eigenvalues_general_matrixT_eigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix (算子)

名称

eigenvalues_general_matrixT_eigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix — 计算通用矩阵的特征值和可选的特征向量。

签名

描述

算子 eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_matrix computes all eigenvalues and, optionally, the left or right eigenvectors of a square, general Matrix. The matrix is defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixIDmatrix_id. The computed eigenvectors have the norm 1.

The operator generates the new matrices EigenvaluesReal and EigenvaluesImag with the real and the imaginary parts of the computed eigenvalues. Each matrix has one column and n rows, where n is the number of rows of the input Matrix. In contrast to the operator eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrix, the order of the eigenvalues is not defined. The operator returns the matrix handles EigenvaluesRealIDEigenvaluesRealIDEigenvaluesRealIDEigenvaluesRealIDeigenvaluesRealIDeigenvalues_real_id and EigenvaluesImagIDEigenvaluesImagIDEigenvaluesImagIDEigenvaluesImagIDeigenvaluesImagIDeigenvalues_imag_id. If desired, the real and imaginary parts of the computed eigenvectors are stored in the new matrices EigenvectorsReal and EigenvectorsImag. For this, the operator returns valid matrix handles EigenvectorsRealIDEigenvectorsRealIDEigenvectorsRealIDEigenvectorsRealIDeigenvectorsRealIDeigenvectors_real_id and EigenvectorsImagIDEigenvectorsImagIDEigenvectorsImagIDEigenvectorsImagIDeigenvectorsImagIDeigenvectors_imag_id.可通过算子 get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrixget_full_matrix 等方式访问该矩阵的元素。

The computation type of eigenvectors can be selected via the parameter ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors. If ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors = 'none'"none""none""none""none""none", no eigenvectors are computed. If 'left'"left""left""left""left""left" is selected, the left eigenvalues are computed. If 'right'"right""right""right""right""right" is selected, the right eigenvalues are computed.

示例：

ComputeEigenvectorsComputeEigenvectorsComputeEigenvectorsComputeEigenvectorscomputeEigenvectorscompute_eigenvectors = 'right'"right""right""right""right""right"

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 eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrixeigenvalues_general_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, get_diagonal_matrixget_diagonal_matrixGetDiagonalMatrixGetDiagonalMatrixGetDiagonalMatrixget_diagonal_matrix

另见

eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrix, generalized_eigenvalues_symmetric_matrixgeneralized_eigenvalues_symmetric_matrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixGeneralizedEigenvaluesSymmetricMatrixgeneralized_eigenvalues_symmetric_matrix, generalized_eigenvalues_general_matrixgeneralized_eigenvalues_general_matrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixGeneralizedEigenvaluesGeneralMatrixgeneralized_eigenvalues_general_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