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 MatrixMatrixMatrixMatrixmatrixmatrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixIDmatrix_id. The operator returns the matrix handle MatrixSIDMatrixSIDMatrixSIDMatrixSIDmatrixSIDmatrix_sid of the matrix MatrixSMatrixSMatrixSMatrixSmatrixSmatrix_s with singular values in descending order. Optionally, the matrices MatrixUMatrixUMatrixUMatrixUmatrixUmatrix_u with the left and MatrixVMatrixVMatrixVMatrixVmatrixVmatrix_v 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 MatrixUMatrixUMatrixUMatrixUmatrixUmatrix_u with the left singular vectors is computed. For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'right'"right""right""right""right""right", the matrix MatrixVMatrixVMatrixVMatrixVmatrixVmatrix_v with the right singular vectors is computed. For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'both'"both""both""both""both""both", the matrices MatrixUMatrixUMatrixUMatrixUmatrixUmatrix_u and MatrixVMatrixVMatrixVMatrixVmatrixVmatrix_v 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 MatrixSMatrixSMatrixSMatrixSmatrixSmatrix_s is a matrix with n rows and one column, where the number n = min(number of rows of the input MatrixMatrixMatrixMatrixmatrixmatrix, number of columns of the input MatrixMatrixMatrixMatrixmatrixmatrix).

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