svd_matrixsvd_matrixSvdMatrixsvd_matrixSvdMatrixSvdMatrix (Operator)

Name

svd_matrixsvd_matrixSvdMatrixsvd_matrixSvdMatrixSvdMatrix — Compute the singular value decomposition of a matrix.

Signature

Description

The operator svd_matrixsvd_matrixSvdMatrixsvd_matrixSvdMatrixSvdMatrix computes a full or reduced singular value decomposition (SVD) of the MatrixMatrixMatrixMatrixMatrixmatrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDMatrixIDmatrixID. The operator returns the matrix handle MatrixSIDMatrixSIDMatrixSIDMatrixSIDMatrixSIDmatrixSID of the matrix MatrixSMatrixSMatrixSMatrixSMatrixSmatrixS with singular values in descending order. Optionally, the matrices MatrixUMatrixUMatrixUMatrixUMatrixUmatrixU with the left and MatrixVMatrixVMatrixVMatrixVMatrixVmatrixV with the right singular vectors are computed and the matrix handles MatrixUIDMatrixUIDMatrixUIDMatrixUIDMatrixUIDmatrixUID and MatrixVIDMatrixVIDMatrixVIDMatrixVIDMatrixVIDmatrixVID are returned. Access to the elements of the matrices is possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix. 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 ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors = 'left'"left""left""left""left""left", the matrix MatrixUMatrixUMatrixUMatrixUMatrixUmatrixU with the left singular vectors is computed. For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors = 'right'"right""right""right""right""right", the matrix MatrixVMatrixVMatrixVMatrixVMatrixVmatrixV with the right singular vectors is computed. For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors = 'both'"both""both""both""both""both", the matrices MatrixUMatrixUMatrixUMatrixUMatrixUmatrixU and MatrixVMatrixVMatrixVMatrixVMatrixVmatrixV with the left and right singular vectors are computed.

For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectors = 'none'"none""none""none""none""none", no matrices with the singular vectors are computed. The matrix MatrixSMatrixSMatrixSMatrixSMatrixSmatrixS 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.

Parallelization

• 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_matrixSvdMatrixsvd_matrixSvdMatrixSvdMatrix returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.

Possible Predecessors

create_matrixcreate_matrixCreateMatrixcreate_matrixCreateMatrixCreateMatrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix, get_value_matrixget_value_matrixGetValueMatrixget_value_matrixGetValueMatrixGetValueMatrix

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