F01 Chapter Contents : NAG Library Manual, Mark 25

Routine Name	Mark of Introduction	Purpose
F01ABF Example Text Example Data	1	nagf_matop_real_symm_posdef_inv Inverse of real symmetric positive definite matrix using iterative refinement
F01ADF Example Text Example Data	2	nagf_matop_real_symm_posdef_inv_noref Inverse of real symmetric positive definite matrix
F01BLF Example Text Example Data	5	nagf_matop_real_gen_pseudinv Pseudo-inverse and rank of real $m$ by $n$ matrix $(m \geq n)$
F01BRF Example Text Example Data	7	nagf_matop_real_gen_sparse_lu $L U$ factorization of real sparse matrix
F01BSF Example Text Example Data	7	nagf_matop_real_gen_sparse_lu_reuse $L U$ factorization of real sparse matrix with known sparsity pattern
F01BUF Example Text Example Data	7	nagf_matop_real_symm_posdef_fac $U L D L^{T} U^{T}$ factorization of real symmetric positive definite band matrix
F01BVF Example Text Example Data	7	nagf_matop_real_symm_posdef_geneig Reduction to standard form, generalized real symmetric-definite banded eigenproblem
F01CKF Example Text Example Data	2	nagf_matop_real_gen_matmul Multiplication of real matrices
F01CRF Example Text Example Data	7	nagf_matop_real_gen_trans_inplace Transposition of a real matrix
F01CTF Example Text Example Data	14	nagf_matop_real_addsub Sum or difference of two real matrices, optional scaling and transposition
F01CWF Example Text Example Data	14	nagf_matop_complex_addsub Sum or difference of two complex matrices, optional scaling and transposition
F01ECF Example Text Example Data	22	nagf_matop_real_gen_matrix_exp Real matrix exponential
F01EDF Example Text Example Data	23	nagf_matop_real_symm_matrix_exp Real symmetric matrix exponential
F01EFF Example Text Example Data	23	nagf_matop_real_symm_matrix_fun Function of a real symmetric matrix
F01EJF Example Text Example Data	24	nagf_matop_real_gen_matrix_log Real matrix logarithm
F01EKF Example Text Example Data	24	nagf_matop_real_gen_matrix_fun_std Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
F01ELF Example Text Example Data	24	nagf_matop_real_gen_matrix_fun_num Function of a real matrix (using numerical differentiation)
F01EMF Example Text Example Data	24	nagf_matop_real_gen_matrix_fun_usd Function of a real matrix (using user-supplied derivatives)
F01ENF Example Text Example Data	25	nagf_matop_real_gen_matrix_sqrt Real matrix square root
F01EPF Example Text Example Data	25	nagf_matop_real_tri_matrix_sqrt Real upper quasi-triangular matrix square root
F01EQF Example Text Example Data	25	nagf_matop_real_gen_matrix_pow General power of a real matrix
F01FCF Example Text Example Data	23	nagf_matop_complex_gen_matrix_exp Complex matrix exponential
F01FDF Example Text Example Data	23	nagf_matop_complex_herm_matrix_exp Complex Hermitian matrix exponential
F01FFF Example Text Example Data	23	nagf_matop_complex_herm_matrix_fun Function of a complex Hermitian matrix
F01FJF Example Text Example Data	24	nagf_matop_complex_gen_matrix_log Complex matrix logarithm
F01FKF Example Text Example Data	24	nagf_matop_complex_gen_matrix_fun_std Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
F01FLF Example Text Example Data	24	nagf_matop_complex_gen_matrix_fun_num Function of a complex matrix (using numerical differentiation)
F01FMF Example Text Example Data	24	nagf_matop_complex_gen_matrix_fun_usd Function of a complex matrix (using user-supplied derivatives)
F01FNF Example Text Example Data	25	nagf_matop_complex_gen_matrix_sqrt Complex matrix square root
F01FPF Example Text Example Data	25	nagf_matop_complex_tri_matrix_sqrt Complex upper triangular matrix square root
F01FQF Example Text Example Data	25	nagf_matop_complex_gen_matrix_pow General power of a complex matrix
F01GAF Example Text Example Data	24	nagf_matop_real_gen_matrix_actexp Action of a real matrix exponential on a real matrix
F01GBF Example Text Example Data	24	nagf_matop_real_gen_matrix_actexp_rcomm Action of a real matrix exponential on a real matrix (reverse communication)
F01HAF Example Text Example Data	24	nagf_matop_complex_gen_matrix_actexp Action of a complex matrix exponential on a complex matrix
F01HBF Example Text Example Data	24	nagf_matop_complex_gen_matrix_actexp_rcomm Action of a complex matrix exponential on a complex matrix (reverse communication)
F01JAF Example Text Example Data	24	nagf_matop_real_gen_matrix_cond_std Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
F01JBF Example Text Example Data	24	nagf_matop_real_gen_matrix_cond_num Condition number for a function of a real matrix (using numerical differentiation)
F01JCF Example Text Example Data	24	nagf_matop_real_gen_matrix_cond_usd Condition number for a function of a real matrix (using user-supplied derivatives)
F01JDF Example Text Example Data	25	nagf_matop_real_gen_matrix_cond_sqrt Condition number for square root of real matrix
F01JEF Example Text Example Data	25	nagf_matop_real_gen_matrix_cond_pow Condition number for real matrix power
F01JFF Example Text Example Data	25	nagf_matop_real_gen_matrix_frcht_pow Fréchet derivative of real matrix power
F01JGF Example Text Example Data	25	nagf_matop_real_gen_matrix_cond_exp Condition number for real matrix exponential
F01JHF Example Text Example Data	25	nagf_matop_real_gen_matrix_frcht_exp Fréchet derivative of real matrix exponential
F01JJF Example Text Example Data	25	nagf_matop_real_gen_matrix_cond_log Condition number for real matrix logarithm
F01JKF Example Text Example Data	25	nagf_matop_real_gen_matrix_frcht_log Fréchet derivative of real matrix logarithm
F01KAF Example Text Example Data	24	nagf_matop_complex_gen_matrix_cond_std Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
F01KBF Example Text Example Data	24	nagf_matop_complex_gen_matrix_cond_num Condition number for a function of a complex matrix (using numerical differentiation)
F01KCF Example Text Example Data	24	nagf_matop_complex_gen_matrix_cond_usd Condition number for a function of a complex matrix (using user-supplied derivatives)
F01KDF Example Text Example Data	25	nagf_matop_complex_gen_matrix_cond_sqrt Condition number for square root of complex matrix
F01KEF Example Text Example Data	25	nagf_matop_complex_gen_matrix_cond_pow Condition number for complex matrix power
F01KFF Example Text Example Data	25	nagf_matop_complex_gen_matrix_frcht_pow Fréchet derivative of complex matrix power
F01KGF Example Text Example Data	25	nagf_matop_complex_gen_matrix_cond_exp Condition number for complex matrix exponential
F01KHF Example Text Example Data	25	nagf_matop_complex_gen_matrix_frcht_exp Fréchet derivative of complex matrix exponential
F01KJF Example Text Example Data	25	nagf_matop_complex_gen_matrix_cond_log Condition number for complex matrix logarithm
F01KKF Example Text Example Data	25	nagf_matop_complex_gen_matrix_frcht_log Fréchet derivative of complex matrix logarithm
F01LEF Example Text Example Data	11	nagf_matop_real_gen_tridiag_lu $L U$ factorization of real tridiagonal matrix
F01LHF Example Text Example Data	13	nagf_matop_real_gen_blkdiag_lu $L U$ factorization of real almost block diagonal matrix
F01MCF Example Text Example Data	8	nagf_matop_real_vband_posdef_fac $L D L^{T}$ factorization of real symmetric positive definite variable-bandwidth matrix
F01QGF Example Text Example Data	14	nagf_matop_real_trapez_rq $R Q$ factorization of real $m$ by $n$ upper trapezoidal matrix $(m \leq n)$
F01QJF Example Text Example Data	14	nagf_matop_real_gen_rq $R Q$ factorization of real $m$ by $n$ matrix $(m \leq n)$
F01QKF Example Text Example Data	14	nagf_matop_real_gen_rq_formq Operations with orthogonal matrices, form rows of $Q$ , after $R Q$ factorization by F01QJF
F01RGF Example Text Example Data	14	nagf_matop_complex_trapez_rq $R Q$ factorization of complex $m$ by $n$ upper trapezoidal matrix $(m \leq n)$
F01RJF Example Text Example Data	14	nagf_matop_complex_gen_rq $R Q$ factorization of complex $m$ by $n$ matrix $(m \leq n)$
F01RKF Example Text Example Data	14	nagf_matop_complex_gen_rq_formq Operations with unitary matrices, form rows of $Q$ , after $R Q$ factorization by F01RJF
F01VAF (DTRTTP) Example Text Example Data	23	DTRTTP nagf_matop_dtrttp Copies a real triangular matrix from full format to packed format
F01VBF (ZTRTTP) Example Text Example Data	23	ZTRTTP nagf_matop_ztrttp Copies a complex triangular matrix from full format to packed format
F01VCF (DTPTTR) Example Text Example Data	23	DTPTTR nagf_matop_dtpttr Copies a real triangular matrix from packed format to full format
F01VDF (ZTPTTR) Example Text Example Data	23	ZTPTTR nagf_matop_ztpttr Copies a complex triangular matrix from packed format to full format
F01VEF (DTRTTF) Example Text Example Data	23	DTRTTF nagf_matop_dtrttf Copies a real triangular matrix from full format to Rectangular Full Packed format
F01VFF (ZTRTTF) Example Text Example Data	23	ZTRTTF nagf_matop_ztrttf Copies a complex triangular matrix from full format to Rectangular Full Packed format
F01VGF (DTFTTR) Example Text Example Data	23	DTFTTR nagf_matop_dtfttr Copies a real triangular matrix from Rectangular Full Packed format to full format
F01VHF (ZTFTTR) Example Text Example Data	23	ZTFTTR nagf_matop_ztfttr Copies a complex triangular matrix from Rectangular Full Packed format to full format
F01VJF (DTPTTF) Example Text Example Data	23	DTPTTF nagf_matop_dtpttf Copies a real triangular matrix from packed format to Rectangular Full Packed format
F01VKF (ZTPTTF) Example Text Example Data	23	ZTPTTF nagf_matop_ztpttf Copies a complex triangular matrix from packed format to Rectangular Full Packed format
F01VLF (DTFTTP) Example Text Example Data	23	DTFTTP nagf_matop_dtfttp Copies a real triangular matrix from Rectangular Full Packed format to packed format
F01VMF (ZTFTTP) Example Text Example Data	23	ZTFTTP nagf_matop_ztfttp Copies a complex triangular matrix from Rectangular Full Packed format to packed format
F01ZAF Example Text Example Data	14	nagf_matop_real_tri_pack Convert real matrix between packed triangular and square storage formats
F01ZBF Example Text Example Data	14	nagf_matop_complex_tri_pack Convert complex matrix between packed triangular and square storage formats
F01ZCF Example Text Example Data	14	nagf_matop_real_band_pack Convert real matrix between packed banded and rectangular storage formats
F01ZDF Example Text Example Data	14	nagf_matop_complex_band_pack Convert complex matrix between packed banded and rectangular storage formats

NAG Library Chapter Contents

F01 – Matrix Operations, Including Inversion

F01 Chapter Introduction

NAG Library Chapter ContentsF01 – Matrix Operations, Including Inversion

F01 Chapter Introduction

NAG Library Chapter Contents

F01 – Matrix Operations, Including Inversion