svd_matrixT_svd_matrixSvdMatrixSvdMatrixsvd_matrix (Operator)

Name

svd_matrixT_svd_matrixSvdMatrixSvdMatrixsvd_matrix — Compute the singular value decomposition of a matrix.

Signature

Description

The operator svd_matrixsvd_matrixSvdMatrixSvdMatrixSvdMatrixsvd_matrix computes a full or reduced singular value decomposition (SVD) of the Matrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixIDmatrix_id. The operator returns the matrix handle MatrixSIDMatrixSIDMatrixSIDMatrixSIDmatrixSIDmatrix_sid of the matrix MatrixS with singular values in descending order. Optionally, the matrices MatrixU with the left and MatrixV with the right singular vectors are computed and the matrix handles MatrixUIDMatrixUIDMatrixUIDMatrixUIDmatrixUIDmatrix_uid and MatrixVIDMatrixVIDMatrixVIDMatrixVIDmatrixVIDmatrix_vid are returned. Access to the elements of the matrices is possible e.g., with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix. The SVD is written

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

Example:

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

Example:

For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'left'"left""left""left""left""left", the matrix MatrixU with the left singular vectors is computed. For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'right'"right""right""right""right""right", the matrix MatrixV with the right singular vectors is computed. For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'both'"both""both""both""both""both", the matrices MatrixU and MatrixV with the left and right singular vectors are computed.

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

Example:

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

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Processed without parallelization.

Parameters

Result

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

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixCreateMatrixcreate_matrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixGetValueMatrixget_value_matrix

References

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.

Module

Foundation