HALCON 23.05.0.0 / HALCON Operator Reference / Matrix / Decomposition
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orthogonal_decompose_matrixT_orthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixorthogonal_decompose_matrix (Operator)

Name

orthogonal_decompose_matrixT_orthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixorthogonal_decompose_matrix — Perform an orthogonal decomposition of a matrix.

Signature

orthogonal_decompose_matrix( : : MatrixID, DecompositionType, OutputMatricesType, ComputeOrthogonal : MatrixOrthogonalID, MatrixTriangularID)

Herror T_orthogonal_decompose_matrix(const Htuple MatrixID, const Htuple DecompositionType, const Htuple OutputMatricesType, const Htuple ComputeOrthogonal, Htuple* MatrixOrthogonalID, Htuple* MatrixTriangularID)

void OrthogonalDecomposeMatrix(const HTuple& MatrixID, const HTuple& DecompositionType, const HTuple& OutputMatricesType, const HTuple& ComputeOrthogonal, HTuple* MatrixOrthogonalID, HTuple* MatrixTriangularID)

HMatrix HMatrix::OrthogonalDecomposeMatrix(const HString& DecompositionType, const HString& OutputMatricesType, const HString& ComputeOrthogonal, HMatrix* MatrixTriangularID) const

HMatrix HMatrix::OrthogonalDecomposeMatrix(const char* DecompositionType, const char* OutputMatricesType, const char* ComputeOrthogonal, HMatrix* MatrixTriangularID) const

HMatrix HMatrix::OrthogonalDecomposeMatrix(const wchar_t* DecompositionType, const wchar_t* OutputMatricesType, const wchar_t* ComputeOrthogonal, HMatrix* MatrixTriangularID) const   ( Windows only)

static void HOperatorSet.OrthogonalDecomposeMatrix(HTuple matrixID, HTuple decompositionType, HTuple outputMatricesType, HTuple computeOrthogonal, out HTuple matrixOrthogonalID, out HTuple matrixTriangularID)

HMatrix HMatrix.OrthogonalDecomposeMatrix(string decompositionType, string outputMatricesType, string computeOrthogonal, out HMatrix matrixTriangularID)

def orthogonal_decompose_matrix(matrix_id: HHandle, decomposition_type: str, output_matrices_type: str, compute_orthogonal: str) -> Tuple[HHandle, HHandle]

Description

The operator orthogonal_decompose_matrixorthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixorthogonal_decompose_matrix decomposes the Matrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixIDmatrix_id. The results are stored in the two generated matrices MatrixOrthogonal and MatrixTriangular. The operator returns the matrix handles MatrixOrthogonalIDMatrixOrthogonalIDMatrixOrthogonalIDMatrixOrthogonalIDmatrixOrthogonalIDmatrix_orthogonal_id and MatrixTriangularIDMatrixTriangularIDMatrixTriangularIDMatrixTriangularIDmatrixTriangularIDmatrix_triangular_id of these two matrices. Access to the elements of the matrices is possible e.g., with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix.

For OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'full'"full""full""full""full""full" all results of the decomposition are stored in the matrices MatrixOrthogonal and MatrixTriangular. For OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'reduced'"reduced""reduced""reduced""reduced""reduced" only a part of result elements of the matrices MatrixOrthogonal and MatrixTriangular are stored. Therefore the sizes of these matrices are smaller than for OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'full'"full""full""full""full""full".

For the parameter ComputeOrthogonalComputeOrthogonalComputeOrthogonalComputeOrthogonalcomputeOrthogonalcompute_orthogonal = 'true'"true""true""true""true""true" both output matrices are computed. For the ComputeOrthogonalComputeOrthogonalComputeOrthogonalComputeOrthogonalcomputeOrthogonalcompute_orthogonal = 'false'"false""false""false""false""false" only the matrix MatrixTriangular is computed. Thus, the runtime of the operation takes fewer time.

The type of the Matrix can be selected via the parameter DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type. For DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'qr'"qr""qr""qr""qr""qr" a QR decomposition (Quadratic/Right) or for DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'ql'"ql""ql""ql""ql""ql" a QL decomposition (Quadratic/Left) is computed. The decomposition is written as

Example:

DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'qr'"qr""qr""qr""qr""qr", OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'full'"full""full""full""full""full"

Example:

DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'qr'"qr""qr""qr""qr""qr", OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'reduced'"reduced""reduced""reduced""reduced""reduced"

Example:

DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'ql'"ql""ql""ql""ql""ql", OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'full'"full""full""full""full""full"

Example:

DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'ql'"ql""ql""ql""ql""ql", OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'reduced'"reduced""reduced""reduced""reduced""reduced"

For DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'rq'"rq""rq""rq""rq""rq" a RQ decomposition (Right/Quadratic) or for DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'lq'"lq""lq""lq""lq""lq" a LQ decomposition (Left/Quadratic) is computed. The decomposition is written as

Example:

DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'rq'"rq""rq""rq""rq""rq", OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'full'"full""full""full""full""full"

Example:

DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'rq'"rq""rq""rq""rq""rq", OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'reduced'"reduced""reduced""reduced""reduced""reduced"

Example:

DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'lq'"lq""lq""lq""lq""lq", OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'full'"full""full""full""full""full"

Example:

DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionTypedecomposition_type = 'lq'"lq""lq""lq""lq""lq", OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesTypeoutput_matrices_type = 'reduced'"reduced""reduced""reduced""reduced""reduced"

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

Execution Information

Parameters

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

Matrix handle of the input matrix.

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

Method of decomposition.

Default: 'qr' "qr" "qr" "qr" "qr" "qr"

List of values: 'lq'"lq""lq""lq""lq""lq", 'ql'"ql""ql""ql""ql""ql", 'qr'"qr""qr""qr""qr""qr", 'rq'"rq""rq""rq""rq""rq"

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

Type of output matrices.

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

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

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

Computation of the orthogonal matrix.

Default: 'true' "true" "true" "true" "true" "true"

List of values: 'false'"false""false""false""false""false", 'true'"true""true""true""true""true"

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

Matrix handle with the orthogonal part of the decomposed input matrix.

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

Matrix handle with the triangular part of the decomposed input matrix.

Result

If the parameters are valid, the operator orthogonal_decompose_matrixorthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixorthogonal_decompose_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

See also

decompose_matrixdecompose_matrixDecomposeMatrixDecomposeMatrixDecomposeMatrixdecompose_matrix, solve_matrixsolve_matrixSolveMatrixSolveMatrixSolveMatrixsolve_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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HALCON Operator Reference 23.05.0.0 Copyright © 1996-2023 MVTec Software GmbH