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;
24: /* Local variables */
25: static double emin, emax;
26: static PetscInt dsgn[6];
27: static double f_max, f_min, stdv;
28: static PetscInt i__, j;
29: static double scale;
30: static PetscInt mh;
31: static PetscInt cancel[6], dnoise;
32: static double err2, est1, est2, est3, est4;
34: /* ********** */
36: /* Subroutine dnest */
38: /* This subroutine estimates the noise in a function */
39: /* and provides estimates of the optimal difference parameter */
40: /* for a forward-difference approximation. */
42: /* The user must provide a difference parameter h, and the */
43: /* function value at nf points centered around the current point. */
44: /* For example, if nf = 7, the user must provide */
46: /* f(x-2*h), f(x-h), f(x), f(x+h), f(x+2*h), */
48: /* in the array fval. The use of nf = 7 function evaluations is */
49: /* recommended. */
51: /* The noise in the function is roughly defined as the variance in */
52: /* the computed value of the function. The noise in the function */
53: /* provides valuable information. For example, function values */
54: /* smaller than the noise should be considered to be zero. */
56: /* This subroutine requires an initial estimate for h. Under estimates */
57: /* are usually preferred. If noise is not detected, the user should */
58: /* increase or decrease h according to the ouput value of info. */
59: /* In most cases, the subroutine detects noise with the initial */
60: /* value of h. */
62: /* The subroutine statement is */
64: /* subroutine dnest(nf,fval,h,hopt,fnoise,info,eps) */
66: /* where */
68: /* nf is an int variable. */
69: /* On entry nf is the number of function values. */
70: /* On exit nf is unchanged. */
72: /* f is a double precision array of dimension nf. */
73: /* On entry f contains the function values. */
74: /* On exit f is overwritten. */
76: /* h is a double precision variable. */
77: /* On entry h is an estimate of the optimal difference parameter. */
78: /* On exit h is unchanged. */
80: /* fnoise is a double precision variable. */
81: /* On entry fnoise need not be specified. */
82: /* On exit fnoise is set to an estimate of the function noise */
83: /* if noise is detected; otherwise fnoise is set to zero. */
85: /* hopt is a double precision variable. */
86: /* On entry hopt need not be specified. */
87: /* On exit hopt is set to an estimate of the optimal difference */
88: /* parameter if noise is detected; otherwise hopt is set to zero. */
90: /* info is an int variable. */
91: /* On entry info need not be specified. */
92: /* On exit info is set as follows: */
94: /* info = 1 Noise has been detected. */
96: /* info = 2 Noise has not been detected; h is too small. */
97: /* Try 100*h for the next value of h. */
99: /* info = 3 Noise has not been detected; h is too large. */
100: /* Try h/100 for the next value of h. */
102: /* info = 4 Noise has been detected but the estimate of hopt */
103: /* is not reliable; h is too small. */
105: /* eps is a double precision work array of dimension nf. */
107: /* MINPACK-2 Project. April 1997. */
108: /* Argonne National Laboratory. */
109: /* Jorge J. More'. */
111: /* ********** */
112: /* Parameter adjustments */
113: --eps;
114: --fval;
116: /* Function Body */
117: *fnoise = 0.;
118: *fder2 = 0.;
119: *hopt = 0.;
120: /* Compute an estimate of the second derivative and */
121: /* determine a bound on the error. */
122: mh = (*nf + 1) / 2;
123: est1 = (fval[mh + 1] - fval[mh] * 2 + fval[mh - 1]) / *h__ / *h__;
124: est2 = (fval[mh + 2] - fval[mh] * 2 + fval[mh - 2]) / (*h__ * 2) / (*h__ * 2);
125: est3 = (fval[mh + 3] - fval[mh] * 2 + fval[mh - 3]) / (*h__ * 3) / (*h__ * 3);
126: est4 = (est1 + est2 + est3) / 3;
127: /* Computing MAX */
128: /* Computing PETSCMAX */
129: d__3 = PetscMax(est1,est2);
130: /* Computing MIN */
131: d__4 = PetscMin(est1,est2);
132: d__1 = PetscMax(d__3,est3) - est4;
133: d__2 = est4 - PetscMin(d__4,est3);
134: err2 = PetscMax(d__1,d__2);
135: /* write (2,123) est1, est2, est3 */
136: /* 123 format ('Second derivative estimates', 3d12.2) */
137: if (err2 <= PetscAbsScalar(est4) * .1) *fder2 = est4;
138: else if (err2 < PetscAbsScalar(est4)) *fder2 = est3;
139: else *fder2 = 0.;
141: /* Compute the range of function values. */
142: f_min = fval[1];
143: f_max = fval[1];
144: i__1 = *nf;
145: for (i__ = 2; i__ <= i__1; ++i__) {
146: /* Computing MIN */
147: d__1 = f_min;
148: d__2 = fval[i__];
149: f_min = PetscMin(d__1,d__2);
151: /* Computing MAX */
152: d__1 = f_max;
153: d__2 = fval[i__];
154: f_max = PetscMax(d__1,d__2);
155: }
156: /* Construct the difference table. */
157: dnoise = FALSE_;
158: for (j = 1; j <= 6; ++j) {
159: dsgn[j - 1] = FALSE_;
160: cancel[j - 1] = FALSE_;
161: scale = 0.;
162: i__1 = *nf - j;
163: for (i__ = 1; i__ <= i__1; ++i__) {
164: fval[i__] = fval[i__ + 1] - fval[i__];
165: if (fval[i__] == 0.) cancel[j - 1] = TRUE_;
167: /* Computing MAX */
168: d__1 = fval[i__];
169: d__2 = scale;
170: d__3 = PetscAbsScalar(d__1);
171: scale = PetscMax(d__2,d__3);
172: }
174: /* Compute the estimates for the noise level. */
175: if (scale == 0.) stdv = 0.;
176: else {
177: stdv = 0.;
178: i__1 = *nf - j;
179: for (i__ = 1; i__ <= i__1; ++i__) {
180: /* Computing 2nd power */
181: d__1 = fval[i__] / scale;
182: stdv += d__1 * d__1;
183: }
184: stdv = scale * PetscSqrtScalar(stdv / (*nf - j));
185: }
186: eps[j] = const__[j - 1] * stdv;
187: /* Determine differences in sign. */
188: i__1 = *nf - j - 1;
189: for (i__ = 1; i__ <= i__1; ++i__) {
190: /* Computing MIN */
191: d__1 = fval[i__];
192: d__2 = fval[i__ + 1];
193: /* Computing MAX */
194: d__3 = fval[i__];
195: d__4 = fval[i__ + 1];
196: if (PetscMin(d__1,d__2) < 0. && PetscMax(d__3,d__4) > 0.) dsgn[j - 1] = TRUE_;
197: }
198: }
199: /* First requirement for detection of noise. */
200: dnoise = dsgn[3];
201: /* Check for h too small or too large. */
202: *info = 0;
203: if (f_max == f_min) *info = 2;
204: else /* if (complicated condition) */ {
205: /* Computing MIN */
206: d__1 = PetscAbsScalar(f_max);
207: d__2 = PetscAbsScalar(f_min);
208: if (f_max - f_min > PetscMin(d__1,d__2) * .1) *info = 3;
209: }
210: if (*info != 0) return(0);
212: /* Determine the noise level. */
213: /* Computing MIN */
214: d__1 = PetscMin(eps[4],eps[5]);
215: emin = PetscMin(d__1,eps[6]);
217: /* Computing MAX */
218: d__1 = PetscMax(eps[4],eps[5]);
219: emax = PetscMax(d__1,eps[6]);
221: if (emax <= emin * 4 && dnoise) {
222: *fnoise = (eps[4] + eps[5] + eps[6]) / 3;
223: if (*fder2 != 0.) {
224: *info = 1;
225: *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68;
226: } else {
227: *info = 4;
228: *hopt = *h__ * 10;
229: }
230: return(0);
231: }
233: /* Computing MIN */
234: d__1 = PetscMin(eps[3],eps[4]);
235: emin = PetscMin(d__1,eps[5]);
237: /* Computing MAX */
238: d__1 = PetscMax(eps[3],eps[4]);
239: emax = PetscMax(d__1,eps[5]);
241: if (emax <= emin * 4 && dnoise) {
242: *fnoise = (eps[3] + eps[4] + eps[5]) / 3;
243: if (*fder2 != 0.) {
244: *info = 1;
245: *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68;
246: } else {
247: *info = 4;
248: *hopt = *h__ * 10;
249: }
250: return(0);
251: }
252: /* Noise not detected; decide if h is too small or too large. */
253: if (!cancel[3]) {
254: if (dsgn[3]) *info = 2;
255: else *info = 3;
256: return(0);
257: }
258: if (!cancel[2]) {
259: if (dsgn[2]) *info = 2;
260: else *info = 3;
261: return(0);
262: }
263: /* If there is cancelllation on the third and fourth column */
264: /* then h is too small */
265: *info = 2;
266: return(0);
267: /* if (cancel .or. dsgn(3)) then */
268: /* info = 2 */
269: /* else */
270: /* info = 3 */
271: /* end if */
272: } /* dnest_ */