# NAG FL InterfaceF01 (Matop)Matrix Operations, Including Inversion

Settings help

FL Name Style:

FL Specification Language:

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

Routine
Mark of
Introduction

Purpose
f01abf 1 nagf_matop_real_symm_posdef_inv
Inverse of real symmetric positive definite matrix using iterative refinement
Inverse of real symmetric positive definite matrix
f01blf 5 nagf_matop_real_gen_pseudinv
Pseudo-inverse and rank of real $m×n$ matrix $\left(m\ge n\right)$
f01brf 7 nagf_matop_real_gen_sparse_lu
$LU$ factorization of real sparse matrix
f01bsf 7 nagf_matop_real_gen_sparse_lu_reuse
$LU$ factorization of real sparse matrix with known sparsity pattern
f01buf 7 nagf_matop_real_symm_posdef_fac
$ULD{L}^{\mathrm{T}}{U}^{\mathrm{T}}$ 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
Sum or difference of two real matrices, optional scaling and transposition
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
$LU$ factorization of real tridiagonal matrix
f01lhf 13 nagf_matop_real_gen_blkdiag_lu
$LU$ factorization of real almost block diagonal matrix
f01mcf 8 nagf_matop_real_vband_posdef_fac
$LD{L}^{\mathrm{T}}$ 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
$RQ$ factorization of real $m×n$ upper trapezoidal matrix $\left(m\le n\right)$
f01qjf 14 nagf_matop_real_gen_rq
$RQ$ factorization of real $m×n$ matrix $\left(m\le n\right)$
f01qkf 14 nagf_matop_real_gen_rq_formq
Operations with orthogonal matrices, form rows of $Q$, after $RQ$ factorization by f01qjf
f01rgf 14 nagf_matop_complex_trapez_rq
$RQ$ factorization of complex $m×n$ upper trapezoidal matrix $\left(m\le n\right)$
f01rjf 14 nagf_matop_complex_gen_rq
$RQ$ factorization of complex $m×n$ matrix $\left(m\le n\right)$
f01rkf 14 nagf_matop_complex_gen_rq_formq
Operations with unitary matrices, form rows of $Q$, after $RQ$ 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