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maint: Update copyright notices for release.
author John W. Eaton <jwe@octave.org>
date Wed, 23 Oct 2013 22:09:27 -0400
parents 1c89599167a6
children 0f912af348e0
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1 ## Copyright (C) 2005-2013 David Bateman
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{d} =} eigs (@var{A})
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21 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{k})
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22 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{k}, @var{sigma})
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23 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{k}, @var{sigma}, @var{opts})
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24 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{B})
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25 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{B}, @var{k})
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26 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{B}, @var{k}, @var{sigma})
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27 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{A}, @var{B}, @var{k}, @var{sigma}, @var{opts})
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28 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n})
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29 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{B})
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30 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{k})
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31 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k})
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32 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{k}, @var{sigma})
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33 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k}, @var{sigma})
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34 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{k}, @var{sigma}, @var{opts})
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35 ## @deftypefnx {Function File} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k}, @var{sigma}, @var{opts})
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36 ## @deftypefnx {Function File} {[@var{V}, @var{d}] =} eigs (@var{A}, @dots{})
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37 ## @deftypefnx {Function File} {[@var{V}, @var{d}] =} eigs (@var{af}, @var{n}, @dots{})
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38 ## @deftypefnx {Function File} {[@var{V}, @var{d}, @var{flag}] =} eigs (@var{A}, @dots{})
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39 ## @deftypefnx {Function File} {[@var{V}, @var{d}, @var{flag}] =} eigs (@var{af}, @var{n}, @dots{})
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40 ## Calculate a limited number of eigenvalues and eigenvectors of @var{A},
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41 ## based on a selection criteria. The number of eigenvalues and eigenvectors to
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42 ## calculate is given by @var{k} and defaults to 6.
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43 ##
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44 ## By default, @code{eigs} solve the equation
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45 ## @tex
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46 ## $A \nu = \lambda \nu$,
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47 ## @end tex
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48 ## @ifinfo
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49 ## @code{A * v = lambda * v},
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50 ## @end ifinfo
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51 ## where
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52 ## @tex
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53 ## $\lambda$ is a scalar representing one of the eigenvalues, and $\nu$
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54 ## @end tex
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55 ## @ifinfo
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56 ## @code{lambda} is a scalar representing one of the eigenvalues, and @code{v}
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57 ## @end ifinfo
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58 ## is the corresponding eigenvector. If given the positive definite matrix
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59 ## @var{B} then @code{eigs} solves the general eigenvalue equation
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60 ## @tex
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61 ## $A \nu = \lambda B \nu$.
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62 ## @end tex
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63 ## @ifinfo
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64 ## @code{A * v = lambda * B * v}.
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65 ## @end ifinfo
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66 ##
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67 ## The argument @var{sigma} determines which eigenvalues are returned.
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68 ## @var{sigma} can be either a scalar or a string. When @var{sigma} is a
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69 ## scalar, the @var{k} eigenvalues closest to @var{sigma} are returned. If
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70 ## @var{sigma} is a string, it must have one of the following values.
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71 ##
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72 ## @table @asis
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73 ## @item @qcode{"lm"}
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74 ## Largest Magnitude (default).
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75 ##
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76 ## @item @qcode{"sm"}
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77 ## Smallest Magnitude.
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78 ##
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79 ## @item @qcode{"la"}
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80 ## Largest Algebraic (valid only for real symmetric problems).
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81 ##
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82 ## @item @qcode{"sa"}
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83 ## Smallest Algebraic (valid only for real symmetric problems).
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84 ##
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85 ## @item @qcode{"be"}
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86 ## Both Ends, with one more from the high-end if @var{k} is odd (valid only for
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87 ## real symmetric problems).
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88 ##
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89 ## @item @qcode{"lr"}
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90 ## Largest Real part (valid only for complex or unsymmetric problems).
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91 ##
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92 ## @item @qcode{"sr"}
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93 ## Smallest Real part (valid only for complex or unsymmetric problems).
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94 ##
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95 ## @item @qcode{"li"}
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96 ## Largest Imaginary part (valid only for complex or unsymmetric problems).
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97 ##
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98 ## @item @qcode{"si"}
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99 ## Smallest Imaginary part (valid only for complex or unsymmetric problems).
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100 ## @end table
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101 ##
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102 ## If @var{opts} is given, it is a structure defining possible options that
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103 ## @code{eigs} should use. The fields of the @var{opts} structure are:
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104 ##
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105 ## @table @code
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106 ## @item issym
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107 ## If @var{af} is given, then flags whether the function @var{af} defines a
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108 ## symmetric problem. It is ignored if @var{A} is given. The default is false.
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109 ##
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110 ## @item isreal
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111 ## If @var{af} is given, then flags whether the function @var{af} defines a
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112 ## real problem. It is ignored if @var{A} is given. The default is true.
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113 ##
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114 ## @item tol
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115 ## Defines the required convergence tolerance, calculated as
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116 ## @code{tol * norm (A)}. The default is @code{eps}.
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117 ##
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118 ## @item maxit
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119 ## The maximum number of iterations. The default is 300.
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120 ##
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121 ## @item p
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122 ## The number of Lanzcos basis vectors to use. More vectors will result in
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123 ## faster convergence, but a greater use of memory. The optimal value of
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124 ## @code{p} is problem dependent and should be in the range @var{k} to @var{n}.
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125 ## The default value is @code{2 * @var{k}}.
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126 ##
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127 ## @item v0
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128 ## The starting vector for the algorithm. An initial vector close to the
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129 ## final vector will speed up convergence. The default is for @sc{arpack}
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130 ## to randomly generate a starting vector. If specified, @code{v0} must be
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131 ## an @var{n}-by-1 vector where @code{@var{n} = rows (@var{A})}
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132 ##
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133 ## @item disp
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134 ## The level of diagnostic printout (0|1|2). If @code{disp} is 0 then
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135 ## diagnostics are disabled. The default value is 0.
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136 ##
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137 ## @item cholB
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138 ## Flag if @code{chol (@var{B})} is passed rather than @var{B}. The default is
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139 ## false.
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140 ##
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141 ## @item permB
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142 ## The permutation vector of the Cholesky@tie{}factorization of @var{B} if
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143 ## @code{cholB} is true. That is @code{chol (@var{B}(permB, permB))}. The
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144 ## default is @code{1:@var{n}}.
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145 ##
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146 ## @end table
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147 ##
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148 ## It is also possible to represent @var{A} by a function denoted @var{af}.
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149 ## @var{af} must be followed by a scalar argument @var{n} defining the length
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150 ## of the vector argument accepted by @var{af}. @var{af} can be
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151 ## a function handle, an inline function, or a string. When @var{af} is a
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152 ## string it holds the name of the function to use.
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153 ##
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154 ## @var{af} is a function of the form @code{y = af (x)}
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155 ## where the required return value of @var{af} is determined by
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156 ## the value of @var{sigma}. The four possible forms are
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157 ##
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158 ## @table @code
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159 ## @item A * x
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160 ## if @var{sigma} is not given or is a string other than "sm".
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161 ##
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162 ## @item A \ x
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163 ## if @var{sigma} is 0 or "sm".
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164 ##
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165 ## @item (A - sigma * I) \ x
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166 ## for the standard eigenvalue problem, where @code{I} is the identity matrix of
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167 ## the same size as @var{A}.
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168 ##
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169 ## @item (A - sigma * B) \ x
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170 ## for the general eigenvalue problem.
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171 ## @end table
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172 ##
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173 ## The return arguments of @code{eigs} depend on the number of return arguments
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174 ## requested. With a single return argument, a vector @var{d} of length @var{k}
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175 ## is returned containing the @var{k} eigenvalues that have been found. With
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176 ## two return arguments, @var{V} is a @var{n}-by-@var{k} matrix whose columns
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177 ## are the @var{k} eigenvectors corresponding to the returned eigenvalues. The
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178 ## eigenvalues themselves are returned in @var{d} in the form of a
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179 ## @var{n}-by-@var{k} matrix, where the elements on the diagonal are the
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180 ## eigenvalues.
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181 ##
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182 ## Given a third return argument @var{flag}, @code{eigs} returns the status
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183 ## of the convergence. If @var{flag} is 0 then all eigenvalues have converged.
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184 ## Any other value indicates a failure to converge.
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185 ##
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186 ## This function is based on the @sc{arpack} package, written by R. Lehoucq,
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187 ## K. Maschhoff, D. Sorensen, and C. Yang. For more information see
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188 ## @url{http://www.caam.rice.edu/software/ARPACK/}.
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189 ##
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190 ## @seealso{eig, svds}
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191 ## @end deftypefn
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192
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193 function varargout = eigs (varargin)
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194
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195 ## For compatibility with Matlab, handle small matrix cases here
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196 ## that ARPACK does not.
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197
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198 if (nargin == 0)
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199 print_usage ();
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200 endif
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201
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202 call_eig = false;
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203 offset = 0;
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204 k = 6;
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205 sigma = "lm";
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206
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207 if (isnumeric (varargin{1}) && issquare (varargin{1}))
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208 a = varargin{1};
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209 if (nargin > 1 && isnumeric (varargin{2})
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210 && issquare (varargin{2}) && size_equal (a, varargin{2}))
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211 b = varargin{2};
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212 offset = 1;
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213 endif
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214
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215 if (rows (a) < 9)
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216 call_eig = true;
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217 endif
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218
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219 if (nargin > 1 + offset)
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220 tmp = varargin{2+offset};
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221 if (isnumeric (tmp) && isscalar (tmp) && isreal (tmp)
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222 && round (tmp) == tmp)
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223 k = tmp;
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224
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225 if (rows (a) - k < 3)
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226 call_eig = true;
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227 endif
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228 else
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229 call_eig = false;
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230 endif
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231
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232 if (nargin > 2 + offset)
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233 tmp = varargin{3+offset};
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234 if (ischar (tmp) || (isnumeric (tmp) && isscalar (tmp)))
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235 sigma = tmp;
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236 else
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237 call_eig = false;
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238 endif
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239 endif
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240 endif
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241 endif
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242
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243 if (call_eig)
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244 varargout = cell (1, min (2, max (1, nargout)));
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245 if (offset)
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246 real_valued = isreal (a) && isreal (b);
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247 symmetric = issymmetric (a) && issymmetric (b);
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248 [varargout{:}] = eig (a, b);
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249 else
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250 real_valued = isreal (a);
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251 symmetric = issymmetric (a);
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252 [varargout{:}] = eig (a);
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253 endif
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254 varargout = select (varargout, k, sigma, real_valued, symmetric);
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255 if (nargout == 3)
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256 varargout{3} = 0;
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257 endif
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258 else
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259 varargout = cell (1, max (1, nargout));
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260 [varargout{:}] = __eigs__ (varargin{:});
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261 endif
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262
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263 endfunction
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264
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265 function out = select (args, k, sigma, real_valued, symmetric)
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266
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267 if (numel (args) == 1)
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268 d = args{1};
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269 else
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270 d = diag (args{2});
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271 endif
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272
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273 if (ischar (sigma))
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274 switch (sigma)
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275 case "lm"
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276 [~, idx] = sort (abs (d), "descend");
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277
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278 case "sm"
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279 [~, idx] = sort (abs (d), "ascend");
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280
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281 case "la"
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282 if (real_valued && symmetric)
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283 [~, idx] = sort (real (d), "descend");
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284 else
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285 error ("sigma = \"la\" requires real symmetric problem");
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286 endif
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287
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288 case "sa"
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289 if (real_valued && symmetric)
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290 [~, idx] = sort (real (d), "ascend");
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291 else
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292 error ("sigma = \"sa\" requires real symmetric problem");
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293 endif
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parents:
diff changeset
294
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parents:
diff changeset
295 case "be"
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parents:
diff changeset
296 if (real_valued && symmetric)
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diff changeset
297 [~, idx] = sort (real (d), "ascend");
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parents:
diff changeset
298 else
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parents:
diff changeset
299 error ("sigma = \"be\" requires real symmetric problem");
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parents:
diff changeset
300 endif
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parents:
diff changeset
301
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parents:
diff changeset
302 case "lr"
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parents:
diff changeset
303 if (! (real_valued || symmetric))
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parents:
diff changeset
304 [~, idx] = sort (real (d), "descend");
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parents:
diff changeset
305 else
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parents:
diff changeset
306 error ("sigma = \"lr\" requires complex or unsymmetric problem");
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parents:
diff changeset
307 endif
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parents:
diff changeset
308
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
309 case "sr"
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parents:
diff changeset
310 if (! (real_valued || symmetric))
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parents:
diff changeset
311 [~, idx] = sort (real (d), "ascend");
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parents:
diff changeset
312 else
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parents:
diff changeset
313 error ("sigma = \"sr\" requires complex or unsymmetric problem");
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parents:
diff changeset
314 endif
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
315
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
316 case "li"
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parents:
diff changeset
317 if (! (real_valued || symmetric))
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parents:
diff changeset
318 [~, idx] = sort (imag (d), "descend");
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parents:
diff changeset
319 else
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parents:
diff changeset
320 error ("sigma = \"li\" requires complex or unsymmetric problem");
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parents:
diff changeset
321 endif
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parents:
diff changeset
322
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
323 case "si"
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parents:
diff changeset
324 if (! (real_valued || symmetric))
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parents:
diff changeset
325 [~, idx] = sort (imag (d), "ascend");
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parents:
diff changeset
326 else
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parents:
diff changeset
327 error ("sigma = \"si\" requires complex or unsymmetric problem");
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parents:
diff changeset
328 endif
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
329
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
330 otherwise
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parents:
diff changeset
331 error ("unrecognized value for sigma: %s", sigma);
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diff changeset
332 endswitch
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parents:
diff changeset
333 endif
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parents:
diff changeset
334
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diff changeset
335 d = d(idx);
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parents:
diff changeset
336
ea9992fd9c89 fix eigs to handle small matrices
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diff changeset
337 n = numel (d);
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parents:
diff changeset
338
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
339 k = min (k, n);
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parents:
diff changeset
340
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
341 if (strcmp (sigma, 'be'))
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parents:
diff changeset
342 tmp = k / 2;
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parents:
diff changeset
343 n1 = floor (tmp);
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diff changeset
344 n2 = n - ceil (tmp) + 1;
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diff changeset
345 selection = [1:floor(k/2), n2:n];
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parents:
diff changeset
346 else
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diff changeset
347 selection = 1:k;
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parents:
diff changeset
348 endif
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parents:
diff changeset
349
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diff changeset
350 d = d(selection);
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parents:
diff changeset
351
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
352 if (numel (args) == 1)
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
353 out{1} = d;
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parents:
diff changeset
354 else
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
355 out{2} = diag (d);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
356
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
357 v = args{1};
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parents:
diff changeset
358 v = v(:,idx);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
359 out{1} = v(selection,:);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
360 endif
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
361
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
362 endfunction
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
363
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 17281
diff changeset
364
17220
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parents:
diff changeset
365 #### SPARSE MATRIX VERSIONS ####
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diff changeset
366
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
367 ## Real positive definite tests, n must be even
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parents:
diff changeset
368 %!shared n, k, A, d0, d2
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diff changeset
369 %! n = 20;
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370 %! k = 4;
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diff changeset
371 %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),4*ones(1,n),ones(1,n-2)]);
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diff changeset
372 %! d0 = eig (A);
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diff changeset
373 %! d2 = sort (d0);
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diff changeset
374 %! [~, idx] = sort (abs (d0));
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diff changeset
375 %! d0 = d0(idx);
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diff changeset
376 %! rand ("state", 42); # initialize generator to make eigs behavior reproducible
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diff changeset
377 %!testif HAVE_ARPACK
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378 %! d1 = eigs (A, k);
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diff changeset
379 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
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diff changeset
380 %!testif HAVE_ARPACK
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diff changeset
381 %! d1 = eigs (A, k+1);
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diff changeset
382 %! assert (d1, d0(end:-1:(end-k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
383 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
384 %! d1 = eigs (A, k, "lm");
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parents:
diff changeset
385 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
386 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
387 %! d1 = eigs (A, k, "sm");
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parents:
diff changeset
388 %! assert (d1, d0(k:-1:1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
389 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
390 %! d1 = eigs (A, k, "la");
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
391 %! assert (d1, d2(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
392 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
393 %! d1 = eigs (A, k, "sa");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
394 %! assert (d1, d2(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
395 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
396 %! d1 = eigs (A, k, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
397 %! assert (d1, d2([1:floor(k/2), (end - ceil(k/2) + 1):end]), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
398 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
399 %! d1 = eigs (A, k+1, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
400 %! assert (d1, d2([1:floor((k+1)/2), (end - ceil((k+1)/2) + 1):end]), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
401 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
402 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
403 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
404 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
405 %! assert (d1(idx1), d0(idx0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
406 %!testif HAVE_ARPACK, HAVE_CHOLMOD
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
407 %! d1 = eigs (A, speye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
408 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
409 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
410 %! assert (eigs (A, k, 4.1), eigs (A, speye (n), k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
411 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
412 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
413 %! d1 = eigs (A, speye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
414 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
415 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
416 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
417 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
418 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
419 %! d1 = eigs (A, speye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
420 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
421 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
422 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
423 %! d1 = eigs (A, speye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
424 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
425 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
426 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
427 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
428 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
429 %! d1 = eigs (A, speye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
430 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
431 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
432 %! assert (eigs (A, k, 4.1), eigs (A, speye (n), k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
433 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
434 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
435 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
436 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
437 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
438 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
439 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
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parents:
diff changeset
440 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
441 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
442 %! assert (d1, d0(k:-1:1), 1e-11);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
443 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
444 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
445 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
446 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
447 %! assert (d1, eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
448 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
449 %! AA = speye (10);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
450 %! fn = @(x) AA * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
451 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
452 %! assert (eigs (fn, 10, AA, 3, "lm", opts), [1; 1; 1], 10*eps);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
453 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
454 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
455 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
456 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
457 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
458 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
459 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
460 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
461 %! d1 = diag (d1);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
462 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
463 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
464 %! endfor
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
465 %!testif HAVE_ARPACK
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
466 %! [v1,d1] = eigs (A, k, "la");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
467 %! d1 = diag (d1);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
468 %! for i=1:k
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
469 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
470 %! endfor
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
471 %!testif HAVE_ARPACK
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
472 %! [v1,d1] = eigs (A, k, "sa");
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
473 %! d1 = diag (d1);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
474 %! for i=1:k
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
475 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
476 %! endfor
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
477 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
478 %! [v1,d1] = eigs (A, k, "be");
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
479 %! d1 = diag (d1);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
480 %! for i=1:k
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
481 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
482 %! endfor
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
483
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
484 ## Real unsymmetric tests
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
485 %!shared n, k, A, d0
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
486 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
487 %! k = 4;
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
488 %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),1:n,-ones(1,n-2)]);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
489 %! d0 = eig (A);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
490 %! [~, idx] = sort (abs (d0));
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
491 %! d0 = d0(idx);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
492 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
493 %!testif HAVE_ARPACK
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
494 %! d1 = eigs (A, k);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
495 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
496 %!testif HAVE_ARPACK
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
497 %! d1 = eigs (A, k+1);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
498 %! assert (abs (d1), abs (d0(end:-1:(end-k))),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
499 %!testif HAVE_ARPACK
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
500 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
501 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
502 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
503 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
504 %! assert (abs (d1), abs (d0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
505 %!testif HAVE_ARPACK
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
506 %! d1 = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
507 %! [~, idx] = sort (real (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
508 %! d2 = d0(idx);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
509 %! assert (real (d1), real (d2(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
510 %!testif HAVE_ARPACK
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
511 %! d1 = eigs (A, k, "sr");
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
512 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
513 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
514 %! assert (real (d1), real (d2(1:k)), 1e-11);
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
515 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
516 %! d1 = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
517 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
518 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
519 %! assert (sort (imag (d1)), sort (imag (d2(end:-1:(end-k+1)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
520 %!testif HAVE_ARPACK
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John W. Eaton <jwe@octave.org>
parents:
diff changeset
521 %! d1 = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
522 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
523 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
524 %! assert (sort (imag (d1)), sort (imag (d2(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
525 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
526 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
527 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
528 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
529 %! assert (abs (d1(idx1)), abs (d0(idx0(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
530 %! assert (sort (imag (d1(idx1))), sort (imag (d0(idx0(1:k)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
531 %!testif HAVE_ARPACK, HAVE_CHOLMOD
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
532 %! d1 = eigs (A, speye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
533 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
534 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
535 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
536 %! d1 = eigs (A, speye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
537 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
538 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
539 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
540 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
541 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
542 %! d1 = eigs (A, speye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
543 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
544 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
545 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
546 %! d1 = eigs (A, speye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
547 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
548 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
549 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
550 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
551 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
552 %! d1 = eigs (A, speye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
553 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
554 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
555 %! assert (abs (eigs (A, k, 4.1)), abs (eigs (A, speye (n), k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
556 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
557 %! assert (sort (imag (eigs (A, k, 4.1))), sort (imag (eigs (A, speye (n), k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
558 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
559 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
560 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
561 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
562 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
563 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
564 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
565 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
566 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
567 %! assert (abs (d1), d0(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
568 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
569 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
570 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
571 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
572 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
573 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
574 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
575 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
576 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
577 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
578 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
579 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
580 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
581 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
582 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
583 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
584 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
585 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
586 %! [v1,d1] = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
587 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
588 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
589 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
590 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
591 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
592 %! [v1,d1] = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
593 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
594 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
595 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
596 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
597 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
598 %! [v1,d1] = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
599 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
600 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
601 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
602 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
603 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
604 %! [v1,d1] = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
605 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
606 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
607 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
608 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
609
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
610
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
611 ## Complex hermitian tests
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
612 %!shared n, k, A, d0
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
613 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
614 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
615 %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[1i*ones(1,n-2),4*ones(1,n),-1i*ones(1,n-2)]);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
616 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
617 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
618 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
619 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
620 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
621 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
622 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
623 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
624 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
625 %! assert (abs (d1), abs (d0(end:-1:(end-k))),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
626 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
627 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
628 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
629 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
630 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
631 %! assert (abs (d1), abs (d0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
632 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
633 %! d1 = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
634 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
635 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
636 %! assert (real (d1), real (d2(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
637 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
638 %! d1 = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
639 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
640 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
641 %! assert (real (d1), real (d2(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
642 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
643 %! d1 = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
644 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
645 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
646 %! assert (sort (imag (d1)), sort (imag (d2(end:-1:(end-k+1)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
647 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
648 %! d1 = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
649 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
650 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
651 %! assert (sort (imag (d1)), sort (imag (d2(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
652 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
653 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
654 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
655 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
656 %! assert (abs (d1(idx1)), abs (d0(idx0(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
657 %! assert (sort (imag (d1(idx1))), sort (imag (d0(idx0(1:k)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
658 %!testif HAVE_ARPACK, HAVE_CHOLMOD
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
659 %! d1 = eigs (A, speye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
660 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
661 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
662 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
663 %! d1 = eigs (A, speye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
664 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
665 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
666 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
667 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
668 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
669 %! d1 = eigs (A, speye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
670 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
671 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
672 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
673 %! d1 = eigs (A, speye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
674 %! assert (abs (abs (d1)), abs (eigs (A, k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
675 %! assert (sort (imag (abs (d1))), sort (imag (eigs (A, k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
676 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
677 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
678 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
679 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
680 %! d1 = eigs (A, speye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
681 %! assert (abs (abs (d1)), abs (eigs (A, k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
682 %! assert (sort (imag (abs (d1))), sort (imag (eigs (A, k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
683 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
684 %! assert (abs (eigs (A, k, 4.1)), abs (eigs (A, speye (n), k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
685 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
686 %! assert (sort (imag (eigs (A, k, 4.1))), sort (imag (eigs (A, speye (n), k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
687 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
688 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
689 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
690 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
691 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
692 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
693 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
694 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
695 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
696 %! assert (abs (d1), d0(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
697 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
698 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
699 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
700 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
701 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
702 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
703 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
704 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
705 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
706 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
707 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
708 %!testif HAVE_ARPACK, HAVE_UMFPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
709 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
710 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
711 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
712 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
713 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
714 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
715 %! [v1,d1] = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
716 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
717 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
718 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
719 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
720 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
721 %! [v1,d1] = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
722 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
723 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
724 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
725 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
726 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
727 %! [v1,d1] = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
728 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
729 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
730 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
731 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
732 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
733 %! [v1,d1] = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
734 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
735 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
736 %! assert (max (abs ((A - d1(i)*speye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
737 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
738
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
739 #### FULL MATRIX VERSIONS ####
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
740
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
741 ## Real positive definite tests, n must be even
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
742 %!shared n, k, A, d0, d2
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
743 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
744 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
745 %! A = full (sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),4*ones(1,n),ones(1,n-2)]));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
746 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
747 %! d2 = sort (d0);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
748 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
749 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
750 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
751 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
752 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
753 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
754 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
755 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
756 %! assert (d1, d0(end:-1:(end-k)),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
757 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
758 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
759 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
760 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
761 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
762 %! assert (d1, d0(k:-1:1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
763 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
764 %! d1 = eigs (A, k, "la");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
765 %! assert (d1, d2(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
766 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
767 %! d1 = eigs (A, k, "sa");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
768 %! assert (d1, d2(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
769 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
770 %! d1 = eigs (A, k, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
771 %! assert (d1, d2([1:floor(k/2), (end - ceil(k/2) + 1):end]), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
772 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
773 %! d1 = eigs (A, k+1, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
774 %! assert (d1, d2([1:floor((k+1)/2), (end - ceil((k+1)/2) + 1):end]), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
775 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
776 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
777 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
778 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
779 %! assert (d1(idx1), d0(idx0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
780 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
781 %! d1 = eigs (A, eye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
782 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
783 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
784 %! assert (eigs (A, k, 4.1), eigs (A, eye (n), k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
785 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
786 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
787 %! d1 = eigs (A, eye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
788 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
789 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
790 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
791 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
792 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
793 %! d1 = eigs (A, eye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
794 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
795 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
796 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
797 %! d1 = eigs (A, eye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
798 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
799 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
800 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
801 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
802 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
803 %! d1 = eigs (A, eye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
804 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
805 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
806 %! assert (eigs (A, k, 4.1), eigs (A, eye (n), k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
807 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
808 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
809 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
810 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
811 %! assert (d1, d0(end:-1:(end-k+1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
812 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
813 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
814 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
815 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
816 %! assert (d1, d0(k:-1:1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
817 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
818 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
819 %! opts.issym = 1; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
820 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
821 %! assert (d1, eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
822 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
823 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
824 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
825 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
826 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
827 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
828 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
829 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
830 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
831 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
832 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
833 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
834 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
835 %! [v1,d1] = eigs (A, k, "la");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
836 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
837 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
838 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
839 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
840 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
841 %! [v1,d1] = eigs (A, k, "sa");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
842 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
843 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
844 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
845 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
846 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
847 %! [v1,d1] = eigs (A, k, "be");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
848 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
849 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
850 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
851 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
852
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
853 ## Real unsymmetric tests
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
854 %!shared n, k, A, d0
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
855 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
856 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
857 %! A = full (sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),1:n,-ones(1,n-2)]));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
858 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
859 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
860 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
861 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
862 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
863 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
864 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
865 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
866 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
867 %! assert (abs (d1), abs (d0(end:-1:(end-k))),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
868 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
869 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
870 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
871 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
872 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
873 %! assert (abs (d1), abs (d0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
874 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
875 %! d1 = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
876 %! [~, idx] = sort (real (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
877 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
878 %! assert (real (d1), real (d2(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
879 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
880 %! d1 = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
881 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
882 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
883 %! assert (real (d1), real (d2(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
884 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
885 %! d1 = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
886 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
887 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
888 %! assert (sort (imag (d1)), sort (imag (d2(end:-1:(end-k+1)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
889 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
890 %! d1 = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
891 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
892 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
893 %! assert (sort (imag (d1)), sort (imag (d2(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
894 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
895 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
896 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
897 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
898 %! assert (abs (d1(idx1)), abs (d0(idx0(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
899 %! assert (sort (imag (d1(idx1))), sort (imag (d0(idx0(1:k)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
900 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
901 %! d1 = eigs (A, eye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
902 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
903 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
904 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
905 %! d1 = eigs (A, eye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
906 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
907 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
908 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
909 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
910 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
911 %! d1 = eigs (A, eye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
912 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
913 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
914 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
915 %! d1 = eigs (A, eye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
916 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
917 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
918 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
919 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
920 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
921 %! d1 = eigs (A, eye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
922 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
923 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
924 %! assert (abs (eigs (A, k, 4.1)), abs (eigs (A, eye (n), k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
925 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
926 %! assert (sort (imag (eigs (A, k, 4.1))), sort (imag (eigs (A, eye (n), k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
927 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
928 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
929 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
930 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
931 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
932 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
933 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
934 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
935 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
936 %! assert (abs (d1), d0(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
937 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
938 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
939 %! opts.issym = 0; opts.isreal = 1;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
940 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
941 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
942 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
943 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
944 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
945 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
946 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
947 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
948 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
949 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
950 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
951 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
952 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
953 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
954 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
955 %! [v1,d1] = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
956 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
957 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
958 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
959 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
960 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
961 %! [v1,d1] = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
962 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
963 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
964 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
965 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
966 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
967 %! [v1,d1] = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
968 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
969 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
970 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
971 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
972 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
973 %! [v1,d1] = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
974 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
975 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
976 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
977 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
978
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
979 ## Complex hermitian tests
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
980 %!shared n, k, A, d0
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
981 %! n = 20;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
982 %! k = 4;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
983 %! A = full (sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[1i*ones(1,n-2),4*ones(1,n),-1i*ones(1,n-2)]));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
984 %! d0 = eig (A);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
985 %! [~, idx] = sort (abs (d0));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
986 %! d0 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
987 %! rand ("state", 42); % initialize generator to make eigs behavior reproducible
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
988 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
989 %! d1 = eigs (A, k);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
990 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
991 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
992 %! d1 = eigs (A, k+1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
993 %! assert (abs (d1), abs (d0(end:-1:(end-k))),1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
994 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
995 %! d1 = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
996 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
997 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
998 %! d1 = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
999 %! assert (abs (d1), abs (d0(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1000 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1001 %! d1 = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1002 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1003 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1004 %! assert (real (d1), real (d2(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1005 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1006 %! d1 = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1007 %! [~, idx] = sort (real (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1008 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1009 %! assert (real (d1), real (d2(1:k)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1010 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1011 %! d1 = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1012 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1013 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1014 %! assert (sort (imag (d1)), sort (imag (d2(end:-1:(end-k+1)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1015 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1016 %! d1 = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1017 %! [~, idx] = sort (imag (abs (d0)));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1018 %! d2 = d0(idx);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1019 %! assert (sort (imag (d1)), sort (imag (d2(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1020 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1021 %! d1 = eigs (A, k, 4.1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1022 %! [~, idx0] = sort (abs (d0 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1023 %! [~, idx1] = sort (abs (d1 - 4.1));
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1024 %! assert (abs (d1(idx1)), abs (d0(idx0(1:k))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1025 %! assert (sort (imag (d1(idx1))), sort (imag (d0(idx0(1:k)))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1026 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1027 %! d1 = eigs (A, eye (n), k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1028 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1029 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1030 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1031 %! d1 = eigs (A, eye (n), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1032 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1033 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1034 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1035 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1036 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1037 %! d1 = eigs (A, eye (n)(q,q), k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1038 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1039 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1040 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1041 %! d1 = eigs (A, eye (n), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1042 %! assert (abs (abs (d1)), abs (eigs (A, k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1043 %! assert (sort (imag (abs (d1))), sort (imag (eigs (A, k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1044 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1045 %! opts.cholB = true;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1046 %! q = [2:n,1];
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1047 %! opts.permB = q;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1048 %! d1 = eigs (A, eye (n)(q,q), k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1049 %! assert (abs (abs (d1)), abs (eigs (A, k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1050 %! assert (sort (imag (abs (d1))), sort (imag (eigs (A, k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1051 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1052 %! assert (abs (eigs (A, k, 4.1)), abs (eigs (A, eye (n), k, 4.1)), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1053 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1054 %! assert (sort (imag (eigs (A, k, 4.1))), sort (imag (eigs (A, eye (n), k, 4.1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1055 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1056 %! fn = @(x) A * x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1057 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1058 %! d1 = eigs (fn, n, k, "lm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1059 %! assert (abs (d1), abs (d0(end:-1:(end-k+1))), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1060 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1061 %! fn = @(x) A \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1062 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1063 %! d1 = eigs (fn, n, k, "sm", opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1064 %! assert (abs (d1), d0(1:k), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1065 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1066 %! fn = @(x) (A - 4.1 * eye (n)) \ x;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1067 %! opts.issym = 0; opts.isreal = 0;
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1068 %! d1 = eigs (fn, n, k, 4.1, opts);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1069 %! assert (abs (d1), eigs (A, k, 4.1), 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1070 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1071 %! [v1,d1] = eigs (A, k, "lm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1072 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1073 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1074 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1075 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1076 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1077 %! [v1,d1] = eigs (A, k, "sm");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1078 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1079 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1080 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1081 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1082 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1083 %! [v1,d1] = eigs (A, k, "lr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1084 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1085 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1086 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1087 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1088 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1089 %! [v1,d1] = eigs (A, k, "sr");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1090 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1091 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1092 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1093 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1094 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1095 %! [v1,d1] = eigs (A, k, "li");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1096 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1097 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1098 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1099 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1100 %!testif HAVE_ARPACK
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1101 %! [v1,d1] = eigs (A, k, "si");
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1102 %! d1 = diag (d1);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1103 %! for i=1:k
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1104 %! assert (max (abs ((A - d1(i)*eye (n))*v1(:,i))), 0, 1e-11);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1105 %! endfor
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1106
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1107 %!assert (eigs (diag (1:5), 5, "sa"), [1;2;3;4;5]);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1108 %!assert (eigs (diag (1:5), 5, "la"), [5;4;3;2;1]);
ea9992fd9c89 fix eigs to handle small matrices
John W. Eaton <jwe@octave.org>
parents:
diff changeset
1109 %!assert (eigs (diag (1:5), 3, "be"), [1;4;5]);
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 17281
diff changeset
1110