ClassesClasses | | Operators

invert_matrix_modinvert_matrix_modInvertMatrixModInvertMatrixMod (Operator)

Name

invert_matrix_modinvert_matrix_modInvertMatrixModInvertMatrixMod — Invert a matrix.

Signature

invert_matrix_mod( : : MatrixID, MatrixType, Epsilon : )

Herror invert_matrix_mod(const Hlong MatrixID, const char* MatrixType, double Epsilon)

Herror T_invert_matrix_mod(const Htuple MatrixID, const Htuple MatrixType, const Htuple Epsilon)

void InvertMatrixMod(const HTuple& MatrixID, const HTuple& MatrixType, const HTuple& Epsilon)

void HMatrix::InvertMatrixMod(const HString& MatrixType, double Epsilon) const

void HMatrix::InvertMatrixMod(const char* MatrixType, double Epsilon) const

static void HOperatorSet.InvertMatrixMod(HTuple matrixID, HTuple matrixType, HTuple epsilon)

void HMatrix.InvertMatrixMod(string matrixType, double epsilon)

Description

The operator invert_matrix_modinvert_matrix_modInvertMatrixModInvertMatrixModInvertMatrixMod computes the inverse of the MatrixMatrixMatrixMatrixmatrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDmatrixID. The input matrix is overwritten with the result. Access to the elements of the matrix is possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix.

For EpsilonEpsilonEpsilonEpsilonepsilon = 0, the inverse is computed. The type of the MatrixMatrixMatrixMatrixmatrix can be selected via MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType. The following values are supported: 'general'"general""general""general""general" for general, 'symmetric'"symmetric""symmetric""symmetric""symmetric" for symmetric, 'positive_definite'"positive_definite""positive_definite""positive_definite""positive_definite" for symmetric positive definite, 'tridiagonal'"tridiagonal""tridiagonal""tridiagonal""tridiagonal" for tridiagonal, 'upper_triangular'"upper_triangular""upper_triangular""upper_triangular""upper_triangular" for upper triangular, 'permuted_upper_triangular'"permuted_upper_triangular""permuted_upper_triangular""permuted_upper_triangular""permuted_upper_triangular" for permuted upper triangular, 'lower_triangular'"lower_triangular""lower_triangular""lower_triangular""lower_triangular" for lower triangular, and 'permuted_lower_triangular'"permuted_lower_triangular""permuted_lower_triangular""permuted_lower_triangular""permuted_lower_triangular" for permuted lower triangular matrices.

Example 1:

Example 2:

Example 3:

For EpsilonEpsilonEpsilonEpsilonepsilon > 0, the pseudo inverse is computed using a singular value decomposition (SVD). During the computation, all singular values less than the value EpsilonEpsilonEpsilonEpsilonepsilon * the largest singular value are set to 0. For these values no internal division is done to prevent a division by zero. If a square matrix is computed with the SVD algorithm the computation takes more time. The type of the matrix must be set to MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'general'"general""general""general""general".

Example:

Note: The relative accuracy of the floating point representation of the used data type (double) is EpsilonEpsilonEpsilonEpsilonepsilon = 2.2204e-16.

It should be also 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.

Attention

For MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'symmetric'"symmetric""symmetric""symmetric""symmetric", 'positive_definite'"positive_definite""positive_definite""positive_definite""positive_definite", or 'upper_triangular'"upper_triangular""upper_triangular""upper_triangular""upper_triangular" the upper triangular part of the input MatrixMatrixMatrixMatrixmatrix must contain the relevant information of the matrix. The strictly lower triangular part of the matrix is not referenced. For MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'lower_triangular'"lower_triangular""lower_triangular""lower_triangular""lower_triangular" the lower triangular part of the input MatrixMatrixMatrixMatrixmatrix must contain the relevant information of the matrix. The strictly upper triangular part of the matrix is not referenced. For MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'tridiagonal'"tridiagonal""tridiagonal""tridiagonal""tridiagonal", only the main diagonal, the superdiagonal, and the subdiagonal of the input MatrixMatrixMatrixMatrixmatrix are used. The other parts of the matrix are not referenced. If the referenced part of the input MatrixMatrixMatrixMatrixmatrix is not of the specified type, an exception is raised.

invert_matrix_modinvert_matrix_modInvertMatrixModInvertMatrixModInvertMatrixMod modifies the content of an already existing matrix.

Execution Information

This operator modifies the state of the following input parameter:

The value of this parameter may not be shared across multiple threads without external synchronization.

Parameters

MatrixIDMatrixIDMatrixIDMatrixIDmatrixID (input_control, state is modified)  matrix HMatrix, HTupleHTupleHtuple (integer) (IntPtr) (Hlong) (Hlong)

Matrix handle of the input matrix.

MatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

The type of the input matrix.

Default value: 'general' "general" "general" "general" "general"

List of values: 'general'"general""general""general""general", 'lower_triangular'"lower_triangular""lower_triangular""lower_triangular""lower_triangular", 'permuted_lower_triangular'"permuted_lower_triangular""permuted_lower_triangular""permuted_lower_triangular""permuted_lower_triangular", 'permuted_upper_triangular'"permuted_upper_triangular""permuted_upper_triangular""permuted_upper_triangular""permuted_upper_triangular", 'positive_definite'"positive_definite""positive_definite""positive_definite""positive_definite", 'symmetric'"symmetric""symmetric""symmetric""symmetric", 'tridiagonal'"tridiagonal""tridiagonal""tridiagonal""tridiagonal", 'upper_triangular'"upper_triangular""upper_triangular""upper_triangular""upper_triangular"

EpsilonEpsilonEpsilonEpsilonepsilon (input_control)  real HTupleHTupleHtuple (real) (double) (double) (double)

Type of inversion.

Default value: 0.0

Suggested values: 0.0, 2.2204e-16

Result

If the parameters are valid, the operator invert_matrix_modinvert_matrix_modInvertMatrixModInvertMatrixModInvertMatrixMod returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.

Possible Predecessors

create_matrixcreate_matrixCreateMatrixCreateMatrixCreateMatrix

Possible Successors

get_full_matrixget_full_matrixGetFullMatrixGetFullMatrixGetFullMatrix, get_value_matrixget_value_matrixGetValueMatrixGetValueMatrixGetValueMatrix

Alternatives

invert_matrixinvert_matrixInvertMatrixInvertMatrixInvertMatrix

See also

transpose_matrixtranspose_matrixTransposeMatrixTransposeMatrixTransposeMatrix, transpose_matrix_modtranspose_matrix_modTransposeMatrixModTransposeMatrixModTransposeMatrixMod

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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