1 /* fnoise/snesdnest.F -- translated by f2c (version 20020314). 2 */ 3 #include "petsc.h" 4 #define FALSE_ 0 5 #define TRUE_ 1 6 7 /* Noise estimation routine, written by Jorge More'. Details are below. */ 8 9 /* Subroutine */ PetscErrorCode dnest_(PetscInt *nf, double *fval,double *h__,double *fnoise, double *fder2, double *hopt, PetscInt *info, double *eps) 10 { 11 /* Initialized data */ 12 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 }; 15 16 /* System generated locals */ 17 PetscInt i__1; 18 double d__1, d__2, d__3, d__4; 19 20 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; 30 31 /* ********** */ 32 33 /* Subroutine dnest */ 34 35 /* This subroutine estimates the noise in a function */ 36 /* and provides estimates of the optimal difference parameter */ 37 /* for a forward-difference approximation. */ 38 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 */ 42 43 /* f(x-2*h), f(x-h), f(x), f(x+h), f(x+2*h), */ 44 45 /* in the array fval. The use of nf = 7 function evaluations is */ 46 /* recommended. */ 47 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. */ 52 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. */ 58 59 /* The subroutine statement is */ 60 61 /* subroutine dnest(nf,fval,h,hopt,fnoise,info,eps) */ 62 63 /* where */ 64 65 /* nf is an int variable. */ 66 /* On entry nf is the number of function values. */ 67 /* On exit nf is unchanged. */ 68 69 /* f is a double precision array of dimension nf. */ 70 /* On entry f contains the function values. */ 71 /* On exit f is overwritten. */ 72 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. */ 76 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. */ 81 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. */ 86 87 /* info is an int variable. */ 88 /* On entry info need not be specified. */ 89 /* On exit info is set as follows: */ 90 91 /* info = 1 Noise has been detected. */ 92 93 /* info = 2 Noise has not been detected; h is too small. */ 94 /* Try 100*h for the next value of h. */ 95 96 /* info = 3 Noise has not been detected; h is too large. */ 97 /* Try h/100 for the next value of h. */ 98 99 /* info = 4 Noise has been detected but the estimate of hopt */ 100 /* is not reliable; h is too small. */ 101 102 /* eps is a double precision work array of dimension nf. */ 103 104 /* MINPACK-2 Project. April 1997. */ 105 /* Argonne National Laboratory. */ 106 /* Jorge J. More'. */ 107 108 /* ********** */ 109 /* Parameter adjustments */ 110 --eps; 111 --fval; 112 113 /* 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 PetscFunctionReturn(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 PetscFunctionReturn(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 PetscFunctionReturn(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 PetscFunctionReturn(0); 255 } 256 if (! cancel[2]) { 257 if (dsgn[2]) { 258 *info = 2; 259 } else { 260 *info = 3; 261 } 262 PetscFunctionReturn(0); 263 } 264 /* If there is cancelllation on the third and fourth column */ 265 /* then h is too small */ 266 *info = 2; 267 PetscFunctionReturn(0); 268 /* if (cancel .or. dsgn(3)) then */ 269 /* info = 2 */ 270 /* else */ 271 /* info = 3 */ 272 /* end if */ 273 } /* dnest_ */ 274 275