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1 /* |
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2 |
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3 Copyright (C) 2005, 2006, 2007 David Bateman |
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4 Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005 Andy Adler |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 3 of the License, or (at your |
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11 option) any later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, see |
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20 <http://www.gnu.org/licenses/>. |
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21 |
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22 */ |
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23 |
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24 #ifdef HAVE_CONFIG_H |
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25 #include <config.h> |
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26 #endif |
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27 |
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28 #include "defun-dld.h" |
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29 #include "error.h" |
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30 #include "gripes.h" |
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31 #include "oct-obj.h" |
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32 #include "utils.h" |
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33 |
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34 #include "oct-sparse.h" |
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35 #include "ov-re-sparse.h" |
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36 #include "ov-cx-sparse.h" |
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37 #include "SparseQR.h" |
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38 #include "SparseCmplxQR.h" |
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39 |
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40 #ifdef IDX_TYPE_LONG |
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41 #define CXSPARSE_NAME(name) cs_dl ## name |
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42 #else |
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43 #define CXSPARSE_NAME(name) cs_di ## name |
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44 #endif |
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45 |
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46 // PKG_ADD: dispatch ("qr", "spqr", "sparse matrix"); |
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47 // PKG_ADD: dispatch ("qr", "spqr", "sparse complex matrix"); |
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48 // PKG_ADD: dispatch ("qr", "spqr", "sparse bool matrix"); |
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49 DEFUN_DLD (spqr, args, nargout, |
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50 "-*- texinfo -*-\n\ |
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51 @deftypefn {Loadable Function} {@var{r} =} spqr (@var{a})\n\ |
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52 @deftypefnx {Loadable Function} {@var{r} =} spqr (@var{a},0)\n\ |
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53 @deftypefnx {Loadable Function} {[@var{c}, @var{r}] =} spqr (@var{a},@var{b})\n\ |
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54 @deftypefnx {Loadable Function} {[@var{c}, @var{r}] =} spqr (@var{a},@var{b},0)\n\ |
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55 @cindex QR factorization\n\ |
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56 Compute the sparse QR factorization of @var{a}, using @sc{CSparse}.\n\ |
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57 As the matrix @var{Q} is in general a full matrix, this function returns\n\ |
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58 the @var{Q}-less factorization @var{r} of @var{a}, such that\n\ |
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59 @code{@var{r} = chol (@var{a}' * @var{a})}.\n\ |
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60 \n\ |
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61 If the final argument is the scalar @code{0} and the number of rows is\n\ |
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62 larger than the number of columns, then an economy factorization is\n\ |
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63 returned. That is @var{r} will have only @code{size (@var{a},1)} rows.\n\ |
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64 \n\ |
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65 If an additional matrix @var{b} is supplied, then @code{spqr} returns\n\ |
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66 @var{c}, where @code{@var{c} = @var{q}' * @var{b}}. This allows the\n\ |
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67 least squares approximation of @code{@var{a} \\ @var{b}} to be calculated\n\ |
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68 as\n\ |
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69 \n\ |
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70 @example\n\ |
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71 [@var{c},@var{r}] = spqr (@var{a},@var{b})\n\ |
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72 @var{x} = @var{r} \\ @var{c}\n\ |
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73 @end example\n\ |
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74 @seealso{spchol, qr}\n\ |
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75 @end deftypefn") |
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76 { |
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77 int nargin = args.length (); |
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78 octave_value_list retval; |
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79 bool economy = false; |
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80 bool is_cmplx = false; |
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81 bool have_b = false; |
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82 |
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83 if (nargin < 1 || nargin > 3) |
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84 print_usage (); |
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85 else |
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86 { |
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87 if (args(0).is_complex_type ()) |
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88 is_cmplx = true; |
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89 if (nargin > 1) |
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90 { |
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91 have_b = true; |
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92 if (args(nargin-1).is_scalar_type ()) |
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93 { |
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94 int val = args(nargin-1).int_value (); |
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95 if (val == 0) |
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96 { |
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97 economy = true; |
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98 have_b = (nargin > 2); |
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99 } |
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100 } |
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101 if (have_b && args(1).is_complex_type ()) |
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102 is_cmplx = true; |
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103 } |
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104 |
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105 if (!error_state) |
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106 { |
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107 if (have_b && nargout < 2) |
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108 error ("spqr: incorrect number of output arguments"); |
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109 else if (is_cmplx) |
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110 { |
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111 SparseComplexQR q (args(0).sparse_complex_matrix_value ()); |
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112 if (!error_state) |
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113 { |
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114 if (have_b) |
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115 { |
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116 retval(1) = q.R (economy); |
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117 retval(0) = q.C (args(1).complex_matrix_value ()); |
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118 if (args(0).rows() < args(0).columns()) |
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119 warning ("spqr: non minimum norm solution for under-determined problem"); |
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120 } |
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121 else |
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122 retval(0) = q.R (economy); |
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123 } |
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124 } |
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125 else |
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126 { |
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127 SparseQR q (args(0).sparse_matrix_value ()); |
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128 if (!error_state) |
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129 { |
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130 if (have_b) |
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131 { |
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132 retval(1) = q.R (economy); |
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133 retval(0) = q.C (args(1).matrix_value ()); |
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134 if (args(0).rows() < args(0).columns()) |
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135 warning ("spqr: non minimum norm solution for under-determined problem"); |
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136 } |
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137 else |
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138 retval(0) = q.R (economy); |
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139 } |
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140 } |
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141 } |
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142 } |
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143 return retval; |
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144 } |
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145 |
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146 /* |
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147 |
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148 The deactivated tests below can't be tested till rectangular back-subs is |
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149 implemented for sparse matrices. |
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150 |
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151 %!testif HAVE_CXSPARSE |
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152 %! n = 20; d= 0.2; |
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153 %! a = sprandn(n,n,d)+speye(n,n); |
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154 %! r = spqr(a); |
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155 %! assert(r'*r,a'*a,1e-10) |
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156 |
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157 %!testif HAVE_CXSPARSE |
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158 %! n = 20; d= 0.2; |
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159 %! a = sprandn(n,n,d)+speye(n,n); |
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160 %! q = symamd(a); |
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161 %! a = a(q,q); |
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162 %! r = spqr(a); |
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163 %! assert(r'*r,a'*a,1e-10) |
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164 |
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165 %!testif HAVE_CXSPARSE |
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166 %! n = 20; d= 0.2; |
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167 %! a = sprandn(n,n,d)+speye(n,n); |
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168 %! [c,r] = spqr(a,ones(n,1)); |
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169 %! assert (r\c,full(a)\ones(n,1),10e-10) |
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170 |
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171 %!testif HAVE_CXSPARSE |
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172 %! n = 20; d= 0.2; |
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173 %! a = sprandn(n,n,d)+speye(n,n); |
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174 %! b = randn(n,2); |
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175 %! [c,r] = spqr(a,b); |
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176 %! assert (r\c,full(a)\b,10e-10) |
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177 |
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178 %% Test under-determined systems!! |
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179 %!#testif HAVE_CXSPARSE |
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180 %! n = 20; d= 0.2; |
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181 %! a = sprandn(n,n+1,d)+speye(n,n+1); |
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182 %! b = randn(n,2); |
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183 %! [c,r] = spqr(a,b); |
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184 %! assert (r\c,full(a)\b,10e-10) |
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185 |
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186 %!testif HAVE_CXSPARSE |
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187 %! n = 20; d= 0.2; |
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188 %! a = 1i*sprandn(n,n,d)+speye(n,n); |
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189 %! r = spqr(a); |
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190 %! assert(r'*r,a'*a,1e-10) |
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191 |
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192 %!testif HAVE_CXSPARSE |
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193 %! n = 20; d= 0.2; |
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194 %! a = 1i*sprandn(n,n,d)+speye(n,n); |
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195 %! q = symamd(a); |
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196 %! a = a(q,q); |
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197 %! r = spqr(a); |
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198 %! assert(r'*r,a'*a,1e-10) |
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199 |
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200 %!testif HAVE_CXSPARSE |
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201 %! n = 20; d= 0.2; |
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202 %! a = 1i*sprandn(n,n,d)+speye(n,n); |
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203 %! [c,r] = spqr(a,ones(n,1)); |
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204 %! assert (r\c,full(a)\ones(n,1),10e-10) |
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205 |
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206 %!testif HAVE_CXSPARSE |
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207 %! n = 20; d= 0.2; |
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208 %! a = 1i*sprandn(n,n,d)+speye(n,n); |
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209 %! b = randn(n,2); |
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210 %! [c,r] = spqr(a,b); |
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211 %! assert (r\c,full(a)\b,10e-10) |
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212 |
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213 %% Test under-determined systems!! |
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214 %!#testif HAVE_CXSPARSE |
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215 %! n = 20; d= 0.2; |
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216 %! a = 1i*sprandn(n,n+1,d)+speye(n,n+1); |
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217 %! b = randn(n,2); |
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218 %! [c,r] = spqr(a,b); |
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219 %! assert (r\c,full(a)\b,10e-10) |
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220 |
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221 %!error spqr(sprandn(10,10,0.2),ones(10,1)); |
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222 |
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223 */ |
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224 |
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225 static RowVector |
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226 put_int (octave_idx_type *p, octave_idx_type n) |
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227 { |
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228 RowVector ret (n); |
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229 for (octave_idx_type i = 0; i < n; i++) |
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230 ret.xelem(i) = p[i] + 1; |
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231 return ret; |
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232 } |
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233 |
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234 #if HAVE_CXSPARSE |
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235 static octave_value_list |
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236 dmperm_internal (bool rank, const octave_value arg, int nargout) |
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237 { |
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238 octave_value_list retval; |
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239 octave_idx_type nr = arg.rows (); |
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240 octave_idx_type nc = arg.columns (); |
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241 SparseMatrix m; |
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242 SparseComplexMatrix cm; |
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243 CXSPARSE_NAME () csm; |
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244 csm.m = nr; |
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245 csm.n = nc; |
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246 csm.x = NULL; |
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247 csm.nz = -1; |
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248 |
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249 if (arg.is_real_type ()) |
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250 { |
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251 m = arg.sparse_matrix_value (); |
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252 csm.nzmax = m.nnz(); |
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253 csm.p = m.xcidx (); |
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254 csm.i = m.xridx (); |
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255 } |
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256 else |
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257 { |
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258 cm = arg.sparse_complex_matrix_value (); |
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259 csm.nzmax = cm.nnz(); |
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260 csm.p = cm.xcidx (); |
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261 csm.i = cm.xridx (); |
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262 } |
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263 |
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264 if (!error_state) |
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265 { |
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266 if (nargout <= 1 || rank) |
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267 { |
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268 #if defined(CS_VER) && (CS_VER >= 2) |
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269 octave_idx_type *jmatch = CXSPARSE_NAME (_maxtrans) (&csm, 0); |
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270 #else |
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271 octave_idx_type *jmatch = CXSPARSE_NAME (_maxtrans) (&csm); |
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272 #endif |
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273 if (rank) |
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274 { |
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275 octave_idx_type r = 0; |
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276 for (octave_idx_type i = 0; i < nc; i++) |
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277 if (jmatch[nr+i] >= 0) |
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278 r++; |
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279 retval(0) = static_cast<double>(r); |
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280 } |
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281 else |
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282 retval(0) = put_int (jmatch + nr, nc); |
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283 CXSPARSE_NAME (_free) (jmatch); |
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284 } |
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285 else |
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286 { |
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287 #if defined(CS_VER) && (CS_VER >= 2) |
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288 CXSPARSE_NAME (d) *dm = CXSPARSE_NAME(_dmperm) (&csm, 0); |
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289 #else |
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290 CXSPARSE_NAME (d) *dm = CXSPARSE_NAME(_dmperm) (&csm); |
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291 #endif |
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292 |
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293 //retval(5) = put_int (dm->rr, 5); |
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294 //retval(4) = put_int (dm->cc, 5); |
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295 #if defined(CS_VER) && (CS_VER >= 2) |
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296 retval(3) = put_int (dm->s, dm->nb+1); |
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297 retval(2) = put_int (dm->r, dm->nb+1); |
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298 retval(1) = put_int (dm->q, nc); |
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299 retval(0) = put_int (dm->p, nr); |
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300 #else |
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301 retval(3) = put_int (dm->S, dm->nb+1); |
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302 retval(2) = put_int (dm->R, dm->nb+1); |
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303 retval(1) = put_int (dm->Q, nc); |
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304 retval(0) = put_int (dm->P, nr); |
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305 #endif |
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306 CXSPARSE_NAME (_dfree) (dm); |
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307 } |
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308 } |
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309 return retval; |
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310 } |
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311 #endif |
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312 |
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313 DEFUN_DLD (dmperm, args, nargout, |
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314 "-*- texinfo -*-\n\ |
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315 @deftypefn {Loadable Function} {@var{p} =} dmperm (@var{s})\n\ |
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316 @deftypefnx {Loadable Function} {[@var{p}, @var{q}, @var{r}, @var{s}] =} dmperm (@var{s})\n\ |
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317 \n\ |
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318 @cindex Dulmage-Mendelsohn decomposition\n\ |
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319 Perform a Dulmage-Mendelsohn permutation on the sparse matrix @var{s}.\n\ |
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320 With a single output argument @dfn{dmperm} performs the row permutations\n\ |
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321 @var{p} such that @code{@var{s} (@var{p},:)} has no zero elements on the\n\ |
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322 diagonal.\n\ |
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323 \n\ |
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324 Called with two or more output arguments, returns the row and column\n\ |
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325 permutations, such that @code{@var{s} (@var{p}, @var{q})} is in block\n\ |
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326 triangular form. The values of @var{r} and @var{s} define the boundaries\n\ |
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327 of the blocks. If @var{s} is square then @code{@var{r} == @var{s}}.\n\ |
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328 \n\ |
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329 The method used is described in: A. Pothen & C.-J. Fan. Computing the block\n\ |
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330 triangular form of a sparse matrix. ACM Trans. Math. Software,\n\ |
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331 16(4):303-324, 1990.\n\ |
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332 @seealso{colamd, ccolamd}\n\ |
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333 @end deftypefn") |
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334 { |
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335 int nargin = args.length(); |
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336 octave_value_list retval; |
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337 |
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338 if (nargin != 1) |
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339 { |
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340 print_usage (); |
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341 return retval; |
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342 } |
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343 |
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344 #if HAVE_CXSPARSE |
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345 retval = dmperm_internal (false, args(0), nargout); |
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346 #else |
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347 error ("dmperm: not available in this version of Octave"); |
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348 #endif |
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349 |
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350 return retval; |
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351 } |
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352 |
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353 /* |
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354 |
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355 %!testif HAVE_CXSPARSE |
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356 %! n=20; |
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357 %! a=speye(n,n);a=a(randperm(n),:); |
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358 %! assert(a(dmperm(a),:),speye(n)) |
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359 |
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360 %!testif HAVE_CXSPARSE |
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361 %! n=20; |
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362 %! d=0.2; |
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363 %! a=tril(sprandn(n,n,d),-1)+speye(n,n); |
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364 %! a=a(randperm(n),randperm(n)); |
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365 %! [p,q,r,s]=dmperm(a); |
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366 %! assert(tril(a(p,q),-1),sparse(n,n)) |
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367 |
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368 */ |
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369 |
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370 DEFUN_DLD (sprank, args, nargout, |
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371 "-*- texinfo -*-\n\ |
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372 @deftypefn {Loadable Function} {@var{p} =} sprank (@var{s})\n\ |
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373 \n\ |
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374 @cindex Structural Rank\n\ |
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375 Calculates the structural rank of a sparse matrix @var{s}. Note that\n\ |
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376 only the structure of the matrix is used in this calculation based on\n\ |
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377 a Dulmage-Mendelsohn to block triangular form. As such the numerical\n\ |
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378 rank of the matrix @var{s} is bounded by @code{sprank (@var{s}) >=\n\ |
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379 rank (@var{s})}. Ignoring floating point errors @code{sprank (@var{s}) ==\n\ |
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380 rank (@var{s})}.\n\ |
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381 @seealso{dmperm}\n\ |
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382 @end deftypefn") |
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383 { |
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384 int nargin = args.length(); |
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385 octave_value_list retval; |
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386 |
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387 if (nargin != 1) |
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388 { |
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389 print_usage (); |
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390 return retval; |
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391 } |
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392 |
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393 #if HAVE_CXSPARSE |
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394 retval = dmperm_internal (true, args(0), nargout); |
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395 #else |
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396 error ("sprank: not available in this version of Octave"); |
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397 #endif |
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398 |
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399 return retval; |
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400 } |
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401 |
|
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402 /* |
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403 |
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404 %!error(sprank(1,2)); |
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7243
|
405 %!testif HAVE_CXSPARSE |
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406 %! assert(sprank(speye(20)), 20) |
|
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407 %!testif HAVE_CXSPARSE |
|
|
408 %! assert(sprank([1,0,2,0;2,0,4,0]),2) |
|
6066
|
409 |
|
|
410 */ |
|
5610
|
411 /* |
|
|
412 ;;; Local Variables: *** |
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413 ;;; mode: C++ *** |
|
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414 ;;; End: *** |
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415 */ |
