Name
invert_matrixinvert_matrixInvertMatrixinvert_matrixInvertMatrixInvertMatrix — Invert a matrix.
The operator invert_matrixinvert_matrixInvertMatrixinvert_matrixInvertMatrixInvertMatrix computes the inverse of the
MatrixMatrixMatrixMatrixMatrixmatrix defined by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDMatrixIDmatrixID. A
new matrix MatrixInvMatrixInvMatrixInvMatrixInvMatrixInvmatrixInv is generated with the result and the
matrix handle MatrixInvIDMatrixInvIDMatrixInvIDMatrixInvIDMatrixInvIDmatrixInvID of this matrix is returned.
Access to the elements of the matrix is possible e.g. with the
operator get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix.
For EpsilonEpsilonEpsilonEpsilonEpsilonepsilon = 0, the inverse is computed. The type of the
MatrixMatrixMatrixMatrixMatrixmatrix can be selected via MatrixTypeMatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType. The
following values are supported: 'general'"general""general""general""general""general" for general,
'symmetric'"symmetric""symmetric""symmetric""symmetric""symmetric" for symmetric, 'positive_definite'"positive_definite""positive_definite""positive_definite""positive_definite""positive_definite" for
symmetric positive definite, 'tridiagonal'"tridiagonal""tridiagonal""tridiagonal""tridiagonal""tridiagonal" for tridiagonal,
'upper_triangular'"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""permuted_upper_triangular" for permuted upper triangular,
'lower_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""permuted_lower_triangular" for permuted lower triangular
matrices.
Example 1:
Example 2:
Example 3:
For EpsilonEpsilonEpsilonEpsilonEpsilonepsilon > 0, the pseudo inverse is computed using a
singular value decomposition (SVD). During the computation, all
singular values less than the value EpsilonEpsilonEpsilonEpsilonEpsilonepsilon *
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
MatrixTypeMatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'general'"general""general""general""general""general".
Example:
Note: The relative accuracy of the floating point representation of
the used data type (double) is EpsilonEpsilonEpsilonEpsilonEpsilonepsilon = 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.
For MatrixTypeMatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'symmetric'"symmetric""symmetric""symmetric""symmetric""symmetric",
'positive_definite'"positive_definite""positive_definite""positive_definite""positive_definite""positive_definite", or 'upper_triangular'"upper_triangular""upper_triangular""upper_triangular""upper_triangular""upper_triangular" the
upper triangular part of the input MatrixMatrixMatrixMatrixMatrixmatrix must contain
the relevant information of the matrix. The strictly lower
triangular part of the matrix is not referenced. For
MatrixTypeMatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType = 'lower_triangular'"lower_triangular""lower_triangular""lower_triangular""lower_triangular""lower_triangular" the lower
triangular part of the input MatrixMatrixMatrixMatrixMatrixmatrix must contain the
relevant information of the matrix. The strictly upper triangular
part of the matrix is not referenced. For MatrixTypeMatrixTypeMatrixTypeMatrixTypeMatrixTypematrixType =
'tridiagonal'"tridiagonal""tridiagonal""tridiagonal""tridiagonal""tridiagonal", only the main diagonal, the superdiagonal,
and the subdiagonal of the input MatrixMatrixMatrixMatrixMatrixmatrix are used. The
other parts of the matrix are not referenced. If the referenced
part of the input MatrixMatrixMatrixMatrixMatrixmatrix is not of the specified type,
an exception is raised.
- Multithreading type: reentrant (runs in parallel with non-exclusive operators).
- Multithreading scope: global (may be called from any thread).
- Processed without parallelization.
Matrix handle of the input matrix.
The type of the input matrix.
Default value:
'general'
"general"
"general"
"general"
"general"
"general"
List of values: 'general'"general""general""general""general""general", 'lower_triangular'"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_lower_triangular", 'permuted_upper_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""positive_definite", 'symmetric'"symmetric""symmetric""symmetric""symmetric""symmetric", 'tridiagonal'"tridiagonal""tridiagonal""tridiagonal""tridiagonal""tridiagonal", 'upper_triangular'"upper_triangular""upper_triangular""upper_triangular""upper_triangular""upper_triangular"
Type of inversion.
Default value: 0.0
Suggested values: 0.0, 2.2204e-16
Matrix handle with the inverse matrix.
If the parameters are valid, the operator invert_matrixinvert_matrixInvertMatrixinvert_matrixInvertMatrixInvertMatrix
returns the value 2 (H_MSG_TRUE). If necessary, an exception is raised.
create_matrixcreate_matrixCreateMatrixcreate_matrixCreateMatrixCreateMatrix
get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix,
get_value_matrixget_value_matrixGetValueMatrixget_value_matrixGetValueMatrixGetValueMatrix
invert_matrix_modinvert_matrix_modInvertMatrixModinvert_matrix_modInvertMatrixModInvertMatrixMod
transpose_matrixtranspose_matrixTransposeMatrixtranspose_matrixTransposeMatrixTransposeMatrix,
transpose_matrix_modtranspose_matrix_modTransposeMatrixModtranspose_matrix_modTransposeMatrixModTransposeMatrixMod
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.
Foundation