-
Notifications
You must be signed in to change notification settings - Fork 63
/
fdjac1.c
189 lines (151 loc) · 5.72 KB
/
fdjac1.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
/* fdjac1.f -- translated by f2c (version 20020621).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "cminpack.h"
#include <math.h>
#include "cminpackP.h"
__cminpack_attr__
int __cminpack_func__(fdjac1)(__cminpack_decl_fcn_nn__ void *p, int n, real *x, const real *
fvec, real *fjac, int ldfjac, int ml,
int mu, real epsfcn, real *wa1, real *wa2)
{
/* System generated locals */
int fjac_dim1, fjac_offset;
/* Local variables */
real h;
int i, j, k;
real eps, temp;
int msum;
real epsmch;
int iflag = 0;
/* ********** */
/* subroutine fdjac1 */
/* this subroutine computes a forward-difference approximation */
/* to the n by n jacobian matrix associated with a specified */
/* problem of n functions in n variables. if the jacobian has */
/* a banded form, then function evaluations are saved by only */
/* approximating the nonzero terms. */
/* the subroutine statement is */
/* subroutine fdjac1(fcn,n,x,fvec,fjac,ldfjac,iflag,ml,mu,epsfcn, */
/* wa1,wa2) */
/* where */
/* fcn is the name of the user-supplied subroutine which */
/* calculates the functions. fcn must be declared */
/* in an external statement in the user calling */
/* program, and should be written as follows. */
/* subroutine fcn(n,x,fvec,iflag) */
/* integer n,iflag */
/* double precision x(n),fvec(n) */
/* ---------- */
/* calculate the functions at x and */
/* return this vector in fvec. */
/* ---------- */
/* return */
/* end */
/* the value of iflag should not be changed by fcn unless */
/* the user wants to terminate execution of fdjac1. */
/* in this case set iflag to a negative integer. */
/* n is a positive integer input variable set to the number */
/* of functions and variables. */
/* x is an input array of length n. */
/* fvec is an input array of length n which must contain the */
/* functions evaluated at x. */
/* fjac is an output n by n array which contains the */
/* approximation to the jacobian matrix evaluated at x. */
/* ldfjac is a positive integer input variable not less than n */
/* which specifies the leading dimension of the array fjac. */
/* iflag is an integer variable which can be used to terminate */
/* the execution of fdjac1. see description of fcn. */
/* ml is a nonnegative integer input variable which specifies */
/* the number of subdiagonals within the band of the */
/* jacobian matrix. if the jacobian is not banded, set */
/* ml to at least n - 1. */
/* epsfcn is an input variable used in determining a suitable */
/* step length for the forward-difference approximation. this */
/* approximation assumes that the relative errors in the */
/* functions are of the order of epsfcn. if epsfcn is less */
/* than the machine precision, it is assumed that the relative */
/* errors in the functions are of the order of the machine */
/* precision. */
/* mu is a nonnegative integer input variable which specifies */
/* the number of superdiagonals within the band of the */
/* jacobian matrix. if the jacobian is not banded, set */
/* mu to at least n - 1. */
/* wa1 and wa2 are work arrays of length n. if ml + mu + 1 is at */
/* least n, then the jacobian is considered dense, and wa2 is */
/* not referenced. */
/* subprograms called */
/* minpack-supplied ... dpmpar */
/* fortran-supplied ... dabs,dmax1,dsqrt */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/* Parameter adjustments */
--wa2;
--wa1;
--fvec;
--x;
fjac_dim1 = ldfjac;
fjac_offset = 1 + fjac_dim1 * 1;
fjac -= fjac_offset;
/* Function Body */
/* epsmch is the machine precision. */
epsmch = __cminpack_func__(dpmpar)(1);
eps = sqrt((max(epsfcn,epsmch)));
msum = ml + mu + 1;
if (msum >= n) {
/* computation of dense approximate jacobian. */
for (j = 1; j <= n; ++j) {
temp = x[j];
h = eps * fabs(temp);
if (h == 0.) {
h = eps;
}
x[j] = temp + h;
/* the last parameter of fcn_nn() is set to 2 to differentiate
calls made to compute the function from calls made to compute
the Jacobian (see fcn() in examples/hybdrv.c, and how njev
is used to compute the number of Jacobian evaluations) */
iflag = fcn_nn(p, n, &x[1], &wa1[1], 2);
if (iflag < 0) {
return iflag;
}
x[j] = temp;
for (i = 1; i <= n; ++i) {
fjac[i + j * fjac_dim1] = (wa1[i] - fvec[i]) / h;
}
}
return 0;
}
/* computation of banded approximate jacobian. */
for (k = 1; k <= msum; ++k) {
for (j = k; j <= n; j += msum) {
wa2[j] = x[j];
h = eps * fabs(wa2[j]);
if (h == 0.) {
h = eps;
}
x[j] = wa2[j] + h;
}
iflag = fcn_nn(p, n, &x[1], &wa1[1], 1);
if (iflag < 0) {
return iflag;
}
for (j = k; j <= n; j += msum) {
x[j] = wa2[j];
h = eps * fabs(wa2[j]);
if (h == 0.) {
h = eps;
}
for (i = 1; i <= n; ++i) {
fjac[i + j * fjac_dim1] = 0.;
if (i >= j - mu && i <= j + ml) {
fjac[i + j * fjac_dim1] = (wa1[i] - fvec[i]) / h;
}
}
}
}
return 0;
/* last card of subroutine fdjac1. */
} /* fdjac1_ */