/// <summary>
/// QR decomposition - raw Lapack output
/// </summary>
/// <param name="A">general input matrix A</param>
/// <returns>orthonormal / unitary matrix Q and upper triangular
/// matrix R packed into single matrix. This is the output of the
/// lapack function ?geqrf.</returns>
/// <remarks><para>Input matrix A will not be altered. </para>
/// <para>The matrix returned is the direct output of the lapack
/// function [d,s,c,z]geqrf respectively. This mean that it contains
/// the decomposition factors Q and R, but they are cmbined into a
/// single matrix for performance reasons. If you need one of the factors,
/// you would use the overloaded function
/// <see cref="ILNumerics.BuiltInFunctions.ILMath.qr(ILArray<double>,ref ILArray<double>)"/>
/// instead, which returns those factors seperately.</para></remarks>
public static /*!HC:inCls1*/ ILArray <double> qr(/*!HC:inCls1*/ ILArray <double> A)
{
if (!A.IsMatrix)
{
throw new ILArgumentException("qr decomposition: A must be a matrix");
}
int m = A.Dimensions[0], n = A.Dimensions[1];
/*!HC:inCls1*/ ILArray <double> ret = (/*!HC:inCls1*/ ILArray <double>)A.Clone();
/*!HC:inArr1*/ double [] tau = new /*!HC:inArr1*/ double [(m < n)?m:n];
int info = 0;
/*!HC:lapack_*geqrf*/ Lapack.dgeqrf(m, n, ret.m_data, m, tau, ref info);
if (info < 0)
{
throw new ILArgumentException("qr: an error occoured during decomposition");
}
return(ret);
}
/*!HC:TYPELIST:
<hycalper>
<type>
<source locate="after">
inArr1
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
dllfunc
</source>
<destination>zgeqp3</destination>
</type>
<type>
<source locate="nextline">
dll1func
</source>
<destination>lapack_zgeqp3 (ref M, ref N, A, ref LDA, JPVT, tau, work, ref lwork, rwork, ref info);</destination>
</type>
<type>
<source locate="nextline">
cmplxRwork
</source>
<destination>double[] rwork = new double[2 * N];</destination>
</type>
</hycalper>
*/
public void /*!HC:dllfunc*/ dgeqp3 ( int M,int N,/*!HC:inArr1*/ double [] A,int LDA,int [] JPVT,/*!HC:inArr1*/ double [] tau, ref int info ) {
/*!HC:inArr1*/ double [] work = new /*!HC:inArr1*/ double [1];
int lwork = -1;
try {
/*!HC:cmplxRwork*/
/*dummy*/
/*!HC:dll1func*/
lapack_dgeqp3 (ref M, ref N, A, ref LDA, JPVT, tau, work, ref lwork, ref info);
lwork = (int)work[0];
if (lwork > 0 && info == 0) {
work = new /*!HC:inArr1*/ double [lwork];
/*!HC:dll1func*/
lapack_dgeqp3 (ref M, ref N, A, ref LDA, JPVT, tau, work, ref lwork, ref info);
} else {
throw new ILException("error in lapack_?geqp3");
}
} catch (OutOfMemoryException e) {
throw new ILException("error on ?geqp3. Not enough memory! " + (lwork * Marshal.SizeOf( work[0] )).ToString() + " bytes has been requested.",e);
}
}
/*!HC:TYPELIST:
<hycalper>
<type>
<source locate="after">
inArr1
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
outArr1
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
dllfunc
</source>
<destination>zungqr</destination>
</type>
<type>
<source locate="after">
lapack_***gqr
</source>
<destination>lapack_zungqr</destination>
</type>
</hycalper>
*/
public void /*!HC:dllfunc*/ dorgqr (int M, int N, int K, /*!HC:inArr1*/ double [] A, int lda, /*!HC:inArr1*/ double [] tau, ref int info) {
/*!HC:inArr1*/ double [] work = new /*!HC:inArr1*/ double [1];
int lwork = -1;
try {
/*!HC:lapack_***gqr*/ lapack_dorgqr (ref M, ref N, ref K, A, ref lda, tau, work, ref lwork, ref info);
lwork = (int)work[0];
if (lwork > 0 && info == 0) {
work = new /*!HC:inArr1*/ double [lwork];
/*!HC:lapack_***gqr*/ lapack_dorgqr (ref M, ref N, ref K, A, ref lda, tau, work, ref lwork, ref info);
} else {
throw new ILException("error in lapack_?[un/or]gqr");
}
} catch (OutOfMemoryException e) {
throw new ILException("error on ?[un/or]gqr. Not enough memory! " + (lwork * Marshal.SizeOf( work[0] )).ToString() + " bytes has been requested.",e);
}
}
/*!HC:TYPELIST:
<hycalper>
<type>
<source locate="after">
inArr1
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
outArrS
</source>
<destination>double</destination>
</type>
<type>
<source locate="after">
outArrU
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
dllfunc
</source>
<destination>zgetri</destination>
</type>
<type>
<source locate="after">
dll1func
</source>
<destination>lapack_zgetri</destination>
</type>
</hycalper>
*/
public void /*!HC:dllfunc*/ dgetri (int N, /*!HC:inArr1*/ double [] A, int LDA, int[] IPIV, ref int info) {
/*!HC:inArr1*/ double [] work = new /*!HC:inArr1*/ double [1];
int lwork = -1;
try {
/*!HC:dll1func*/ lapack_dgetri (ref N, A, ref LDA, IPIV, work, ref lwork, ref info);
lwork = (int)work[0];
if (lwork > 0 && info == 0) {
work = new /*!HC:inArr1*/ double [lwork];
/*!HC:dll1func*/ lapack_dgetri (ref N, A, ref LDA, IPIV, work, ref lwork, ref info);
} else {
throw new ILException("error in lapack_dgetri");
}
} catch (OutOfMemoryException e) {
throw new ILException("error on dgetri. Not enough memory! " + (lwork * Marshal.SizeOf( work[0] )).ToString() + " bytes has been requested.",e);
}
}
/*!HC:TYPELIST:
<hycalper>
<type>
<source locate="after">
inArr1
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
outArrS
</source>
<destination>double</destination>
</type>
<type>
<source locate="after">
outArrU
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
dllfunc
</source>
<destination>zgesvd</destination>
</type>
<type>
<source locate="after">
dll1func
</source>
<destination>lapack_zgesvd</destination>
</type>
</hycalper>
*/
/// <summary>
/// singular value decomposition
/// </summary>
/// <param name="jobz"></param>
/// <param name="m"></param>
/// <param name="n"></param>
/// <param name="a"></param>
/// <param name="lda"></param>
/// <param name="s"></param>
/// <param name="u"></param>
/// <param name="ldu"></param>
/// <param name="vt"></param>
/// <param name="ldvt"></param>
/// <param name="info"></param>
public void /*!HC:dllfunc*/ dgesvd (char jobz, int m, int n, /*!HC:inArr1*/ double [] a, int lda,
/*!HC:outArrS*/ double [] s, /*!HC:outArrU*/ double [] u, int ldu, /*!HC:outArrU*/ double [] vt, int ldvt, ref int info) {
if (jobz != 'A' && jobz != 'S' && jobz != 'N')
throw new ILArgumentException("Argument jobz must be one of 'A','S' or 'N'");
try {
/*!HC:inArr1*/ double [] work = new /*!HC:inArr1*/ double [1] { (/*!HC:inArr1*/ double )0.0 };
int lwork = -1;
int[] iwork = new int[((m < n) ? m : n) * 8];
/*!HC:dll1func*/ lapack_dgesvd (ref jobz, ref jobz, ref m, ref n, a, ref lda, s, u, ref ldu, vt, ref ldvt, work, ref lwork, iwork, ref info);
if (work[0] != 0) {
work = new /*!HC:inArr1*/ double [(int)work[0]];
lwork = work.Length;
/*!HC:dll1func*/ lapack_dgesvd (ref jobz, ref jobz, ref m, ref n, a, ref lda, s, u, ref ldu, vt, ref ldvt, work, ref lwork, iwork, ref info);
}
} catch (Exception e) {
if (e is OutOfMemoryException) {
throw new ILMemoryException("Not enough memory for given arguments.");
}
throw new ILException("Unable to do gesvd.", e);
}
}
/*!HC:TYPELIST:
<hycalper>
<type>
<source locate="after">
inArr1
</source>
<destination>fcomplex</destination>
<destination>complex</destination>
<destination>float</destination>
</type>
<type>
<source locate="after">
dllfunc
</source>
<destination>cgeqrf</destination>
<destination>zgeqrf</destination>
<destination>sgeqrf</destination>
</type>
<type>
<source locate="after">
dll1func
</source>
<destination>mkl_cgeqrf</destination>
<destination>mkl_zgeqrf</destination>
<destination>mkl_sgeqrf</destination>
</type>
</hycalper>
*/
public void /*!HC:dllfunc*/ dgeqrf (int M, int N, /*!HC:inArr1*/ double [] A, int lda, /*!HC:inArr1*/ double [] tau, ref int info) {
/*!HC:inArr1*/ double [] work = new /*!HC:inArr1*/ double [1];
int lwork = -1;
try {
/*!HC:dll1func*/ mkl_dgeqrf (ref M, ref N, A, ref lda, tau, work, ref lwork, ref info);
lwork = (int)work[0];
if (lwork > 0 && info == 0) {
work = new /*!HC:inArr1*/ double [lwork];
/*!HC:dll1func*/ mkl_dgeqrf (ref M, ref N, A, ref lda, tau, work, ref lwork, ref info);
} else {
throw new ILException("error in mkl_?geqrf");
}
} catch (OutOfMemoryException e) {
throw new ILException("error on ?geqrf. Not enough memory! " + (lwork * Marshal.SizeOf( work[0] )).ToString() + " bytes has been requested.",e);
}
}
/*!HC:TYPELIST:
<hycalper>
<type>
<source locate="after">
inArr1
</source>
<destination>float</destination>
</type>
<type>
<source locate="after">
outArrS
</source>
<destination>float</destination>
</type>
<type>
<source locate="after">
outArrU
</source>
<destination>float</destination>
</type>
<type>
<source locate="after">
dllfunc
</source>
<destination>sgesdd</destination>
</type>
<type>
<source locate="after">
dllQuotefunc
</source>
<destination><![CDATA["sgesdd"]]></destination>
</type>
<type>
<source locate="after">
dll1func
</source>
<destination>mkl_sgesdd</destination>
</type>
<type>
<source locate="after">
dll2func
</source>
<destination>sgesvd</destination>
</type>
</hycalper>
*/
public void /*!HC:dllfunc*/ dgesdd (char jobz, int m, int n, /*!HC:inArr1*/ double [] a, int lda, /*!HC:outArrS*/ double [] s, /*!HC:outArrU*/ double [] u, int ldu, /*!HC:outArrU*/ double [] vt, int ldvt, ref int info) {
try {
/*!HC:inArr1*/ double [] work = new /*!HC:inArr1*/ double [1] { (/*!HC:inArr1*/ double )0.0 };
int lwork = -1;
int[] iwork = new int[((m < n) ? m : n) * 8];
/*!HC:dll1func*/ mkl_dgesdd (ref jobz, ref m, ref n, a, ref lda, s, u, ref ldu, vt, ref ldvt, work, ref lwork, iwork, ref info);
if (work[0] != 0) {
work = new /*!HC:inArr1*/ double [(int)work[0]];
lwork = work.Length;
/*!HC:dll1func*/ mkl_dgesdd (ref jobz, ref m, ref n, a, ref lda, s, u, ref ldu, vt, ref ldvt, work, ref lwork, iwork, ref info);
}
} catch (Exception e) {
if (e is OutOfMemoryException) {
/*!HC:dll2func*/ dgesvd (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, ref info);
}
throw new ILException("Unable to do " + /*!HC:dllQuotefunc*/ "dgesdd" + ".", e);
}
}
/// <summary>
/// singular value decomposition
/// </summary>
/// <param name="X">matrix X. The elements of X will not be altered.</param>
/// <param name="U">(return value) left singular vectors of X as columns of matrix U.
/// If this parameter is set, it must be not null. It might be an empty array. On return
/// it will be set to a physical array accordingly.</param>
/// <param name="V">right singular vectors of X as rows of matrix V.
/// If this parameter is set, it must be not null. It might be an empty array. On return
/// it will be set to a physical array accordingly.</param>
/// <param name="small">if true: return only first min(M,N) columns of U and S will be
/// of size [min(M,N),min(M,N)]</param>
/// <param name="discardFiniteTest">if true: the matrix given will not be checked for infinte or NaN values. If such elements
/// are contained nevertheless, this may result in failing convergence or error. In worst case
/// the function may hang inside the Lapack lib. Use with care! </param>
/// <returns>singluar values as diagonal matrix of same size as X</returns>
/// <remarks>the right singular vectors V will be returned as reference array.</remarks>
public static /*!HC:outClsS*/ ILArray <double> svd(/*!HC:inCls1*/ ILArray <double> X, ref /*!HC:outClsU*/ ILArray <double> U, ref /*!HC:outClsV*/ ILArray <double> V, bool small, bool discardFiniteTest)
{
if (!X.IsMatrix)
{
throw new ILArgumentSizeException("svd is defined for matrices only!");
}
// early exit for small matrices
if (X.Dimensions[1] < 4 && X.Dimensions[0] == X.Dimensions[1])
{
switch (X.Dimensions[0])
{
case 1:
if (!Object.Equals(U, null))
{
U = (/*!HC:outArrU*/ double )1.0;
}
if (!Object.Equals(V, null))
{
V = (/*!HC:outArrV*/ double )1.0;
}
return(new /*!HC:outClsS*/ ILArray <double> (ILMath.abs(X)));
//case 2:
// return -1;
//case 3:
// return -1;
}
}
if (!discardFiniteTest && !all(all(isfinite(X))))
{
throw new ILArgumentException("svd: input must have only finite elements!");
}
if (Lapack == null)
{
throw new ILMathException("No Lapack package available.");
}
// parameter evaluation
int M = X.Dimensions[0]; int N = X.Dimensions[1];
int minMN = (M < N) ? M : N;
int LDU = M; int LDVT = N;
int LDA = M;
/*!HC:outArrS*/ double [] dS = new /*!HC:outArrS*/ double [minMN];
char jobz = (small) ? 'S' : 'A';
/*!HC:outArrU*/ double [] dU = null;
/*!HC:outArrV*/ double [] dVT = null;
int info = 0;
if (!Object.Equals(U, null) || !Object.Equals(V, null))
{
// need to return U and VT
if (small)
{
dU = new /*!HC:outArrU*/ double [M * minMN];
dVT = new /*!HC:outArrV*/ double [N * minMN];
}
else
{
dU = new /*!HC:outArrU*/ double [M * M];
dVT = new /*!HC:outArrV*/ double [N * N];
}
}
else
{
jobz = 'N';
}
// must create copy of input !
/*!HC:inArr1*/ double [] dInput = new /*!HC:inArr1*/ double [X.m_data.Length];
System.Array.Copy(X.m_data, dInput, X.m_data.Length);
/*!HC:lapack_dgesdd*/
Lapack.dgesdd(jobz, M, N, dInput, LDA, dS, dU, LDU, dVT, LDVT, ref info);
if (info < 0)
{
throw new ILArgumentException("ILMath.svd: the " + (-info).ToString() + "th argument was invalid.");
}
if (info > 0)
{
throw new ILArgumentException("svd was not converging!");
}
/*!HC:outClsS*/ ILArray <double> ret = null;
if (info == 0)
{
// success
if (!Object.Equals(U, null) || !Object.Equals(V, null))
{
if (small)
{
ret = /*!HC:outClsS*/ ILArray <double> .zeros(minMN, minMN);
}
else
{
ret = /*!HC:outClsS*/ ILArray <double> .zeros(M, N);
}
for (int i = 0; i < minMN; i++)
{
ret.SetValue(dS[i], i, i);
}
if (!Object.Equals(U, null))
{
U = new /*!HC:outClsU*/ ILArray <double> (dU, M, dU.Length / M);
}
if (!Object.Equals(V, null))
{
/*!HC:complxConj*/
V = new ILArray <double> (dVT, N, dVT.Length / N).T;
}
}
else
{
ret = new /*!HC:outClsS*/ ILArray <double> (dS, minMN, 1);
}
}
return(ret);
}
/// <summary>
/// QR decomposition, returning Q and R, optionally economical sized
/// </summary>
/// <param name="A">general input matrix A of size [m x n]</param>
/// <param name="R">output parameter. Upper triangular matrix R as
/// result of decomposition. Size [m x n] or [min(m,n) x n] (see remarks). </param>
/// <param name="economySize">if true, the size of Q and R will
/// be [m x m] and [m x n] respectively. However, if m < n,
/// the economySize parameter has no effect. </param>
/// <returns>Orthonormal real / unitary complex matrix Q as result
/// of decomposition. Size [m x m] or [m x min(m,n)], depending
/// on <paramref name="economySize"/> (see remarks below)</returns>
/// <remarks>The function returns Q and R such that the equation
/// <para>A = Q * R</para> holds with roundoff errors. ('*'
/// denotes matrix multiplication.)
/// <para>Q and R will be solid ILArray's.</para></remarks>
public static /*!HC:inCls1*/ ILArray<double> qr(
/*!HC:inCls1*/ ILArray<double> A,
ref /*!HC:inCls1*/ ILArray<double> R, bool economySize) {
if (Object.Equals(R,null)) {
return qr(A);
}
int m = A.Dimensions[0];
int n = A.Dimensions[1];
if (m < n && economySize) return qr(A,ref R, false);
/*!HC:inCls1*/ ILArray<double> ret;
if (m == 0 || n == 0) {
R = new /*!HC:inCls1*/ ILArray<double> (new /*!HC:inArr1*/ double [0],m,n);
return /*!HC:inCls1*/ ILArray<double> .empty(A.Dimensions);
}
int minMN = (m<n)?m:n;
int info = 0;
/*!HC:inArr1*/ double [] tau = new /*!HC:inArr1*/ double [minMN];
/*!HC:inArr1*/ double [] QArr;
if (m >= n) {
ret = new /*!HC:inCls1*/ ILArray<double> (
new /*!HC:inArr1*/ double [(economySize)? minMN * m : m * m],
m,(economySize)? minMN: m);
} else {
// economySize is always false ... !
// a temporary array is needed for extraction of the compact lapack Q (?geqrf)
ret = new /*!HC:inCls1*/ ILArray<double> (
new /*!HC:inArr1*/ double [m * n],m,n);
}
QArr = ret.m_data;
for (int i = m*n; i-->0;) {
QArr[i] = A.GetValue(i);
}
/*!HC:lapack_*geqrf*/ Lapack.dgeqrf (m,n,QArr,m,tau,ref info);
if (info != 0) {
throw new ILArgumentException("qr: error inside lapack library (?geqrf). info=" + info.ToString());
}
// extract R, Q
if (economySize) {
R = copyUpperTriangle(QArr,m,n,minMN);
/*!HC:lapack_*orgqr*/ Lapack.dorgqr (m,minMN,tau.Length,QArr,m,tau,ref info);
} else {
R = copyUpperTriangle(QArr,m,n,m);
/*!HC:lapack_*orgqr*/ Lapack.dorgqr (m,m,tau.Length,QArr,m,tau,ref info);
if (m < n)
ret = ret[":;0:" + (m-1)];
}
if (info != 0)
throw new ILArgumentException("qr: error in lapack library (???gqr). info=" + info.ToString());
return ret;
}
/// <summary>
/// QR decomposition with pivoting, possibly economical sized
/// </summary>
/// <param name="A">general input matrix A of size [m x n]</param>
/// <param name="R">output parameter. Upper triangular matrix R as
/// result of decomposition. Size [m x n] or [min(m,n) x n] depending
/// on <paramref name="economySize"/> (see remarks). </param>
/// <param name="economySize"><para>if true, <list type="bullet">
/// <item>the size of Q and R will be [m x m] and [m x n] respectively.
/// However, if m < n, the economySize parameter has no effect on
/// those sizes.</item>
/// <item>the output parameter E will be returned as row permutation
/// vector rather than as permutation matrix</item></list></para>
/// <para>if false, this function acts exactly as its overload
/// <see cref="ILNumerics.BuiltInFunctions.ILMath.qr(ILArray<double>,ref ILArray<double>,ref ILArray<double>)"/></para>
/// </param>
/// <param name="E">permutation matrix from pivoting. Size [m x m].
/// If this is not null, the permutation matrix/ vector E will be returned.
/// <para>E is of size [n x n], if <paramref name="economySize"/> is
/// true, a row vector of length n otherwise</para></param>
/// <returns>Orthonormal / unitary matrix Q as result of decomposition.
/// Size [m x m] or [m x min(m,n)], depending on <paramref name="economySize"/>
/// (see remarks below)</returns>
/// <remarks><para> If <paramref name="economySize"/> is false, the function
/// returns Q, R and E such that the equation A * E = Q * R holds except
/// roundoff errors. </para>
/// <para>If <paramref name="economySize"/> is true, E will be a permutation
/// vector and the equation A[null,E] == Q * R holds (except roundoff).</para>
/// <para>E reflects the pivoting of A done inside LAPACK in order to give R
/// increasingly diagonal elements.</para>
/// <para>Q, R and E will be solid ILArray's.</para></remarks>
public static /*!HC:inCls1*/ ILArray<double> qr(
/*!HC:inCls1*/ ILArray<double> A,
ref /*!HC:inCls1*/ ILArray<double> R,
ref /*!HC:inCls1*/ ILArray<double> E,
bool economySize) {
if (Object.Equals(R,null)) {
return qr(A);
}
int m = A.Dimensions[0];
int n = A.Dimensions[1];
if (m < n && economySize) return qr(A,ref R, false);
/*!HC:inCls1*/ ILArray<double> ret;
if (m == 0 || n == 0) {
R = new /*!HC:inCls1*/ ILArray<double> (new /*!HC:inArr1*/ double [0],m,n);
E = new /*!HC:inCls1*/ ILArray<double> (new /*!HC:inArr1*/ double [0],1,0);
return /*!HC:inCls1*/ ILArray<double> .empty(A.Dimensions);
}
// prepare IPVT
if (object.Equals(E,null))
return qr(A,ref R,economySize);
if (!economySize) {
E = new /*!HC:inCls1*/ ILArray<double> (new /*!HC:inArr1*/ double [n * n],n,n);
} else {
E = new /*!HC:inCls1*/ ILArray<double> (new /*!HC:inArr1*/ double [n],1,n);
}
int [] ipvt = new int[n];
int minMN = (m<n)?m:n;
int info = 0;
/*!HC:inArr1*/ double [] tau = new /*!HC:inArr1*/ double [minMN];
/*!HC:inArr1*/ double [] QArr;
if (m >= n) {
ret = new /*!HC:inCls1*/ ILArray<double> (
new /*!HC:inArr1*/ double [(economySize)? minMN * m : m * m],
m,(economySize)? minMN: m);
} else {
// economySize is always false ... !
// a temporary array is needed for extraction of the compact lapack Q (?geqrf)
ret = new /*!HC:inCls1*/ ILArray<double> (
new /*!HC:inArr1*/ double [m * n],m,n);
}
QArr = ret.m_data;
for (int i = m*n; i-->0;) {
QArr[i] = A.GetValue(i);
}
/*!HC:lapack_*geqp3*/ Lapack.dgeqp3 (m,n,QArr,m,ipvt,tau,ref info);
if (info != 0) {
throw new ILArgumentException("qr: error inside lapack library (?geqrf). info=" + info.ToString());
}
// extract R, Q
if (economySize) {
R = copyUpperTriangle(QArr,m,n,minMN);
/*!HC:lapack_*orgqr*/ Lapack.dorgqr (m,minMN,tau.Length,QArr,m,tau,ref info);
// transform E into out typed vector
for (int i = 0; i < n; i++) {
E.m_data[i] = ipvt[i] - 1;
}
} else {
R = copyUpperTriangle(QArr,m,n,m);
/*!HC:lapack_*orgqr*/ Lapack.dorgqr (m,m,tau.Length,QArr,m,tau,ref info);
if (m < n)
ret = ret[":;0:" + (m-1)];
// transform E into matrix
for (int i = 0; i < n; i++) {
E.m_data[(ipvt[i]-1) + n * i] = /*!HC:unityValNoCmplx*/ 1.0 ;
}
}
if (info != 0)
throw new ILArgumentException("qr: error in lapack library (???gqr). info=" + info.ToString());
return ret;
}
/// <summary>
/// QR decomposition - raw Lapack output
/// </summary>
/// <param name="A">general input matrix A</param>
/// <returns>orthonormal / unitary matrix Q and upper triangular
/// matrix R packed into single matrix. This is the output of the
/// lapack function ?geqrf.</returns>
/// <remarks><para>Input matrix A will not be altered. </para>
/// <para>The matrix returned is the direct output of the lapack
/// function [d,s,c,z]geqrf respectively. This mean that it contains
/// the decomposition factors Q and R, but they are cmbined into a
/// single matrix for performance reasons. If you need one of the factors,
/// you would use the overloaded function
/// <see cref="ILNumerics.BuiltInFunctions.ILMath.qr(ILArray<double>,ref ILArray<double>)"/>
/// instead, which returns those factors seperately.</para></remarks>
public static /*!HC:inCls1*/ ILArray<double> qr(/*!HC:inCls1*/ ILArray<double> A) {
if (!A.IsMatrix)
throw new ILArgumentException("qr decomposition: A must be a matrix");
int m = A.Dimensions[0], n = A.Dimensions[1];
/*!HC:inCls1*/ ILArray<double> ret = (/*!HC:inCls1*/ ILArray<double> )A.Clone();
/*!HC:inArr1*/ double [] tau = new /*!HC:inArr1*/ double [(m<n)?m:n];
int info = 0;
/*!HC:lapack_*geqrf*/ Lapack.dgeqrf (m,n,ret.m_data,m,tau,ref info);
if (info < 0)
throw new ILArgumentException("qr: an error occoured during decomposition");
return ret;
}
/// <summary>
/// QR decomposition with pivoting, possibly economical sized
/// </summary>
/// <param name="A">general input matrix A of size [m x n]</param>
/// <param name="R">output parameter. Upper triangular matrix R as
/// result of decomposition. Size [m x n] or [min(m,n) x n] depending
/// on <paramref name="economySize"/> (see remarks). </param>
/// <param name="economySize"><para>if true, <list type="bullet">
/// <item>the size of Q and R will be [m x m] and [m x n] respectively.
/// However, if m < n, the economySize parameter has no effect on
/// those sizes.</item>
/// <item>the output parameter E will be returned as row permutation
/// vector rather than as permutation matrix</item></list></para>
/// <para>if false, this function acts exactly as its overload
/// <see cref="ILNumerics.BuiltInFunctions.ILMath.qr(ILArray<double>,ref ILArray<double>,ref ILArray<double>)"/></para>
/// </param>
/// <param name="E">permutation matrix from pivoting. Size [m x m].
/// If this is not null, the permutation matrix/ vector E will be returned.
/// <para>E is of size [n x n], if <paramref name="economySize"/> is
/// true, a row vector of length n otherwise</para></param>
/// <returns>Orthonormal / unitary matrix Q as result of decomposition.
/// Size [m x m] or [m x min(m,n)], depending on <paramref name="economySize"/>
/// (see remarks below)</returns>
/// <remarks><para> If <paramref name="economySize"/> is false, the function
/// returns Q, R and E such that the equation A * E = Q * R holds except
/// roundoff errors. </para>
/// <para>If <paramref name="economySize"/> is true, E will be a permutation
/// vector and the equation A[null,E] == Q * R holds (except roundoff).</para>
/// <para>E reflects the pivoting of A done inside LAPACK in order to give R
/// increasingly diagonal elements.</para>
/// <para>Q, R and E will be solid ILArray's.</para></remarks>
public static /*!HC:inCls1*/ ILArray <double> qr(
/*!HC:inCls1*/ ILArray <double> A,
ref /*!HC:inCls1*/ ILArray <double> R,
ref /*!HC:inCls1*/ ILArray <double> E,
bool economySize)
{
if (Object.Equals(R, null))
{
return(qr(A));
}
int m = A.Dimensions[0];
int n = A.Dimensions[1];
if (m < n && economySize)
{
return(qr(A, ref R, false));
}
/*!HC:inCls1*/ ILArray <double> ret;
if (m == 0 || n == 0)
{
R = new /*!HC:inCls1*/ ILArray <double> (new /*!HC:inArr1*/ double [0], m, n);
E = new /*!HC:inCls1*/ ILArray <double> (new /*!HC:inArr1*/ double [0], 1, 0);
return /*!HC:inCls1*/ (ILArray <double> .empty(A.Dimensions));
}
// prepare IPVT
if (object.Equals(E, null))
{
return(qr(A, ref R, economySize));
}
if (!economySize)
{
E = new /*!HC:inCls1*/ ILArray <double> (new /*!HC:inArr1*/ double [n * n], n, n);
}
else
{
E = new /*!HC:inCls1*/ ILArray <double> (new /*!HC:inArr1*/ double [n], 1, n);
}
int [] ipvt = new int[n];
int minMN = (m < n)?m:n;
int info = 0;
/*!HC:inArr1*/ double [] tau = new /*!HC:inArr1*/ double [minMN];
/*!HC:inArr1*/ double [] QArr;
if (m >= n)
{
ret = new /*!HC:inCls1*/ ILArray <double> (
new /*!HC:inArr1*/ double [(economySize)? minMN * m : m * m],
m, (economySize)? minMN: m);
}
else
{
// economySize is always false ... !
// a temporary array is needed for extraction of the compact lapack Q (?geqrf)
ret = new /*!HC:inCls1*/ ILArray <double> (
new /*!HC:inArr1*/ double [m * n], m, n);
}
QArr = ret.m_data;
for (int i = m * n; i-- > 0;)
{
QArr[i] = A.GetValue(i);
}
/*!HC:lapack_*geqp3*/ Lapack.dgeqp3(m, n, QArr, m, ipvt, tau, ref info);
if (info != 0)
{
throw new ILArgumentException("qr: error inside lapack library (?geqrf). info=" + info.ToString());
}
// extract R, Q
if (economySize)
{
R = copyUpperTriangle(QArr, m, n, minMN);
/*!HC:lapack_*orgqr*/ Lapack.dorgqr(m, minMN, tau.Length, QArr, m, tau, ref info);
// transform E into out typed vector
for (int i = 0; i < n; i++)
{
E.m_data[i] = ipvt[i] - 1;
}
}
else
{
R = copyUpperTriangle(QArr, m, n, m);
/*!HC:lapack_*orgqr*/ Lapack.dorgqr(m, m, tau.Length, QArr, m, tau, ref info);
if (m < n)
{
ret = ret[":;0:" + (m - 1)];
}
// transform E into matrix
for (int i = 0; i < n; i++)
{
E.m_data[(ipvt[i] - 1) + n * i] = /*!HC:unityValNoCmplx*/ 1.0;
}
}
if (info != 0)
{
throw new ILArgumentException("qr: error in lapack library (???gqr). info=" + info.ToString());
}
return(ret);
}
/// <summary>
/// QR decomposition, returning Q and R, optionally economical sized
/// </summary>
/// <param name="A">general input matrix A of size [m x n]</param>
/// <param name="R">output parameter. Upper triangular matrix R as
/// result of decomposition. Size [m x n] or [min(m,n) x n] (see remarks). </param>
/// <param name="economySize">if true, the size of Q and R will
/// be [m x m] and [m x n] respectively. However, if m < n,
/// the economySize parameter has no effect. </param>
/// <returns>Orthonormal real / unitary complex matrix Q as result
/// of decomposition. Size [m x m] or [m x min(m,n)], depending
/// on <paramref name="economySize"/> (see remarks below)</returns>
/// <remarks>The function returns Q and R such that the equation
/// <para>A = Q * R</para> holds with roundoff errors. ('*'
/// denotes matrix multiplication.)
/// <para>Q and R will be solid ILArray's.</para></remarks>
public static /*!HC:inCls1*/ ILArray <double> qr(
/*!HC:inCls1*/ ILArray <double> A,
ref /*!HC:inCls1*/ ILArray <double> R, bool economySize)
{
if (Object.Equals(R, null))
{
return(qr(A));
}
int m = A.Dimensions[0];
int n = A.Dimensions[1];
if (m < n && economySize)
{
return(qr(A, ref R, false));
}
/*!HC:inCls1*/ ILArray <double> ret;
if (m == 0 || n == 0)
{
R = new /*!HC:inCls1*/ ILArray <double> (new /*!HC:inArr1*/ double [0], m, n);
return /*!HC:inCls1*/ (ILArray <double> .empty(A.Dimensions));
}
int minMN = (m < n)?m:n;
int info = 0;
/*!HC:inArr1*/ double [] tau = new /*!HC:inArr1*/ double [minMN];
/*!HC:inArr1*/ double [] QArr;
if (m >= n)
{
ret = new /*!HC:inCls1*/ ILArray <double> (
new /*!HC:inArr1*/ double [(economySize)? minMN * m : m * m],
m, (economySize)? minMN: m);
}
else
{
// economySize is always false ... !
// a temporary array is needed for extraction of the compact lapack Q (?geqrf)
ret = new /*!HC:inCls1*/ ILArray <double> (
new /*!HC:inArr1*/ double [m * n], m, n);
}
QArr = ret.m_data;
for (int i = m * n; i-- > 0;)
{
QArr[i] = A.GetValue(i);
}
/*!HC:lapack_*geqrf*/ Lapack.dgeqrf(m, n, QArr, m, tau, ref info);
if (info != 0)
{
throw new ILArgumentException("qr: error inside lapack library (?geqrf). info=" + info.ToString());
}
// extract R, Q
if (economySize)
{
R = copyUpperTriangle(QArr, m, n, minMN);
/*!HC:lapack_*orgqr*/ Lapack.dorgqr(m, minMN, tau.Length, QArr, m, tau, ref info);
}
else
{
R = copyUpperTriangle(QArr, m, n, m);
/*!HC:lapack_*orgqr*/ Lapack.dorgqr(m, m, tau.Length, QArr, m, tau, ref info);
if (m < n)
{
ret = ret[":;0:" + (m - 1)];
}
}
if (info != 0)
{
throw new ILArgumentException("qr: error in lapack library (???gqr). info=" + info.ToString());
}
return(ret);
}
/*!HC:TYPELIST:
<hycalper>
<type>
<source locate="after">
inArr1
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
inArr2
</source>
<destination>double</destination>
</type>
<type>
<source locate="after">
dllfunc
</source>
<destination>zgelsd </destination>
</type>
<type>
<source locate="after">
dll1func
</source>
<destination>lapack_zgeqrf</destination>
</type>
<type>
<source locate="after">
lapack_?gelsd
</source>
<destination>lapack_zgelsd</destination>
</type>
<type>
<source locate="nextline">
HycalpTag1
</source>
<destination>double [] rwork = new double [1]; lapack_zgelsd (ref m, ref n, ref nrhs, A, ref lda, B, ref ldb, S,ref RCond, ref rank, work, ref lwork, rwork, iwork, ref info);</destination>
</type>
<type>
<source locate="nextline">
HycalpTag2
</source>
<destination>rwork = new double [(int)rwork[0]]; lapack_zgelsd (ref m, ref n, ref nrhs, A, ref lda, B, ref ldb, S,ref RCond, ref rank, work, ref lwork, rwork, iwork, ref info);</destination>
</type>
</hycalper>
*/
public void /*!HC:dllfunc*/ dgelsd (int m, int n, int nrhs, /*!HC:inArr1*/ double [] A, int lda, /*!HC:inArr1*/ double [] B, int ldb, /*!HC:inArr2*/ double [] S, /*!HC:inArr2*/ double RCond, ref int rank, ref int info) {
/*!HC:inArr1*/ double [] work = new /*!HC:inArr1*/ double [1];
int [] iwork = new int[1];
int lwork = -1;
/*HC:HycalpTag1*/
lapack_dgelsd (ref m, ref n, ref nrhs, A, ref lda, B, ref ldb, S,ref RCond, ref rank, work, ref lwork, iwork, ref info);
if (info != 0)
throw new ILArgumentException("dgelsd: invalid parameter: #" + (-info).ToString());
lwork = ILAENV(9, "dgelsd", " ",0,0,0,0);
if (lwork <= 0)
throw new ILArgumentException("dgelsd: unknown error determining working size liwork");
iwork = new int[lwork];
lwork = (int)work[0];
work = new /*!HC:inArr1*/ double [lwork];
/*HC:HycalpTag2*/
lapack_dgelsd (ref m, ref n, ref nrhs, A, ref lda, B, ref ldb, S,ref RCond, ref rank, work, ref lwork, iwork, ref info);
}
// DO NOT EDIT INSIDE THIS REGION !! CHANGES WILL BE LOST !!
#endregion HYCALPER AUTO GENERATED CODE
#region HYCALPER LOOPSTART Matrix_multiply
/*!HC:TYPELIST:
* <hycalper>
* <type>
* <source locate="after">
* inArr1
* </source>
* <destination>complex</destination>
* </type>
* <type>
* <source locate="after">
* inArr2
* </source>
* <destination>complex</destination>
* </type>
* <type>
* <source locate="after">
* outArr1
* </source>
* <destination>complex</destination>
* </type>
* <type>
* <source locate="after">
* inCls1
* </source>
* <destination><![CDATA[ILArray<complex>]]></destination>
* </type>
* <type>
* <source locate="after">
* inCls2
* </source>
* <destination><![CDATA[ILArray<complex>]]></destination>
* </type>
* <type>
* <source locate="after">
* outCls1
* </source>
* <destination><![CDATA[ILArray<complex>]]></destination>
* </type>
* <type>
* <source locate="after">
* lapackfunc
* </source>
* <destination>Lapack.zgemm</destination>
* </type>
* </hycalper>
*/
/// <summary>
/// GEneral Matrix Multiply this array
/// </summary>
/// <overloads>General Matrix Multiply for double, float, complex and fcomplex arrays</overloads>
/// <param name="A"><![CDATA[ILArray<>]]> matrix A</param>
/// <param name="B"><![CDATA[ILArray<>]]> matrix B</param>
/// <returns><![CDATA[ILArray<double>]]> new array - result of matrix multiplication</returns>
/// <remarks>Both arrays must be matrices. The matrix will be multiplied only
/// if dimensions match accordingly. Therefore B's number of rows must
/// equal A's number of columns. An Exception will be thrown otherwise.
/// The multiplication will carried out on BLAS libraries, if availiable and the
/// storage memory structure meets BLAS's requirements. If not it will be done inside .NET's
/// framework 'by hand'. This is especially true for referencing storages with
/// irregular dimensions. However, even GEMM on those reference storages linking into
/// a physical storage can (an will) be carried out via BLAS dll's, if the spacing
/// into dimensions matches the requirements of BLAS. Those are:
/// <list>
/// <item>the elements of one dimension will be adjecently layed out, and</item>
/// <item>the elements of the second dimension must be regular (evenly) spaced</item>
/// </list>
/// <para>For reference arrays where the spacing between adjecent elements do not meet the
/// requirements above, the matrix multiplication will be made without optimization and
/// therefore suffer from low performance in relation to solid arrays. See <a href="http://ilnumerics.net?site=5142">online documentation: referencing for ILNumerics.Net</a></para>
/// </remarks>
/// <exception cref="ILNumerics.Exceptions.ILArgumentSizeException">if at least one arrays is not a matrix</exception>
/// <exception cref="ILNumerics.Exceptions.ILDimensionMismatchException">if the size of both matrices do not match</exception>
public static /*!HC:outCls1*/ ILArray <double> multiply(/*!HC:inCls1*/ ILArray <double> A, /*!HC:inCls2*/ ILArray <double> B)
{
/*!HC:outCls1*/ ILArray <double> ret = null;
if (A.Dimensions.NumberOfDimensions != 2 ||
B.Dimensions.NumberOfDimensions != 2)
{
throw new ILArgumentSizeException("Matrix multiply: arguments must be 2-d.");
}
if (A.Dimensions[1] != B.Dimensions[0])
{
throw new ILDimensionMismatchException("Matrix multiply: inner matrix dimensions must match.");
}
// decide wich method to use
// test auf Regelmigkeit der Dimensionen
int spacingA0;
int spacingA1;
int spacingB0;
int spacingB1;
char transA, transB;
/*!HC:inArr1*/ double [] retArr = null;
isSuitableForLapack(A, B, out spacingA0, out spacingA1, out spacingB0, out spacingB1, out transA, out transB);
if (A.m_dimensions.NumberOfElements > ILAtlasMinimumElementSize ||
B.m_dimensions.NumberOfElements > ILAtlasMinimumElementSize)
{
// do BLAS GEMM
retArr = new /*!HC:inArr1*/ double [A.m_dimensions[0] * B.m_dimensions[1]];
if (((spacingA0 == 1 && spacingA1 > int.MinValue) || (spacingA1 == 1 && spacingA0 > int.MinValue)) &&
((spacingB0 == 1 && spacingB1 > int.MinValue) || (spacingB1 == 1 && spacingB0 > int.MinValue)))
{
ret = new /*!HC:outCls1*/ ILArray <double> (retArr, new ILDimension(A.m_dimensions[0], B.m_dimensions[1]));
if (transA == 't')
{
spacingA1 = spacingA0;
}
if (transB == 't')
{
spacingB1 = spacingB0;
}
unsafe
{
fixed(/*!HC:outArr1*/ double *ptrC = retArr)
fixed(/*!HC:inArr1*/ double *pA = A.m_data)
fixed(/*!HC:inArr2*/ double *pB = B.m_data)
{
/*!HC:inArr1*/ double *ptrA = pA + A.getBaseIndex(0);
/*!HC:inArr2*/ double *ptrB = pB + B.getBaseIndex(0);
if (transA == 't')
{
spacingA1 = spacingA0;
}
if (transB == 't')
{
spacingB1 = spacingB0;
}
/*!HC:lapackfunc*/ Lapack.dgemm(transA, transB, A.m_dimensions[0], B.m_dimensions[1],
A.m_dimensions[1], (/*!HC:inArr1*/ double )1.0, (IntPtr)ptrA, spacingA1,
(IntPtr)ptrB, spacingB1, (/*!HC:inArr1*/ double )1.0, retArr, A.m_dimensions[0]);
}
}
return(ret);
}
}
// do GEMM by hand
retArr = new /*!HC:outArr1*/ double [A.m_dimensions[0] * B.m_dimensions[1]];
ret = new /*!HC:outCls1*/ ILArray <double> (retArr, A.m_dimensions[0], B.m_dimensions[1]);
unsafe {
int in2Len1 = B.m_dimensions[1];
int in1Len0 = A.m_dimensions[0];
int in1Len1 = A.m_dimensions[1];
fixed(/*!HC:outArr1*/ double *ptrC = retArr)
{
/*!HC:outArr1*/ double *pC = ptrC;
for (int c = 0; c < in2Len1; c++)
{
for (int r = 0; r < in1Len0; r++)
{
for (int n = 0; n < in1Len1; n++)
{
*pC += A.GetValue(r, n) * B.GetValue(n, c);
}
pC++;
}
}
}
}
return(ret);
}
/*!HC:TYPELIST:
<hycalper>
<type>
<source locate="after">
inArr1
</source>
<destination>complex</destination>
</type>
<type>
<source locate="after">
inArr2
</source>
<destination>double</destination>
</type>
<type>
<source locate="after">
dllfunc
</source>
<destination>zgelsy </destination>
</type>
<type>
<source locate="nextline">
lapack_?gelsy
</source>
<destination>lapack_zgelsy (ref m,ref n,ref nrhs,A,ref lda,B,ref ldb,JPVT0,ref RCond,ref rank,work,ref lwork, rwork, ref info);</destination>
</type>
<type>
<source locate="after">
hycalpRwork1
</source>
<destination>double[] rwork = new double[1];</destination>
</type>
<type>
<source locate="after">
hycalpRwork2
</source>
<destination>rwork = new double[lwork];</destination>
</type>
</hycalper>
*/
public void /*!HC:dllfunc*/ dgelsy (int m, int n, int nrhs, /*!HC:inArr1*/ double [] A, int lda, /*!HC:inArr1*/ double [] B, int ldb, int[] JPVT0, /*!HC:inArr2*/ double RCond, ref int rank, ref int info) {
int lwork = -1;
/*!HC:inArr1*/ double [] work = new /*!HC:inArr1*/ double [1];
/*!HC:hycalpRwork1*/ //
/*!HC:lapack_?gelsy*/
lapack_dgelsy (ref m,ref n,ref nrhs,A,ref lda,B,ref ldb,JPVT0,ref RCond,ref rank,work,ref lwork,ref info);
if (info != 0)
throw new ILArgumentException("?gelsy: unable to determine optimal block size. cancelling...");
lwork = (int) work[0];
work = new /*!HC:inArr1*/ double [lwork];
/*!HC:hycalpRwork2*/ //
/*!HC:lapack_?gelsy*/
lapack_dgelsy (ref m,ref n,ref nrhs,A,ref lda,B,ref ldb,JPVT0,ref RCond,ref rank,work,ref lwork,ref info);
}
/// <summary>
/// singular value decomposition
/// </summary>
/// <param name="X">matrix X. The elements of X will not be altered.</param>
/// <param name="U">(return value) left singular vectors of X as columns of matrix U.
/// If this parameter is set, it must be not null. It might be an empty array. On return
/// it will be set to a physical array accordingly.</param>
/// <param name="V">right singular vectors of X as rows of matrix V.
/// If this parameter is set, it must be not null. It might be an empty array. On return
/// it will be set to a physical array accordingly.</param>
/// <param name="small">if true: return only first min(M,N) columns of U and S will be
/// of size [min(M,N),min(M,N)]</param>
/// <param name="discardFiniteTest">if true: the matrix given will not be checked for infinte or NaN values. If such elements
/// are contained nevertheless, this may result in failing convergence or error. In worst case
/// the function may hang inside the Lapack lib. Use with care! </param>
/// <returns>singluar values as diagonal matrix of same size as X</returns>
/// <remarks>the right singular vectors V will be returned as reference array.</remarks>
public static /*!HC:outClsS*/ ILArray<double> svd(/*!HC:inCls1*/ ILArray<double> X, ref /*!HC:outClsU*/ ILArray<double> U, ref /*!HC:outClsV*/ ILArray<double> V, bool small, bool discardFiniteTest) {
if (!X.IsMatrix)
throw new ILArgumentSizeException("svd is defined for matrices only!");
// early exit for small matrices
if (X.Dimensions[1] < 4 && X.Dimensions[0] == X.Dimensions[1]) {
switch (X.Dimensions[0]) {
case 1:
if (!Object.Equals(U,null))
U = (/*!HC:outArrU*/ double ) 1.0;
if (!Object.Equals(V,null))
V = (/*!HC:outArrV*/ double ) 1.0;
return new /*!HC:outClsS*/ ILArray<double> ( ILMath.abs(X));
//case 2:
// return -1;
//case 3:
// return -1;
}
}
if (!discardFiniteTest && !all(all(isfinite( X ))))
throw new ILArgumentException("svd: input must have only finite elements!");
if (Lapack == null)
throw new ILMathException("No Lapack package available.");
// parameter evaluation
int M = X.Dimensions[0]; int N = X.Dimensions[1];
int minMN = (M < N) ? M : N;
int LDU = M; int LDVT = N;
int LDA = M;
/*!HC:outArrS*/ double [] dS = new /*!HC:outArrS*/ double [minMN];
char jobz = (small) ? 'S' : 'A';
/*!HC:outArrU*/ double [] dU = null;
/*!HC:outArrV*/ double [] dVT = null;
int info = 0;
if (!Object.Equals(U, null) || !Object.Equals(V, null)) {
// need to return U and VT
if (small) {
dU = new /*!HC:outArrU*/ double [M * minMN];
dVT = new /*!HC:outArrV*/ double [N * minMN];
} else {
dU = new /*!HC:outArrU*/ double [M * M];
dVT = new /*!HC:outArrV*/ double [N * N];
}
} else {
jobz = 'N';
}
if (X.IsReference) {
X.Detach();
}
// must create copy of input !
/*!HC:inArr1*/ double [] dInput = new /*!HC:inArr1*/ double [X.m_data.Length];
System.Array.Copy(X.m_data, dInput, X.m_data.Length);
/*!HC:lapack_dgesdd*/
Lapack.dgesdd(jobz, M, N, dInput, LDA, dS, dU, LDU, dVT, LDVT, ref info);
if (info < 0)
throw new ILArgumentException ("ILMath.svd: the " + (-info).ToString() +"th argument was invalid.");
if (info > 0)
throw new ILArgumentException("svd was not converging!");
/*!HC:outClsS*/ ILArray<double> ret = null;
if (info == 0) {
// success
if (!Object.Equals(U, null) || !Object.Equals(V, null)) {
if (small) {
ret = /*!HC:outClsS*/ ILArray<double> .zeros(minMN,minMN);
} else {
ret = /*!HC:outClsS*/ ILArray<double> .zeros(M, N);
}
for (int i = 0; i < minMN; i++) {
ret.SetValue(dS[i],i,i);
}
if (!Object.Equals(U, null))
U = new /*!HC:outClsU*/ ILArray<double> (dU,M,dU.Length / M);
if (!Object.Equals(V, null)) {
/*!HC:complxConj*/
V = new ILArray<double> (dVT,N,dVT.Length / N).T;
}
} else {
ret = new /*!HC:outClsS*/ ILArray<double> (dS,minMN,1);
}
}
return ret;
}
