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[project @ 2005-02-25 19:55:24 by jwe]
author jwe
date Fri, 25 Feb 2005 19:55:28 +0000
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5163:9f3299378193 5164:57077d0ddc8e
1 /* ========================================================================== */
2 /* === UMFPACK_get_determinant ============================================== */
3 /* ========================================================================== */
4
5 /* -------------------------------------------------------------------------- */
6 /* UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis. CISE Dept, */
7 /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
8 /* web: http://www.cise.ufl.edu/research/sparse/umfpack */
9 /* -------------------------------------------------------------------------- */
10
11 int umfpack_di_get_determinant
12 (
13 double *Mx,
14 double *Ex,
15 void *NumericHandle,
16 double User_Info [UMFPACK_INFO]
17 ) ;
18
19 long umfpack_dl_get_determinant
20 (
21 double *Mx,
22 double *Ex,
23 void *NumericHandle,
24 double User_Info [UMFPACK_INFO]
25 ) ;
26
27 int umfpack_zi_get_determinant
28 (
29 double *Mx,
30 double *Mz,
31 double *Ex,
32 void *NumericHandle,
33 double User_Info [UMFPACK_INFO]
34 ) ;
35
36 long umfpack_zl_get_determinant
37 (
38 double *Mx,
39 double *Mz,
40 double *Ex,
41 void *NumericHandle,
42 double User_Info [UMFPACK_INFO]
43 ) ;
44
45 /*
46 double int Syntax:
47
48 #include "umfpack.h"
49 void *Numeric ;
50 int status ;
51 double Mx, Ex, Info [UMFPACK_INFO] ;
52 status = umfpack_di_get_determinant (&Mx, &Ex, Numeric, Info) ;
53
54 double long Syntax:
55
56 #include "umfpack.h"
57 void *Numeric ;
58 long status ;
59 double Mx, Ex, Info [UMFPACK_INFO] ;
60 status = umfpack_dl_get_determinant (&Mx, &Ex, Numeric, Info) ;
61
62 complex int Syntax:
63
64 #include "umfpack.h"
65 void *Numeric ;
66 int status ;
67 double Mx, Mz, Ex, Info [UMFPACK_INFO] ;
68 status = umfpack_zi_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ;
69
70 complex int Syntax:
71
72 #include "umfpack.h"
73 void *Numeric ;
74 long status ;
75 double *Mx, *Mz, *Ex, Info [UMFPACK_INFO] ;
76 status = umfpack_zl_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ;
77
78 packed complex int Syntax:
79
80 Same as above, except Mz is NULL.
81
82 Purpose:
83
84 Using the LU factors and the permutation vectors contained in the Numeric
85 object, calculate the determinant of the matrix A.
86
87 The value of the determinant can be returned in two forms, depending on
88 whether Ex is NULL or not. If Ex is NULL then the value of the determinant
89 is returned on Mx and Mz for the real and imaginary parts. However, to
90 avoid over- or underflows, the determinant can be split into a mantissa
91 and exponent, and the parts returned separately, in which case Ex is not
92 NULL. The actual determinant is then given by
93
94 double det ;
95 det = Mx * pow (10.0, Ex) ;
96
97 for the double case, or
98
99 double det [2] ;
100 det [0] = Mx * pow (10.0, Ex) ; // real part
101 det [1] = Mz * pow (10.0, Ex) ; // imaginary part
102
103 for the complex case. Information on if the determinant will or has
104 over or under-flowed is given by Info [UMFPACK_STATUS].
105
106 In the "packed complex" syntax, Mx [0] holds the real part and Mx [1]
107 holds the imaginary part. Mz is not used (it is NULL).
108
109 Returns:
110
111 Returns UMFPACK_OK if sucessful. Returns UMFPACK_ERROR_out_of_memory if
112 insufficient memory is available for the n_row integer workspace that
113 umfpack_*_get_determinant allocates to construct pivots from the
114 permutation vectors. Returns UMFPACK_ERROR_invalid_Numeric_object if the
115 Numeric object provided as input is invalid. Returns
116 UMFPACK_WARNING_singular_matrix if the determinant is zero. Returns
117 UMFPACK_WARNING_determinant_underflow or
118 UMFPACK_WARNING_determinant_overflow if the determinant has underflowed
119 overflowed (for the case when Ex is NULL), or will overflow if Ex is not
120 NULL and det is computed (see above) in the user program.
121
122 Arguments:
123
124 double *Mx ; Output argument (array of size 1, or size 2 if Mz is NULL)
125 double *Mz ; Output argument (optional)
126 double *Ex ; Output argument (optional)
127
128 The determinant returned in mantissa/exponent form, as discussed above.
129 If Mz is NULL, then both the original and imaginary parts will be
130 returned in Mx. If Ex is NULL then the determinant is returned directly
131 in Mx and Mz (or Mx [0] and Mx [1] if Mz is NULL), rather than in
132 mantissa/exponent form.
133
134 void *Numeric ; Input argument, not modified.
135
136 Numeric must point to a valid Numeric object, computed by
137 umfpack_*_numeric.
138
139 double Info [UMFPACK_INFO] ; Output argument.
140
141 Contains information about the calculation of the determinant. If a
142 (double *) NULL pointer is passed, then no statistics are returned in
143 Info (this is not an error condition). The following statistics are
144 computed in umfpack_*_determinant:
145
146 Info [UMFPACK_STATUS]: status code. This is also the return value,
147 whether or not Info is present.
148
149 UMFPACK_OK
150
151 The determinant was successfully found.
152
153 UMFPACK_ERROR_out_of_memory
154
155 Insufficient memory to solve the linear system.
156
157 UMFPACK_ERROR_argument_missing
158
159 Mx is missing (NULL).
160
161 UMFPACK_ERROR_invalid_Numeric_object
162
163 The Numeric object is not valid.
164
165 UMFPACK_ERROR_invalid_system
166
167 The matrix is rectangular. Only square systems can be
168 handled.
169
170 UMFPACK_WARNING_singluar_matrix
171
172 The determinant is zero or NaN. The matrix is singular.
173
174 UMFPACK_WARNING_determinant_underflow
175
176 When passing from mantissa/exponent form to the determinant
177 an underflow has or will occur. If the mantissa/exponent from
178 of obtaining the determinant is used, the underflow will occur
179 in the user program. If the single argument method of
180 obtaining the determinant is used, the underflow has already
181 occurred.
182
183 UMFPACK_WARNING_determinant_overflow
184
185 When passing from mantissa/exponent form to the determinant
186 an overflow has or will occur. If the mantissa/exponent from
187 of obtaining the determinant is used, the overflow will occur
188 in the user program. If the single argument method of
189 obtaining the determinant is used, the overflow has already
190 occurred.
191
192 */