1 2 /* fnoise/snesdnest.F -- translated by f2c (version 20020314). 3 */ 4 #include <petscsys.h> 5 #define FALSE_ 0 6 #define TRUE_ 1 7 8 /* Noise estimation routine, written by Jorge More'. Details are below. */ 9 10 PETSC_INTERN PetscErrorCode SNESNoise_dnest_(PetscInt*,PetscScalar*,PetscScalar*,PetscScalar*,PetscScalar*,PetscScalar*,PetscInt*,PetscScalar*); 11 12 PetscErrorCode SNESNoise_dnest_(PetscInt *nf, double *fval,double *h__,double *fnoise, double *fder2, double *hopt, PetscInt *info, double *eps) 13 { 14 /* Initialized data */ 15 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 }; 18 19 /* System generated locals */ 20 PetscInt i__1; 21 double d__1, d__2, d__3, d__4; 22 23 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; 33 34 /* ********** */ 35 36 /* Subroutine dnest */ 37 38 /* This subroutine estimates the noise in a function */ 39 /* and provides estimates of the optimal difference parameter */ 40 /* for a forward-difference approximation. */ 41 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 */ 45 46 /* f(x-2*h), f(x-h), f(x), f(x+h), f(x+2*h), */ 47 48 /* in the array fval. The use of nf = 7 function evaluations is */ 49 /* recommended. */ 50 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. */ 55 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. */ 61 62 /* The subroutine statement is */ 63 64 /* subroutine dnest(nf,fval,h,hopt,fnoise,info,eps) */ 65 66 /* where */ 67 68 /* nf is a PetscInt variable. */ 69 /* On entry nf is the number of function values. */ 70 /* On exit nf is unchanged. */ 71 72 /* f is a double precision array of dimension nf. */ 73 /* On entry f contains the function values. */ 74 /* On exit f is overwritten. */ 75 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. */ 79 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. */ 84 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. */ 89 90 /* info is a PetscInt variable. */ 91 /* On entry info need not be specified. */ 92 /* On exit info is set as follows: */ 93 94 /* info = 1 Noise has been detected. */ 95 96 /* info = 2 Noise has not been detected; h is too small. */ 97 /* Try 100*h for the next value of h. */ 98 99 /* info = 3 Noise has not been detected; h is too large. */ 100 /* Try h/100 for the next value of h. */ 101 102 /* info = 4 Noise has been detected but the estimate of hopt */ 103 /* is not reliable; h is too small. */ 104 105 /* eps is a double precision work array of dimension nf. */ 106 107 /* MINPACK-2 Project. April 1997. */ 108 /* Argonne National Laboratory. */ 109 /* Jorge J. More'. */ 110 111 /* ********** */ 112 /* Parameter adjustments */ 113 --eps; 114 --fval; 115 116 /* 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.; 140 141 /* 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); 150 151 /* 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_; 166 167 /* 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 } 173 174 /* 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) 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]); 216 217 /* Computing MAX */ 218 d__1 = PetscMax(eps[4],eps[5]); 219 emax = PetscMax(d__1,eps[6]); 220 221 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 PetscFunctionReturn(0); 231 } 232 233 /* Computing MIN */ 234 d__1 = PetscMin(eps[3],eps[4]); 235 emin = PetscMin(d__1,eps[5]); 236 237 /* Computing MAX */ 238 d__1 = PetscMax(eps[3],eps[4]); 239 emax = PetscMax(d__1,eps[5]); 240 241 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 PetscFunctionReturn(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 PetscFunctionReturn(0); 257 } 258 if (!cancel[2]) { 259 if (dsgn[2]) *info = 2; 260 else *info = 3; 261 PetscFunctionReturn(0); 262 } 263 /* If there is cancelllation on the third and fourth column */ 264 /* then h is too small */ 265 *info = 2; 266 PetscFunctionReturn(0); 267 /* if (cancel .or. dsgn(3)) then */ 268 /* info = 2 */ 269 /* else */ 270 /* info = 3 */ 271 /* end if */ 272 } /* dnest_ */ 273 274