Actual source code: snesdnest.c
2: /* fnoise/snesdnest.F -- translated by f2c (version 20020314).
3: */
4: #include <petscsys.h>
5: #define FALSE_ 0
6: #define TRUE_ 1
8: /* Noise estimation routine, written by Jorge More'. Details are below. */
10: PETSC_INTERN PetscErrorCode SNESNoise_dnest_(PetscInt*,PetscScalar*,PetscScalar*,PetscScalar*,PetscScalar*,PetscScalar*,PetscInt*,PetscScalar*);
12: PetscErrorCode SNESNoise_dnest_(PetscInt *nf, double *fval,double *h__,double *fnoise, double *fder2, double *hopt, PetscInt *info, double *eps)
13: {
14: /* Initialized data */
16: static double const__[15] = { .71,.41,.23,.12,.063,.033,.018,.0089,
17: .0046,.0024,.0012,6.1e-4,3.1e-4,1.6e-4,8e-5 };
19: /* System generated locals */
20: PetscInt i__1;
21: double d__1, d__2, d__3, d__4;
23: /* Local variables */
24: static double emin, emax;
25: static PetscInt dsgn[6];
26: static double f_max, f_min, stdv;
27: static PetscInt i__, j;
28: static double scale;
29: static PetscInt mh;
30: static PetscInt cancel[6], dnoise;
31: static double err2, est1, est2, est3, est4;
33: /* ********** */
35: /* Subroutine dnest */
37: /* This subroutine estimates the noise in a function */
38: /* and provides estimates of the optimal difference parameter */
39: /* for a forward-difference approximation. */
41: /* The user must provide a difference parameter h, and the */
42: /* function value at nf points centered around the current point. */
43: /* For example, if nf = 7, the user must provide */
45: /* f(x-2*h), f(x-h), f(x), f(x+h), f(x+2*h), */
47: /* in the array fval. The use of nf = 7 function evaluations is */
48: /* recommended. */
50: /* The noise in the function is roughly defined as the variance in */
51: /* the computed value of the function. The noise in the function */
52: /* provides valuable information. For example, function values */
53: /* smaller than the noise should be considered to be zero. */
55: /* This subroutine requires an initial estimate for h. Under estimates */
56: /* are usually preferred. If noise is not detected, the user should */
57: /* increase or decrease h according to the ouput value of info. */
58: /* In most cases, the subroutine detects noise with the initial */
59: /* value of h. */
61: /* The subroutine statement is */
63: /* subroutine dnest(nf,fval,h,hopt,fnoise,info,eps) */
65: /* where */
67: /* nf is a PetscInt variable. */
68: /* On entry nf is the number of function values. */
69: /* On exit nf is unchanged. */
71: /* f is a double precision array of dimension nf. */
72: /* On entry f contains the function values. */
73: /* On exit f is overwritten. */
75: /* h is a double precision variable. */
76: /* On entry h is an estimate of the optimal difference parameter. */
77: /* On exit h is unchanged. */
79: /* fnoise is a double precision variable. */
80: /* On entry fnoise need not be specified. */
81: /* On exit fnoise is set to an estimate of the function noise */
82: /* if noise is detected; otherwise fnoise is set to zero. */
84: /* hopt is a double precision variable. */
85: /* On entry hopt need not be specified. */
86: /* On exit hopt is set to an estimate of the optimal difference */
87: /* parameter if noise is detected; otherwise hopt is set to zero. */
89: /* info is a PetscInt variable. */
90: /* On entry info need not be specified. */
91: /* On exit info is set as follows: */
93: /* info = 1 Noise has been detected. */
95: /* info = 2 Noise has not been detected; h is too small. */
96: /* Try 100*h for the next value of h. */
98: /* info = 3 Noise has not been detected; h is too large. */
99: /* Try h/100 for the next value of h. */
101: /* info = 4 Noise has been detected but the estimate of hopt */
102: /* is not reliable; h is too small. */
104: /* eps is a double precision work array of dimension nf. */
106: /* MINPACK-2 Project. April 1997. */
107: /* Argonne National Laboratory. */
108: /* Jorge J. More'. */
110: /* ********** */
111: /* Parameter adjustments */
112: --eps;
113: --fval;
115: /* Function Body */
116: *fnoise = 0.;
117: *fder2 = 0.;
118: *hopt = 0.;
119: /* Compute an estimate of the second derivative and */
120: /* determine a bound on the error. */
121: mh = (*nf + 1) / 2;
122: est1 = (fval[mh + 1] - fval[mh] * 2 + fval[mh - 1]) / *h__ / *h__;
123: est2 = (fval[mh + 2] - fval[mh] * 2 + fval[mh - 2]) / (*h__ * 2) / (*h__ * 2);
124: est3 = (fval[mh + 3] - fval[mh] * 2 + fval[mh - 3]) / (*h__ * 3) / (*h__ * 3);
125: est4 = (est1 + est2 + est3) / 3;
126: /* Computing MAX */
127: /* Computing PETSCMAX */
128: d__3 = PetscMax(est1,est2);
129: /* Computing MIN */
130: d__4 = PetscMin(est1,est2);
131: d__1 = PetscMax(d__3,est3) - est4;
132: d__2 = est4 - PetscMin(d__4,est3);
133: err2 = PetscMax(d__1,d__2);
134: /* write (2,123) est1, est2, est3 */
135: /* 123 format ('Second derivative estimates', 3d12.2) */
136: if (err2 <= PetscAbsScalar(est4) * .1) *fder2 = est4;
137: else if (err2 < PetscAbsScalar(est4)) *fder2 = est3;
138: else *fder2 = 0.;
140: /* Compute the range of function values. */
141: f_min = fval[1];
142: f_max = fval[1];
143: i__1 = *nf;
144: for (i__ = 2; i__ <= i__1; ++i__) {
145: /* Computing MIN */
146: d__1 = f_min;
147: d__2 = fval[i__];
148: f_min = PetscMin(d__1,d__2);
150: /* Computing MAX */
151: d__1 = f_max;
152: d__2 = fval[i__];
153: f_max = PetscMax(d__1,d__2);
154: }
155: /* Construct the difference table. */
156: dnoise = FALSE_;
157: for (j = 1; j <= 6; ++j) {
158: dsgn[j - 1] = FALSE_;
159: cancel[j - 1] = FALSE_;
160: scale = 0.;
161: i__1 = *nf - j;
162: for (i__ = 1; i__ <= i__1; ++i__) {
163: fval[i__] = fval[i__ + 1] - fval[i__];
164: if (fval[i__] == 0.) cancel[j - 1] = TRUE_;
166: /* Computing MAX */
167: d__1 = fval[i__];
168: d__2 = scale;
169: d__3 = PetscAbsScalar(d__1);
170: scale = PetscMax(d__2,d__3);
171: }
173: /* Compute the estimates for the noise level. */
174: if (scale == 0.) stdv = 0.;
175: else {
176: stdv = 0.;
177: i__1 = *nf - j;
178: for (i__ = 1; i__ <= i__1; ++i__) {
179: /* Computing 2nd power */
180: d__1 = fval[i__] / scale;
181: stdv += d__1 * d__1;
182: }
183: stdv = scale * PetscSqrtScalar(stdv / (*nf - j));
184: }
185: eps[j] = const__[j - 1] * stdv;
186: /* Determine differences in sign. */
187: i__1 = *nf - j - 1;
188: for (i__ = 1; i__ <= i__1; ++i__) {
189: /* Computing MIN */
190: d__1 = fval[i__];
191: d__2 = fval[i__ + 1];
192: /* Computing MAX */
193: d__3 = fval[i__];
194: d__4 = fval[i__ + 1];
195: if (PetscMin(d__1,d__2) < 0. && PetscMax(d__3,d__4) > 0.) dsgn[j - 1] = TRUE_;
196: }
197: }
198: /* First requirement for detection of noise. */
199: dnoise = dsgn[3];
200: /* Check for h too small or too large. */
201: *info = 0;
202: if (f_max == f_min) *info = 2;
203: else /* if (complicated condition) */ {
204: /* Computing MIN */
205: d__1 = PetscAbsScalar(f_max);
206: d__2 = PetscAbsScalar(f_min);
207: if (f_max - f_min > PetscMin(d__1,d__2) * .1) *info = 3;
208: }
209: if (*info != 0) return(0);
211: /* Determine the noise level. */
212: /* Computing MIN */
213: d__1 = PetscMin(eps[4],eps[5]);
214: emin = PetscMin(d__1,eps[6]);
216: /* Computing MAX */
217: d__1 = PetscMax(eps[4],eps[5]);
218: emax = PetscMax(d__1,eps[6]);
220: if (emax <= emin * 4 && dnoise) {
221: *fnoise = (eps[4] + eps[5] + eps[6]) / 3;
222: if (*fder2 != 0.) {
223: *info = 1;
224: *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68;
225: } else {
226: *info = 4;
227: *hopt = *h__ * 10;
228: }
229: return(0);
230: }
232: /* Computing MIN */
233: d__1 = PetscMin(eps[3],eps[4]);
234: emin = PetscMin(d__1,eps[5]);
236: /* Computing MAX */
237: d__1 = PetscMax(eps[3],eps[4]);
238: emax = PetscMax(d__1,eps[5]);
240: if (emax <= emin * 4 && dnoise) {
241: *fnoise = (eps[3] + eps[4] + eps[5]) / 3;
242: if (*fder2 != 0.) {
243: *info = 1;
244: *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68;
245: } else {
246: *info = 4;
247: *hopt = *h__ * 10;
248: }
249: return(0);
250: }
251: /* Noise not detected; decide if h is too small or too large. */
252: if (!cancel[3]) {
253: if (dsgn[3]) *info = 2;
254: else *info = 3;
255: return(0);
256: }
257: if (!cancel[2]) {
258: if (dsgn[2]) *info = 2;
259: else *info = 3;
260: return(0);
261: }
262: /* If there is cancelllation on the third and fourth column */
263: /* then h is too small */
264: *info = 2;
265: return(0);
266: /* if (cancel .or. dsgn(3)) then */
267: /* info = 2 */
268: /* else */
269: /* info = 3 */
270: /* end if */
271: } /* dnest_ */