Name
pow_matrixpow_matrixPowMatrixpow_matrixPowMatrixPowMatrix — Compute the power functions of a matrix.
The operator pow_matrixpow_matrixPowMatrixpow_matrixPowMatrixPowMatrix computes the power of the input
MatrixMatrixMatrixMatrixMatrixmatrix by a constant value. The input MatrixMatrixMatrixMatrixMatrixmatrix
is given by the matrix handle MatrixIDMatrixIDMatrixIDMatrixIDMatrixIDmatrixID. The power value
is given by the parameter PowerPowerPowerPowerPowerpower. A new matrix
MatrixPowMatrixPowMatrixPowMatrixPowMatrixPowmatrixPow is generated with the result. The operator
returns the matrix handle MatrixPowIDMatrixPowIDMatrixPowIDMatrixPowIDMatrixPowIDmatrixPowID of the matrix
MatrixPowMatrixPowMatrixPowMatrixPowMatrixPowmatrixPow. Access to the elements of the matrix is
possible e.g. with the operator get_full_matrixget_full_matrixGetFullMatrixget_full_matrixGetFullMatrixGetFullMatrix.
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,
'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. The formula for the calculation of the
result is:
MatrixPower
MatrixPow = Matrix .
Example:
/ 3.0 1.0 2.0 \
Matrix = | 5.0 7.0 2.0 | Power = [ 2.0 ] MatrixType = 'general'
\ 9.0 4.0 1.0 /
/ 32.0 18.0 10.0 \
-> MatrixPow = | 68.0 62.0 26.0 |
\ 56.0 41.0 27.0 /
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. 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", 'upper_triangular'"upper_triangular""upper_triangular""upper_triangular""upper_triangular""upper_triangular"
The power.
Default value: 2.0
Suggested values: 0.1, 0.2, 0.3, 0.5, 0.7, 1.0, 1.5, 2.0, 3.0, 5.0, 10.0
Matrix handle with the raised powered matrix.
If the parameters are valid, the operator pow_matrixpow_matrixPowMatrixpow_matrixPowMatrixPowMatrix
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
pow_matrix_modpow_matrix_modPowMatrixModpow_matrix_modPowMatrixModPowMatrixMod,
eigenvalues_symmetric_matrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixeigenvalues_symmetric_matrixEigenvaluesSymmetricMatrixEigenvaluesSymmetricMatrix,
eigenvalues_general_matrixeigenvalues_general_matrixEigenvaluesGeneralMatrixeigenvalues_general_matrixEigenvaluesGeneralMatrixEigenvaluesGeneralMatrix
sqrt_matrixsqrt_matrixSqrtMatrixsqrt_matrixSqrtMatrixSqrtMatrix,
sqrt_matrix_modsqrt_matrix_modSqrtMatrixModsqrt_matrix_modSqrtMatrixModSqrtMatrixMod
Foundation