/// <summary>
/// Creates a new object that is a copy of the current instance.
/// </summary>
/// <returns>
/// A new object that is a copy of this instance.
/// </returns>
public object Clone()
{
var clone = new QrDecompositionF();
clone.qr = (Single[, ])qr.Clone();
clone.Rdiag = (Single[])Rdiag.Clone();
return(clone);
}
/// <summary>
/// Construct an eigenvalue decomposition.</summary>
/// <param name="value">
/// The matrix to be decomposed.</param>
/// <param name="assumeSymmetric">
/// Defines if the matrix should be assumed as being symmetric
/// regardless if it is or not. Default is <see langword="false"/>.</param>
/// <param name="inPlace">
/// Pass <see langword="true"/> to perform the decomposition in place. The matrix
/// <paramref name="value"/> will be destroyed in the process, resulting in less
/// memory comsumption.</param>
public EigenvalueDecompositionF(Single[,] value, bool assumeSymmetric, bool inPlace)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if (value.GetLength(0) != value.GetLength(1))
{
throw new ArgumentException("Matrix is not a square matrix.", "value");
}
n = value.GetLength(1);
V = new Single[n, n];
d = new Single[n];
e = new Single[n];
this.symmetric = assumeSymmetric;
if (this.symmetric)
{
V = inPlace ? value : (Single[, ])value.Clone();
// Tridiagonalize.
this.tred2();
// Diagonalize.
this.tql2();
}
else
{
H = inPlace ? value : (Single[, ])value.Clone();
ort = new Single[n];
// Reduce to Hessenberg form.
this.orthes();
// Reduce Hessenberg to real Schur form.
this.hqr2();
}
}
/// <summary>
/// Creates a new object that is a copy of the current instance.
/// </summary>
/// <returns>
/// A new object that is a copy of this instance.
/// </returns>
///
public object Clone()
{
var svd = new SingularValueDecompositionF();
svd.m = m;
svd.n = n;
svd.s = (Single[])s.Clone();
svd.si = (int[])si.Clone();
svd.swapped = swapped;
if (u != null)
{
svd.u = (Single[, ])u.Clone();
}
if (v != null)
{
svd.v = (Single[, ])u.Clone();
}
return(svd);
}
/// <summary>
/// Creates a new object that is a copy of the current instance.
/// </summary>
/// <returns>
/// A new object that is a copy of this instance.
/// </returns>
///
public object Clone()
{
var clone = new CholeskyDecompositionF();
clone.L = (Single[, ])L.Clone();
clone.D = (Single[])D.Clone();
clone.n = n;
clone.robust = robust;
clone.positiveDefinite = positiveDefinite;
clone.symmetric = symmetric;
return(clone);
}
/// <summary>
/// Creates a new object that is a copy of the current instance.
/// </summary>
/// <returns>
/// A new object that is a copy of this instance.
/// </returns>
public object Clone()
{
var clone = new EigenvalueDecompositionF();
clone.d = (Single[])d.Clone();
clone.e = (Single[])e.Clone();
clone.H = (Single[, ])H.Clone();
clone.n = n;
clone.ort = (Single[])ort;
clone.symmetric = symmetric;
clone.V = (Single[, ])V.Clone();
return(clone);
}
/// <summary>
/// Constructs a new singular value decomposition.
/// </summary>
///
/// <param name="value">
/// The matrix to be decomposed.</param>
/// <param name="computeLeftSingularVectors">
/// Pass <see langword="true"/> if the left singular vector matrix U
/// should be computed. Pass <see langword="false"/> otherwise. Default
/// is <see langword="true"/>.</param>
/// <param name="computeRightSingularVectors">
/// Pass <see langword="true"/> if the right singular vector matrix V
/// should be computed. Pass <see langword="false"/> otherwise. Default
/// is <see langword="true"/>.</param>
/// <param name="autoTranspose">
/// Pass <see langword="true"/> to automatically transpose the value matrix in
/// case JAMA's assumptions about the dimensionality of the matrix are violated.
/// Pass <see langword="false"/> otherwise. Default is <see langword="false"/>.</param>
/// <param name="inPlace">
/// Pass <see langword="true"/> to perform the decomposition in place. The matrix
/// <paramref name="value"/> will be destroyed in the process, resulting in less
/// memory comsumption.</param>
///
public unsafe SingularValueDecompositionF(Single[,] value,
bool computeLeftSingularVectors, bool computeRightSingularVectors, bool autoTranspose, bool inPlace)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
Single[,] a;
m = value.GetLength(0); // rows
n = value.GetLength(1); // cols
if (m == 0 || n == 0)
{
throw new ArgumentException("Matrix does not have any rows or columns.", "value");
}
if (m < n) // Check if we are violating JAMA's assumption
{
if (!autoTranspose) // Yes, check if we should correct it
{
// Warning! This routine is not guaranteed to work when A has less rows
// than columns. If this is the case, you should compute SVD on the
// transpose of A and then swap the left and right eigenvectors.
// However, as the solution found can still be useful, the exception below
// will not be thrown, and only a warning will be output in the trace.
// throw new ArgumentException("Matrix should have more rows than columns.");
System.Diagnostics.Trace.WriteLine(
"WARNING: Computing SVD on a matrix with more columns than rows.");
// Proceed anyway
a = inPlace ? value : (Single[, ])value.Clone();
}
else
{
// Transposing and swapping
a = value.Transpose(inPlace && m == n);
m = value.GetLength(1);
n = value.GetLength(0);
swapped = true;
bool aux = computeLeftSingularVectors;
computeLeftSingularVectors = computeRightSingularVectors;
computeRightSingularVectors = aux;
}
}
else
{
// Input matrix is ok
a = inPlace ? value : (Single[, ])value.Clone();
}
int nu = System.Math.Min(m, n);
int ni = System.Math.Min(m + 1, n);
s = new Single[ni];
u = new Single[m, nu];
v = new Single[n, n];
Single[] e = new Single[n];
Single[] work = new Single[m];
bool wantu = computeLeftSingularVectors;
bool wantv = computeRightSingularVectors;
fixed(Single *U = u)
fixed(Single * V = v)
fixed(Single * A = a)
{
// Will store ordered sequence of indices after sorting.
si = new int[ni]; for (int i = 0; i < ni; i++)
{
si[i] = i;
}
// Reduce A to bidiagonal form, storing the diagonal elements in s and the super-diagonal elements in e.
int nct = System.Math.Min(m - 1, n);
int nrt = System.Math.Max(0, System.Math.Min(n - 2, m));
for (int k = 0; k < System.Math.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.
s[k] = 0;
for (int i = k; i < m; i++)
{
s[k] = Accord.Math.Tools.Hypotenuse(s[k], a[i, k]);
}
if (s[k] != 0)
{
if (a[k, k] < 0)
{
s[k] = -s[k];
}
for (int i = k; i < m; i++)
{
a[i, k] /= s[k];
}
a[k, k] += 1;
}
s[k] = -s[k];
}
for (int j = k + 1; j < n; j++)
{
Single *ptr_ak = A + k * n + k; // A[k,k]
Single *ptr_aj = A + k * n + j; // A[k,j]
if ((k < nct) & (s[k] != 0))
{
// Apply the transformation.
Single t = 0;
Single *ak = ptr_ak;
Single *aj = ptr_aj;
for (int i = k; i < m; i++)
{
t += (*ak) * (*aj);
ak += n; aj += n;
}
t = -t / *ptr_ak;
ak = ptr_ak;
aj = ptr_aj;
for (int i = k; i < m; i++)
{
*aj += t * (*ak);
ak += n; aj += n;
}
}
// Place the k-th row of A into e for the subsequent calculation of the row transformation.
e[j] = *ptr_aj;
}
if (wantu & (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] = Accord.Math.Tools.Hypotenuse(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;
}
int k1 = k + 1;
for (int i = k1; i < m; i++)
{
Single *ai = A + (i * n) + k1;
for (int j = k1; j < n; j++, ai++)
{
work[i] += e[j] * (*ai);
}
}
for (int j = k1; j < n; j++)
{
Single t = -e[j] / e[k1];
Single *aj = A + (k1 * n) + j;
for (int i = k1; i < m; i++, aj += n)
{
*aj += t * work[i];
}
}
}
if (wantv)
{
// 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 = System.Math.Min(n, m + 1);
if (nct < n)
{
s[nct] = a[nct, nct];
}
if (m < p)
{
s[p - 1] = 0;
}
if (nrt + 1 < p)
{
e[nrt] = a[nrt, p - 1];
}
e[p - 1] = 0;
// If required, generate U.
if (wantu)
{
for (int j = nct; j < nu; 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 (s[k] != 0)
{
Single *ptr_uk = U + k * nu + k; // u[k,k]
Single *uk, uj;
for (int j = k + 1; j < nu; j++)
{
Single *ptr_uj = U + k * nu + j; // u[k,j]
Single t = 0;
uk = ptr_uk;
uj = ptr_uj;
for (int i = k; i < m; i++)
{
t += *uk * *uj;
uk += nu; uj += nu;
}
t = -t / *ptr_uk;
uk = ptr_uk; uj = ptr_uj;
for (int i = k; i < m; i++)
{
*uj += t * (*uk);
uk += nu; uj += nu;
}
}
uk = ptr_uk;
for (int i = k; i < m; i++)
{
*uk = -(*uk);
uk += nu;
}
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;
}
}
}
// If required, generate V.
if (wantv)
{
for (int k = n - 1; k >= 0; k--)
{
if ((k < nrt) & (e[k] != 0))
{
// TODO: The following is a pseudo correction to make SVD
// work on matrices with n > m (less rows than columns).
// For the proper correction, compute the decomposition of the
// transpose of A and swap the left and right eigenvectors
// Original line:
// for (int j = k + 1; j < nu; j++)
// Pseudo correction:
// for (int j = k + 1; j < n; j++)
for (int j = k + 1; j < n; j++) // pseudo-correction
{
Single *ptr_vk = V + (k + 1) * n + k; // v[k + 1, k]
Single *ptr_vj = V + (k + 1) * n + j; // v[k + 1, j]
Single t = 0;
Single *vk = ptr_vk;
Single *vj = ptr_vj;
for (int i = k + 1; i < n; i++)
{
t += *vk * *vj;
vk += n; vj += n;
}
t = -t / *ptr_vk;
vk = ptr_vk; vj = ptr_vj;
for (int i = k + 1; i < n; i++)
{
*vj += t * (*vk);
vk += n; vj += n;
}
}
}
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;
int iter = 0;
while (p > 0)
{
int k, 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 >= -1; k--)
{
if (k == -1)
{
break;
}
if (System.Math.Abs(e[k]) <=
tiny + eps * (System.Math.Abs(s[k]) + System.Math.Abs(s[k + 1])))
{
e[k] = 0;
break;
}
}
if (k == p - 2)
{
kase = 4;
}
else
{
int ks;
for (ks = p - 1; ks >= k; ks--)
{
if (ks == k)
{
break;
}
Single t = (ks != p ? System.Math.Abs(e[ks]) : 0) +
(ks != k + 1 ? System.Math.Abs(e[ks - 1]) : 0);
if (System.Math.Abs(s[ks]) <= tiny + eps * t)
{
s[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:
{
Single f = e[p - 2];
e[p - 2] = 0;
for (int j = p - 2; j >= k; j--)
{
Single t = Accord.Math.Tools.Hypotenuse(s[j], f);
Single cs = s[j] / t;
Single sn = f / t;
s[j] = t;
if (j != k)
{
f = -sn * e[j - 1];
e[j - 1] = cs * e[j - 1];
}
if (wantv)
{
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:
{
Single f = e[k - 1];
e[k - 1] = 0;
for (int j = k; j < p; j++)
{
Single t = Accord.Math.Tools.Hypotenuse(s[j], f);
Single cs = s[j] / t;
Single sn = f / t;
s[j] = t;
f = -sn * e[j];
e[j] = cs * e[j];
if (wantu)
{
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.
Single scale = System.Math.Max(System.Math.Max(System.Math.Max(System.Math.Max(System.Math.Abs(s[p - 1]), System.Math.Abs(s[p - 2])), System.Math.Abs(e[p - 2])), System.Math.Abs(s[k])), System.Math.Abs(e[k]));
Single sp = s[p - 1] / scale;
Single spm1 = s[p - 2] / scale;
Single epm1 = e[p - 2] / scale;
Single sk = s[k] / scale;
Single ek = e[k] / scale;
Single b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2;
Single c = (sp * epm1) * (sp * epm1);
double shift = 0;
if ((b != 0) | (c != 0))
{
if (b < 0)
{
shift = -System.Math.Sqrt(b * b + c);
}
else
{
shift = System.Math.Sqrt(b * b + c);
}
shift = c / (b + shift);
}
Single f = (sk + sp) * (sk - sp) + (Single)shift;
Single g = sk * ek;
// Chase zeros.
for (int j = k; j < p - 1; j++)
{
Single t = Accord.Math.Tools.Hypotenuse(f, g);
Single cs = f / t;
Single sn = g / t;
if (j != k)
{
e[j - 1] = t;
}
f = cs * s[j] + sn * e[j];
e[j] = cs * e[j] - sn * s[j];
g = sn * s[j + 1];
s[j + 1] = cs * s[j + 1];
if (wantv)
{
unsafe
{
fixed(Single *ptr_vj = &v[0, j])
{
Single *vj = ptr_vj;
Single *vj1 = ptr_vj + 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;*/
Single vij = *vj;
Single vij1 = *vj1;
t = cs * vij + sn * vij1;
*vj1 = -sn * vij + cs * vij1;
*vj = t;
vj += n; vj1 += n;
}
}
}
}
t = Accord.Math.Tools.Hypotenuse(f, g);
cs = f / t;
sn = g / t;
s[j] = t;
f = cs * e[j] + sn * s[j + 1];
s[j + 1] = -sn * e[j] + cs * s[j + 1];
g = sn * e[j + 1];
e[j + 1] = cs * e[j + 1];
if (wantu && (j < m - 1))
{
fixed(Single *ptr_uj = &u[0, j])
{
Single *uj = ptr_uj;
Single *uj1 = ptr_uj + 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;*/
Single uij = *uj;
Single uij1 = *uj1;
t = cs * uij + sn * uij1;
*uj1 = -sn * uij + cs * uij1;
*uj = t;
uj += nu; uj1 += nu;
}
}
}
}
e[p - 2] = f;
iter = iter + 1;
}
break;
// Convergence.
case 4:
{
// Make the singular values positive.
if (s[k] <= 0)
{
s[k] = (s[k] < 0 ? -s[k] : 0);
if (wantv)
{
for (int i = 0; i <= pp; i++)
{
v[i, k] = -v[i, k];
}
}
}
// Order the singular values.
while (k < pp)
{
if (s[k] >= s[k + 1])
{
break;
}
Single t = s[k];
s[k] = s[k + 1];
s[k + 1] = t;
int ti = si[k];
si[k] = si[k + 1];
si[k + 1] = ti;
if (wantv && (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 (wantu && (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++;
}
iter = 0;
p--;
}
break;
}
}
}
// If we are violating JAMA's assumption about
// the input dimension, we need to swap u and v.
if (swapped)
{
Single[,] temp = this.u;
this.u = this.v;
this.v = temp;
}
}
/// <summary>Constructs a QR decomposition.</summary>
/// <param name="value">The matrix A to be decomposed.</param>
/// <param name="transpose">True if the decomposition should be performed on
/// the transpose of A rather than A itself, false otherwise. Default is false.</param>
public QrDecompositionF(Single[,] value, bool transpose)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if ((!transpose && value.GetLength(0) < value.GetLength(1)) ||
(transpose && value.GetLength(1) < value.GetLength(0)))
{
throw new ArgumentException("Matrix has more columns than rows.", "value");
}
this.qr = transpose ? value.Transpose() : (Single[, ])value.Clone();
int rows = qr.GetLength(0);
int cols = qr.GetLength(1);
this.Rdiag = new Single[cols];
for (int k = 0; k < cols; k++)
{
// Compute 2-norm of k-th column without under/overflow.
Single nrm = 0;
for (int i = k; i < rows; i++)
{
nrm = Tools.Hypotenuse(nrm, qr[i, k]);
}
if (nrm != 0)
{
// Form k-th Householder vector.
if (qr[k, k] < 0)
{
nrm = -nrm;
}
for (int i = k; i < rows; i++)
{
qr[i, k] /= nrm;
}
qr[k, k] += 1;
// Apply transformation to remaining columns.
for (int j = k + 1; j < cols; j++)
{
Single s = 0;
for (int i = k; i < rows; i++)
{
s += qr[i, k] * qr[i, j];
}
s = -s / qr[k, k];
for (int i = k; i < rows; i++)
{
qr[i, j] += s * qr[i, k];
}
}
}
this.Rdiag[k] = -nrm;
}
}
/// <summary>Least squares solution of <c>A * X = B</c></summary>
/// <param name="value">Right-hand-side matrix with as many rows as <c>A</c> and any number of columns.</param>
/// <returns>A matrix that minimized the two norm of <c>Q * R * X - B</c>.</returns>
/// <exception cref="T:System.ArgumentException">Matrix row dimensions must be the same.</exception>
/// <exception cref="T:System.InvalidOperationException">Matrix is rank deficient.</exception>
public Single[,] Solve(Single[,] value)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if (value.GetLength(0) != qr.GetLength(0))
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!this.FullRank)
{
throw new InvalidOperationException("Matrix is rank deficient.");
}
// Copy right hand side
int count = value.GetLength(1);
var X = (Single[, ])value.Clone();
int m = qr.GetLength(0);
int n = qr.GetLength(1);
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < count; j++)
{
Single s = 0;
for (int i = k; i < m; i++)
{
s += qr[i, k] * X[i, j];
}
s = -s / qr[k, k];
for (int i = k; i < m; i++)
{
X[i, j] += s * qr[i, k];
}
}
}
// Solve R*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
X[k, j] /= Rdiag[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * qr[i, k];
}
}
}
var r = new Single[n, count];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < count; j++)
{
r[i, j] = X[i, j];
}
}
return(r);
}
/// <summary>
/// Constructs a new LU decomposition.
/// </summary>
/// <param name="value">The matrix A to be decomposed.</param>
/// <param name="transpose">True if the decomposition should be performed on
/// the transpose of A rather than A itself, false otherwise. Default is false.</param>
/// <param name="inPlace">True if the decomposition should be performed over the
/// <paramref name="value"/> matrix rather than on a copy of it. If true, the
/// matrix will be destroyed during the decomposition. Default is false.</param>
///
public LuDecompositionF(Single[,] value, bool transpose, bool inPlace)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if (transpose)
{
this.lu = value.Transpose(inPlace);
}
else
{
this.lu = inPlace ? value : (Single[, ])value.Clone();
}
this.rows = lu.GetLength(0);
this.cols = lu.GetLength(1);
this.pivotSign = 1;
this.pivotVector = new int[rows];
for (int i = 0; i < rows; i++)
{
pivotVector[i] = i;
}
var LUcolj = new Single[rows];
unsafe
{
fixed(Single *LU = lu)
{
// Outer loop.
for (int j = 0; j < cols; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < rows; i++)
{
LUcolj[i] = lu[i, j];
}
// Apply previous transformations.
for (int i = 0; i < rows; i++)
{
Single s = 0;
// Most of the time is spent in
// the following dot product:
int kmax = Math.Min(i, j);
Single *LUrowi = &LU[i * cols];
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 < rows; i++)
{
if (Math.Abs(LUcolj[i]) > Math.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < cols; k++)
{
var t = lu[p, k];
lu[p, k] = lu[j, k];
lu[j, k] = t;
}
int v = pivotVector[p];
pivotVector[p] = pivotVector[j];
pivotVector[j] = v;
pivotSign = -pivotSign;
}
// Compute multipliers.
if (j < rows && lu[j, j] != 0)
{
for (int i = j + 1; i < rows; i++)
{
lu[i, j] /= lu[j, j];
}
}
}
}
}
}
/// <summary>Solves a set of equation systems of type <c>A * X = B</c>.</summary>
/// <param name="value">Right hand side matrix with as many rows as <c>A</c> and any number of columns.</param>
/// <returns>Matrix <c>X</c> so that <c>L * L' * X = B</c>.</returns>
/// <exception cref="T:System.ArgumentException">Matrix dimensions do not match.</exception>
/// <exception cref="T:System.NonSymmetricMatrixException">Matrix is not symmetric.</exception>
/// <exception cref="T:System.NonPositiveDefiniteMatrixException">Matrix is not positive-definite.</exception>
/// <param name="inPlace">True to compute the solving in place, false otherwise.</param>
///
public Single[,] Solve(Single[,] value, bool inPlace)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.GetLength(0) != n)
{
throw new ArgumentException("Argument matrix should have the same number of rows as the decomposed matrix.", "value");
}
if (!symmetric)
{
throw new NonSymmetricMatrixException("Decomposed matrix is not symmetric.");
}
if (!robust && !positiveDefinite)
{
throw new NonPositiveDefiniteMatrixException("Decomposed matrix is not positive definite.");
}
int count = value.GetLength(1);
Single[,] B = inPlace ? value : (Single[, ])value.Clone();
// Solve L*Y = B;
for (int k = 0; k < n; k++)
{
for (int j = 0; j < count; j++)
{
for (int i = 0; i < k; i++)
{
B[k, j] -= B[i, j] * L[k, i];
}
B[k, j] /= L[k, k];
}
}
if (robust)
{
for (int k = 0; k < n; k++)
{
for (int j = 0; j < count; j++)
{
B[k, j] /= D[k];
}
}
}
// Solve L'*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
for (int i = k + 1; i < n; i++)
{
B[k, j] -= B[i, j] * L[i, k];
}
B[k, j] /= L[k, k];
}
}
return(B);
}
/// <summary>
/// Construct an eigenvalue decomposition.</summary>
///
/// <param name="value">
/// The matrix to be decomposed.</param>
/// <param name="assumeSymmetric">
/// Defines if the matrix should be assumed as being symmetric
/// regardless if it is or not. Default is <see langword="false"/>.</param>
/// <param name="inPlace">
/// Pass <see langword="true"/> to perform the decomposition in place. The matrix
/// <paramref name="value"/> will be destroyed in the process, resulting in less
/// memory comsumption.</param>
/// <param name="sort">
/// Pass <see langword="true"/> to sort the eigenvalues and eigenvectors at the end
/// of the decomposition.</param>
///
public EigenvalueDecompositionF(Single[,] value, bool assumeSymmetric,
bool inPlace = false, bool sort = false)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if (value.GetLength(0) != value.GetLength(1))
{
throw new ArgumentException("Matrix is not a square matrix.", "value");
}
n = value.GetLength(1);
V = new Single[n, n];
d = new Single[n];
e = new Single[n];
this.symmetric = assumeSymmetric;
if (this.symmetric)
{
V = inPlace ? value : (Single[, ])value.Clone();
// Tridiagonalize.
this.tred2();
// Diagonalize.
this.tql2();
}
else
{
H = inPlace ? value : (Single[, ])value.Clone();
ort = new Single[n];
// Reduce to Hessenberg form.
this.orthes();
// Reduce Hessenberg to real Schur form.
this.hqr2();
}
if (sort)
{
// Sort eigenvalues and vectors in descending order
var idx = Vector.Range(n);
Array.Sort(idx, (i, j) =>
{
if (Math.Abs(d[i]) == Math.Abs(d[j]))
{
return(-Math.Abs(e[i]).CompareTo(Math.Abs(e[j])));
}
return(-Math.Abs(d[i]).CompareTo(Math.Abs(d[j])));
});
this.d = this.d.Get(idx);
this.e = this.e.Get(idx);
this.V = this.V.Get(null, idx);
}
}