NAG Library Chapter Contents

F01 (matop)
Matrix Operations, Including Inversion


F01 (matop) Chapter Introduction – a description of the Chapter and an overview of the algorithms available

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 mn
f01brf
Example Text
Example Data
7 nagf_matop_real_gen_sparse_lu
LU factorization of real sparse matrix
f01bsf
Example Text
Example Data
7 nagf_matop_real_gen_sparse_lu_reuse
LU factorization of real sparse matrix with known sparsity pattern
f01buf
Example Text
Example Data
7 nagf_matop_real_symm_posdef_fac
ULDLTUT 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
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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
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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
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Example Data
24 nagf_matop_real_gen_matrix_log
Real matrix logarithm
f01ekf
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Example Data
24 nagf_matop_real_gen_matrix_fun_std
Exponential, sine, cosine, sinh or cosh of a real matrix (Schur–Parlett algorithm)
f01elf
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Example Data
24 nagf_matop_real_gen_matrix_fun_num
Function of a real matrix (using numerical differentiation)
f01emf
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Example Data
24 nagf_matop_real_gen_matrix_fun_usd
Function of a real matrix (using user-supplied derivatives)
f01enf
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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
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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
LU factorization of real tridiagonal matrix
f01lhf
Example Text
Example Data
13 nagf_matop_real_gen_blkdiag_lu
LU factorization of real almost block diagonal matrix
f01mcf
Example Text
Example Data
8 nagf_matop_real_vband_posdef_fac
LDLT factorization of real symmetric positive definite variable-bandwidth matrix
f01qgf
Example Text
Example Data
14 nagf_matop_real_trapez_rq
RQ factorization of real m by n upper trapezoidal matrix mn
f01qjf
Example Text
Example Data
14 nagf_matop_real_gen_rq
RQ factorization of real m by n matrix mn
f01qkf
Example Text
Example Data
14 nagf_matop_real_gen_rq_formq
Operations with orthogonal matrices, form rows of Q, after RQ factorization by f01qjf
f01rgf
Example Text
Example Data
14 nagf_matop_complex_trapez_rq
RQ factorization of complex m by n upper trapezoidal matrix mn
f01rjf
Example Text
Example Data
14 nagf_matop_complex_gen_rq
RQ factorization of complex m by n matrix mn
f01rkf
Example Text
Example Data
14 nagf_matop_complex_gen_rq_formq
Operations with unitary matrices, form rows of Q, after RQ 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