NAG FL Interface
F01 (Matop)
Matrix Operations, Including Inversion

F01 (Matop) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Routine
Mark of
Introduction

Purpose
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1 nagf_matop_real_symm_posdef_inv
Inverse of real symmetric positive definite matrix using iterative refinement
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2 nagf_matop_real_symm_posdef_inv_noref
Inverse of real symmetric positive definite matrix
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5 nagf_matop_real_gen_pseudinv
Pseudo-inverse and rank of real m by n matrix mn
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7 nagf_matop_real_gen_sparse_lu
LU factorization of real sparse matrix
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7 nagf_matop_real_gen_sparse_lu_reuse
LU factorization of real sparse matrix with known sparsity pattern
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7 nagf_matop_real_symm_posdef_fac
ULDLTUT factorization of real symmetric positive definite band matrix
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7 nagf_matop_real_symm_posdef_geneig
Reduction to standard form, generalized real symmetric-definite banded eigenproblem
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2 nagf_matop_real_gen_matmul
Multiplication of real matrices
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7 nagf_matop_real_gen_trans_inplace
Transposition of a real matrix
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14 nagf_matop_real_addsub
Sum or difference of two real matrices, optional scaling and transposition
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14 nagf_matop_complex_addsub
Sum or difference of two complex matrices, optional scaling and transposition
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27 nagf_matop_real_tri_matmul_inplace
Matrix-matrix product, two real lower or upper triangular matrices
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27 nagf_matop_complex_tri_matmul_inplace
Matrix-matrix product, two complex lower or upper triangular matrices
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22 nagf_matop_real_gen_matrix_exp
Real matrix exponential
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23 nagf_matop_real_symm_matrix_exp
Real symmetric matrix exponential
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23 nagf_matop_real_symm_matrix_fun
Function of a real symmetric matrix
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24 nagf_matop_real_gen_matrix_log
Real matrix logarithm
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24 nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
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24 nagf_matop_real_gen_matrix_fun_num
Function of a real matrix (using numerical differentiation)
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24 nagf_matop_real_gen_matrix_fun_usd
Function of a real matrix (using user-supplied derivatives)
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25 nagf_matop_real_gen_matrix_sqrt
Real matrix square root
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25 nagf_matop_real_tri_matrix_sqrt
Real upper quasi-triangular matrix square root
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25 nagf_matop_real_gen_matrix_pow
General power of a real matrix
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23 nagf_matop_complex_gen_matrix_exp
Complex matrix exponential
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23 nagf_matop_complex_herm_matrix_exp
Complex Hermitian matrix exponential
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23 nagf_matop_complex_herm_matrix_fun
Function of a complex Hermitian matrix
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24 nagf_matop_complex_gen_matrix_log
Complex matrix logarithm
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24 nagf_matop_complex_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
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24 nagf_matop_complex_gen_matrix_fun_num
Function of a complex matrix (using numerical differentiation)
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24 nagf_matop_complex_gen_matrix_fun_usd
Function of a complex matrix (using user-supplied derivatives)
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25 nagf_matop_complex_gen_matrix_sqrt
Complex matrix square root
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25 nagf_matop_complex_tri_matrix_sqrt
Complex upper triangular matrix square root
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25 nagf_matop_complex_gen_matrix_pow
General power of a complex matrix
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24 nagf_matop_real_gen_matrix_actexp
Action of a real matrix exponential on a real matrix
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24 nagf_matop_real_gen_matrix_actexp_rcomm
Action of a real matrix exponential on a real matrix (reverse communication)
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24 nagf_matop_complex_gen_matrix_actexp
Action of a complex matrix exponential on a complex matrix
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24 nagf_matop_complex_gen_matrix_actexp_rcomm
Action of a complex matrix exponential on a complex matrix (reverse communication)
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24 nagf_matop_real_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
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24 nagf_matop_real_gen_matrix_cond_num
Condition number for a function of a real matrix (using numerical differentiation)
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24 nagf_matop_real_gen_matrix_cond_usd
Condition number for a function of a real matrix (using user-supplied derivatives)
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25 nagf_matop_real_gen_matrix_cond_sqrt
Condition number for square root of real matrix
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25 nagf_matop_real_gen_matrix_cond_pow
Condition number for real matrix power
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25 nagf_matop_real_gen_matrix_frcht_pow
Fréchet derivative of real matrix power
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25 nagf_matop_real_gen_matrix_cond_exp
Condition number for real matrix exponential
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25 nagf_matop_real_gen_matrix_frcht_exp
Fréchet derivative of real matrix exponential
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25 nagf_matop_real_gen_matrix_cond_log
Condition number for real matrix logarithm
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25 nagf_matop_real_gen_matrix_frcht_log
Fréchet derivative of real matrix logarithm
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24 nagf_matop_complex_gen_matrix_cond_std
Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
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24 nagf_matop_complex_gen_matrix_cond_num
Condition number for a function of a complex matrix (using numerical differentiation)
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24 nagf_matop_complex_gen_matrix_cond_usd
Condition number for a function of a complex matrix (using user-supplied derivatives)
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25 nagf_matop_complex_gen_matrix_cond_sqrt
Condition number for square root of complex matrix
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25 nagf_matop_complex_gen_matrix_cond_pow
Condition number for complex matrix power
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25 nagf_matop_complex_gen_matrix_frcht_pow
Fréchet derivative of complex matrix power
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25 nagf_matop_complex_gen_matrix_cond_exp
Condition number for complex matrix exponential
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25 nagf_matop_complex_gen_matrix_frcht_exp
Fréchet derivative of complex matrix exponential
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25 nagf_matop_complex_gen_matrix_cond_log
Condition number for complex matrix logarithm
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25 nagf_matop_complex_gen_matrix_frcht_log
Fréchet derivative of complex matrix logarithm
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11 nagf_matop_real_gen_tridiag_lu
LU factorization of real tridiagonal matrix
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13 nagf_matop_real_gen_blkdiag_lu
LU factorization of real almost block diagonal matrix
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8 nagf_matop_real_vband_posdef_fac
LDLT factorization of real symmetric positive definite variable-bandwidth matrix
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14 nagf_matop_real_trapez_rq
RQ factorization of real m by n upper trapezoidal matrix mn
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14 nagf_matop_real_gen_rq
RQ factorization of real m by n matrix mn
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14 nagf_matop_real_gen_rq_formq
Operations with orthogonal matrices, form rows of Q, after RQ factorization by f01qjf
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14 nagf_matop_complex_trapez_rq
RQ factorization of complex m by n upper trapezoidal matrix mn
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14 nagf_matop_complex_gen_rq
RQ factorization of complex m by n matrix mn
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14 nagf_matop_complex_gen_rq_formq
Operations with unitary matrices, form rows of Q, after RQ factorization by f01rjf
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27 nagf_matop_real_nmf
Non-negative matrix factorization of real non-negative matrix
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27 nagf_matop_real_nmf_rcomm
Non-negative matrix factorization of real non-negative matrix (reverse communication)
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23 dtrttp
nagf_matop_dtrttp
Copies a real triangular matrix from full format to packed format
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23 ztrttp
nagf_matop_ztrttp
Copies a complex triangular matrix from full format to packed format
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23 dtpttr
nagf_matop_dtpttr
Copies a real triangular matrix from packed format to full format
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23 ztpttr
nagf_matop_ztpttr
Copies a complex triangular matrix from packed format to full format
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23 dtrttf
nagf_matop_dtrttf
Copies a real triangular matrix from full format to Rectangular Full Packed format
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23 ztrttf
nagf_matop_ztrttf
Copies a complex triangular matrix from full format to Rectangular Full Packed format
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23 dtfttr
nagf_matop_dtfttr
Copies a real triangular matrix from Rectangular Full Packed format to full format
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23 ztfttr
nagf_matop_ztfttr
Copies a complex triangular matrix from Rectangular Full Packed format to full format
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23 dtpttf
nagf_matop_dtpttf
Copies a real triangular matrix from packed format to Rectangular Full Packed format
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23 ztpttf
nagf_matop_ztpttf
Copies a complex triangular matrix from packed format to Rectangular Full Packed format
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23 dtfttp
nagf_matop_dtfttp
Copies a real triangular matrix from Rectangular Full Packed format to packed format
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23 ztfttp
nagf_matop_ztfttp
Copies a complex triangular matrix from Rectangular Full Packed format to packed format
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14 nagf_matop_real_tri_pack
Convert real matrix between packed triangular and square storage formats
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14 nagf_matop_complex_tri_pack
Convert complex matrix between packed triangular and square storage formats
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14 nagf_matop_real_band_pack
Convert real matrix between packed banded and rectangular storage formats
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14 nagf_matop_complex_band_pack
Convert complex matrix between packed banded and rectangular storage formats