F01 Chapter Contents : NAG Library Manual, Mark 27

Routine	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
f01dgf Example Text Example Data	27	nagf_matop_real_tri_matmul_inplace Matrix-matrix product, two real lower or upper triangular matrices
f01duf Example Text Example Data	27	nagf_matop_complex_tri_matmul_inplace Matrix-matrix product, two complex lower or upper triangular matrices
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
f01saf Example Text Example Data	27	nagf_matop_real_nmf Non-negative matrix factorization of real non-negative matrix
f01sbf Example Text Example Data	27	nagf_matop_real_nmf_rcomm Non-negative matrix factorization of real non-negative matrix (reverse communication)
f01vaf Example Text Example Data	23	dtrttp nagf_matop_dtrttp Copies a real triangular matrix from full format to packed format
f01vbf Example Text Example Data	23	ztrttp nagf_matop_ztrttp Copies a complex triangular matrix from full format to packed format
f01vcf Example Text Example Data	23	dtpttr nagf_matop_dtpttr Copies a real triangular matrix from packed format to full format
f01vdf Example Text Example Data	23	ztpttr nagf_matop_ztpttr Copies a complex triangular matrix from packed format to full format
f01vef Example Text Example Data	23	dtrttf nagf_matop_dtrttf Copies a real triangular matrix from full format to Rectangular Full Packed format
f01vff Example Text Example Data	23	ztrttf nagf_matop_ztrttf Copies a complex triangular matrix from full format to Rectangular Full Packed format
f01vgf Example Text Example Data	23	dtfttr nagf_matop_dtfttr Copies a real triangular matrix from Rectangular Full Packed format to full format
f01vhf Example Text Example Data	23	ztfttr nagf_matop_ztfttr Copies a complex triangular matrix from Rectangular Full Packed format to full format
f01vjf Example Text Example Data	23	dtpttf nagf_matop_dtpttf Copies a real triangular matrix from packed format to Rectangular Full Packed format
f01vkf Example Text Example Data	23	ztpttf nagf_matop_ztpttf Copies a complex triangular matrix from packed format to Rectangular Full Packed format
f01vlf Example Text Example Data	23	dtfttp nagf_matop_dtfttp Copies a real triangular matrix from Rectangular Full Packed format to packed format
f01vmf 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 FL InterfaceF01 (Matop)Matrix Operations, Including Inversion

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