orthogonal_decompose_matrixT_orthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixorthogonal_decompose_matrix (算子)

名称

orthogonal_decompose_matrixT_orthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixorthogonal_decompose_matrix — 对矩阵进行正交分解。

签名

描述

算子 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

示例：

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

示例：

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

示例：

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

示例：

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

示例：

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

示例：

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

示例：

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

示例：

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.

执行信息

• 多线程类型：可重入（与非独占算子并行运行）。
• 多线程作用域：全局（可从任何线程调用）。
• 未采用并行化处理。

参数

结果

如果参数有效，算子 orthogonal_decompose_matrixorthogonal_decompose_matrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixOrthogonalDecomposeMatrixorthogonal_decompose_matrix 返回值 2 ( H_MSG_TRUE )。如有必要，则抛出异常。

可能的前趋

create_matrixcreate_matrixCreateMatrixCreateMatrixCreateMatrixcreate_matrix

可能的后继

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixGetValueMatrixget_value_matrix

另见

decompose_matrixdecompose_matrixDecomposeMatrixDecomposeMatrixDecomposeMatrixdecompose_matrix, solve_matrixsolve_matrixSolveMatrixSolveMatrixSolveMatrixsolve_matrix

参考文献

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.

模块

基础

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