orthogonal_decompose_matrixT_orthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrix (Operator)

Name

orthogonal_decompose_matrixT_orthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrix — Perform an orthogonal decomposition of a matrix.

Signature

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

The operator orthogonal_decompose_matrixorthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrix decomposes the MatrixMatrixMatrixMatrixmatrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixID. The results are stored in the two generated matrices MatrixOrthogonalMatrixOrthogonalMatrixOrthogonalMatrixOrthogonalmatrixOrthogonal and MatrixTriangularMatrixTriangularMatrixTriangularMatrixTriangularmatrixTriangular. The operator returns the matrix handles MatrixOrthogonalIDMatrixOrthogonalIDMatrixOrthogonalIDMatrixOrthogonalIDmatrixOrthogonalID and MatrixTriangularIDMatrixTriangularIDMatrixTriangularIDMatrixTriangularIDmatrixTriangularID of these two matrices. Access to the elements of the matrices is possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix.

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

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

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

  MatrixMatrixMatrixMatrixmatrix = MatrixOrthogonalMatrixOrthogonalMatrixOrthogonalMatrixOrthogonalmatrixOrthogonal * MatrixTriangularMatrixTriangularMatrixTriangularMatrixTriangularmatrixTriangular.

Example for DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionType = 'qr'"qr""qr""qr""qr" and OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesType = 'full'"full""full""full""full":

Example for DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionType = 'ql'"ql""ql""ql""ql" and OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesType = 'full'"full""full""full""full":

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

  MatrixMatrixMatrixMatrixmatrix = MatrixTriangularMatrixTriangularMatrixTriangularMatrixTriangularmatrixTriangular * MatrixOrthogonalMatrixOrthogonalMatrixOrthogonalMatrixOrthogonalmatrixOrthogonal.

Example for DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionType = 'rq'"rq""rq""rq""rq" and OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesType = 'full'"full""full""full""full":

Example for DecompositionTypeDecompositionTypeDecompositionTypeDecompositionTypedecompositionType = 'lq'"lq""lq""lq""lq" and OutputMatricesTypeOutputMatricesTypeOutputMatricesTypeOutputMatricesTypeoutputMatricesType = 'full'"full""full""full""full":

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.