Operator Reference

HALCON Operator Reference / Matrix / Decomposition

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svd_matrixT_svd_matrixSvdMatrixSvdMatrixsvd_matrix (Operator)

svd_matrixT_svd_matrixSvdMatrixSvdMatrixsvd_matrix — Compute the singular value decomposition of a matrix.

Signature

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

HMatrix HMatrix::SvdMatrix(const wchar_t* SVDType, const wchar_t* ComputeSingularVectors, HMatrix* MatrixSID, HMatrix* MatrixVID) const   ( Windows only)

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)

def svd_matrix(matrix_id: HHandle, svdtype: str, compute_singular_vectors: str) -> Tuple[HHandle, HHandle, HHandle]

Description

The operator svd_matrixsvd_matrixSvdMatrixSvdMatrixsvd_matrix computes a full or reduced singular value decomposition (SVD) of the Matrix defined by the matrix handle MatrixIDMatrixIDMatrixIDmatrixIDmatrix_id. The operator returns the matrix handle MatrixSIDMatrixSIDMatrixSIDmatrixSIDmatrix_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 MatrixUIDMatrixUIDMatrixUIDmatrixUIDmatrix_uid and MatrixVIDMatrixVIDMatrixVIDmatrixVIDmatrix_vid are returned. Access to the elements of the matrices is possible e.g., with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixget_full_matrix. The SVD is written

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

Example:

SVDTypeSVDTypeSVDTypeSVDTypesvdtype = 'full'"full""full""full""full", ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'both'"both""both""both""both"

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

Example:

SVDTypeSVDTypeSVDTypeSVDTypesvdtype = 'reduced'"reduced""reduced""reduced""reduced", ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'both'"both""both""both""both"

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

For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = '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:

SVDTypeSVDTypeSVDTypeSVDTypesvdtype = 'reduced'"reduced""reduced""reduced""reduced" or 'full'"full""full""full""full", ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'none'"none""none""none""none"

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

MatrixIDMatrixIDMatrixIDmatrixIDmatrix_id (input_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle of the input matrix.

SVDTypeSVDTypeSVDTypeSVDTypesvdtype (input_control)  string → HTuplestrHTupleHtuple (string) (string) (HString) (char*)

Type of computation.

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

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

ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors (input_control)  string → HTuplestrHTupleHtuple (string) (string) (HString) (char*)

Computation of singular values.

Default: '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"

MatrixUIDMatrixUIDMatrixUIDmatrixUIDmatrix_uid (output_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle with the left singular vectors.

MatrixSIDMatrixSIDMatrixSIDmatrixSIDmatrix_sid (output_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle with singular values.

MatrixVIDMatrixVIDMatrixVIDmatrixVIDmatrix_vid (output_control)  matrix → HMatrix, HTupleHHandleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

Matrix handle with the right singular vectors.

Result

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

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixcreate_matrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixget_full_matrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixget_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

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