.\" Automatically generated by Pod::Man 4.14 (Pod::Simple 3.43) .\" .\" Standard preamble: .\" ======================================================================== .de Sp \" Vertical space (when we can't use .PP) .if t .sp .5v .if n .sp .. .de Vb \" Begin verbatim text .ft CW .nf .ne \\$1 .. .de Ve \" End verbatim text .ft R .fi .. .\" Set up some character translations and predefined strings. \*(-- will .\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left .\" double quote, and \*(R" will give a right double quote. \*(C+ will .\" give a nicer C++. Capital omega is used to do unbreakable dashes and .\" therefore won't be available. \*(C` and \*(C' expand to `' in nroff, .\" nothing in troff, for use with C<>. .tr \(*W- .ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p' .ie n \{\ . ds -- \(*W- . ds PI pi . if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch . if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch . ds L" "" . ds R" "" . ds C` "" . ds C' "" 'br\} .el\{\ . ds -- \|\(em\| . ds PI \(*p . ds L" `` . ds R" '' . ds C` . ds C' 'br\} .\" .\" Escape single quotes in literal strings from groff's Unicode transform. .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" .\" If the F register is >0, we'll generate index entries on stderr for .\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index .\" entries marked with X<> in POD. Of course, you'll have to process the .\" output yourself in some meaningful fashion. .\" .\" Avoid warning from groff about undefined register 'F'. .de IX .. .nr rF 0 .if \n(.g .if rF .nr rF 1 .if (\n(rF:(\n(.g==0)) \{\ . if \nF \{\ . de IX . tm Index:\\$1\t\\n%\t"\\$2" .. . if !\nF==2 \{\ . nr % 0 . nr F 2 . \} . \} .\} .rr rF .\" ======================================================================== .\" .IX Title "LINALG 3pm" .TH LINALG 3pm "2023-06-17" "perl v5.36.0" "User Contributed Perl Documentation" .\" For nroff, turn off justification. Always turn off hyphenation; it makes .\" way too many mistakes in technical documents. .if n .ad l .nh .SH "NAME" PDL::GSL::LINALG \- PDL interface to linear algebra routines in GSL .SH "SYNOPSIS" .IX Header "SYNOPSIS" .Vb 10 \& use PDL::LiteF; \& use PDL::MatrixOps; # for \*(Aqx\*(Aq \& use PDL::GSL::LINALG; \& my $A = pdl [ \& [0.18, 0.60, 0.57, 0.96], \& [0.41, 0.24, 0.99, 0.58], \& [0.14, 0.30, 0.97, 0.66], \& [0.51, 0.13, 0.19, 0.85], \& ]; \& my $B = sequence(2,4); # column vectors \& LU_decomp(my $lu=$A\->copy, my $p=null, my $signum=null); \& # transpose so first dim means is vector, higher dims broadcast \& LU_solve($lu, $p, $B\->transpose, my $x=null); \& $x = $x\->inplace\->transpose; # now can be matrix\-multiplied .Ve .SH "DESCRIPTION" .IX Header "DESCRIPTION" This is an interface to the linear algebra package present in the \&\s-1GNU\s0 Scientific Library. Functions are named as in \s-1GSL,\s0 but with the initial \f(CW\*(C`gsl_linalg_\*(C'\fR removed. They are provided in both real and complex double precision. .PP Currently only \s-1LU\s0 decomposition interfaces here. Pull requests welcome! #line 60 \*(L"\s-1LINALG\s0.pm\*(R" .SH "FUNCTIONS" .IX Header "FUNCTIONS" .SS "LU_decomp" .IX Subsection "LU_decomp" .Vb 1 \& Signature: ([io,phys]A(n,m); indx [o,phys]ipiv(p); int [o,phys]signum()) .Ve .PP \&\s-1LU\s0 decomposition of the given (real or complex) matrix. .PP LU_decomp ignores the bad-value flag of the input ndarrays. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "LU_solve" .IX Subsection "LU_solve" .Vb 1 \& Signature: ([phys]LU(n,m); indx [phys]ipiv(p); [phys]B(n); [o,phys]x(n)) .Ve .PP Solve \f(CW\*(C`A x = B\*(C'\fR using the \s-1LU\s0 and permutation from \*(L"LU_decomp\*(R", real or complex. .PP LU_solve ignores the bad-value flag of the input ndarrays. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "LU_det" .IX Subsection "LU_det" .Vb 1 \& Signature: ([phys]LU(n,m); int [phys]signum(); [o]det()) .Ve .PP Find the determinant from the \s-1LU\s0 decomp. .PP LU_det ignores the bad-value flag of the input ndarrays. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "solve_tridiag" .IX Subsection "solve_tridiag" .Vb 1 \& Signature: ([phys]diag(n); [phys]superdiag(n); [phys]subdiag(n); [phys]B(n); [o,phys]x(n)) .Ve .PP Solve \f(CW\*(C`A x = B\*(C'\fR where A is a tridiagonal system. Real only, because \&\s-1GSL\s0 does not have a complex function. .PP solve_tridiag ignores the bad-value flag of the input ndarrays. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SH "SEE ALSO" .IX Header "SEE ALSO" \&\s-1PDL\s0 .PP The \s-1GSL\s0 documentation for linear algebra is online at