F01 Chapter Contents (PDF version)
F01 Chapter Introduction
NAG Library Manual

NAG Library Chapter Contents

F01 – Matrix Operations, Including Inversion


F01 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
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
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

F01 Chapter Contents (PDF version)
F01 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016