/// <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>
/// 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;
}