Actual source code: snesdnest.c
1: /* fnoise/snesdnest.F -- translated by f2c (version 20020314).
2: */
3: #include petsc.h
4: #define FALSE_ 0
5: #define TRUE_ 1
7: /* Noise estimation routine, written by Jorge More'. Details are below. */
9: /* Subroutine */ PetscErrorCode dnest_(PetscInt *nf, double *fval,double *h__,double *fnoise, double *fder2, double *hopt, PetscInt *info, double *eps)
10: {
11: /* Initialized data */
13: static double const__[15] = { .71,.41,.23,.12,.063,.033,.018,.0089,
14: .0046,.0024,.0012,6.1e-4,3.1e-4,1.6e-4,8e-5 };
16: /* System generated locals */
17: PetscInt i__1;
18: double d__1, d__2, d__3, d__4;
21: /* Local variables */
22: static double emin, emax;
23: static PetscInt dsgn[6];
24: static double f_max, f_min, stdv;
25: static PetscInt i__, j;
26: static double scale;
27: static PetscInt mh;
28: static PetscInt cancel[6], dnoise;
29: static double err2, est1, est2, est3, est4;
31: /* ********** */
33: /* Subroutine dnest */
35: /* This subroutine estimates the noise in a function */
36: /* and provides estimates of the optimal difference parameter */
37: /* for a forward-difference approximation. */
39: /* The user must provide a difference parameter h, and the */
40: /* function value at nf points centered around the current point. */
41: /* For example, if nf = 7, the user must provide */
43: /* f(x-2*h), f(x-h), f(x), f(x+h), f(x+2*h), */
45: /* in the array fval. The use of nf = 7 function evaluations is */
46: /* recommended. */
48: /* The noise in the function is roughly defined as the variance in */
49: /* the computed value of the function. The noise in the function */
50: /* provides valuable information. For example, function values */
51: /* smaller than the noise should be considered to be zero. */
53: /* This subroutine requires an initial estimate for h. Under estimates */
54: /* are usually preferred. If noise is not detected, the user should */
55: /* increase or decrease h according to the ouput value of info. */
56: /* In most cases, the subroutine detects noise with the initial */
57: /* value of h. */
59: /* The subroutine statement is */
61: /* subroutine dnest(nf,fval,h,hopt,fnoise,info,eps) */
63: /* where */
65: /* nf is an int variable. */
66: /* On entry nf is the number of function values. */
67: /* On exit nf is unchanged. */
69: /* f is a double precision array of dimension nf. */
70: /* On entry f contains the function values. */
71: /* On exit f is overwritten. */
73: /* h is a double precision variable. */
74: /* On entry h is an estimate of the optimal difference parameter. */
75: /* On exit h is unchanged. */
77: /* fnoise is a double precision variable. */
78: /* On entry fnoise need not be specified. */
79: /* On exit fnoise is set to an estimate of the function noise */
80: /* if noise is detected; otherwise fnoise is set to zero. */
82: /* hopt is a double precision variable. */
83: /* On entry hopt need not be specified. */
84: /* On exit hopt is set to an estimate of the optimal difference */
85: /* parameter if noise is detected; otherwise hopt is set to zero. */
87: /* info is an int variable. */
88: /* On entry info need not be specified. */
89: /* On exit info is set as follows: */
91: /* info = 1 Noise has been detected. */
93: /* info = 2 Noise has not been detected; h is too small. */
94: /* Try 100*h for the next value of h. */
96: /* info = 3 Noise has not been detected; h is too large. */
97: /* Try h/100 for the next value of h. */
99: /* info = 4 Noise has been detected but the estimate of hopt */
100: /* is not reliable; h is too small. */
102: /* eps is a double precision work array of dimension nf. */
104: /* MINPACK-2 Project. April 1997. */
105: /* Argonne National Laboratory. */
106: /* Jorge J. More'. */
108: /* ********** */
109: /* Parameter adjustments */
110: --eps;
111: --fval;
113: /* Function Body */
114: *fnoise = 0.;
115: *fder2 = 0.;
116: *hopt = 0.;
117: /* Compute an estimate of the second derivative and */
118: /* determine a bound on the error. */
119: mh = (*nf + 1) / 2;
120: est1 = (fval[mh + 1] - fval[mh] * 2 + fval[mh - 1]) / *h__ / *h__;
121: est2 = (fval[mh + 2] - fval[mh] * 2 + fval[mh - 2]) / (*h__ * 2) / (*h__ *
122: 2);
123: est3 = (fval[mh + 3] - fval[mh] * 2 + fval[mh - 3]) / (*h__ * 3) / (*h__ *
124: 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, d__2 = est4 - PetscMin(d__4,est3);
132: err2 = PetscMax(d__1,d__2);
133: /* write (2,123) est1, est2, est3 */
134: /* 123 format ('Second derivative estimates', 3d12.2) */
135: if (err2 <= PetscAbsScalar(est4) * .1) {
136: *fder2 = est4;
137: } else if (err2 < PetscAbsScalar(est4)) {
138: *fder2 = est3;
139: } else {
140: *fder2 = 0.;
141: }
142: /* Compute the range of function values. */
143: f_min = fval[1];
144: f_max = fval[1];
145: i__1 = *nf;
146: for (i__ = 2; i__ <= i__1; ++i__) {
147: /* Computing MIN */
148: d__1 = f_min, d__2 = fval[i__];
149: f_min = PetscMin(d__1,d__2);
150: /* Computing MAX */
151: d__1 = f_max, d__2 = fval[i__];
152: f_max = PetscMax(d__1,d__2);
153: }
154: /* Construct the difference table. */
155: dnoise = FALSE_;
156: for (j = 1; j <= 6; ++j) {
157: dsgn[j - 1] = FALSE_;
158: cancel[j - 1] = FALSE_;
159: scale = 0.;
160: i__1 = *nf - j;
161: for (i__ = 1; i__ <= i__1; ++i__) {
162: fval[i__] = fval[i__ + 1] - fval[i__];
163: if (fval[i__] == 0.) {
164: cancel[j - 1] = TRUE_;
165: }
166: /* Computing MAX */
167: d__2 = scale, d__3 = (d__1 = fval[i__], PetscAbsScalar(d__1));
168: scale = PetscMax(d__2,d__3);
169: }
170: /* Compute the estimates for the noise level. */
171: if (scale == 0.) {
172: stdv = 0.;
173: } else {
174: stdv = 0.;
175: i__1 = *nf - j;
176: for (i__ = 1; i__ <= i__1; ++i__) {
177: /* Computing 2nd power */
178: d__1 = fval[i__] / scale;
179: stdv += d__1 * d__1;
180: }
181: stdv = scale * PetscSqrtScalar(stdv / (*nf - j));
182: }
183: eps[j] = const__[j - 1] * stdv;
184: /* Determine differences in sign. */
185: i__1 = *nf - j - 1;
186: for (i__ = 1; i__ <= i__1; ++i__) {
187: /* Computing MIN */
188: d__1 = fval[i__], d__2 = fval[i__ + 1];
189: /* Computing MAX */
190: d__3 = fval[i__], d__4 = fval[i__ + 1];
191: if (PetscMin(d__1,d__2) < 0. && PetscMax(d__3,d__4) > 0.) {
192: dsgn[j - 1] = TRUE_;
193: }
194: }
195: }
196: /* First requirement for detection of noise. */
197: dnoise = dsgn[3];
198: /* Check for h too small or too large. */
199: *info = 0;
200: if (f_max == f_min) {
201: *info = 2;
202: } else /* if(complicated condition) */ {
203: /* Computing MIN */
204: d__1 = PetscAbsScalar(f_max), d__2 = PetscAbsScalar(f_min);
205: if (f_max - f_min > PetscMin(d__1,d__2) * .1) {
206: *info = 3;
207: }
208: }
209: if (*info != 0) {
210: return(0);
211: }
212: /* Determine the noise level. */
213: /* Computing MIN */
214: d__1 = PetscMin(eps[4],eps[5]);
215: emin = PetscMin(d__1,eps[6]);
216: /* Computing MAX */
217: d__1 = PetscMax(eps[4],eps[5]);
218: emax = PetscMax(d__1,eps[6]);
219: if (emax <= emin * 4 && dnoise) {
220: *fnoise = (eps[4] + eps[5] + eps[6]) / 3;
221: if (*fder2 != 0.) {
222: *info = 1;
223: *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68;
224: } else {
225: *info = 4;
226: *hopt = *h__ * 10;
227: }
228: return(0);
229: }
230: /* Computing MIN */
231: d__1 = PetscMin(eps[3],eps[4]);
232: emin = PetscMin(d__1,eps[5]);
233: /* Computing MAX */
234: d__1 = PetscMax(eps[3],eps[4]);
235: emax = PetscMax(d__1,eps[5]);
236: if (emax <= emin * 4 && dnoise) {
237: *fnoise = (eps[3] + eps[4] + eps[5]) / 3;
238: if (*fder2 != 0.) {
239: *info = 1;
240: *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68;
241: } else {
242: *info = 4;
243: *hopt = *h__ * 10;
244: }
245: return(0);
246: }
247: /* Noise not detected; decide if h is too small or too large. */
248: if (! cancel[3]) {
249: if (dsgn[3]) {
250: *info = 2;
251: } else {
252: *info = 3;
253: }
254: return(0);
255: }
256: if (! cancel[2]) {
257: if (dsgn[2]) {
258: *info = 2;
259: } else {
260: *info = 3;
261: }
262: return(0);
263: }
264: /* If there is cancelllation on the third and fourth column */
265: /* then h is too small */
266: *info = 2;
267: return(0);
268: /* if (cancel .or. dsgn(3)) then */
269: /* info = 2 */
270: /* else */
271: /* info = 3 */
272: /* end if */
273: } /* dnest_ */