F01 Chapter Contents : NAG Library Manual, Mark 26

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 (matop)
Matrix Operations, Including Inversion

NAG Library Chapter Contents

F01 (matop)Matrix Operations, Including Inversion

F01 (matop)
Matrix Operations, Including Inversion