1# This file was automatically generated by SWIG (http://www.swig.org).
2# Version 4.0.1
3#
4# Do not make changes to this file unless you know what you are doing--modify
5# the SWIG interface file instead.
6
7package Math::GSL::Linalg;
8use base qw(Exporter);
9use base qw(DynaLoader);
10package Math::GSL::Linalgc;
11bootstrap Math::GSL::Linalg;
12package Math::GSL::Linalg;
13@EXPORT = qw();
14
15# ---------- BASE METHODS -------------
16
17package Math::GSL::Linalg;
18
19sub TIEHASH {
20    my ($classname,$obj) = @_;
21    return bless $obj, $classname;
22}
23
24sub CLEAR { }
25
26sub FIRSTKEY { }
27
28sub NEXTKEY { }
29
30sub FETCH {
31    my ($self,$field) = @_;
32    my $member_func = "swig_${field}_get";
33    $self->$member_func();
34}
35
36sub STORE {
37    my ($self,$field,$newval) = @_;
38    my $member_func = "swig_${field}_set";
39    $self->$member_func($newval);
40}
41
42sub this {
43    my $ptr = shift;
44    return tied(%$ptr);
45}
46
47
48# ------- FUNCTION WRAPPERS --------
49
50package Math::GSL::Linalg;
51
52*gsl_error = *Math::GSL::Linalgc::gsl_error;
53*gsl_stream_printf = *Math::GSL::Linalgc::gsl_stream_printf;
54*gsl_strerror = *Math::GSL::Linalgc::gsl_strerror;
55*gsl_set_error_handler = *Math::GSL::Linalgc::gsl_set_error_handler;
56*gsl_set_error_handler_off = *Math::GSL::Linalgc::gsl_set_error_handler_off;
57*gsl_set_stream_handler = *Math::GSL::Linalgc::gsl_set_stream_handler;
58*gsl_set_stream = *Math::GSL::Linalgc::gsl_set_stream;
59*gsl_linalg_matmult = *Math::GSL::Linalgc::gsl_linalg_matmult;
60*gsl_linalg_matmult_mod = *Math::GSL::Linalgc::gsl_linalg_matmult_mod;
61*gsl_linalg_exponential_ss = *Math::GSL::Linalgc::gsl_linalg_exponential_ss;
62*gsl_linalg_householder_transform = *Math::GSL::Linalgc::gsl_linalg_householder_transform;
63*gsl_linalg_complex_householder_transform = *Math::GSL::Linalgc::gsl_linalg_complex_householder_transform;
64*gsl_linalg_householder_hm = *Math::GSL::Linalgc::gsl_linalg_householder_hm;
65*gsl_linalg_householder_mh = *Math::GSL::Linalgc::gsl_linalg_householder_mh;
66*gsl_linalg_householder_hv = *Math::GSL::Linalgc::gsl_linalg_householder_hv;
67*gsl_linalg_householder_hm1 = *Math::GSL::Linalgc::gsl_linalg_householder_hm1;
68*gsl_linalg_complex_householder_hm = *Math::GSL::Linalgc::gsl_linalg_complex_householder_hm;
69*gsl_linalg_complex_householder_mh = *Math::GSL::Linalgc::gsl_linalg_complex_householder_mh;
70*gsl_linalg_complex_householder_hv = *Math::GSL::Linalgc::gsl_linalg_complex_householder_hv;
71*gsl_linalg_hessenberg_decomp = *Math::GSL::Linalgc::gsl_linalg_hessenberg_decomp;
72*gsl_linalg_hessenberg_unpack = *Math::GSL::Linalgc::gsl_linalg_hessenberg_unpack;
73*gsl_linalg_hessenberg_unpack_accum = *Math::GSL::Linalgc::gsl_linalg_hessenberg_unpack_accum;
74*gsl_linalg_hessenberg_set_zero = *Math::GSL::Linalgc::gsl_linalg_hessenberg_set_zero;
75*gsl_linalg_hessenberg_submatrix = *Math::GSL::Linalgc::gsl_linalg_hessenberg_submatrix;
76*gsl_linalg_hesstri_decomp = *Math::GSL::Linalgc::gsl_linalg_hesstri_decomp;
77*gsl_linalg_SV_decomp = *Math::GSL::Linalgc::gsl_linalg_SV_decomp;
78*gsl_linalg_SV_decomp_mod = *Math::GSL::Linalgc::gsl_linalg_SV_decomp_mod;
79*gsl_linalg_SV_decomp_jacobi = *Math::GSL::Linalgc::gsl_linalg_SV_decomp_jacobi;
80*gsl_linalg_SV_solve = *Math::GSL::Linalgc::gsl_linalg_SV_solve;
81*gsl_linalg_LU_decomp = *Math::GSL::Linalgc::gsl_linalg_LU_decomp;
82*gsl_linalg_LU_solve = *Math::GSL::Linalgc::gsl_linalg_LU_solve;
83*gsl_linalg_LU_svx = *Math::GSL::Linalgc::gsl_linalg_LU_svx;
84*gsl_linalg_LU_refine = *Math::GSL::Linalgc::gsl_linalg_LU_refine;
85*gsl_linalg_LU_invert = *Math::GSL::Linalgc::gsl_linalg_LU_invert;
86*gsl_linalg_LU_det = *Math::GSL::Linalgc::gsl_linalg_LU_det;
87*gsl_linalg_LU_lndet = *Math::GSL::Linalgc::gsl_linalg_LU_lndet;
88*gsl_linalg_LU_sgndet = *Math::GSL::Linalgc::gsl_linalg_LU_sgndet;
89*gsl_linalg_complex_LU_decomp = *Math::GSL::Linalgc::gsl_linalg_complex_LU_decomp;
90*gsl_linalg_complex_LU_solve = *Math::GSL::Linalgc::gsl_linalg_complex_LU_solve;
91*gsl_linalg_complex_LU_svx = *Math::GSL::Linalgc::gsl_linalg_complex_LU_svx;
92*gsl_linalg_complex_LU_refine = *Math::GSL::Linalgc::gsl_linalg_complex_LU_refine;
93*gsl_linalg_complex_LU_invert = *Math::GSL::Linalgc::gsl_linalg_complex_LU_invert;
94*gsl_linalg_complex_LU_det = *Math::GSL::Linalgc::gsl_linalg_complex_LU_det;
95*gsl_linalg_complex_LU_lndet = *Math::GSL::Linalgc::gsl_linalg_complex_LU_lndet;
96*gsl_linalg_complex_LU_sgndet = *Math::GSL::Linalgc::gsl_linalg_complex_LU_sgndet;
97*gsl_linalg_QR_decomp = *Math::GSL::Linalgc::gsl_linalg_QR_decomp;
98*gsl_linalg_QR_solve = *Math::GSL::Linalgc::gsl_linalg_QR_solve;
99*gsl_linalg_QR_svx = *Math::GSL::Linalgc::gsl_linalg_QR_svx;
100*gsl_linalg_QR_lssolve = *Math::GSL::Linalgc::gsl_linalg_QR_lssolve;
101*gsl_linalg_QR_QRsolve = *Math::GSL::Linalgc::gsl_linalg_QR_QRsolve;
102*gsl_linalg_QR_Rsolve = *Math::GSL::Linalgc::gsl_linalg_QR_Rsolve;
103*gsl_linalg_QR_Rsvx = *Math::GSL::Linalgc::gsl_linalg_QR_Rsvx;
104*gsl_linalg_QR_update = *Math::GSL::Linalgc::gsl_linalg_QR_update;
105*gsl_linalg_QR_QTvec = *Math::GSL::Linalgc::gsl_linalg_QR_QTvec;
106*gsl_linalg_QR_Qvec = *Math::GSL::Linalgc::gsl_linalg_QR_Qvec;
107*gsl_linalg_QR_QTmat = *Math::GSL::Linalgc::gsl_linalg_QR_QTmat;
108*gsl_linalg_QR_unpack = *Math::GSL::Linalgc::gsl_linalg_QR_unpack;
109*gsl_linalg_R_solve = *Math::GSL::Linalgc::gsl_linalg_R_solve;
110*gsl_linalg_R_svx = *Math::GSL::Linalgc::gsl_linalg_R_svx;
111*gsl_linalg_QRPT_decomp = *Math::GSL::Linalgc::gsl_linalg_QRPT_decomp;
112*gsl_linalg_QRPT_decomp2 = *Math::GSL::Linalgc::gsl_linalg_QRPT_decomp2;
113*gsl_linalg_QRPT_solve = *Math::GSL::Linalgc::gsl_linalg_QRPT_solve;
114*gsl_linalg_QRPT_svx = *Math::GSL::Linalgc::gsl_linalg_QRPT_svx;
115*gsl_linalg_QRPT_QRsolve = *Math::GSL::Linalgc::gsl_linalg_QRPT_QRsolve;
116*gsl_linalg_QRPT_Rsolve = *Math::GSL::Linalgc::gsl_linalg_QRPT_Rsolve;
117*gsl_linalg_QRPT_Rsvx = *Math::GSL::Linalgc::gsl_linalg_QRPT_Rsvx;
118*gsl_linalg_QRPT_update = *Math::GSL::Linalgc::gsl_linalg_QRPT_update;
119*gsl_linalg_LQ_decomp = *Math::GSL::Linalgc::gsl_linalg_LQ_decomp;
120*gsl_linalg_LQ_solve_T = *Math::GSL::Linalgc::gsl_linalg_LQ_solve_T;
121*gsl_linalg_LQ_svx_T = *Math::GSL::Linalgc::gsl_linalg_LQ_svx_T;
122*gsl_linalg_LQ_lssolve_T = *Math::GSL::Linalgc::gsl_linalg_LQ_lssolve_T;
123*gsl_linalg_LQ_Lsolve_T = *Math::GSL::Linalgc::gsl_linalg_LQ_Lsolve_T;
124*gsl_linalg_LQ_Lsvx_T = *Math::GSL::Linalgc::gsl_linalg_LQ_Lsvx_T;
125*gsl_linalg_L_solve_T = *Math::GSL::Linalgc::gsl_linalg_L_solve_T;
126*gsl_linalg_LQ_vecQ = *Math::GSL::Linalgc::gsl_linalg_LQ_vecQ;
127*gsl_linalg_LQ_vecQT = *Math::GSL::Linalgc::gsl_linalg_LQ_vecQT;
128*gsl_linalg_LQ_unpack = *Math::GSL::Linalgc::gsl_linalg_LQ_unpack;
129*gsl_linalg_LQ_update = *Math::GSL::Linalgc::gsl_linalg_LQ_update;
130*gsl_linalg_LQ_LQsolve = *Math::GSL::Linalgc::gsl_linalg_LQ_LQsolve;
131*gsl_linalg_PTLQ_decomp = *Math::GSL::Linalgc::gsl_linalg_PTLQ_decomp;
132*gsl_linalg_PTLQ_decomp2 = *Math::GSL::Linalgc::gsl_linalg_PTLQ_decomp2;
133*gsl_linalg_PTLQ_solve_T = *Math::GSL::Linalgc::gsl_linalg_PTLQ_solve_T;
134*gsl_linalg_PTLQ_svx_T = *Math::GSL::Linalgc::gsl_linalg_PTLQ_svx_T;
135*gsl_linalg_PTLQ_LQsolve_T = *Math::GSL::Linalgc::gsl_linalg_PTLQ_LQsolve_T;
136*gsl_linalg_PTLQ_Lsolve_T = *Math::GSL::Linalgc::gsl_linalg_PTLQ_Lsolve_T;
137*gsl_linalg_PTLQ_Lsvx_T = *Math::GSL::Linalgc::gsl_linalg_PTLQ_Lsvx_T;
138*gsl_linalg_PTLQ_update = *Math::GSL::Linalgc::gsl_linalg_PTLQ_update;
139*gsl_linalg_cholesky_decomp = *Math::GSL::Linalgc::gsl_linalg_cholesky_decomp;
140*gsl_linalg_cholesky_solve = *Math::GSL::Linalgc::gsl_linalg_cholesky_solve;
141*gsl_linalg_cholesky_svx = *Math::GSL::Linalgc::gsl_linalg_cholesky_svx;
142*gsl_linalg_cholesky_invert = *Math::GSL::Linalgc::gsl_linalg_cholesky_invert;
143*gsl_linalg_cholesky_decomp_unit = *Math::GSL::Linalgc::gsl_linalg_cholesky_decomp_unit;
144*gsl_linalg_complex_cholesky_decomp = *Math::GSL::Linalgc::gsl_linalg_complex_cholesky_decomp;
145*gsl_linalg_complex_cholesky_solve = *Math::GSL::Linalgc::gsl_linalg_complex_cholesky_solve;
146*gsl_linalg_complex_cholesky_svx = *Math::GSL::Linalgc::gsl_linalg_complex_cholesky_svx;
147*gsl_linalg_complex_cholesky_invert = *Math::GSL::Linalgc::gsl_linalg_complex_cholesky_invert;
148*gsl_linalg_symmtd_decomp = *Math::GSL::Linalgc::gsl_linalg_symmtd_decomp;
149*gsl_linalg_symmtd_unpack = *Math::GSL::Linalgc::gsl_linalg_symmtd_unpack;
150*gsl_linalg_symmtd_unpack_T = *Math::GSL::Linalgc::gsl_linalg_symmtd_unpack_T;
151*gsl_linalg_hermtd_decomp = *Math::GSL::Linalgc::gsl_linalg_hermtd_decomp;
152*gsl_linalg_hermtd_unpack = *Math::GSL::Linalgc::gsl_linalg_hermtd_unpack;
153*gsl_linalg_hermtd_unpack_T = *Math::GSL::Linalgc::gsl_linalg_hermtd_unpack_T;
154*gsl_linalg_HH_solve = *Math::GSL::Linalgc::gsl_linalg_HH_solve;
155*gsl_linalg_HH_svx = *Math::GSL::Linalgc::gsl_linalg_HH_svx;
156*gsl_linalg_solve_symm_tridiag = *Math::GSL::Linalgc::gsl_linalg_solve_symm_tridiag;
157*gsl_linalg_solve_tridiag = *Math::GSL::Linalgc::gsl_linalg_solve_tridiag;
158*gsl_linalg_solve_symm_cyc_tridiag = *Math::GSL::Linalgc::gsl_linalg_solve_symm_cyc_tridiag;
159*gsl_linalg_solve_cyc_tridiag = *Math::GSL::Linalgc::gsl_linalg_solve_cyc_tridiag;
160*gsl_linalg_bidiag_decomp = *Math::GSL::Linalgc::gsl_linalg_bidiag_decomp;
161*gsl_linalg_bidiag_unpack = *Math::GSL::Linalgc::gsl_linalg_bidiag_unpack;
162*gsl_linalg_bidiag_unpack2 = *Math::GSL::Linalgc::gsl_linalg_bidiag_unpack2;
163*gsl_linalg_bidiag_unpack_B = *Math::GSL::Linalgc::gsl_linalg_bidiag_unpack_B;
164*gsl_linalg_balance_matrix = *Math::GSL::Linalgc::gsl_linalg_balance_matrix;
165*gsl_linalg_balance_accum = *Math::GSL::Linalgc::gsl_linalg_balance_accum;
166*gsl_linalg_balance_columns = *Math::GSL::Linalgc::gsl_linalg_balance_columns;
167*gsl_permutation_alloc = *Math::GSL::Linalgc::gsl_permutation_alloc;
168*gsl_permutation_calloc = *Math::GSL::Linalgc::gsl_permutation_calloc;
169*gsl_permutation_init = *Math::GSL::Linalgc::gsl_permutation_init;
170*gsl_permutation_free = *Math::GSL::Linalgc::gsl_permutation_free;
171*gsl_permutation_memcpy = *Math::GSL::Linalgc::gsl_permutation_memcpy;
172*gsl_permutation_fread = *Math::GSL::Linalgc::gsl_permutation_fread;
173*gsl_permutation_fwrite = *Math::GSL::Linalgc::gsl_permutation_fwrite;
174*gsl_permutation_fscanf = *Math::GSL::Linalgc::gsl_permutation_fscanf;
175*gsl_permutation_fprintf = *Math::GSL::Linalgc::gsl_permutation_fprintf;
176*gsl_permutation_size = *Math::GSL::Linalgc::gsl_permutation_size;
177*gsl_permutation_data = *Math::GSL::Linalgc::gsl_permutation_data;
178*gsl_permutation_swap = *Math::GSL::Linalgc::gsl_permutation_swap;
179*gsl_permutation_valid = *Math::GSL::Linalgc::gsl_permutation_valid;
180*gsl_permutation_reverse = *Math::GSL::Linalgc::gsl_permutation_reverse;
181*gsl_permutation_inverse = *Math::GSL::Linalgc::gsl_permutation_inverse;
182*gsl_permutation_next = *Math::GSL::Linalgc::gsl_permutation_next;
183*gsl_permutation_prev = *Math::GSL::Linalgc::gsl_permutation_prev;
184*gsl_permutation_mul = *Math::GSL::Linalgc::gsl_permutation_mul;
185*gsl_permutation_linear_to_canonical = *Math::GSL::Linalgc::gsl_permutation_linear_to_canonical;
186*gsl_permutation_canonical_to_linear = *Math::GSL::Linalgc::gsl_permutation_canonical_to_linear;
187*gsl_permutation_inversions = *Math::GSL::Linalgc::gsl_permutation_inversions;
188*gsl_permutation_linear_cycles = *Math::GSL::Linalgc::gsl_permutation_linear_cycles;
189*gsl_permutation_canonical_cycles = *Math::GSL::Linalgc::gsl_permutation_canonical_cycles;
190*gsl_permutation_get = *Math::GSL::Linalgc::gsl_permutation_get;
191*gsl_complex_polar = *Math::GSL::Linalgc::gsl_complex_polar;
192*gsl_complex_rect = *Math::GSL::Linalgc::gsl_complex_rect;
193*gsl_complex_arg = *Math::GSL::Linalgc::gsl_complex_arg;
194*gsl_complex_abs = *Math::GSL::Linalgc::gsl_complex_abs;
195*gsl_complex_abs2 = *Math::GSL::Linalgc::gsl_complex_abs2;
196*gsl_complex_logabs = *Math::GSL::Linalgc::gsl_complex_logabs;
197*gsl_complex_add = *Math::GSL::Linalgc::gsl_complex_add;
198*gsl_complex_sub = *Math::GSL::Linalgc::gsl_complex_sub;
199*gsl_complex_mul = *Math::GSL::Linalgc::gsl_complex_mul;
200*gsl_complex_div = *Math::GSL::Linalgc::gsl_complex_div;
201*gsl_complex_add_real = *Math::GSL::Linalgc::gsl_complex_add_real;
202*gsl_complex_sub_real = *Math::GSL::Linalgc::gsl_complex_sub_real;
203*gsl_complex_mul_real = *Math::GSL::Linalgc::gsl_complex_mul_real;
204*gsl_complex_div_real = *Math::GSL::Linalgc::gsl_complex_div_real;
205*gsl_complex_add_imag = *Math::GSL::Linalgc::gsl_complex_add_imag;
206*gsl_complex_sub_imag = *Math::GSL::Linalgc::gsl_complex_sub_imag;
207*gsl_complex_mul_imag = *Math::GSL::Linalgc::gsl_complex_mul_imag;
208*gsl_complex_div_imag = *Math::GSL::Linalgc::gsl_complex_div_imag;
209*gsl_complex_conjugate = *Math::GSL::Linalgc::gsl_complex_conjugate;
210*gsl_complex_inverse = *Math::GSL::Linalgc::gsl_complex_inverse;
211*gsl_complex_negative = *Math::GSL::Linalgc::gsl_complex_negative;
212*gsl_complex_sqrt = *Math::GSL::Linalgc::gsl_complex_sqrt;
213*gsl_complex_sqrt_real = *Math::GSL::Linalgc::gsl_complex_sqrt_real;
214*gsl_complex_pow = *Math::GSL::Linalgc::gsl_complex_pow;
215*gsl_complex_pow_real = *Math::GSL::Linalgc::gsl_complex_pow_real;
216*gsl_complex_exp = *Math::GSL::Linalgc::gsl_complex_exp;
217*gsl_complex_log = *Math::GSL::Linalgc::gsl_complex_log;
218*gsl_complex_log10 = *Math::GSL::Linalgc::gsl_complex_log10;
219*gsl_complex_log_b = *Math::GSL::Linalgc::gsl_complex_log_b;
220*gsl_complex_sin = *Math::GSL::Linalgc::gsl_complex_sin;
221*gsl_complex_cos = *Math::GSL::Linalgc::gsl_complex_cos;
222*gsl_complex_sec = *Math::GSL::Linalgc::gsl_complex_sec;
223*gsl_complex_csc = *Math::GSL::Linalgc::gsl_complex_csc;
224*gsl_complex_tan = *Math::GSL::Linalgc::gsl_complex_tan;
225*gsl_complex_cot = *Math::GSL::Linalgc::gsl_complex_cot;
226*gsl_complex_arcsin = *Math::GSL::Linalgc::gsl_complex_arcsin;
227*gsl_complex_arcsin_real = *Math::GSL::Linalgc::gsl_complex_arcsin_real;
228*gsl_complex_arccos = *Math::GSL::Linalgc::gsl_complex_arccos;
229*gsl_complex_arccos_real = *Math::GSL::Linalgc::gsl_complex_arccos_real;
230*gsl_complex_arcsec = *Math::GSL::Linalgc::gsl_complex_arcsec;
231*gsl_complex_arcsec_real = *Math::GSL::Linalgc::gsl_complex_arcsec_real;
232*gsl_complex_arccsc = *Math::GSL::Linalgc::gsl_complex_arccsc;
233*gsl_complex_arccsc_real = *Math::GSL::Linalgc::gsl_complex_arccsc_real;
234*gsl_complex_arctan = *Math::GSL::Linalgc::gsl_complex_arctan;
235*gsl_complex_arccot = *Math::GSL::Linalgc::gsl_complex_arccot;
236*gsl_complex_sinh = *Math::GSL::Linalgc::gsl_complex_sinh;
237*gsl_complex_cosh = *Math::GSL::Linalgc::gsl_complex_cosh;
238*gsl_complex_sech = *Math::GSL::Linalgc::gsl_complex_sech;
239*gsl_complex_csch = *Math::GSL::Linalgc::gsl_complex_csch;
240*gsl_complex_tanh = *Math::GSL::Linalgc::gsl_complex_tanh;
241*gsl_complex_coth = *Math::GSL::Linalgc::gsl_complex_coth;
242*gsl_complex_arcsinh = *Math::GSL::Linalgc::gsl_complex_arcsinh;
243*gsl_complex_arccosh = *Math::GSL::Linalgc::gsl_complex_arccosh;
244*gsl_complex_arccosh_real = *Math::GSL::Linalgc::gsl_complex_arccosh_real;
245*gsl_complex_arcsech = *Math::GSL::Linalgc::gsl_complex_arcsech;
246*gsl_complex_arccsch = *Math::GSL::Linalgc::gsl_complex_arccsch;
247*gsl_complex_arctanh = *Math::GSL::Linalgc::gsl_complex_arctanh;
248*gsl_complex_arctanh_real = *Math::GSL::Linalgc::gsl_complex_arctanh_real;
249*gsl_complex_arccoth = *Math::GSL::Linalgc::gsl_complex_arccoth;
250
251############# Class : Math::GSL::Linalg::gsl_permutation_struct ##############
252
253package Math::GSL::Linalg::gsl_permutation_struct;
254use vars qw(@ISA %OWNER %ITERATORS %BLESSEDMEMBERS);
255@ISA = qw( Math::GSL::Linalg );
256%OWNER = ();
257%ITERATORS = ();
258*swig_size_get = *Math::GSL::Linalgc::gsl_permutation_struct_size_get;
259*swig_size_set = *Math::GSL::Linalgc::gsl_permutation_struct_size_set;
260*swig_data_get = *Math::GSL::Linalgc::gsl_permutation_struct_data_get;
261*swig_data_set = *Math::GSL::Linalgc::gsl_permutation_struct_data_set;
262sub new {
263    my $pkg = shift;
264    my $self = Math::GSL::Linalgc::new_gsl_permutation_struct(@_);
265    bless $self, $pkg if defined($self);
266}
267
268sub DESTROY {
269    return unless $_[0]->isa('HASH');
270    my $self = tied(%{$_[0]});
271    return unless defined $self;
272    delete $ITERATORS{$self};
273    if (exists $OWNER{$self}) {
274        Math::GSL::Linalgc::delete_gsl_permutation_struct($self);
275        delete $OWNER{$self};
276    }
277}
278
279sub DISOWN {
280    my $self = shift;
281    my $ptr = tied(%$self);
282    delete $OWNER{$ptr};
283}
284
285sub ACQUIRE {
286    my $self = shift;
287    my $ptr = tied(%$self);
288    $OWNER{$ptr} = 1;
289}
290
291
292############# Class : Math::GSL::Linalg::gsl_complex ##############
293
294package Math::GSL::Linalg::gsl_complex;
295use vars qw(@ISA %OWNER %ITERATORS %BLESSEDMEMBERS);
296@ISA = qw( Math::GSL::Linalg );
297%OWNER = ();
298%ITERATORS = ();
299*swig_dat_get = *Math::GSL::Linalgc::gsl_complex_dat_get;
300*swig_dat_set = *Math::GSL::Linalgc::gsl_complex_dat_set;
301sub new {
302    my $pkg = shift;
303    my $self = Math::GSL::Linalgc::new_gsl_complex(@_);
304    bless $self, $pkg if defined($self);
305}
306
307sub DESTROY {
308    return unless $_[0]->isa('HASH');
309    my $self = tied(%{$_[0]});
310    return unless defined $self;
311    delete $ITERATORS{$self};
312    if (exists $OWNER{$self}) {
313        Math::GSL::Linalgc::delete_gsl_complex($self);
314        delete $OWNER{$self};
315    }
316}
317
318sub DISOWN {
319    my $self = shift;
320    my $ptr = tied(%$self);
321    delete $OWNER{$ptr};
322}
323
324sub ACQUIRE {
325    my $self = shift;
326    my $ptr = tied(%$self);
327    $OWNER{$ptr} = 1;
328}
329
330
331############# Class : Math::GSL::Linalg::gsl_complex_long_double ##############
332
333package Math::GSL::Linalg::gsl_complex_long_double;
334use vars qw(@ISA %OWNER %ITERATORS %BLESSEDMEMBERS);
335@ISA = qw( Math::GSL::Linalg );
336%OWNER = ();
337%ITERATORS = ();
338*swig_dat_get = *Math::GSL::Linalgc::gsl_complex_long_double_dat_get;
339*swig_dat_set = *Math::GSL::Linalgc::gsl_complex_long_double_dat_set;
340sub new {
341    my $pkg = shift;
342    my $self = Math::GSL::Linalgc::new_gsl_complex_long_double(@_);
343    bless $self, $pkg if defined($self);
344}
345
346sub DESTROY {
347    return unless $_[0]->isa('HASH');
348    my $self = tied(%{$_[0]});
349    return unless defined $self;
350    delete $ITERATORS{$self};
351    if (exists $OWNER{$self}) {
352        Math::GSL::Linalgc::delete_gsl_complex_long_double($self);
353        delete $OWNER{$self};
354    }
355}
356
357sub DISOWN {
358    my $self = shift;
359    my $ptr = tied(%$self);
360    delete $OWNER{$ptr};
361}
362
363sub ACQUIRE {
364    my $self = shift;
365    my $ptr = tied(%$self);
366    $OWNER{$ptr} = 1;
367}
368
369
370############# Class : Math::GSL::Linalg::gsl_complex_float ##############
371
372package Math::GSL::Linalg::gsl_complex_float;
373use vars qw(@ISA %OWNER %ITERATORS %BLESSEDMEMBERS);
374@ISA = qw( Math::GSL::Linalg );
375%OWNER = ();
376%ITERATORS = ();
377*swig_dat_get = *Math::GSL::Linalgc::gsl_complex_float_dat_get;
378*swig_dat_set = *Math::GSL::Linalgc::gsl_complex_float_dat_set;
379sub new {
380    my $pkg = shift;
381    my $self = Math::GSL::Linalgc::new_gsl_complex_float(@_);
382    bless $self, $pkg if defined($self);
383}
384
385sub DESTROY {
386    return unless $_[0]->isa('HASH');
387    my $self = tied(%{$_[0]});
388    return unless defined $self;
389    delete $ITERATORS{$self};
390    if (exists $OWNER{$self}) {
391        Math::GSL::Linalgc::delete_gsl_complex_float($self);
392        delete $OWNER{$self};
393    }
394}
395
396sub DISOWN {
397    my $self = shift;
398    my $ptr = tied(%$self);
399    delete $OWNER{$ptr};
400}
401
402sub ACQUIRE {
403    my $self = shift;
404    my $ptr = tied(%$self);
405    $OWNER{$ptr} = 1;
406}
407
408
409# ------- VARIABLE STUBS --------
410
411package Math::GSL::Linalg;
412
413*GSL_VERSION = *Math::GSL::Linalgc::GSL_VERSION;
414*GSL_MAJOR_VERSION = *Math::GSL::Linalgc::GSL_MAJOR_VERSION;
415*GSL_MINOR_VERSION = *Math::GSL::Linalgc::GSL_MINOR_VERSION;
416*GSL_POSZERO = *Math::GSL::Linalgc::GSL_POSZERO;
417*GSL_NEGZERO = *Math::GSL::Linalgc::GSL_NEGZERO;
418*GSL_SUCCESS = *Math::GSL::Linalgc::GSL_SUCCESS;
419*GSL_FAILURE = *Math::GSL::Linalgc::GSL_FAILURE;
420*GSL_CONTINUE = *Math::GSL::Linalgc::GSL_CONTINUE;
421*GSL_EDOM = *Math::GSL::Linalgc::GSL_EDOM;
422*GSL_ERANGE = *Math::GSL::Linalgc::GSL_ERANGE;
423*GSL_EFAULT = *Math::GSL::Linalgc::GSL_EFAULT;
424*GSL_EINVAL = *Math::GSL::Linalgc::GSL_EINVAL;
425*GSL_EFAILED = *Math::GSL::Linalgc::GSL_EFAILED;
426*GSL_EFACTOR = *Math::GSL::Linalgc::GSL_EFACTOR;
427*GSL_ESANITY = *Math::GSL::Linalgc::GSL_ESANITY;
428*GSL_ENOMEM = *Math::GSL::Linalgc::GSL_ENOMEM;
429*GSL_EBADFUNC = *Math::GSL::Linalgc::GSL_EBADFUNC;
430*GSL_ERUNAWAY = *Math::GSL::Linalgc::GSL_ERUNAWAY;
431*GSL_EMAXITER = *Math::GSL::Linalgc::GSL_EMAXITER;
432*GSL_EZERODIV = *Math::GSL::Linalgc::GSL_EZERODIV;
433*GSL_EBADTOL = *Math::GSL::Linalgc::GSL_EBADTOL;
434*GSL_ETOL = *Math::GSL::Linalgc::GSL_ETOL;
435*GSL_EUNDRFLW = *Math::GSL::Linalgc::GSL_EUNDRFLW;
436*GSL_EOVRFLW = *Math::GSL::Linalgc::GSL_EOVRFLW;
437*GSL_ELOSS = *Math::GSL::Linalgc::GSL_ELOSS;
438*GSL_EROUND = *Math::GSL::Linalgc::GSL_EROUND;
439*GSL_EBADLEN = *Math::GSL::Linalgc::GSL_EBADLEN;
440*GSL_ENOTSQR = *Math::GSL::Linalgc::GSL_ENOTSQR;
441*GSL_ESING = *Math::GSL::Linalgc::GSL_ESING;
442*GSL_EDIVERGE = *Math::GSL::Linalgc::GSL_EDIVERGE;
443*GSL_EUNSUP = *Math::GSL::Linalgc::GSL_EUNSUP;
444*GSL_EUNIMPL = *Math::GSL::Linalgc::GSL_EUNIMPL;
445*GSL_ECACHE = *Math::GSL::Linalgc::GSL_ECACHE;
446*GSL_ETABLE = *Math::GSL::Linalgc::GSL_ETABLE;
447*GSL_ENOPROG = *Math::GSL::Linalgc::GSL_ENOPROG;
448*GSL_ENOPROGJ = *Math::GSL::Linalgc::GSL_ENOPROGJ;
449*GSL_ETOLF = *Math::GSL::Linalgc::GSL_ETOLF;
450*GSL_ETOLX = *Math::GSL::Linalgc::GSL_ETOLX;
451*GSL_ETOLG = *Math::GSL::Linalgc::GSL_ETOLG;
452*GSL_EOF = *Math::GSL::Linalgc::GSL_EOF;
453*GSL_LINALG_MOD_NONE = *Math::GSL::Linalgc::GSL_LINALG_MOD_NONE;
454*GSL_LINALG_MOD_TRANSPOSE = *Math::GSL::Linalgc::GSL_LINALG_MOD_TRANSPOSE;
455*GSL_LINALG_MOD_CONJUGATE = *Math::GSL::Linalgc::GSL_LINALG_MOD_CONJUGATE;
456
457@EXPORT_OK = qw/$GSL_LINALG_MOD_NONE $GSL_LINALG_MOD_TRANSPOSE $GSL_LINALG_MOD_CONJUGATE
458                gsl_linalg_matmult gsl_linalg_matmult_mod
459                gsl_linalg_exponential_ss
460                gsl_linalg_householder_transform
461                gsl_linalg_complex_householder_transform
462                gsl_linalg_householder_hm
463                gsl_linalg_householder_mh
464                gsl_linalg_householder_hv
465                gsl_linalg_householder_hm1
466                gsl_linalg_complex_householder_hm
467                gsl_linalg_complex_householder_mh
468                gsl_linalg_complex_householder_hv
469                gsl_linalg_hessenberg_decomp
470                gsl_linalg_hessenberg_unpack
471                gsl_linalg_hessenberg_unpack_accum
472                gsl_linalg_hessenberg_set_zero
473                gsl_linalg_hessenberg_submatrix
474                gsl_linalg_hessenberg
475                gsl_linalg_hesstri_decomp
476                gsl_linalg_SV_decomp
477                gsl_linalg_SV_decomp_mod
478                gsl_linalg_SV_decomp_jacobi
479                gsl_linalg_SV_solve
480                gsl_linalg_LU_decomp
481                gsl_linalg_LU_solve
482                gsl_linalg_LU_svx
483                gsl_linalg_LU_refine
484                gsl_linalg_LU_invert
485                gsl_linalg_LU_det
486                gsl_linalg_LU_lndet
487                gsl_linalg_LU_sgndet
488                gsl_linalg_complex_LU_decomp
489                gsl_linalg_complex_LU_solve
490                gsl_linalg_complex_LU_svx
491                gsl_linalg_complex_LU_refine
492                gsl_linalg_complex_LU_invert
493                gsl_linalg_complex_LU_det
494                gsl_linalg_complex_LU_lndet
495                gsl_linalg_complex_LU_sgndet
496                gsl_linalg_QR_decomp
497                gsl_linalg_QR_solve
498                gsl_linalg_QR_svx
499                gsl_linalg_QR_lssolve
500                gsl_linalg_QR_QRsolve
501                gsl_linalg_QR_Rsolve
502                gsl_linalg_QR_Rsvx
503                gsl_linalg_QR_update
504                gsl_linalg_QR_QTvec
505                gsl_linalg_QR_Qvec
506                gsl_linalg_QR_QTmat
507                gsl_linalg_QR_unpack
508                gsl_linalg_R_solve
509                gsl_linalg_R_svx
510                gsl_linalg_QRPT_decomp
511                gsl_linalg_QRPT_decomp2
512                gsl_linalg_QRPT_solve
513                gsl_linalg_QRPT_svx
514                gsl_linalg_QRPT_QRsolve
515                gsl_linalg_QRPT_Rsolve
516                gsl_linalg_QRPT_Rsvx
517                gsl_linalg_QRPT_update
518                gsl_linalg_LQ_decomp
519                gsl_linalg_LQ_solve_T
520                gsl_linalg_LQ_svx_T
521                gsl_linalg_LQ_lssolve_T
522                gsl_linalg_LQ_Lsolve_T
523                gsl_linalg_LQ_Lsvx_T
524                gsl_linalg_L_solve_T
525                gsl_linalg_LQ_vecQ
526                gsl_linalg_LQ_vecQT
527                gsl_linalg_LQ_unpack
528                gsl_linalg_LQ_update
529                gsl_linalg_LQ_LQsolve
530                gsl_linalg_PTLQ_decomp
531                gsl_linalg_PTLQ_decomp2
532                gsl_linalg_PTLQ_solve_T
533                gsl_linalg_PTLQ_svx_T
534                gsl_linalg_PTLQ_LQsolve_T
535                gsl_linalg_PTLQ_Lsolve_T
536                gsl_linalg_PTLQ_Lsvx_T
537                gsl_linalg_PTLQ_update
538                gsl_linalg_cholesky_decomp
539                gsl_linalg_cholesky_solve
540                gsl_linalg_cholesky_svx
541                gsl_linalg_cholesky_decomp_unit
542                gsl_linalg_complex_cholesky_decomp
543                gsl_linalg_complex_cholesky_solve
544                gsl_linalg_complex_cholesky_svx
545                gsl_linalg_symmtd_decomp
546                gsl_linalg_symmtd_unpack
547                gsl_linalg_symmtd_unpack_T
548                gsl_linalg_hermtd_decomp
549                gsl_linalg_hermtd_unpack
550                gsl_linalg_hermtd_unpack_T
551                gsl_linalg_HH_solve
552                gsl_linalg_HH_svx
553                gsl_linalg_solve_symm_tridiag
554                gsl_linalg_solve_tridiag
555                gsl_linalg_solve_symm_cyc_tridiag
556                gsl_linalg_solve_cyc_tridiag
557                gsl_linalg_bidiag_decomp
558                gsl_linalg_bidiag_unpack
559                gsl_linalg_bidiag_unpack2
560                gsl_linalg_bidiag_unpack_B
561                gsl_linalg_balance_matrix
562                gsl_linalg_balance_accum
563                gsl_linalg_balance_columns
564                gsl_linalg_givens gsl_linalg_givens_gv
565       /;
566%EXPORT_TAGS = ( all =>[ @EXPORT_OK ] );
567
568__END__
569
570=encoding utf8
571
572=head1 NAME
573
574Math::GSL::Linalg - Functions for solving linear systems
575
576=head1 SYNOPSIS
577
578    use Math::GSL::Linalg qw/:all/;
579
580=head1 DESCRIPTION
581
582
583Here is a list of all the functions included in this module :
584
585=over
586
587=item gsl_linalg_matmult
588
589=item gsl_linalg_matmult_mod
590
591=item gsl_linalg_exponential_ss
592
593=item gsl_linalg_householder_transform
594
595=item gsl_linalg_complex_householder_transform
596
597=item gsl_linalg_householder_hm($tau, $v, $A) - This function applies the Householder matrix P defined by the scalar $tau and the vector $v to the left-hand side of the matrix $A. On output the result P A is stored in $A. The function returns 0 if it succeded, 1 otherwise.
598
599=item gsl_linalg_householder_mh($tau, $v, $A) - This function applies the Householder matrix P defined by the scalar $tau and the vector $v to the right-hand side of the matrix $A. On output the result A P is stored in $A.
600
601=item gsl_linalg_householder_hv($tau, $v, $w) - This function applies the Householder transformation P defined by the scalar $tau and the vector $v to the vector $w. On output the result P w is stored in $w.
602
603=item gsl_linalg_householder_hm1
604
605=item gsl_linalg_givens($a,$b,$c,$s)
606
607Performs a Givens rotation on the vector ($a,$b) and stores the answer in $c and $s.
608
609=item gsl_linalg_givens_gv($v, $i,$j, $c, $s)
610
611Performs a Givens rotation on the $i and $j-th elements of $v, storing them in $c and $s.
612
613=item gsl_linalg_complex_householder_hm($tau, $v, $A) - Does the same operation than gsl_linalg_householder_hm but with the complex matrix $A, the complex value $tau and the complex vector $v.
614
615=item gsl_linalg_complex_householder_mh($tau, $v, $A) - Does the same operation than gsl_linalg_householder_mh but with the complex matrix $A, the complex value $tau and the complex vector $v.
616
617=item gsl_linalg_complex_householder_hv($tau, $v, $w) - Does the same operation than gsl_linalg_householder_hv but with the complex value $tau and the complex vectors $v and $w.
618
619=item gsl_linalg_hessenberg_decomp($A, $tau) - This function computes the Hessenberg decomposition of the matrix $A by applying the similarity transformation H = U^T A U. On output, H is stored in the upper portion of $A. The information required to construct the matrix U is stored in the lower triangular portion of $A. U is a product of N - 2 Householder matrices. The Householder vectors are stored in the lower portion of $A (below the subdiagonal) and the Householder coefficients are stored in the vector $tau. tau must be of length N. The function returns 0 if it succeded, 1 otherwise.
620
621=item gsl_linalg_hessenberg_unpack($H, $tau, $U) - This function constructs the orthogonal matrix $U from the information stored in the Hessenberg matrix $H along with the vector $tau. $H and $tau are outputs from gsl_linalg_hessenberg_decomp.
622
623=item gsl_linalg_hessenberg_unpack_accum($H, $tau, $V) - This function is similar to gsl_linalg_hessenberg_unpack, except it accumulates the matrix U into $V, so that V' = VU. The matrix $V must be initialized prior to calling this function. Setting $V to the identity matrix provides the same result as gsl_linalg_hessenberg_unpack. If $H is order N, then $V must have N columns but may have any number of rows.
624
625=item gsl_linalg_hessenberg_set_zero($H) - This function sets the lower triangular portion of $H, below the subdiagonal, to zero. It is useful for clearing out the Householder vectors after calling gsl_linalg_hessenberg_decomp.
626
627=item gsl_linalg_hessenberg_submatrix
628
629=item gsl_linalg_hessenberg
630
631=item gsl_linalg_hesstri_decomp($A, $B, $U, $V, $work) - This function computes the Hessenberg-Triangular decomposition of the matrix pair ($A, $B). On output, H is stored in $A, and R is stored in $B. If $U and $V are provided (they may be null), the similarity transformations are stored in them. Additional workspace of length N is needed in the vector $work.
632
633=item gsl_linalg_SV_decomp($A, $V, $S, $work) - This function factorizes the M-by-N matrix $A into the singular value decomposition A = U S V^T for M >= N. On output the matrix $A is replaced by U. The diagonal elements of the singular value matrix S are stored in the vector $S. The singular values are non-negative and form a non-increasing sequence from S_1 to S_N. The matrix $V contains the elements of V in untransposed form. To form the product U S V^T it is necessary to take the transpose of V. A workspace of length N is required in vector $work. This routine uses the Golub-Reinsch SVD algorithm.
634
635=item gsl_linalg_SV_decomp_mod($A, $X, $V, $S, $work) - This function computes the SVD using the modified Golub-Reinsch algorithm, which is faster for M>>N. It requires the vector $work of length N and the N-by-N matrix $X as additional working space. $A and $V are matrices while $S is a vector.
636
637=item gsl_linalg_SV_decomp_jacobi($A, $V, $S) - This function computes the SVD of the M-by-N matrix $A using one-sided Jacobi orthogonalization for M >= N. The Jacobi method can compute singular values to higher relative accuracy than Golub-Reinsch algorithms. $V is a matrix while $S is a vector.
638
639=item gsl_linalg_SV_solve($U, $V, $S, $b, $x) - This function solves the system A x = b using the singular value decomposition ($U, $S, $V) of A given by gsl_linalg_SV_decomp. Only non-zero singular values are used in computing the solution. The parts of the solution corresponding to singular values of zero are ignored. Other singular values can be edited out by setting them to zero before calling this function. In the over-determined case where A has more rows than columns the system is solved in the least squares sense, returning the solution x which minimizes ||A x - b||_2.
640
641=item gsl_linalg_LU_decomp($a, $p) - factorize the matrix $a into the LU decomposition PA = LU. On output the diagonal and upper triangular part of the input matrix A contain the matrix U. The lower triangular part of the input matrix (excluding the diagonal) contains L. The diagonal elements of L are unity, and are not stored. The function returns two value, the first is 0 if the operation succeeded, 1 otherwise, and the second is the sign of the permutation.
642
643=item gsl_linalg_LU_solve($LU, $p, $b, $x) - This function solves the square system A x = b using the LU decomposition of the matrix A into (LU, p) given by gsl_linalg_LU_decomp. $LU is a matrix, $p a permutation and $b and $x are vectors. The function returns 1 if the operation succeded, 0 otherwise.
644
645=item gsl_linalg_LU_svx($LU, $p, $x) - This function solves the square system A x = b in-place using the LU decomposition of A into (LU,p). On input $x should contain the right-hand side b, which is replaced by the solution on output. $LU is a matrix, $p a permutation and $x is a vector. The function returns 1 if the operation succeded, 0 otherwise.
646
647=item gsl_linalg_LU_refine($A, $LU, $p, $b, $x, $residual) - This function apply an iterative improvement to $x, the solution of $A $x = $b, using the LU decomposition of $A into ($LU,$p). The initial residual $r = $A $x - $b (where $x and $b are vectors) is also computed and stored in the vector $residual.
648
649=item gsl_linalg_LU_invert($LU, $p, $inverse) - This function computes the inverse of a matrix A from its LU decomposition stored in the matrix $LU and the permutation $p, storing the result in the matrix $inverse.
650
651=item gsl_linalg_LU_det($LU, $signum) - This function returns the determinant of a matrix A from its LU decomposition stored in the $LU matrix. It needs the integer $signum which is the sign of the permutation returned by gsl_linalg_LU_decomp.
652
653=item gsl_linalg_LU_lndet($LU) - This function returns the logarithm of the absolute value of the determinant of a matrix A, from its LU decomposition stored in the $LU matrix.
654
655=item gsl_linalg_LU_sgndet($LU, $signum) - This functions computes the sign or phase factor of the determinant of a matrix A, det(A)/|det(A)|, from its LU decomposition, $LU.
656
657=item gsl_linalg_complex_LU_decomp($A, $p) - Does the same operation than gsl_linalg_LU_decomp but on the complex matrix $A.
658
659=item gsl_linalg_complex_LU_solve($LU, $p, $b, $x) - This functions solve the square system A x = b using the LU decomposition of A into ($LU, $p) given by  gsl_linalg_complex_LU_decomp.
660
661=item gsl_linalg_complex_LU_svx($LU, $p, $x) - Does the same operation than gsl_linalg_LU_svx but on the complex matrix $LU and the complex vector $x.
662
663=item gsl_linalg_complex_LU_refine($A, $LU, $p, $b, $x, $residual) - Does the same operation than gsl_linalg_LU_refine but on the complex matrices $A and $LU and with the complex vectors $b, $x and $residual.
664
665=item gsl_linalg_complex_LU_invert($LU, $p, $inverse) - Does the same operation than gsl_linalg_LU_invert but on the complex matrces $LU and $inverse.
666
667=item gsl_linalg_complex_LU_det($LU, $signum) - Does the same operation than gsl_linalg_LU_det but on the complex matrix $LU.
668
669=item gsl_linalg_complex_LU_lndet($LU) - Does the same operation than gsl_linalg_LU_det but on the complex matrix $LU.
670
671=item gsl_linalg_complex_LU_sgndet($LU, $signum) - Does the same operation than gsl_linalg_LU_sgndet but on the complex matrix $LU.
672
673=item gsl_linalg_QR_decomp($a, $tau) - factorize the M-by-N matrix A into the QR decomposition A = Q R. On output the diagonal and upper triangular part of the input matrix $a contain the matrix R. The vector $tau and the columns of the lower triangular part of the matrix $a contain the Householder coefficients and Householder vectors which encode the orthogonal matrix Q. The vector tau must be of length k= min(M,N).
674
675=item gsl_linalg_QR_solve($QR, $tau, $b, $x) - This function solves the square system A x = b using the QR decomposition of A into (QR, tau) given by gsl_linalg_QR_decomp. $QR is matrix, and $tau, $b and $x are vectors.
676
677=item gsl_linalg_QR_svx($QR, $tau, $x) - This function solves the square system A x = b in-place using the QR decomposition of A into the matrix $QR and the vector $tau given by gsl_linalg_QR_decomp. On input, the vector $x should contain the right-hand side b, which is replaced by the solution on output.
678
679=item gsl_linalg_QR_lssolve($QR, $tau, $b, $x, $residual) - This function finds the least squares solution to the overdetermined system $A $x = $b where the matrix $A has more rows than columns. The least squares solution minimizes the Euclidean norm of the residual, ||Ax - b||.The routine uses the $QR decomposition of $A into ($QR, $tau) given by gsl_linalg_QR_decomp. The solution is returned in $x. The residual is computed as a by-product and stored in residual. The function returns 0 if it succeded, 1 otherwise.
680
681=item gsl_linalg_QR_QRsolve($Q, $R, $b, $x) - This function solves the system $R $x = $Q**T $b for $x. It can be used when the $QR decomposition of a matrix is available in unpacked form as ($Q, $R). The function returns 0 if it succeded, 1 otherwise.
682
683=item gsl_linalg_QR_Rsolve($QR, $b, $x) - This function solves the triangular system R $x = $b for $x. It may be useful if the product b' = Q^T b has already been computed using gsl_linalg_QR_QTvec.
684
685=item gsl_linalg_QR_Rsvx($QR, $x) - This function solves the triangular system R $x = b for $x in-place. On input $x should contain the right-hand side b and is replaced by the solution on output. This function may be useful if the product b' = Q^T b has already been computed using gsl_linalg_QR_QTvec. The function returns 0 if it succeded, 1 otherwise.
686
687=item gsl_linalg_QR_update($Q, $R, $b, $x) - This function performs a rank-1 update $w $v**T of the QR decomposition ($Q, $R). The update is given by Q'R' = Q R + w v^T where the output matrices Q' and R' are also orthogonal and right triangular. Note that w is destroyed by the update. The function returns 0 if it succeded, 1 otherwise.
688
689=item gsl_linalg_QR_QTvec($QR, $tau, $v) - This function applies the matrix Q^T encoded in the decomposition ($QR,$tau) to the vector $v, storing the result Q^T v in $v. The matrix multiplication is carried out directly using the encoding of the Householder vectors without needing to form the full matrix Q^T. The function returns 0 if it succeded, 1 otherwise.
690
691=item gsl_linalg_QR_Qvec($QR, $tau, $v) - This function applies the matrix Q encoded in the decomposition ($QR,$tau) to the vector $v, storing the result Q v in $v. The matrix multiplication is carried out directly using the encoding of the Householder vectors without needing to form the full matrix Q. The function returns 0 if it succeded, 1 otherwise.
692
693=item gsl_linalg_QR_QTmat($QR, $tau, $A) - This function applies the matrix Q^T encoded in the decomposition ($QR,$tau) to the matrix $A, storing the result Q^T A in $A. The matrix multiplication is carried out directly using the encoding of the Householder vectors without needing to form the full matrix Q^T. The function returns 0 if it succeded, 1 otherwise.
694
695=item gsl_linalg_QR_unpack($QR, $tau, $Q, $R) - This function unpacks the encoded QR decomposition ($QR,$tau) into the matrices $Q and $R, where $Q is M-by-M and $R is M-by-N. The function returns 0 if it succeded, 1 otherwise.
696
697=item gsl_linalg_R_solve($R, $b, $x) - This function solves the triangular system $R $x = $b for the N-by-N matrix $R. The function returns 0 if it succeded, 1 otherwise.
698
699=item gsl_linalg_R_svx($R, $x) - This function solves the triangular system $R $x = b in-place. On input $x should contain the right-hand side b, which is replaced by the solution on output. The function returns 0 if it succeded, 1 otherwise.
700
701=item gsl_linalg_QRPT_decomp($A, $tau, $p, $norm) - This function factorizes the M-by-N matrix $A into the QRP^T decomposition A = Q R P^T. On output the diagonal and upper triangular part of the input matrix contain the matrix R. The permutation matrix P is stored in the permutation $p. There's two value returned by this function : the first is 0 if the operation succeeded, 1 otherwise. The second is sign of the permutation. It has the value (-1)^n, where n is the number of interchanges in the permutation. The vector $tau and the columns of the lower triangular part of the matrix $A contain the Householder coefficients and vectors which encode the orthogonal matrix Q. The vector tau must be of length k=\min(M,N). The matrix Q is related to these components by, Q = Q_k ... Q_2 Q_1 where Q_i = I - \tau_i v_i v_i^T and v_i is the Householder vector v_i = (0,...,1,A(i+1,i),A(i+2,i),...,A(m,i)). This is the same storage scheme as used by lapack. The vector norm is a workspace of length N used for column pivoting. The algorithm used to perform the decomposition is Householder QR with column pivoting (Golub & Van Loan, Matrix Computations, Algorithm 5.4.1).
702
703=item gsl_linalg_QRPT_decomp2($A, $q, $r, $tau, $p, $norm)  - This function factorizes the matrix $A into the decomposition A = Q R P^T without modifying $A itself and storing the output in the separate matrices $q and $r. For the rest, it operates exactly like gsl_linalg_QRPT_decomp
704
705=item gsl_linalg_QRPT_solve
706
707=item gsl_linalg_QRPT_svx
708
709=item gsl_linalg_QRPT_QRsolve
710
711=item gsl_linalg_QRPT_Rsolve
712
713=item gsl_linalg_QRPT_Rsvx
714
715=item gsl_linalg_QRPT_update
716
717=item gsl_linalg_LQ_decomp
718
719=item gsl_linalg_LQ_solve_T
720
721=item gsl_linalg_LQ_svx_T
722
723=item gsl_linalg_LQ_lssolve_T
724
725=item gsl_linalg_LQ_Lsolve_T
726
727=item gsl_linalg_LQ_Lsvx_T
728
729=item gsl_linalg_L_solve_T
730
731=item gsl_linalg_LQ_vecQ
732
733=item gsl_linalg_LQ_vecQT
734
735=item gsl_linalg_LQ_unpack
736
737=item gsl_linalg_LQ_update
738
739=item gsl_linalg_LQ_LQsolve
740
741=item gsl_linalg_PTLQ_decomp
742
743=item gsl_linalg_PTLQ_decomp2
744
745=item gsl_linalg_PTLQ_solve_T
746
747=item gsl_linalg_PTLQ_svx_T
748
749=item gsl_linalg_PTLQ_LQsolve_T
750
751=item gsl_linalg_PTLQ_Lsolve_T
752
753=item gsl_linalg_PTLQ_Lsvx_T
754
755=item gsl_linalg_PTLQ_update
756
757=item gsl_linalg_cholesky_decomp($A) - Factorize the symmetric, positive-definite square matrix $A into the Cholesky decomposition A = L L^T and stores it into the matrix $A. The function returns 0 if the operation succeeded, 0 otherwise.
758
759=item gsl_linalg_cholesky_solve($cholesky, $b, $x) - This function solves the system A x = b using the Cholesky decomposition of A into the matrix $cholesky given by gsl_linalg_cholesky_decomp. $b and $x are vectors. The function returns 0 if the operation succeeded, 0 otherwise.
760
761=item gsl_linalg_cholesky_svx($cholesky, $x) - This function solves the system A x = b in-place using the Cholesky decomposition of A into the matrix $cholesky given by gsl_linalg_cholesky_decomp. On input the vector $x should contain the right-hand side b, which is replaced by the solution on output. The function returns 0 if the operation succeeded, 0 otherwise.
762
763=item gsl_linalg_cholesky_decomp_unit
764
765=item gsl_linalg_complex_cholesky_decomp($A) - Factorize the symmetric, positive-definite square matrix $A which contains complex numbers into the Cholesky decomposition A = L L^T and stores it into the matrix $A. The function returns 0 if the operation succeeded, 0 otherwise.
766
767=item gsl_linalg_complex_cholesky_solve($cholesky, $b, $x) - This function solves the system A x = b using the Cholesky decomposition of A into the matrix $cholesky given by gsl_linalg_complex_cholesky_decomp. $b and $x are vectors. The function returns 0 if the operation succeeded, 0 otherwise.
768
769=item gsl_linalg_complex_cholesky_svx($cholesky, $x) - This function solves the system A x = b in-place using the Cholesky decomposition of A into the matrix $cholesky given by gsl_linalg_complex_cholesky_decomp. On input the vector $x should contain the right-hand side b, which is replaced by the solution on output. The function returns 0 if the operation succeeded, 0 otherwise.
770
771=item gsl_linalg_symmtd_decomp($A, $tau) - This function factorizes the symmetric square matrix $A into the symmetric tridiagonal decomposition Q T Q^T. On output the diagonal and subdiagonal part of the input matrix $A contain the tridiagonal matrix T. The remaining lower triangular part of the input matrix contains the Householder vectors which, together with the Householder coefficients $tau, encode the orthogonal matrix Q. This storage scheme is the same as used by lapack. The upper triangular part of $A is not referenced. $tau is a vector.
772
773=item gsl_linalg_symmtd_unpack($A, $tau, $Q, $diag, $subdiag) - This function unpacks the encoded symmetric tridiagonal decomposition ($A, $tau) obtained from gsl_linalg_symmtd_decomp into the orthogonal matrix $Q, the vector of diagonal elements $diag and the vector of subdiagonal elements $subdiag.
774
775=item gsl_linalg_symmtd_unpack_T($A, $diag, $subdiag) - This function unpacks the diagonal and subdiagonal of the encoded symmetric tridiagonal decomposition ($A, $tau) obtained from gsl_linalg_symmtd_decomp into the vectors $diag and $subdiag.
776
777=item gsl_linalg_hermtd_decomp($A, $tau) - This function factorizes the hermitian matrix $A into the symmetric tridiagonal decomposition U T U^T. On output the real parts of the diagonal and subdiagonal part of the input matrix $A contain the tridiagonal matrix T. The remaining lower triangular part of the input matrix contains the Householder vectors which, together with the Householder coefficients $tau, encode the orthogonal matrix Q. This storage scheme is the same as used by lapack. The upper triangular part of $A and imaginary parts of the diagonal are not referenced. $A is a complex matrix and $tau a complex vector.
778
779=item gsl_linalg_hermtd_unpack($A, $tau, $U, $diag, $subdiag) - This function unpacks the encoded tridiagonal decomposition ($A, $tau) obtained from gsl_linalg_hermtd_decomp into the unitary complex  matrix $U, the real vector of diagonal elements $diag and the real vector of subdiagonal elements $subdiag.
780
781=item gsl_linalg_hermtd_unpack_T($A, $diag, $subdiag) - This function unpacks the diagonal and subdiagonal of the encoded tridiagonal decomposition (A, tau) obtained from the gsl_linalg_hermtd_decomp into the real vectors $diag and $subdiag.
782
783=item gsl_linalg_HH_solve($a, $b, $x) - This function solves the system $A $x = $b directly using Householder transformations where $A is a matrix, $b and $x vectors. On output the solution is stored in $x and $b is not modified. $A is destroyed by the Householder transformations.
784
785=item gsl_linalg_HH_svx($A, $x) - This function solves the system $A $x = b in-place using Householder transformations where $A is a matrix, $b is a vector. On input $x should contain the right-hand side b, which is replaced by the solution on output. The matrix $A is destroyed by the Householder transformations.
786
787=item gsl_linalg_solve_symm_tridiag
788
789=item gsl_linalg_solve_tridiag
790
791=item gsl_linalg_solve_symm_cyc_tridiag
792
793=item gsl_linalg_solve_cyc_tridiag
794
795=item gsl_linalg_bidiag_decomp
796
797=item gsl_linalg_bidiag_unpack
798
799=item gsl_linalg_bidiag_unpack2
800
801=item gsl_linalg_bidiag_unpack_B
802
803=item gsl_linalg_balance_matrix
804
805=item gsl_linalg_balance_accum
806
807=item gsl_linalg_balance_columns
808
809
810 You have to add the functions you want to use inside the qw /put_function_here / with spaces between each function. You can also write use Math::GSL::Complex qw/:all/ to use all available functions of the module.
811
812For more informations on the functions, we refer you to the GSL official documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>
813
814
815=back
816
817=head1 EXAMPLES
818
819This example shows how to compute the determinant of a matrix with the LU decomposition:
820
821 use Math::GSL::Matrix qw/:all/;
822 use Math::GSL::Permutation qw/:all/;
823 use Math::GSL::Linalg qw/:all/;
824
825 my $Matrix = gsl_matrix_alloc(4,4);
826 map { gsl_matrix_set($Matrix, 0, $_, $_+1) } (0..3);
827
828 gsl_matrix_set($Matrix,1, 0, 2);
829 gsl_matrix_set($Matrix, 1, 1, 3);
830 gsl_matrix_set($Matrix, 1, 2, 4);
831 gsl_matrix_set($Matrix, 1, 3, 1);
832
833 gsl_matrix_set($Matrix, 2, 0, 3);
834 gsl_matrix_set($Matrix, 2, 1, 4);
835 gsl_matrix_set($Matrix, 2, 2, 1);
836 gsl_matrix_set($Matrix, 2, 3, 2);
837
838 gsl_matrix_set($Matrix, 3, 0, 4);
839 gsl_matrix_set($Matrix, 3, 1, 1);
840 gsl_matrix_set($Matrix, 3, 2, 2);
841 gsl_matrix_set($Matrix, 3, 3, 3);
842
843 my $permutation = gsl_permutation_alloc(4);
844 gsl_permutation_init($permutation);
845 my ($result, $signum) = gsl_linalg_LU_decomp($Matrix, $permutation);
846 my $det = gsl_linalg_LU_det($Matrix, $signum);
847 print "The value of the determinant of the matrix is $det \n";
848
849=head1 AUTHORS
850
851Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
852
853=head1 COPYRIGHT AND LICENSE
854
855Copyright (C) 2008-2021 Jonathan "Duke" Leto and Thierry Moisan
856
857This program is free software; you can redistribute it and/or modify it
858under the same terms as Perl itself.
859
860=cut
8611;
862