svd_matrixT_svd_matrixSvdMatrixSvdMatrixsvd_matrix (算子)

名称

svd_matrixT_svd_matrixSvdMatrixSvdMatrixsvd_matrix — 计算矩阵的奇异值分解。

签名

描述

算子 svd_matrixsvd_matrixSvdMatrixSvdMatrixSvdMatrixsvd_matrix computes a full or reduced singular value decomposition (SVD) of the Matrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixIDmatrix_id. The operator returns the matrix handle MatrixSIDMatrixSIDMatrixSIDMatrixSIDmatrixSIDmatrix_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 MatrixUIDMatrixUIDMatrixUIDMatrixUIDmatrixUIDmatrix_uid and MatrixVIDMatrixVIDMatrixVIDMatrixVIDmatrixVIDmatrix_vid are returned. Access to the elements of the matrices is possible e.g., with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix。The SVD is written

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

示例：

SVDTypeSVDTypeSVDTypeSVDTypeSVDTypesvdtype = 'full'"full""full""full""full""full", ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'both'"both""both""both""both""both"

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

示例：

SVDTypeSVDTypeSVDTypeSVDTypeSVDTypesvdtype = 'reduced'"reduced""reduced""reduced""reduced""reduced", ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'both'"both""both""both""both""both"

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

For ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'none'"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).

示例：

SVDTypeSVDTypeSVDTypeSVDTypeSVDTypesvdtype = 'reduced'"reduced""reduced""reduced""reduced""reduced" or 'full'"full""full""full""full""full", ComputeSingularVectorsComputeSingularVectorsComputeSingularVectorsComputeSingularVectorscomputeSingularVectorscompute_singular_vectors = 'none'"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.

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 svd_matrixsvd_matrixSvdMatrixSvdMatrixSvdMatrixsvd_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

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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