ClassesClasses | | Operators

svd_matrixsvd_matrixSvdMatrixSvdMatrix (Operator)


svd_matrixsvd_matrixSvdMatrixSvdMatrix — Compute the singular value decomposition of a matrix.


svd_matrix( : : MatrixID, SVDType, ComputeSingularVectors : MatrixUID, MatrixSID, MatrixVID)

Herror svd_matrix(const Hlong MatrixID, const char* SVDType, const char* ComputeSingularVectors, Hlong* MatrixUID, Hlong* MatrixSID, Hlong* MatrixVID)

Herror T_svd_matrix(const Htuple MatrixID, const Htuple SVDType, const Htuple ComputeSingularVectors, Htuple* MatrixUID, Htuple* MatrixSID, Htuple* MatrixVID)

void SvdMatrix(const HTuple& MatrixID, const HTuple& SVDType, const HTuple& ComputeSingularVectors, HTuple* MatrixUID, HTuple* MatrixSID, HTuple* MatrixVID)

HMatrix HMatrix::SvdMatrix(const HString& SVDType, const HString& ComputeSingularVectors, HMatrix* MatrixSID, HMatrix* MatrixVID) const

HMatrix HMatrix::SvdMatrix(const char* SVDType, const char* ComputeSingularVectors, HMatrix* MatrixSID, HMatrix* MatrixVID) const

static void HOperatorSet.SvdMatrix(HTuple matrixID, HTuple SVDType, HTuple computeSingularVectors, out HTuple matrixUID, out HTuple matrixSID, out HTuple matrixVID)

HMatrix HMatrix.SvdMatrix(string SVDType, string computeSingularVectors, out HMatrix matrixSID, out HMatrix matrixVID)


The operator svd_matrixsvd_matrixSvdMatrixSvdMatrixSvdMatrix computes a full or reduced singular value decomposition (SVD) of the MatrixMatrixMatrixMatrixmatrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixID. The operator returns the matrix handle MatrixSIDMatrixSIDMatrixSIDMatrixSIDmatrixSID of the matrix MatrixSMatrixSMatrixSMatrixSmatrixS with singular values in descending order. Optionally, the matrices MatrixUMatrixUMatrixUMatrixUmatrixU with the left and MatrixVMatrixVMatrixVMatrixVmatrixV with the right singular vectors are computed and the matrix handles MatrixUIDMatrixUIDMatrixUIDMatrixUIDmatrixUID and MatrixVIDMatrixVIDMatrixVIDMatrixVIDmatrixVID are returned. Access to the elements of the matrices is possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix. The SVD is written

For SVDTypeSVDTypeSVDTypeSVDTypeSVDType = 'full'"full""full""full""full", a full SVD is computed.


For SVDTypeSVDTypeSVDTypeSVDTypeSVDType = 'reduced'"reduced""reduced""reduced""reduced", a reduced SVD is computed.


For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors = 'left'"left""left""left""left", the matrix MatrixUMatrixUMatrixUMatrixUmatrixU with the left singular vectors is computed. For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors = 'right'"right""right""right""right", the matrix MatrixVMatrixVMatrixVMatrixVmatrixV with the right singular vectors is computed. For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors = 'both'"both""both""both""both", the matrices MatrixUMatrixUMatrixUMatrixUmatrixU and MatrixVMatrixVMatrixVMatrixVmatrixV with the left and right singular vectors are computed.

For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors = 'none'"none""none""none""none", no matrices with the singular vectors are computed. The matrix MatrixSMatrixSMatrixSMatrixSmatrixS is a matrix with n rows and one column, where the number n = min(number of rows of the input MatrixMatrixMatrixMatrixmatrix, number of columns of the input MatrixMatrixMatrixMatrixmatrix).


It should be noted that in the examples there are differences in the meaning of the values of the output matrices: If a value is shown as an integer number, e.g., 0 or 1, the value of this element is per definition this certain value. If the number is shown as a floating point number, e.g., 0.0 or 1.0, the value is computed by the operator.

Execution Information


MatrixIDMatrixIDMatrixIDMatrixIDmatrixID (input_control)  matrix HMatrix, HTupleHTupleHtuple (integer) (IntPtr) (Hlong) (Hlong)

Matrix handle of the input matrix.

SVDTypeSVDTypeSVDTypeSVDTypeSVDType (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Type of computation.

Default value: 'full' "full" "full" "full" "full"

List of values: 'full'"full""full""full""full", 'reduced'"reduced""reduced""reduced""reduced"

ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Computation of singular values.

Default value: 'both' "both" "both" "both" "both"

List of values: 'both'"both""both""both""both", 'left'"left""left""left""left", 'none'"none""none""none""none", 'right'"right""right""right""right"

MatrixUIDMatrixUIDMatrixUIDMatrixUIDmatrixUID (output_control)  matrix HMatrix, HTupleHTupleHtuple (integer) (IntPtr) (Hlong) (Hlong)

Matrix handle with the left singular vectors.

MatrixSIDMatrixSIDMatrixSIDMatrixSIDmatrixSID (output_control)  matrix HMatrix, HTupleHTupleHtuple (integer) (IntPtr) (Hlong) (Hlong)

Matrix handle with singular values.

MatrixVIDMatrixVIDMatrixVIDMatrixVIDmatrixVID (output_control)  matrix HMatrix, HTupleHTupleHtuple (integer) (IntPtr) (Hlong) (Hlong)

Matrix handle with the right singular vectors.


If the parameters are valid, the operator svd_matrixsvd_matrixSvdMatrixSvdMatrixSvdMatrix returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.

Possible Predecessors


Possible Successors

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixGetValueMatrix


David Poole: “Linear Algebra: A Modern Introduction”; Thomson; Belmont; 2006.
Gene H. Golub, Charles F. van Loan: “Matrix Computations”; The Johns Hopkins University Press; Baltimore and London; 1996.



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