annotate scripts/sparse/bicg.m @ 27918:b442ec6dda5c

use centralized file for copyright info for individual contributors * COPYRIGHT.md: New file. * In most other files, use "Copyright (C) YYYY-YYYY The Octave Project Developers" instead of tracking individual names in separate source files. The motivation is to reduce the effort required to update the notices each year. Until now, the Octave source files contained copyright notices that list individual contributors. I adopted these file-scope copyright notices because that is what everyone was doing 30 years ago in the days before distributed version control systems. But now, with many contributors and modern version control systems, having these file-scope copyright notices causes trouble when we update copyright years or refactor code. Over time, the file-scope copyright notices may become outdated as new contributions are made or code is moved from one file to another. Sometimes people contribute significant patches but do not add a line claiming copyright. Other times, people add a copyright notice for their contribution but then a later refactoring moves part or all of their contribution to another file and the notice is not moved with the code. As a practical matter, moving such notices is difficult -- determining what parts are due to a particular contributor requires a time-consuming search through the project history. Even managing the yearly update of copyright years is problematic. We have some contributors who are no longer living. Should we update the copyright dates for their contributions when we release new versions? Probably not, but we do still want to claim copyright for the project as a whole. To minimize the difficulty of maintaining the copyright notices, I would like to change Octave's sources to use what is described here: https://softwarefreedom.org/resources/2012/ManagingCopyrightInformation.html in the section "Maintaining centralized copyright notices": The centralized notice approach consolidates all copyright notices in a single location, usually a top-level file. This file should contain all of the copyright notices provided project contributors, unless the contribution was clearly insignificant. It may also credit -- without a copyright notice -- anyone who helped with the project but did not contribute code or other copyrighted material. This approach captures less information about contributions within individual files, recognizing that the DVCS is better equipped to record those details. As we mentioned before, it does have one disadvantage as compared to the file-scope approach: if a single file is separated from the distribution, the recipient won't see the contributors' copyright notices. But this can be easily remedied by including a single copyright notice in each file's header, pointing to the top-level file: Copyright YYYY-YYYY The Octave Project Developers See the COPYRIGHT file at the top-level directory of this distribution or at https://octave.org/COPYRIGHT.html. followed by the usual GPL copyright statement. For more background, see the discussion here: https://lists.gnu.org/archive/html/octave-maintainers/2020-01/msg00009.html Most files in the following directories have been skipped intentinally in this changeset: doc libgui/qterminal liboctave/external m4
author John W. Eaton <jwe@octave.org>
date Mon, 06 Jan 2020 15:38:17 -0500
parents 4e632e942e84
children 1891570abac8
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1 ## Copyright (C) 2006-2019 The Octave Project Developers
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2 ##
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution
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4 ## or <https://octave.org/COPYRIGHT.html/>.
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5 ##
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6 ##
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7 ## This file is part of Octave.
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8 ##
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9 ## Octave is free software: you can redistribute it and/or modify it
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10 ## under the terms of the GNU General Public License as published by
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11 ## the Free Software Foundation, either version 3 of the License, or
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12 ## (at your option) any later version.
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13 ##
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14 ## Octave is distributed in the hope that it will be useful, but
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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17 ## GNU General Public License for more details.
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18 ##
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19 ## You should have received a copy of the GNU General Public License
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20 ## along with Octave; see the file COPYING. If not, see
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21 ## <https://www.gnu.org/licenses/>.
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22
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23 ## -*- texinfo -*-
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24 ## @deftypefn {} {@var{x} =} bicg (@var{A}, @var{b})
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25 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol})
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26 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit})
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27 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M})
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28 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2})
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29 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M}, [], @var{x0})
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30 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
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31 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M}, [], @var{x0}, @dots{})
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32 ## @deftypefnx {} {@var{x} =} bicg (@var{A}, @var{b}, @var{tol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0}, @dots{})
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33 ## @deftypefnx {} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} bicg (@var{A}, @var{b}, @dots{})
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34 ## Solve the linear system of equations @w{@code{@var{A} * @var{x} = @var{b}}}
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35 ## by means of the Bi-Conjugate Gradient iterative method.
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36 ##
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37 ## The input arguments are:
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38 ##
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39 ## @itemize
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40 ##
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41 ## @item @var{A} is the matrix of the linear system and it must be square.
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42 ## @var{A} can be passed as a matrix, function handle, or inline function
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43 ## @code{Afun} such that @w{@code{Afun (x, "notransp") = A * x}} and
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44 ## @w{@code{Afun (x, "transp") = A' * x}}. Additional parameters to
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45 ## @code{Afun} may be passed after @var{x0}.
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46 ##
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47 ## @item @var{b} is the right-hand side vector. It must be a column vector
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48 ## with the same number of rows as @var{A}.
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49 ##
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50 ## @item
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51 ## @var{tol} is the required relative tolerance for the residual error,
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52 ## @w{@code{@var{b} - @var{A} * @var{x}}}. The iteration stops if
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53 ## @w{@code{norm (@var{b} - @var{A} * @var{x})} @leq{}
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54 ## @w{@code{@var{tol} * norm (@var{b})}}}.
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55 ## If @var{tol} is omitted or empty, then a tolerance of 1e-6 is used.
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56 ##
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57 ## @item
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58 ## @var{maxit} is the maximum allowed number of iterations; if @var{maxit}
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59 ## is omitted or empty then a value of 20 is used.
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60 ##
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61 ## @item
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62 ## @var{M1}, @var{M2} are the preconditioners. The preconditioner @var{M} is
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63 ## given as @code{@var{M} = @var{M1} * @var{M2}}. Both @var{M1} and @var{M2}
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64 ## can be passed as a matrix or as a function handle or inline function
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65 ## @code{g} such that @w{@code{g (@var{x}, "notransp") = @var{M1} \ @var{x}}}
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66 ## or @w{@code{g (@var{x}, "notransp") = @var{M2} \ @var{x}}} and
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67 ## @w{@code{g (@var{x}, "transp") = @var{M1}' \ @var{x}}} or
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68 ## @w{@code{g (@var{x}, "transp") = @var{M2}' \ @var{x}}}.
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69 ## If @var{M1} is omitted or empty, then preconditioning is not applied.
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70 ## The preconditioned system is theoretically equivalent to applying the
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71 ## @code{bicg} method to the linear system
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72 ## @code{inv (@var{M1}) * A * inv (@var{M2}) * @var{y} = inv
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73 ## (@var{M1}) * @var{b}} and
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74 ## @code{inv (@var{M2'}) * A' * inv (@var{M1'}) * @var{z} =
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75 ## inv (@var{M2'}) * @var{b}} and then setting
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76 ## @code{@var{x} = inv (@var{M2}) * @var{y}}.
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77 ##
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78 ## @item
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79 ## @var{x0} is the initial guess. If @var{x0} is omitted or empty then the
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80 ## function sets @var{x0} to a zero vector by default.
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81 ## @end itemize
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82 ##
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83 ## Any arguments which follow @var{x0} are treated as parameters, and passed in
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84 ## an appropriate manner to any of the functions (@var{Afun} or @var{Mfun}) or
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85 ## that have been given to @code{bicg}.
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86 ##
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87 ## The output parameters are:
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88 ##
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89 ## @itemize
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90 ##
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91 ## @item
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92 ## @var{x} is the computed approximation to the solution of
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93 ## @w{@code{@var{A} * @var{x} = @var{b}}}. If the algorithm did not converge,
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94 ## then @var{x} is the iteration which has the minimum residual.
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95 ##
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96 ## @item
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97 ## @var{flag} indicates the exit status:
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98 ##
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99 ## @itemize
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100 ## @item 0: The algorithm converged to within the prescribed tolerance.
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101 ##
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102 ## @item 1: The algorithm did not converge and it reached the maximum number of
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103 ## iterations.
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104 ##
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105 ## @item 2: The preconditioner matrix is singular.
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106 ##
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107 ## @item 3: The algorithm stagnated, i.e., the absolute value of the
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108 ## difference between the current iteration @var{x} and the previous is less
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109 ## than @code{eps * norm (@var{x},2)}.
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110 ##
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111 ## @item 4: The algorithm could not continue because intermediate values
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112 ## became too small or too large for reliable computation.
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113 ## @end itemize
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114 ##
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115 ## @item
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116 ## @var{relres} is the ratio of the final residual to its initial value,
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117 ## measured in the Euclidean norm.
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118 ##
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119 ## @item
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120 ## @var{iter} is the iteration which @var{x} is computed.
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121 ##
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122 ## @item
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123 ## @var{resvec} is a vector containing the residual at each iteration.
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124 ## The total number of iterations performed is given by
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125 ## @code{length (@var{resvec}) - 1}.
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126 ## @end itemize
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127 ##
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128 ## Consider a trivial problem with a tridiagonal matrix
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129 ##
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130 ## @example
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131 ## @group
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132 ## n = 20;
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133 ## A = toeplitz (sparse ([1, 1], [1, 2], [2, 1] * n ^ 2, 1, n)) + ...
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134 ## toeplitz (sparse (1, 2, -1, 1, n) * n / 2, ...
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135 ## sparse (1, 2, 1, 1, n) * n / 2);
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136 ## b = A * ones (n, 1);
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137 ## restart = 5;
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138 ## [M1, M2] = ilu (A); # in this tridiag case, it corresponds to lu (A)
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139 ## M = M1 * M2;
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140 ## Afun = @@(x, string) strcmp (string, "notransp") * (A * x) + ...
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141 ## strcmp (string, "transp") * (A' * x);
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142 ## Mfun = @@(x, string) strcmp (string, "notransp") * (M \ x) + ...
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143 ## strcmp (string, "transp") * (M' \ x);
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144 ## M1fun = @@(x, string) strcmp (string, "notransp") * (M1 \ x) + ...
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145 ## strcmp (string, "transp") * (M1' \ x);
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146 ## M2fun = @@(x, string) strcmp (string, "notransp") * (M2 \ x) + ...
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147 ## strcmp (string, "transp") * (M2' \ x);
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148 ## @end group
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149 ## @end example
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150 ##
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151 ## @sc{Example 1:} simplest usage of @code{bicg}
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152 ##
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153 ## @example
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154 ## x = bicg (A, b)
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155 ## @end example
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156 ##
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157 ## @sc{Example 2:} @code{bicg} with a function that computes
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158 ## @code{@var{A}*@var{x}} and @code{@var{A'}*@var{x}}
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159 ##
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160 ## @example
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161 ## x = bicg (Afun, b, [], n)
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162 ## @end example
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163 ##
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164 ## @sc{Example 3:} @code{bicg} with a preconditioner matrix @var{M}
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165 ##
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166 ## @example
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167 ## x = bicg (A, b, 1e-6, n, M)
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168 ## @end example
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169 ##
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170 ## @sc{Example 4:} @code{bicg} with a function as preconditioner
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171 ##
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172 ## @example
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173 ## x = bicg (Afun, b, 1e-6, n, Mfun)
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174 ## @end example
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175 ##
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176 ## @sc{Example 5:} @code{bicg} with preconditioner matrices @var{M1}
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177 ## and @var{M2}
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178 ##
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179 ## @example
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180 ## x = bicg (A, b, 1e-6, n, M1, M2)
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181 ## @end example
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182 ##
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183 ## @sc{Example 6:} @code{bicg} with functions as preconditioners
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184 ##
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185 ## @example
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186 ## x = bicg (Afun, b, 1e-6, n, M1fun, M2fun)
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187 ## @end example
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188 ##
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189 ## @sc{Example 7:} @code{bicg} with as input a function requiring an argument
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190 ##
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191 ## @example
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192 ## @group
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193 ## function y = Ap (A, x, string, z)
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194 ## ## compute A^z * x or (A^z)' * x
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195 ## y = x;
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196 ## if (strcmp (string, "notransp"))
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197 ## for i = 1:z
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198 ## y = A * y;
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199 ## endfor
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200 ## elseif (strcmp (string, "transp"))
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201 ## for i = 1:z
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202 ## y = A' * y;
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203 ## endfor
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204 ## endif
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205 ## endfunction
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206 ##
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207 ## Apfun = @@(x, string, p) Ap (A, x, string, p);
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208 ## x = bicg (Apfun, b, [], [], [], [], [], 2);
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209 ## @end group
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210 ## @end example
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211 ##
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212 ## References:
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213 ##
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214 ## @enumerate
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215 ##
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216 ## @item @nospell{Y. Saad}, @cite{Iterative Methods for Sparse Linear Systems},
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217 ## Second edition, 2003, SIAM.
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218 ##
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219 ## @end enumerate
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220 ##
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221 ## @seealso{bicgstab, cgs, gmres, pcg, qmr, tfqmr}
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222 ## @end deftypefn
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223
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224 function [x_min, flag, relres, iter_min, resvec] = ...
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225 bicg (A, b, tol = [], maxit = [], M1 = [], M2 = [], x0 = [], varargin)
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226
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227 [Afun, M1fun, M2fun] = __alltohandles__ (A, b, M1, M2, "bicg");
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228
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229 [tol, maxit, x0] = __default__input__ ({1e-06, min(rows(b), 20), ...
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230 zeros(rows (b),1)}, tol, maxit, x0);
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231
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232 if (columns (b) == 2)
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233 c = b(:,2);
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234 b = b(:,1);
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235 else
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236 c = b;
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237 endif
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238 norm_b = norm (b, 2);
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239
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240 if (norm_b == 0) # the only (only iff det(A) == 0) solution is x = 0
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241 if (nargout < 2)
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242 printf ("The right hand side vector is all zero so bicg\n")
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243 printf ("returned an all zero solution without iterating.\n")
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244 endif
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245 x_min = zeros (numel (b), 1);
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246 flag = 0;
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247 relres = 0;
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248 iter_min = 0;
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249 resvec = 0;
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250 return;
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251 endif
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252
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253 x = x_min = x_pr = x0;
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254 iter = iter_min = 0;
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255 flag = 1; # Default flag is "maximum number of iterations reached"
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256 resvec = zeros (maxit + 1, 1);
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257 r0 = b - Afun (x, "notransp", varargin{:}); # Residual of the system
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258 s0 = c - Afun (x, "transp", varargin{:}); # Res. of the "dual system"
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259 resvec(1) = norm (r0, 2);
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260
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261 try
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262 warning ("error", "Octave:singular-matrix", "local")
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263 prec_r0 = M1fun (r0, "notransp", varargin{:}); # r0 preconditioned
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264 prec_s0 = s0;
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265 prec_r0 = M2fun (prec_r0, "notransp", varargin{:});
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266 prec_s0 = M2fun (prec_s0, "transp", varargin{:});
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267 prec_s0 = M1fun (prec_s0, "transp", varargin{:}); # s0 preconditioned
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268 p = prec_r0; # Direction of the system
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269 q = prec_s0; # Direction of the "dual system"
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270 catch
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271 flag = 2;
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272 end_try_catch
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273
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274 while ((flag != 2) && (iter < maxit) && (resvec(iter+1) >= norm_b * tol))
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275 v = Afun (p, "notransp", varargin{:});
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276 prod_qv = q' * v;
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277 alpha = (s0' * prec_r0);
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278 if (abs (prod_qv) <= eps * abs (alpha))
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279 flag = 4;
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280 break
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281 endif
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282 alpha ./= prod_qv;
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283 x += alpha * p;
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284 prod_rs = (s0' * prec_r0); # Product between r0 and s0
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285 r0 -= alpha * v;
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286 s0 -= conj (alpha) * Afun (q, "transp", varargin{:});
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287 prec_r0 = M1fun (r0, "notransp", varargin{:});
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288 prec_s0 = s0;
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289 prec_r0 = M2fun (prec_r0, "notransp", varargin{:});
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290 beta = s0' * prec_r0;
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291 if (abs (prod_rs) <= abs (beta))
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292 flag = 4;
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293 break;
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294 endif
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295 beta ./= prod_rs;
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296 prec_s0 = M2fun (prec_s0, "transp", varargin{:});
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297 prec_s0 = M1fun (prec_s0, "transp", varargin{:});
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298 iter += 1;
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299 resvec(iter+1) = norm (r0);
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300 if (resvec(iter+1) <= resvec(iter_min+1))
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301 x_min = x;
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302 iter_min = iter;
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303 endif
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304 if (norm (x - x_pr) <= norm (x) * eps)
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305 flag = 3;
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306 break;
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307 endif
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308 p = prec_r0 + beta*p;
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309 q = prec_s0 + conj (beta) * q;
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310 endwhile
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311 resvec = resvec(1:iter+1,1);
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312
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313 if (flag == 2)
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314 relres = 1;
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315 else
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316 relres = resvec(iter_min+1) / norm_b;
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317 endif
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
318
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319 if ((flag == 1) && (relres <= tol))
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320 flag = 0;
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321 endif
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322
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323 if (nargout < 2)
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324 switch (flag)
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325 case 0
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326 printf ("bicg converged at iteration %i ", iter_min);
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327 printf ("to a solution with relative residual %e\n", relres);
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328 case 1
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329 printf ("bicg stopped at iteration %i ", iter);
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330 printf ("without converging to the desired tolerance %e\n", tol);
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331 printf ("because the maximum number of iterations was reached. ");
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332 printf ("The iterate returned (number %i) has ", iter_min);
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333 printf ("relative residual %e\n", relres);
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334 case 2
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335 printf ("bicg stopped at iteration %i ", iter);
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336 printf ("without converging to the desired tolerance %e\n", tol);
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337 printf ("because the preconditioner matrix is singular.\n");
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338 printf ("The iterate returned (number %i) ", iter_min);
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339 printf ("has relative residual %e\n", relres);
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340 case 3
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341 printf ("bicg stopped at iteration %i ", iter);
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342 printf ("without converging to the desired tolerance %e\n", tol);
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343 printf ("because the method stagnated.\n");
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344 printf ("The iterate returned (number %i) ", iter_min);
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345 printf ("has relative residual %e\n", relres);
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346 case 4
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347 printf ("bicg stopped at iteration %i ", iter);
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348 printf ("without converging to the desired tolerance %e\n", tol);
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349 printf ("because the method can't continue.\n");
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350 printf ("The iterate returned (number %i) ", iter_min);
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351 printf ("has relative residual %e\n", relres);
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352 endswitch
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353 endif
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354
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355 endfunction
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356
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357
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358 %!demo
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359 %! ## simplest use case
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360 %! n = 20;
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361 %! A = toeplitz (sparse ([1, 1], [1, 2], [2, 1] * n ^ 2, 1, n)) + ...
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362 %! toeplitz (sparse (1, 2, -1, 1, n) * n / 2, ...
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363 %! sparse (1, 2, 1, 1, n) * n / 2);
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364 %! b = A * ones (n, 1);
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365 %! [M1, M2] = ilu (A + 0.1 * eye (n));
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366 %! M = M1 * M2;
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367 %! x = bicg (A, b, [], n);
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368 %! function y = Ap (A, x, string, z)
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369 %! ## compute A^z * x or (A^z)' * x
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370 %! y = x;
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371 %! if (strcmp (string, "notransp"))
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372 %! for i = 1:z
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373 %! y = A * y;
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374 %! endfor
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375 %! elseif (strcmp (string, "transp"))
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376 %! for i = 1:z
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377 %! y = A' * y;
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378 %! endfor
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379 %! endif
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380 %! endfunction
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381 %!
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382 %! Afun = @(x, string) Ap (A, x, string, 1);
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383 %! x = bicg (Afun, b, [], n);
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384 %! x = bicg (A, b, 1e-6, n, M);
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385 %! x = bicg (A, b, 1e-6, n, M1, M2);
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386 %! function y = Mfun (M, x, string)
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387 %! if (strcmp (string, "notransp"))
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388 %! y = M \ x;
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389 %! else
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390 %! y = M' \ x;
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391 %! endif
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392 %! endfunction
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393 %!
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394 %! M1fun = @(x, string) Mfun (M, x, string);
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395 %! x = bicg (Afun, b, 1e-6, n, M1fun);
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396 %! M1fun = @(x, string) Mfun (M1, x, string);
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397 %! M2fun = @(x, string) Mfun (M2, x, string);
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398 %! x = bicg (Afun, b, 1e-6, n, M1fun, M2fun);
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399 %! Afun = @(x, string, p) Ap (A, x, string, p);
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400 %! ## Solution of A^2 * x = b
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401 %! x = bicg (Afun, b, [], 2*n, [], [], [], 2);
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
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diff changeset
402
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403 %!test
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404 %! ## Check that all type of inputs work
25152
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405 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
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406 %! b = A * ones (5, 1);
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407 %! M1 = diag (sqrt (diag (A)));
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408 %! M2 = M1;
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409 %! Afun = @(z, string) strcmp (string, "notransp") * (A * z) + ...
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410 %! strcmp (string, "transp") * (A' * z);
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411 %! M1_fun = @(z, string) strcmp (string,"notransp") * (M1 \ z) + ...
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diff changeset
412 %! strcmp (string, "transp") * (M1' \ z);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
413 %! M2_fun = @(z, string) strcmp (string, "notransp") * (M2 \ z) + ...
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
414 %! strcmp (string, "transp") * (M2' \ z);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
415 %! [x, flag] = bicg (A, b);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
416 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
417 %! [x, flag] = bicg (A, b, [], [], M1, M2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
418 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
419 %! [x, flag] = bicg (A, b, [], [], M1_fun, M2_fun);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
420 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
421 %! [x, flag] = bicg (A, b,[], [], M1_fun, M2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
422 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
423 %! [x, flag] = bicg (A, b,[], [], M1, M2_fun);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
424 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
425 %! [x, flag] = bicg (Afun, b);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
426 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
427 %! [x, flag] = bicg (Afun, b,[], [], M1, M2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
428 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
429 %! [x, flag] = bicg (Afun, b,[], [], M1_fun, M2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
430 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
431 %! [x, flag] = bicg (Afun, b,[], [], M1, M2_fun);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
432 %! assert (flag, 0);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
433 %! [x, flag] = bicg (Afun, b,[], [], M1_fun, M2_fun);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
434 %! assert (flag, 0);
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
435
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
436 %!test
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
437 %! n = 100;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
438 %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
439 %! b = sum (A, 2);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
440 %! tol = 1e-8;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
441 %! maxit = 15;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
442 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
443 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
444 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, maxit, M1, M2);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
445 %! assert (norm (b - A*x) / norm (b), 0, tol);
13796
53674ceb9133 maint: fix function definition in test
John W. Eaton <jwe@octave.org>
parents: 13141
diff changeset
446
53674ceb9133 maint: fix function definition in test
John W. Eaton <jwe@octave.org>
parents: 13141
diff changeset
447 %!function y = afun (x, t, a)
16933
e39f00a32dc7 maint: Use parentheses around condition for switch(),while(),if() statements.
Rik <rik@octave.org>
parents: 16816
diff changeset
448 %! switch (t)
17174
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
449 %! case "notransp"
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
450 %! y = a * x;
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
451 %! case "transp"
c3c1ebfaa7dc maint: Use common indentation for switch statement.
Rik <rik@octave.org>
parents: 16933
diff changeset
452 %! y = a' * x;
13796
53674ceb9133 maint: fix function definition in test
John W. Eaton <jwe@octave.org>
parents: 13141
diff changeset
453 %! endswitch
53674ceb9133 maint: fix function definition in test
John W. Eaton <jwe@octave.org>
parents: 13141
diff changeset
454 %!endfunction
53674ceb9133 maint: fix function definition in test
John W. Eaton <jwe@octave.org>
parents: 13141
diff changeset
455 %!
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
456 %!test
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
457 %! n = 100;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
458 %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
459 %! b = sum (A, 2);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
460 %! tol = 1e-8;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
461 %! maxit = 15;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
462 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
463 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
464 %!
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
465 %! [x, flag, relres, iter, resvec] = bicg (@(x, t) afun (x, t, A),
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
466 %! b, tol, maxit, M1, M2);
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
467 %! assert (x, ones (size (b)), 1e-7);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
468
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
469 %!test
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
470 %! n = 100;
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
471 %! tol = 1e-8;
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
472 %! a = sprand (n, n, .1);
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
473 %! A = a' * a + 100 * eye (n);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
474 %! b = sum (A, 2);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
475 %! [x, flag, relres, iter, resvec] = bicg (A, b, tol, [], diag (diag (A)));
13021
d55d396a9a55 Add an implementation of the biconjugate gradient iterative method
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
476 %! assert (x, ones (size (b)), 1e-7);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
477
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
478 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
479 %! ## Check that if the preconditioner is singular, the method doesn't work
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
480 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
481 %! b = ones (5,1);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
482 %! M = ones (5);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
483 %! [x, flag] = bicg (A, b, [], [], M);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
484 %! assert (flag, 2);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
485
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
486 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
487 %! ## If A singular, the algorithm doesn't work due to division by zero
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
488 %! A = ones (5);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
489 %! b = [1:5]';
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
490 %! [x, flag] = bicg (A, b);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
491 %! assert (flag, 4);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
492
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
493 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
494 %! ## test for a complex linear system
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
495 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]) + ...
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
496 %! 1i * toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
497 %! b = sum (A, 2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
498 %! [x, flag] = bicg (A, b);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
499 %! assert (flag, 0);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
500
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
501 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
502 %! A = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
503 %! b = 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
504 %! [x, flag] = bicg (A, b);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
505 %! assert (class (x), "single");
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
506
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
507 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
508 %! A = 1;
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
509 %! b = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
510 %! [x, flag] = bicg (A, b);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
511 %! assert (class (x), "single");
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
512
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
513 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
514 %! A = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
515 %! b = single (1);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
516 %! [x, flag] = bicg (A, b);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
517 %! assert (class (x), "single");
24860
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Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
518
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
519 %!test
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
520 %!function y = Afun (x, trans)
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
521 %! A = sparse (toeplitz ([2, 1, 0, 0], [2, -1, 0, 0]));
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
522 %! if (strcmp (trans, "notransp"))
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
523 %! y = A * x;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
524 %! else
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
525 %! y = A' * x;
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
526 %! endif
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
527 %!endfunction
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
528 %!
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
529 %! [x, flag] = bicg ("Afun", [1; 2; 2; 3]);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
530 %! assert (x, ones (4, 1), 1e-6);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
531
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
532 %!test
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
533 %! ## unpreconditioned residual
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
534 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
535 %! b = sum (A, 2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
536 %! M = magic (5);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
537 %! [x, flag, relres] = bicg (A, b, [], 2, M);
26160
b9debf4436aa bicg.m: Relax BIST test by 1eps to pass on some systems (bug #55132).
Rik <rik@octave.org>
parents: 25579
diff changeset
538 %! assert (norm (b - A * x) / norm (b), 0, relres + eps);
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
539
24863
009ed89dd0fa test: make bicg and pcg tests conditional on CHOLMOD and UMFPACK
Mike Miller <mtmiller@octave.org>
parents: 24860
diff changeset
540 ## Preconditioned technique
009ed89dd0fa test: make bicg and pcg tests conditional on CHOLMOD and UMFPACK
Mike Miller <mtmiller@octave.org>
parents: 24860
diff changeset
541 %!testif HAVE_UMFPACK
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
542 %! A = sparse (toeplitz ([2, 1, 0, 0, 0], [2, -1, 0, 0, 0]));
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
543 %! b = sum (A, 2);
25159
b8279dd83664 Turn off warning about sparse lu factorization in bicg BIST test (bug #53390).
Marco Caliari <marco.caliari@univr.it>
parents: 25152
diff changeset
544 %! warning ("off", "Octave:lu:sparse_input", "local");
24860
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
545 %! [M1, M2] = lu (A + eye (5));
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
546 %! [x, flag] = bicg (A, b, [], 1, M1, M2);
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
547 %! ## b has two columns!
6266e321ef22 Merge code from SoCiS 2016 "Improve iterative methods" project (http://socis16octave-improveiterativemethods.blogspot.com)
Cristiano Dorigo <cristiano.dorigo@hotmail.it>
parents: 24534
diff changeset
548 %! [y, flag] = bicg (M1 \ A / M2, [M1 \ b, M2' \ b], [], 1);
25152
ad37f04a2eb7 bicg.m: Overhaul GSOC-improved code to conform to Octave conventions.
Rik <rik@octave.org>
parents: 25054
diff changeset
549 %! assert (x, M2 \ y, 8 * eps);