
int n = qrt.Length;
int m = qrt[0].Length;
double[][] qta = new double[m][];
/*
* Q = Q1 Q2 ... Q_m, so Q is formed by first constructing Q_m and then
* applying the Householder transformations Q_(m-1),Q_(m-2),...,Q1 in
* succession to the result
*/
for (int minor = m - 1; minor >= FastMath.min(m, n); minor--)
{
qta[minor][minor] = 1.0d;
}
for (int minor = FastMath.min(m, n) - 1; minor >= 0; minor--)
{
double[] qrtMinor = qrt[minor];
qta[minor][minor] = 1.0d;
if (qrtMinor[minor] != 0.0)
{
for (int col = minor; col < m; col++)
{
double alpha = 0;
for (int row = minor; row < m; row++)
{
alpha -= qta[col][row] * qrtMinor[row];
}
alpha /= rDiag[minor] * qrtMinor[minor];
for (int row = minor; row < m; row++)
{
qta[col][row] += -alpha * qrtMinor[row];
}
}
}
}
cachedQT = MatrixUtils.createRealMatrix(qta);
}
// return the cached matrix
return(cachedQT);
}
/// <summary>
/// Returns the transpose of the matrix Q of the transform.
/// <para>Q is an orthogonal matrix, i.e. its transpose is also its inverse.</para>
/// </summary>
/// <returns>the Q matrix</returns>
public RealMatrix getQT()
{
if (cachedQt == null)
{
int m = householderVectors.Length;
double[][] qta = new double[m][];
// build up first part of the matrix by applying Householder transforms
for (int k = m - 1; k >= 1; --k)
{
double[] hK = householderVectors[k - 1];
qta[k][k] = 1;
if (hK[k] != 0.0)
{
double inv = 1.0 / (secondary[k - 1] * hK[k]);
double beta = 1.0 / secondary[k - 1];
qta[k][k] = 1 + beta * hK[k];
for (int i = k + 1; i < m; ++i)
{
qta[k][i] = beta * hK[i];
}
for (int j = k + 1; j < m; ++j)
{
beta = 0;
for (int i = k + 1; i < m; ++i)
{
beta += qta[j][i] * hK[i];
}
beta *= inv;
qta[j][k] = beta * hK[k];
for (int i = k + 1; i < m; ++i)
{
qta[j][i] += beta * hK[i];
}
}
}
}
qta[0][0] = 1;
cachedQt = MatrixUtils.createRealMatrix(qta);
}
// return the cached matrix
return(cachedQt);
}
/// <summary>
/// Returns the Householder reflector vectors.
/// <para>H is a lower trapezoidal matrix whose columns represent
/// each successive Householder reflector vector. This matrix is used
/// to compute Q.</para>
/// </summary>
/// <returns>a matrix containing the Householder reflector vectors</returns>
public RealMatrix getH()
{
if (cachedH == null)
{
int n = qrt.Length;
int m = qrt[0].Length;
double[][] ha = new double[m][];
for (int i = 0; i < m; ++i)
{
for (int j = 0; j < FastMath.min(i + 1, n); ++j)
{
ha[i][j] = qrt[j][i] / -rDiag[j];
}
}
cachedH = MatrixUtils.createRealMatrix(ha);
}
// return the cached matrix
return(cachedH);
}
/// <summary>
/// Returns the matrix R of the decomposition.
/// <para>R is an upper-triangular matrix</para>
/// </summary>
/// <returns>the R matrix</returns>
public RealMatrix getR()
{
if (cachedR == null)
{
// R is supposed to be m x n
int n = qrt.Length;
int m = qrt[0].Length;
double[][] ra = new double[m][];
// copy the diagonal from rDiag and the upper triangle of qr
for (int row = FastMath.min(m, n) - 1; row >= 0; row--)
{
ra[row][row] = rDiag[row];
for (int col = row + 1; col < n; col++)
{
ra[row][col] = qrt[col][row];
}
}
cachedR = MatrixUtils.createRealMatrix(ra);
}
// return the cached matrix
return(cachedR);
}
/// <summary>
/// Returns the tridiagonal matrix T of the transform.
/// </summary>
/// <returns>the T matrix</returns>
public RealMatrix getT()
{
if (cachedT == null)
{
int m = main.Length;
double[][] ta = new double[m][];
for (int i = 0; i < m; ++i)
{
ta[i][i] = main[i];
if (i > 0)
{
ta[i][i - 1] = secondary[i - 1];
}
if (i < main.Length - 1)
{
ta[i][i + 1] = secondary[i];
}
}
cachedT = MatrixUtils.createRealMatrix(ta);
}
// return the cached matrix
return(cachedT);
}
/// <summary>
/// Calculates the compact Singular Value Decomposition of the given matrix.
/// </summary>
/// <param name="matrix">Matrix to decompose.</param>
public SingularValueDecomposition(RealMatrix matrix)
{
double[][] A;
// "m" is always the largest dimension.
if (matrix.getRowDimension() < matrix.getColumnDimension())
{
transposed = true;
A = matrix.transpose().getData();
m = matrix.getColumnDimension();
n = matrix.getRowDimension();
}
else
{
transposed = false;
A = matrix.getData();
m = matrix.getRowDimension();
n = matrix.getColumnDimension();
}
singularValues = new double[n];
double[][] U = new double[m][];
double[][] V = new double[n][];
double[] e = new double[n];
double[] work = new double[m];
// Reduce A to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
int nct = FastMath.min(m - 1, n);
int nrt = FastMath.max(0, n - 2);
for (int k = 0; k < FastMath.max(nct, nrt); k++)
{
if (k < nct)
{
// Compute the transformation for the k-th column and
// place the k-th diagonal in s[k].
// Compute 2-norm of k-th column without under/overflow.
singularValues[k] = 0;
for (int i = k; i < m; i++)
{
singularValues[k] = FastMath.hypot(singularValues[k], A[i][k]);
}
if (singularValues[k] != 0)
{
if (A[k][k] < 0)
{
singularValues[k] = -singularValues[k];
}
for (int i = k; i < m; i++)
{
A[i][k] /= singularValues[k];
}
A[k][k] += 1;
}
singularValues[k] = -singularValues[k];
}
for (int j = k + 1; j < n; j++)
{
if (k < nct &&
singularValues[k] != 0)
{
// Apply the transformation.
double t = 0;
for (int i = k; i < m; i++)
{
t += A[i][k] * A[i][j];
}
t = -t / A[k][k];
for (int i = k; i < m; i++)
{
A[i][j] += t * A[i][k];
}
}
// Place the k-th row of A into e for the
// subsequent calculation of the row transformation.
e[j] = A[k][j];
}
if (k < nct)
{
// Place the transformation in U for subsequent back
// multiplication.
for (int i = k; i < m; i++)
{
U[i][k] = A[i][k];
}
}
if (k < nrt)
{
// Compute the k-th row transformation and place the
// k-th super-diagonal in e[k].
// Compute 2-norm without under/overflow.
e[k] = 0;
for (int i = k + 1; i < n; i++)
{
e[k] = FastMath.hypot(e[k], e[i]);
}
if (e[k] != 0)
{
if (e[k + 1] < 0)
{
e[k] = -e[k];
}
for (int i = k + 1; i < n; i++)
{
e[i] /= e[k];
}
e[k + 1] += 1;
}
e[k] = -e[k];
if (k + 1 < m &&
e[k] != 0)
{
// Apply the transformation.
for (int i = k + 1; i < m; i++)
{
work[i] = 0;
}
for (int j = k + 1; j < n; j++)
{
for (int i = k + 1; i < m; i++)
{
work[i] += e[j] * A[i][j];
}
}
for (int j = k + 1; j < n; j++)
{
double t = -e[j] / e[k + 1];
for (int i = k + 1; i < m; i++)
{
A[i][j] += t * work[i];
}
}
}
// Place the transformation in V for subsequent
// back multiplication.
for (int i = k + 1; i < n; i++)
{
V[i][k] = e[i];
}
}
}
// Set up the final bidiagonal matrix or order p.
int p = n;
if (nct < n)
{
singularValues[nct] = A[nct][nct];
}
if (m < p)
{
singularValues[p - 1] = 0;
}
if (nrt + 1 < p)
{
e[nrt] = A[nrt][p - 1];
}
e[p - 1] = 0;
// Generate U.
for (int j = nct; j < n; j++)
{
for (int i = 0; i < m; i++)
{
U[i][j] = 0;
}
U[j][j] = 1;
}
for (int k = nct - 1; k >= 0; k--)
{
if (singularValues[k] != 0)
{
for (int j = k + 1; j < n; j++)
{
double t = 0;
for (int i = k; i < m; i++)
{
t += U[i][k] * U[i][j];
}
t = -t / U[k][k];
for (int i = k; i < m; i++)
{
U[i][j] += t * U[i][k];
}
}
for (int i = k; i < m; i++)
{
U[i][k] = -U[i][k];
}
U[k][k] = 1 + U[k][k];
for (int i = 0; i < k - 1; i++)
{
U[i][k] = 0;
}
}
else
{
for (int i = 0; i < m; i++)
{
U[i][k] = 0;
}
U[k][k] = 1;
}
}
// Generate V.
for (int k = n - 1; k >= 0; k--)
{
if (k < nrt &&
e[k] != 0)
{
for (int j = k + 1; j < n; j++)
{
double t = 0;
for (int i = k + 1; i < n; i++)
{
t += V[i][k] * V[i][j];
}
t = -t / V[k + 1][k];
for (int i = k + 1; i < n; i++)
{
V[i][j] += t * V[i][k];
}
}
}
for (int i = 0; i < n; i++)
{
V[i][k] = 0;
}
V[k][k] = 1;
}
// Main iteration loop for the singular values.
int pp = p - 1;
while (p > 0)
{
int k;
int kase;
// Here is where a test for too many iterations would go.
// This section of the program inspects for
// negligible elements in the s and e arrays. On
// completion the variables kase and k are set as follows.
// kase = 1 if s(p) and e[k-1] are negligible and k<p
// kase = 2 if s(k) is negligible and k<p
// kase = 3 if e[k-1] is negligible, k<p, and
// s(k), ..., s(p) are not negligible (qr step).
// kase = 4 if e(p-1) is negligible (convergence).
for (k = p - 2; k >= 0; k--)
{
double threshold
= TINY + EPS * (FastMath.abs(singularValues[k]) +
FastMath.abs(singularValues[k + 1]));
// the following condition is written this way in order
// to break out of the loop when NaN occurs, writing it
// as "if (FastMath.abs(e[k]) <= threshold)" would loop
// indefinitely in case of NaNs because comparison on NaNs
// always return false, regardless of what is checked
// see issue MATH-947
if (!(FastMath.abs(e[k]) > threshold))
{
e[k] = 0;
break;
}
}
if (k == p - 2)
{
kase = 4;
}
else
{
int ks;
for (ks = p - 1; ks >= k; ks--)
{
if (ks == k)
{
break;
}
double t = (ks != p ? FastMath.abs(e[ks]) : 0) +
(ks != k + 1 ? FastMath.abs(e[ks - 1]) : 0);
if (FastMath.abs(singularValues[ks]) <= TINY + EPS * t)
{
singularValues[ks] = 0;
break;
}
}
if (ks == k)
{
kase = 3;
}
else if (ks == p - 1)
{
kase = 1;
}
else
{
kase = 2;
k = ks;
}
}
k++;
// Perform the task indicated by kase.
switch (kase)
{
// Deflate negligible s(p).
case 1:
{
double f = e[p - 2];
e[p - 2] = 0;
for (int j = p - 2; j >= k; j--)
{
double t = FastMath.hypot(singularValues[j], f);
double cs = singularValues[j] / t;
double sn = f / t;
singularValues[j] = t;
if (j != k)
{
f = -sn * e[j - 1];
e[j - 1] = cs * e[j - 1];
}
for (int i = 0; i < n; i++)
{
t = cs * V[i][j] + sn * V[i][p - 1];
V[i][p - 1] = -sn * V[i][j] + cs * V[i][p - 1];
V[i][j] = t;
}
}
}
break;
// Split at negligible s(k).
case 2:
{
double f = e[k - 1];
e[k - 1] = 0;
for (int j = k; j < p; j++)
{
double t = FastMath.hypot(singularValues[j], f);
double cs = singularValues[j] / t;
double sn = f / t;
singularValues[j] = t;
f = -sn * e[j];
e[j] = cs * e[j];
for (int i = 0; i < m; i++)
{
t = cs * U[i][j] + sn * U[i][k - 1];
U[i][k - 1] = -sn * U[i][j] + cs * U[i][k - 1];
U[i][j] = t;
}
}
}
break;
// Perform one qr step.
case 3:
{
// Calculate the shift.
double maxPm1Pm2 = FastMath.max(FastMath.abs(singularValues[p - 1]),
FastMath.abs(singularValues[p - 2]));
double scale = FastMath.max(FastMath.max(FastMath.max(maxPm1Pm2,
FastMath.abs(e[p - 2])),
FastMath.abs(singularValues[k])),
FastMath.abs(e[k]));
double sp = singularValues[p - 1] / scale;
double spm1 = singularValues[p - 2] / scale;
double epm1 = e[p - 2] / scale;
double sk = singularValues[k] / scale;
double ek = e[k] / scale;
double b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2.0;
double c = (sp * epm1) * (sp * epm1);
double shift = 0;
if (b != 0 ||
c != 0)
{
shift = FastMath.sqrt(b * b + c);
if (b < 0)
{
shift = -shift;
}
shift = c / (b + shift);
}
double f = (sk + sp) * (sk - sp) + shift;
double g = sk * ek;
// Chase zeros.
for (int j = k; j < p - 1; j++)
{
double t = FastMath.hypot(f, g);
double cs = f / t;
double sn = g / t;
if (j != k)
{
e[j - 1] = t;
}
f = cs * singularValues[j] + sn * e[j];
e[j] = cs * e[j] - sn * singularValues[j];
g = sn * singularValues[j + 1];
singularValues[j + 1] = cs * singularValues[j + 1];
for (int i = 0; i < n; i++)
{
t = cs * V[i][j] + sn * V[i][j + 1];
V[i][j + 1] = -sn * V[i][j] + cs * V[i][j + 1];
V[i][j] = t;
}
t = FastMath.hypot(f, g);
cs = f / t;
sn = g / t;
singularValues[j] = t;
f = cs * e[j] + sn * singularValues[j + 1];
singularValues[j + 1] = -sn * e[j] + cs * singularValues[j + 1];
g = sn * e[j + 1];
e[j + 1] = cs * e[j + 1];
if (j < m - 1)
{
for (int i = 0; i < m; i++)
{
t = cs * U[i][j] + sn * U[i][j + 1];
U[i][j + 1] = -sn * U[i][j] + cs * U[i][j + 1];
U[i][j] = t;
}
}
}
e[p - 2] = f;
}
break;
// Convergence.
default:
{
// Make the singular values positive.
if (singularValues[k] <= 0)
{
singularValues[k] = singularValues[k] < 0 ? -singularValues[k] : 0;
for (int i = 0; i <= pp; i++)
{
V[i][k] = -V[i][k];
}
}
// Order the singular values.
while (k < pp)
{
if (singularValues[k] >= singularValues[k + 1])
{
break;
}
double t = singularValues[k];
singularValues[k] = singularValues[k + 1];
singularValues[k + 1] = t;
if (k < n - 1)
{
for (int i = 0; i < n; i++)
{
t = V[i][k + 1];
V[i][k + 1] = V[i][k];
V[i][k] = t;
}
}
if (k < m - 1)
{
for (int i = 0; i < m; i++)
{
t = U[i][k + 1];
U[i][k + 1] = U[i][k];
U[i][k] = t;
}
}
k++;
}
p--;
}
break;
}
}
// Set the small value tolerance used to calculate rank and pseudo-inverse
tol = FastMath.max(m * singularValues[0] * EPS,
FastMath.sqrt(Precision.SAFE_MIN));
if (!transposed)
{
cachedU = MatrixUtils.createRealMatrix(U);
cachedV = MatrixUtils.createRealMatrix(V);
}
else
{
cachedU = MatrixUtils.createRealMatrix(V);
cachedV = MatrixUtils.createRealMatrix(U);
}
}
/// <summary>
/// Parse a string to produce a <see cref="RealMatrix"/> object.
/// </summary>
/// <param name="source">String to parse.</param>
/// <param name="pos">input/ouput parsing parameter.</param>
/// <returns>the parsed <see cref="RealMatrix"/> object.</returns>
public RealMatrix parse(String source, ref Int32 pos)
{
int initialIndex = pos;
String trimmedPrefix = prefix.Trim();
String trimmedSuffix = suffix.Trim();
String trimmedRowPrefix = rowPrefix.Trim();
String trimmedRowSuffix = rowSuffix.Trim();
String trimmedColumnSeparator = columnSeparator.Trim();
String trimmedRowSeparator = rowSeparator.Trim();
// parse prefix
CompositeFormat.parseAndIgnoreWhitespace(source, pos);
if (!CompositeFormat.parseFixedstring(source, trimmedPrefix))
{
return(null);
}
// parse components
List <List <double> > matrix = new List <List <double> >();
List <double> rowComponents = new List <double>();
for (Boolean loop = true; loop;)
{
if (rowComponents.Count != 0)
{
CompositeFormat.parseAndIgnoreWhitespace(source, pos);
if (!CompositeFormat.parseFixedstring(source, trimmedColumnSeparator))
{
if (trimmedRowSuffix.Length != 0 &&
!CompositeFormat.parseFixedstring(source, trimmedRowSuffix))
{
return(null);
}
else
{
CompositeFormat.parseAndIgnoreWhitespace(source, pos);
if (CompositeFormat.parseFixedstring(source, trimmedRowSeparator))
{
matrix.Add(rowComponents);
rowComponents = new List <double>();
continue;
}
else
{
loop = false;
}
}
}
}
else
{
CompositeFormat.parseAndIgnoreWhitespace(source, pos);
if (trimmedRowPrefix.Length != 0 &&
!CompositeFormat.parseFixedstring(source, trimmedRowPrefix))
{
return(null);
}
}
if (loop)
{
CompositeFormat.parseAndIgnoreWhitespace(source, pos);
double component = CompositeFormat.parseNumber(source, CultureInfo.CurrentCulture);
if (Double.IsNaN(component))
{
rowComponents.Add(component);
}
else
{
if (rowComponents.Count == 0)
{
loop = false;
}
else
{
// invalid component
// set index back to initial, error index should already be set
pos = initialIndex;
return(null);
}
}
}
}
if (rowComponents.Count != 0)
{
matrix.Add(rowComponents);
}
// parse suffix
CompositeFormat.parseAndIgnoreWhitespace(source, pos);
if (!CompositeFormat.parseFixedstring(source, trimmedSuffix))
{
return(null);
}
// do not allow an empty matrix
if (matrix.Count == 0)
{
pos = initialIndex;
return(null);
}
// build vector
double[][] data = new double[matrix.Count][];
int row = 0;
foreach (List <double> rowList in matrix)
{
data[row] = new double[rowList.Count];
for (int i = 0; i < rowList.Count; i++)
{
data[row][i] = rowList[i];
}
row++;
}
return(MatrixUtils.createRealMatrix(data));
}