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1 /* ========================================================================== */ |
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2 /* === UMFPACK_get_determinant ============================================== */ |
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3 /* ========================================================================== */ |
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4 |
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5 /* -------------------------------------------------------------------------- */ |
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6 /* UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE Dept, */ |
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7 /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ |
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8 /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ |
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9 /* -------------------------------------------------------------------------- */ |
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10 |
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11 int umfpack_di_get_determinant |
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12 ( |
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13 double *Mx, |
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14 double *Ex, |
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15 void *NumericHandle, |
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16 double User_Info [UMFPACK_INFO] |
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17 ) ; |
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18 |
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19 long umfpack_dl_get_determinant |
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20 ( |
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21 double *Mx, |
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22 double *Ex, |
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23 void *NumericHandle, |
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24 double User_Info [UMFPACK_INFO] |
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25 ) ; |
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26 |
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27 int umfpack_zi_get_determinant |
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28 ( |
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29 double *Mx, |
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30 double *Mz, |
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31 double *Ex, |
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32 void *NumericHandle, |
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33 double User_Info [UMFPACK_INFO] |
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34 ) ; |
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35 |
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36 long umfpack_zl_get_determinant |
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37 ( |
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38 double *Mx, |
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39 double *Mz, |
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40 double *Ex, |
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41 void *NumericHandle, |
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42 double User_Info [UMFPACK_INFO] |
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43 ) ; |
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44 |
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45 /* |
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46 double int Syntax: |
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47 |
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48 #include "umfpack.h" |
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49 void *Numeric ; |
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50 int status ; |
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51 double Mx, Ex, Info [UMFPACK_INFO] ; |
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52 status = umfpack_di_get_determinant (&Mx, &Ex, Numeric, Info) ; |
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53 |
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54 double long Syntax: |
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55 |
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56 #include "umfpack.h" |
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57 void *Numeric ; |
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58 long status ; |
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59 double Mx, Ex, Info [UMFPACK_INFO] ; |
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60 status = umfpack_dl_get_determinant (&Mx, &Ex, Numeric, Info) ; |
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61 |
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62 complex int Syntax: |
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63 |
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64 #include "umfpack.h" |
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65 void *Numeric ; |
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66 int status ; |
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67 double Mx, Mz, Ex, Info [UMFPACK_INFO] ; |
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68 status = umfpack_zi_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ; |
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69 |
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70 complex int Syntax: |
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71 |
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72 #include "umfpack.h" |
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73 void *Numeric ; |
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74 long status ; |
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75 double *Mx, *Mz, *Ex, Info [UMFPACK_INFO] ; |
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76 status = umfpack_zl_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ; |
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77 |
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78 packed complex int Syntax: |
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79 |
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80 Same as above, except Mz is NULL. |
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81 |
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82 Purpose: |
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83 |
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84 Using the LU factors and the permutation vectors contained in the Numeric |
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85 object, calculate the determinant of the matrix A. |
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86 |
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87 The value of the determinant can be returned in two forms, depending on |
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88 whether Ex is NULL or not. If Ex is NULL then the value of the determinant |
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89 is returned on Mx and Mz for the real and imaginary parts. However, to |
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90 avoid over- or underflows, the determinant can be split into a mantissa |
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91 and exponent, and the parts returned separately, in which case Ex is not |
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92 NULL. The actual determinant is then given by |
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93 |
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94 double det ; |
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95 det = Mx * pow (10.0, Ex) ; |
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96 |
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97 for the double case, or |
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98 |
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99 double det [2] ; |
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100 det [0] = Mx * pow (10.0, Ex) ; // real part |
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101 det [1] = Mz * pow (10.0, Ex) ; // imaginary part |
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102 |
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103 for the complex case. Information on if the determinant will or has |
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104 over or under-flowed is given by Info [UMFPACK_STATUS]. |
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105 |
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106 In the "packed complex" syntax, Mx [0] holds the real part and Mx [1] |
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107 holds the imaginary part. Mz is not used (it is NULL). |
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108 |
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109 Returns: |
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110 |
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111 Returns UMFPACK_OK if sucessful. Returns UMFPACK_ERROR_out_of_memory if |
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112 insufficient memory is available for the n_row integer workspace that |
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113 umfpack_*_get_determinant allocates to construct pivots from the |
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114 permutation vectors. Returns UMFPACK_ERROR_invalid_Numeric_object if the |
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115 Numeric object provided as input is invalid. Returns |
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116 UMFPACK_WARNING_singular_matrix if the determinant is zero. Returns |
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117 UMFPACK_WARNING_determinant_underflow or |
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118 UMFPACK_WARNING_determinant_overflow if the determinant has underflowed |
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119 overflowed (for the case when Ex is NULL), or will overflow if Ex is not |
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120 NULL and det is computed (see above) in the user program. |
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121 |
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122 Arguments: |
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123 |
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124 double *Mx ; Output argument (array of size 1, or size 2 if Mz is NULL) |
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125 double *Mz ; Output argument (optional) |
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126 double *Ex ; Output argument (optional) |
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127 |
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128 The determinant returned in mantissa/exponent form, as discussed above. |
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129 If Mz is NULL, then both the original and imaginary parts will be |
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130 returned in Mx. If Ex is NULL then the determinant is returned directly |
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131 in Mx and Mz (or Mx [0] and Mx [1] if Mz is NULL), rather than in |
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132 mantissa/exponent form. |
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133 |
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134 void *Numeric ; Input argument, not modified. |
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135 |
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136 Numeric must point to a valid Numeric object, computed by |
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137 umfpack_*_numeric. |
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138 |
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139 double Info [UMFPACK_INFO] ; Output argument. |
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140 |
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141 Contains information about the calculation of the determinant. If a |
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142 (double *) NULL pointer is passed, then no statistics are returned in |
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143 Info (this is not an error condition). The following statistics are |
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144 computed in umfpack_*_determinant: |
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145 |
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146 Info [UMFPACK_STATUS]: status code. This is also the return value, |
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147 whether or not Info is present. |
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148 |
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149 UMFPACK_OK |
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150 |
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151 The determinant was successfully found. |
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152 |
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153 UMFPACK_ERROR_out_of_memory |
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154 |
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155 Insufficient memory to solve the linear system. |
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156 |
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157 UMFPACK_ERROR_argument_missing |
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158 |
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159 Mx is missing (NULL). |
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160 |
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161 UMFPACK_ERROR_invalid_Numeric_object |
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162 |
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163 The Numeric object is not valid. |
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164 |
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165 UMFPACK_ERROR_invalid_system |
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166 |
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167 The matrix is rectangular. Only square systems can be |
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168 handled. |
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169 |
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170 UMFPACK_WARNING_singluar_matrix |
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171 |
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172 The determinant is zero or NaN. The matrix is singular. |
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173 |
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174 UMFPACK_WARNING_determinant_underflow |
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175 |
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176 When passing from mantissa/exponent form to the determinant |
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177 an underflow has or will occur. If the mantissa/exponent from |
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178 of obtaining the determinant is used, the underflow will occur |
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179 in the user program. If the single argument method of |
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180 obtaining the determinant is used, the underflow has already |
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181 occurred. |
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182 |
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183 UMFPACK_WARNING_determinant_overflow |
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184 |
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185 When passing from mantissa/exponent form to the determinant |
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186 an overflow has or will occur. If the mantissa/exponent from |
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187 of obtaining the determinant is used, the overflow will occur |
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188 in the user program. If the single argument method of |
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189 obtaining the determinant is used, the overflow has already |
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190 occurred. |
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191 |
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192 */ |
