F01 Chapter Contents : NAG Library Manual, Mark 28

Routine	Mark of Introduction	Purpose
f01abf	1	nagf_matop_real_symm_posdef_inv Inverse of real symmetric positive definite matrix using iterative refinement
f01adf	2	nagf_matop_real_symm_posdef_inv_noref Inverse of real symmetric positive definite matrix
f01blf	5	nagf_matop_real_gen_pseudinv Pseudo-inverse and rank of real $m \times n$ matrix $(m \geq n)$
f01brf	7	nagf_matop_real_gen_sparse_lu $L U$ factorization of real sparse matrix
f01bsf	7	nagf_matop_real_gen_sparse_lu_reuse $L U$ factorization of real sparse matrix with known sparsity pattern
f01buf	7	nagf_matop_real_symm_posdef_fac $U L D L^{T} U^{T}$ factorization of real symmetric positive definite band matrix
f01bvf	7	nagf_matop_real_symm_posdef_geneig Reduction to standard form, generalized real symmetric-definite banded eigenproblem
f01ckf	2	nagf_matop_real_gen_matmul Multiplication of real matrices
f01crf	7	nagf_matop_real_gen_trans_inplace Transposition of a real matrix
f01ctf	14	nagf_matop_real_addsub Sum or difference of two real matrices, optional scaling and transposition
f01cwf	14	nagf_matop_complex_addsub Sum or difference of two complex matrices, optional scaling and transposition
f01dff	27.1	nagf_matop_real_tri_matmul Matrix-matrix product, two real triangular matrices, update third matrix
f01dgf	27	nagf_matop_real_tri_matmul_inplace Matrix-matrix product, two real lower or upper triangular matrices
f01dtf	27.1	nagf_matop_complex_tri_matmul Matrix-matrix product, two complex triangular matrices, update third matrix
f01duf	27	nagf_matop_complex_tri_matmul_inplace Matrix-matrix product, two complex lower or upper triangular matrices
f01ecf	22	nagf_matop_real_gen_matrix_exp Real matrix exponential
f01edf	23	nagf_matop_real_symm_matrix_exp Real symmetric matrix exponential
f01eff	23	nagf_matop_real_symm_matrix_fun Function of a real symmetric matrix
f01ejf	24	nagf_matop_real_gen_matrix_log Real matrix logarithm
f01ekf	24	nagf_matop_real_gen_matrix_fun_std Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
f01elf	24	nagf_matop_real_gen_matrix_fun_num Function of a real matrix (using numerical differentiation)
f01emf	24	nagf_matop_real_gen_matrix_fun_usd Function of a real matrix (using user-supplied derivatives)
f01enf	25	nagf_matop_real_gen_matrix_sqrt Real matrix square root
f01epf	25	nagf_matop_real_tri_matrix_sqrt Real upper quasi-triangular matrix square root
f01eqf	25	nagf_matop_real_gen_matrix_pow General power of a real matrix
f01fcf	23	nagf_matop_complex_gen_matrix_exp Complex matrix exponential
f01fdf	23	nagf_matop_complex_herm_matrix_exp Complex Hermitian matrix exponential
f01fff	23	nagf_matop_complex_herm_matrix_fun Function of a complex Hermitian matrix
f01fjf	24	nagf_matop_complex_gen_matrix_log Complex matrix logarithm
f01fkf	24	nagf_matop_complex_gen_matrix_fun_std Exponential, sine, cosine, sinh or cosh of a complex matrix (Schur–Parlett algorithm)
f01flf	24	nagf_matop_complex_gen_matrix_fun_num Function of a complex matrix (using numerical differentiation)
f01fmf	24	nagf_matop_complex_gen_matrix_fun_usd Function of a complex matrix (using user-supplied derivatives)
f01fnf	25	nagf_matop_complex_gen_matrix_sqrt Complex matrix square root
f01fpf	25	nagf_matop_complex_tri_matrix_sqrt Complex upper triangular matrix square root
f01fqf	25	nagf_matop_complex_gen_matrix_pow General power of a complex matrix
f01gaf	24	nagf_matop_real_gen_matrix_actexp Action of a real matrix exponential on a real matrix
f01gbf	24	nagf_matop_real_gen_matrix_actexp_rcomm Action of a real matrix exponential on a real matrix (reverse communication)
f01haf	24	nagf_matop_complex_gen_matrix_actexp Action of a complex matrix exponential on a complex matrix
f01hbf	24	nagf_matop_complex_gen_matrix_actexp_rcomm Action of a complex matrix exponential on a complex matrix (reverse communication)
f01jaf	24	nagf_matop_real_gen_matrix_cond_std Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a real matrix
f01jbf	24	nagf_matop_real_gen_matrix_cond_num Condition number for a function of a real matrix (using numerical differentiation)
f01jcf	24	nagf_matop_real_gen_matrix_cond_usd Condition number for a function of a real matrix (using user-supplied derivatives)
f01jdf	25	nagf_matop_real_gen_matrix_cond_sqrt Condition number for square root of real matrix
f01jef	25	nagf_matop_real_gen_matrix_cond_pow Condition number for real matrix power
f01jff	25	nagf_matop_real_gen_matrix_frcht_pow Fréchet derivative of real matrix power
f01jgf	25	nagf_matop_real_gen_matrix_cond_exp Condition number for real matrix exponential
f01jhf	25	nagf_matop_real_gen_matrix_frcht_exp Fréchet derivative of real matrix exponential
f01jjf	25	nagf_matop_real_gen_matrix_cond_log Condition number for real matrix logarithm
f01jkf	25	nagf_matop_real_gen_matrix_frcht_log Fréchet derivative of real matrix logarithm
f01kaf	24	nagf_matop_complex_gen_matrix_cond_std Condition number for the exponential, logarithm, sine, cosine, sinh or cosh of a complex matrix
f01kbf	24	nagf_matop_complex_gen_matrix_cond_num Condition number for a function of a complex matrix (using numerical differentiation)
f01kcf	24	nagf_matop_complex_gen_matrix_cond_usd Condition number for a function of a complex matrix (using user-supplied derivatives)
f01kdf	25	nagf_matop_complex_gen_matrix_cond_sqrt Condition number for square root of complex matrix
f01kef	25	nagf_matop_complex_gen_matrix_cond_pow Condition number for complex matrix power
f01kff	25	nagf_matop_complex_gen_matrix_frcht_pow Fréchet derivative of complex matrix power
f01kgf	25	nagf_matop_complex_gen_matrix_cond_exp Condition number for complex matrix exponential
f01khf	25	nagf_matop_complex_gen_matrix_frcht_exp Fréchet derivative of complex matrix exponential
f01kjf	25	nagf_matop_complex_gen_matrix_cond_log Condition number for complex matrix logarithm
f01kkf	25	nagf_matop_complex_gen_matrix_frcht_log Fréchet derivative of complex matrix logarithm
f01lef	11	nagf_matop_real_gen_tridiag_lu $L U$ factorization of real tridiagonal matrix
f01lhf	13	nagf_matop_real_gen_blkdiag_lu $L U$ factorization of real almost block diagonal matrix
f01mcf	8	nagf_matop_real_vband_posdef_fac $L D L^{T}$ factorization of real symmetric positive definite variable-bandwidth matrix
f01mdf	27.1	nagf_matop_real_modified_cholesky Computes the modified Cholesky factorization of a real symmetric matrix
f01mef	27.1	nagf_matop_real_mod_chol_perturbed_a Computes the positive definite perturbed matrix $A + E$ from the factors of a modified Cholesky factorization of a real symmetric matrix
f01qgf	14	nagf_matop_real_trapez_rq $R Q$ factorization of real $m \times n$ upper trapezoidal matrix $(m \leq n)$
f01qjf	14	nagf_matop_real_gen_rq $R Q$ factorization of real $m \times n$ matrix $(m \leq n)$
f01qkf	14	nagf_matop_real_gen_rq_formq Operations with orthogonal matrices, form rows of $Q$ , after $R Q$ factorization by f01qjf
f01rgf	14	nagf_matop_complex_trapez_rq $R Q$ factorization of complex $m \times n$ upper trapezoidal matrix $(m \leq n)$
f01rjf	14	nagf_matop_complex_gen_rq $R Q$ factorization of complex $m \times n$ matrix $(m \leq n)$
f01rkf	14	nagf_matop_complex_gen_rq_formq Operations with unitary matrices, form rows of $Q$ , after $R Q$ factorization by f01rjf
f01saf	27	nagf_matop_real_nmf Non-negative matrix factorization of real non-negative matrix
f01sbf	27	nagf_matop_real_nmf_rcomm Non-negative matrix factorization of real non-negative matrix (reverse communication)
f01vaf	23	dtrttp nagf_matop_dtrttp Copies a real triangular matrix from full format to packed format
f01vbf	23	ztrttp nagf_matop_ztrttp Copies a complex triangular matrix from full format to packed format
f01vcf	23	dtpttr nagf_matop_dtpttr Copies a real triangular matrix from packed format to full format
f01vdf	23	ztpttr nagf_matop_ztpttr Copies a complex triangular matrix from packed format to full format
f01vef	23	dtrttf nagf_matop_dtrttf Copies a real triangular matrix from full format to Rectangular Full Packed format
f01vff	23	ztrttf nagf_matop_ztrttf Copies a complex triangular matrix from full format to Rectangular Full Packed format
f01vgf	23	dtfttr nagf_matop_dtfttr Copies a real triangular matrix from Rectangular Full Packed format to full format
f01vhf	23	ztfttr nagf_matop_ztfttr Copies a complex triangular matrix from Rectangular Full Packed format to full format
f01vjf	23	dtpttf nagf_matop_dtpttf Copies a real triangular matrix from packed format to Rectangular Full Packed format
f01vkf	23	ztpttf nagf_matop_ztpttf Copies a complex triangular matrix from packed format to Rectangular Full Packed format
f01vlf	23	dtfttp nagf_matop_dtfttp Copies a real triangular matrix from Rectangular Full Packed format to packed format
f01vmf	23	ztfttp nagf_matop_ztfttp Copies a complex triangular matrix from Rectangular Full Packed format to packed format
f01zaf	14	nagf_matop_real_tri_pack Convert real matrix between packed triangular and square storage formats
f01zbf	14	nagf_matop_complex_tri_pack Convert complex matrix between packed triangular and square storage formats
f01zcf	14	nagf_matop_real_band_pack Convert real matrix between packed banded and rectangular storage formats
f01zdf	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