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1 /* |
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2 |
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3 Copyright (C) 2005 David Bateman |
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4 Copyright (C) 1998-2005 Andy Adler |
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5 |
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6 Octave is free software; you can redistribute it and/or modify it |
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7 under the terms of the GNU General Public License as published by the |
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8 Free Software Foundation; either version 2, or (at your option) any |
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9 later version. |
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10 |
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11 Octave is distributed in the hope that it will be useful, but WITHOUT |
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12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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14 for more details. |
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15 |
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16 You should have received a copy of the GNU General Public License |
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17 along with this program; see the file COPYING. If not, write to the |
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18 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, |
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19 Boston, MA 02110-1301, USA. |
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20 |
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21 */ |
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22 |
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23 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include "defun-dld.h" |
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28 #include "error.h" |
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29 #include "gripes.h" |
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30 #include "oct-obj.h" |
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31 #include "utils.h" |
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32 |
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33 #include "oct-sparse.h" |
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34 #include "ov-re-sparse.h" |
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35 #include "ov-cx-sparse.h" |
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36 #include "SparseQR.h" |
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37 #include "SparseCmplxQR.h" |
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38 |
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39 #ifdef IDX_TYPE_LONG |
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40 #define CXSPARSE_NAME(name) cs_dl ## name |
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41 #else |
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42 #define CXSPARSE_NAME(name) cs_di ## name |
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43 #endif |
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44 |
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45 // PKG_ADD: dispatch ("qr", "spqr", "sparse matrix"); |
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46 // PKG_ADD: dispatch ("qr", "spqr", "sparse complex matrix"); |
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47 // PKG_ADD: dispatch ("qr", "spqr", "sparse bool matrix"); |
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48 DEFUN_DLD (spqr, args, nargout, |
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49 "-*- texinfo -*-\n\ |
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50 @deftypefn {Loadable Function} {@var{r} =} spqr (@var{a})\n\ |
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51 @deftypefnx {Loadable Function} {@var{r} =} spqr (@var{a},0)\n\ |
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52 @deftypefnx {Loadable Function} {[@var{c}, @var{r}] =} spqr (@var{a},@var{b})\n\ |
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53 @deftypefnx {Loadable Function} {[@var{c}, @var{r}] =} spqr (@var{a},@var{b},0)\n\ |
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54 @cindex QR factorization\n\ |
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55 Compute the sparse QR factorization of @var{a}, using @sc{CSparse}.\n\ |
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56 As the matrix @var{Q} is in general a full matrix, this function returns\n\ |
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57 the @var{Q}-less factorization @var{r} of @var{a}, such that\n\ |
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58 @code{@var{r} = chol (@var{a}' * @var{a})}.\n\ |
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59 \n\ |
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60 If the final argument is the scalar @code{0} and the number of rows is\n\ |
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61 larger than the number of columns, then an economy factorization is\n\ |
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62 returned. That is @var{r} will have only @code{size (@var{a},1)} rows.\n\ |
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63 \n\ |
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64 If an additional matrix @var{b} is supplied, then @code{spqr} returns\n\ |
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65 @var{c}, where @code{@var{c} = @var{q}' * @var{b}}. This allows the\n\ |
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66 least squares approximation of @code{@var{a} \\ @var{b}} to be calculated\n\ |
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67 as\n\ |
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68 \n\ |
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69 @example\n\ |
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70 [@var{c},@var{r}] = spqr (@var{a},@var{b})\n\ |
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71 @var{x} = @var{r} \\ @var{c}\n\ |
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72 @end example\n\ |
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73 @seealso{spchol, qr}\n\ |
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74 @end deftypefn") |
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75 { |
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76 int nargin = args.length (); |
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77 octave_value_list retval; |
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78 bool economy = false; |
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79 bool is_cmplx = false; |
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80 bool have_b = false; |
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81 |
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82 if (nargin < 1 || nargin > 3) |
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83 print_usage (); |
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84 else |
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85 { |
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86 if (args(0).is_complex_type ()) |
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87 is_cmplx = true; |
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88 if (nargin > 1) |
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89 { |
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90 have_b = true; |
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91 if (args(nargin-1).is_scalar_type ()) |
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92 { |
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93 int val = args(nargin-1).int_value (); |
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94 if (val == 0) |
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95 { |
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96 economy = true; |
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97 have_b = (nargin > 2); |
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98 } |
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99 } |
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100 if (have_b && args(1).is_complex_type ()) |
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101 is_cmplx = true; |
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102 } |
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103 |
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104 if (!error_state) |
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105 { |
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106 if (have_b && nargout < 2) |
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107 error ("spqr: incorrect number of output arguments"); |
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108 else if (is_cmplx) |
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109 { |
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110 SparseComplexQR q (args(0).sparse_complex_matrix_value ()); |
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111 if (!error_state) |
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112 { |
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113 if (have_b) |
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114 { |
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115 retval(1) = q.R (economy); |
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116 retval(0) = q.C (args(1).complex_matrix_value ()); |
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117 if (args(0).rows() < args(0).columns()) |
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118 warning ("spqr: non minimum norm solution for under-determined problem"); |
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119 } |
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120 else |
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121 retval(0) = q.R (economy); |
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122 } |
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123 } |
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124 else |
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125 { |
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126 SparseQR q (args(0).sparse_matrix_value ()); |
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127 if (!error_state) |
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128 { |
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129 if (have_b) |
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130 { |
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131 retval(1) = q.R (economy); |
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132 retval(0) = q.C (args(1).matrix_value ()); |
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133 if (args(0).rows() < args(0).columns()) |
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134 warning ("spqr: non minimum norm solution for under-determined problem"); |
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135 } |
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136 else |
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137 retval(0) = q.R (economy); |
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138 } |
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139 } |
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140 } |
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141 } |
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142 return retval; |
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143 } |
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144 |
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145 /* |
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146 |
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147 The deactivated tests below can't be tested till rectangular back-subs is |
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148 implemented for sparse matrices. |
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149 |
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150 %!test |
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151 %! n = 20; d= 0.2; |
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152 %! a = sprandn(n,n,d)+speye(n,n); |
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153 %! r = spqr(a); |
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154 %! assert(r'*r,a'*a,1e-10) |
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155 |
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156 %!test |
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157 %! n = 20; d= 0.2; |
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158 %! a = sprandn(n,n,d)+speye(n,n); |
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159 %! q = symamd(a); |
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160 %! a = a(q,q); |
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161 %! r = spqr(a); |
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162 %! assert(r'*r,a'*a,1e-10) |
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163 |
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164 %!test |
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165 %! n = 20; d= 0.2; |
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166 %! a = sprandn(n,n,d)+speye(n,n); |
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167 %! [c,r] = spqr(a,ones(n,1)); |
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168 %! assert (r\c,full(a)\ones(n,1),10e-10) |
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169 |
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170 %!test |
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171 %! n = 20; d= 0.2; |
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172 %! a = sprandn(n,n,d)+speye(n,n); |
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173 %! b = randn(n,2); |
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174 %! [c,r] = spqr(a,b); |
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175 %! assert (r\c,full(a)\b,10e-10) |
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176 |
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177 %% Test under-determined systems!! |
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178 %!#test |
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179 %! n = 20; d= 0.2; |
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180 %! a = sprandn(n,n+1,d)+speye(n,n+1); |
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181 %! b = randn(n,2); |
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182 %! [c,r] = spqr(a,b); |
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183 %! assert (r\c,full(a)\b,10e-10) |
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184 |
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185 %!test |
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186 %! n = 20; d= 0.2; |
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187 %! a = 1i*sprandn(n,n,d)+speye(n,n); |
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188 %! r = spqr(a); |
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189 %! assert(r'*r,a'*a,1e-10) |
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190 |
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191 %!test |
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192 %! n = 20; d= 0.2; |
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193 %! a = 1i*sprandn(n,n,d)+speye(n,n); |
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194 %! q = symamd(a); |
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195 %! a = a(q,q); |
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196 %! r = spqr(a); |
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197 %! assert(r'*r,a'*a,1e-10) |
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198 |
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199 %!test |
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200 %! n = 20; d= 0.2; |
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201 %! a = 1i*sprandn(n,n,d)+speye(n,n); |
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202 %! [c,r] = spqr(a,ones(n,1)); |
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203 %! assert (r\c,full(a)\ones(n,1),10e-10) |
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204 |
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205 %!test |
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206 %! n = 20; d= 0.2; |
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207 %! a = 1i*sprandn(n,n,d)+speye(n,n); |
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208 %! b = randn(n,2); |
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209 %! [c,r] = spqr(a,b); |
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210 %! assert (r\c,full(a)\b,10e-10) |
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211 |
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212 %% Test under-determined systems!! |
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213 %!#test |
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214 %! n = 20; d= 0.2; |
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215 %! a = 1i*sprandn(n,n+1,d)+speye(n,n+1); |
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216 %! b = randn(n,2); |
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217 %! [c,r] = spqr(a,b); |
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218 %! assert (r\c,full(a)\b,10e-10) |
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219 |
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220 %!error spqr(sprandn(10,10,0.2),ones(10,1)); |
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221 |
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222 */ |
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223 |
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224 static RowVector |
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225 put_int (octave_idx_type *p, octave_idx_type n) |
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226 { |
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227 RowVector ret (n); |
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228 for (octave_idx_type i = 0; i < n; i++) |
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229 ret.xelem(i) = p[i] + 1; |
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230 return ret; |
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231 } |
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232 |
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233 #if HAVE_CXSPARSE |
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234 static octave_value_list |
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235 dmperm_internal (bool rank, const octave_value arg, int nargout) |
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236 { |
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237 octave_value_list retval; |
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238 octave_idx_type nr = arg.rows (); |
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239 octave_idx_type nc = arg.columns (); |
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240 SparseMatrix m; |
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241 SparseComplexMatrix cm; |
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242 CXSPARSE_NAME () csm; |
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243 csm.m = nr; |
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244 csm.n = nc; |
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245 csm.x = NULL; |
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246 csm.nz = -1; |
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247 |
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248 if (arg.is_real_type ()) |
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249 { |
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250 m = arg.sparse_matrix_value (); |
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251 csm.nzmax = m.nnz(); |
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252 csm.p = m.xcidx (); |
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253 csm.i = m.xridx (); |
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254 } |
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255 else |
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256 { |
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257 cm = arg.sparse_complex_matrix_value (); |
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258 csm.nzmax = cm.nnz(); |
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259 csm.p = cm.xcidx (); |
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260 csm.i = cm.xridx (); |
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261 } |
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262 |
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263 if (!error_state) |
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264 { |
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265 if (nargout <= 1 || rank) |
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266 { |
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267 #if defined(CS_VER) && (CS_VER >= 2) |
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268 octave_idx_type *jmatch = CXSPARSE_NAME (_maxtrans) (&csm, 0); |
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269 #else |
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270 octave_idx_type *jmatch = CXSPARSE_NAME (_maxtrans) (&csm); |
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271 #endif |
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272 if (rank) |
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273 { |
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274 octave_idx_type r = 0; |
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275 for (octave_idx_type i = 0; i < nc; i++) |
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276 if (jmatch[nr+i] >= 0) |
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277 r++; |
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278 retval(0) = static_cast<double>(r); |
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279 } |
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280 else |
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281 retval(0) = put_int (jmatch + nr, nc); |
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282 CXSPARSE_NAME (_free) (jmatch); |
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283 } |
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284 else |
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285 { |
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286 #if defined(CS_VER) && (CS_VER >= 2) |
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287 CXSPARSE_NAME (d) *dm = CXSPARSE_NAME(_dmperm) (&csm, 0); |
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288 #else |
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289 CXSPARSE_NAME (d) *dm = CXSPARSE_NAME(_dmperm) (&csm); |
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290 #endif |
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291 |
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292 //retval(5) = put_int (dm->rr, 5); |
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293 //retval(4) = put_int (dm->cc, 5); |
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294 #if defined(CS_VER) && (CS_VER >= 2) |
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295 retval(3) = put_int (dm->s, dm->nb+1); |
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296 retval(2) = put_int (dm->r, dm->nb+1); |
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297 retval(1) = put_int (dm->q, nc); |
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298 retval(0) = put_int (dm->p, nr); |
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299 #else |
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300 retval(3) = put_int (dm->S, dm->nb+1); |
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301 retval(2) = put_int (dm->R, dm->nb+1); |
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302 retval(1) = put_int (dm->Q, nc); |
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303 retval(0) = put_int (dm->P, nr); |
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304 #endif |
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305 CXSPARSE_NAME (_dfree) (dm); |
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306 } |
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307 } |
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308 return retval; |
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309 } |
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310 #endif |
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311 |
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312 DEFUN_DLD (dmperm, args, nargout, |
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313 "-*- texinfo -*-\n\ |
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314 @deftypefn {Loadable Function} {@var{p} =} dmperm (@var{s})\n\ |
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315 @deftypefnx {Loadable Function} {[@var{p}, @var{q}, @var{r}, @var{s}] =} dmperm (@var{s})\n\ |
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316 \n\ |
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317 @cindex Dulmage-Mendelsohn decomposition\n\ |
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318 Perform a Dulmage-Mendelsohn permutation on the sparse matrix @var{s}.\n\ |
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319 With a single output argument @dfn{dmperm} performs the row permutations\n\ |
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320 @var{p} such that @code{@var{s} (@var{p},:)} has no zero elements on the\n\ |
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321 diagonal.\n\ |
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322 \n\ |
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323 Called with two or more output arguments, returns the row and column\n\ |
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324 permutations, such that @code{@var{s} (@var{p}, @var{q})} is in block\n\ |
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325 triangular form. The values of @var{r} and @var{s} define the boundaries\n\ |
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326 of the blocks. If @var{s} is square then @code{@var{r} == @var{s}}.\n\ |
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327 \n\ |
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328 The method used is described in: A. Pothen & C.-J. Fan. Computing the block\n\ |
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329 triangular form of a sparse matrix. ACM Trans. Math. Software,\n\ |
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330 16(4):303-324, 1990.\n\ |
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331 @seealso{colamd, ccolamd}\n\ |
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332 @end deftypefn") |
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333 { |
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334 int nargin = args.length(); |
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335 octave_value_list retval; |
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336 |
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337 if (nargin != 1) |
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338 { |
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339 print_usage (); |
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340 return retval; |
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341 } |
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342 |
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343 #if HAVE_CXSPARSE |
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344 retval = dmperm_internal (false, args(0), nargout); |
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345 #else |
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346 error ("dmperm: not available in this version of Octave"); |
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347 #endif |
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348 |
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349 return retval; |
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350 } |
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351 |
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352 /* |
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353 |
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354 %!test |
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355 %! n=20; |
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356 %! a=speye(n,n);a=a(randperm(n),:); |
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357 %! assert(a(dmperm(a),:),speye(n)) |
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358 |
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359 %!test |
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360 %! n=20; |
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361 %! d=0.2; |
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362 %! a=tril(sprandn(n,n,d),-1)+speye(n,n); |
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363 %! a=a(randperm(n),randperm(n)); |
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364 %! [p,q,r,s]=dmperm(a); |
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365 %! assert(tril(a(p,q),-1),sparse(n,n)) |
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366 |
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367 */ |
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368 |
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369 DEFUN_DLD (sprank, args, nargout, |
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370 "-*- texinfo -*-\n\ |
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371 @deftypefn {Loadable Function} {@var{p} =} sprank (@var{s})\n\ |
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372 \n\ |
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373 @cindex Structural Rank\n\ |
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374 Calculates the structural rank of a sparse matrix @var{s}. Note that\n\ |
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375 only the structure of the matrix is used in this calculation based on\n\ |
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376 a Dulmage-Mendelsohn to block triangular form. As such the numerical\n\ |
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377 rank of the matrix @var{s} is bounded by @code{sprank (@var{s}) >=\n\ |
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378 rank (@var{s})}. Ignoring floating point errors @code{sprank (@var{s}) ==\n\ |
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379 rank (@var{s})}.\n\ |
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380 @seealso{dmperm}\n\ |
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381 @end deftypefn") |
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382 { |
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383 int nargin = args.length(); |
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384 octave_value_list retval; |
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385 |
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386 if (nargin != 1) |
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387 { |
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388 print_usage (); |
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389 return retval; |
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390 } |
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391 |
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392 #if HAVE_CXSPARSE |
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393 retval = dmperm_internal (true, args(0), nargout); |
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394 #else |
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395 error ("sprank: not available in this version of Octave"); |
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396 #endif |
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397 |
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398 return retval; |
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399 } |
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400 |
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401 /* |
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402 |
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403 %!error(sprank(1,2)); |
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404 %!assert(sprank(speye(20)), 20) |
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405 %!assert(sprank([1,0,2,0;2,0,4,0]),2) |
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406 |
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407 */ |
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408 /* |
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409 ;;; Local Variables: *** |
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410 ;;; mode: C++ *** |
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411 ;;; End: *** |
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412 */ |
