Date: 2013-07-02T14:49:23+00:00

Actual source code: snesdnest.c
petsc-3.4.2 2013-07-02

      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: /* Subroutine */ PetscErrorCode SNESNoise_dnest_(PetscInt *nf, double *fval,double *h__,double *fnoise, double *fder2, double *hopt, PetscInt *info, double *eps)
     11: {
     12:   /* Initialized data */

     14:   static double const__[15] = { .71,.41,.23,.12,.063,.033,.018,.0089,
     15:                                 .0046,.0024,.0012,6.1e-4,3.1e-4,1.6e-4,8e-5 };

     17:   /* System generated locals */
     18:   PetscInt i__1;
     19:   double   d__1, d__2, d__3, d__4;

     22:   /* Local variables */
     23:   static double   emin, emax;
     24:   static PetscInt dsgn[6];
     25:   static double   f_max, f_min, stdv;
     26:   static PetscInt i__, j;
     27:   static double   scale;
     28:   static PetscInt mh;
     29:   static PetscInt cancel[6], dnoise;
     30:   static double   err2, est1, est2, est3, est4;

     32: /*     ********** */

     34: /*     Subroutine dnest */

     36: /*     This subroutine estimates the noise in a function */
     37: /*     and provides estimates of the optimal difference parameter */
     38: /*     for a forward-difference approximation. */

     40: /*     The user must provide a difference parameter h, and the */
     41: /*     function value at nf points centered around the current point. */
     42: /*     For example, if nf = 7, the user must provide */

     44: /*        f(x-2*h), f(x-h), f(x), f(x+h),  f(x+2*h), */

     46: /*     in the array fval. The use of nf = 7 function evaluations is */
     47: /*     recommended. */

     49: /*     The noise in the function is roughly defined as the variance in */
     50: /*     the computed value of the function. The noise in the function */
     51: /*     provides valuable information. For example, function values */
     52: /*     smaller than the noise should be considered to be zero. */

     54: /*     This subroutine requires an initial estimate for h. Under estimates */
     55: /*     are usually preferred. If noise is not detected, the user should */
     56: /*     increase or decrease h according to the ouput value of info. */
     57: /*     In most cases, the subroutine detects noise with the initial */
     58: /*     value of h. */

     60: /*     The subroutine statement is */

     62: /*       subroutine dnest(nf,fval,h,hopt,fnoise,info,eps) */

     64: /*     where */

     66: /*       nf is an int variable. */
     67: /*         On entry nf is the number of function values. */
     68: /*         On exit nf is unchanged. */

     70: /*       f is a double precision array of dimension nf. */
     71: /*         On entry f contains the function values. */
     72: /*         On exit f is overwritten. */

     74: /*       h is a double precision variable. */
     75: /*         On entry h is an estimate of the optimal difference parameter. */
     76: /*         On exit h is unchanged. */

     78: /*       fnoise is a double precision variable. */
     79: /*         On entry fnoise need not be specified. */
     80: /*         On exit fnoise is set to an estimate of the function noise */
     81: /*            if noise is detected; otherwise fnoise is set to zero. */

     83: /*       hopt is a double precision variable. */
     84: /*         On entry hopt need not be specified. */
     85: /*         On exit hopt is set to an estimate of the optimal difference */
     86: /*            parameter if noise is detected; otherwise hopt is set to zero. */

     88: /*       info is an int variable. */
     89: /*         On entry info need not be specified. */
     90: /*         On exit info is set as follows: */

     92: /*            info = 1  Noise has been detected. */

     94: /*            info = 2  Noise has not been detected; h is too small. */
     95: /*                      Try 100*h for the next value of h. */

     97: /*            info = 3  Noise has not been detected; h is too large. */
     98: /*                      Try h/100 for the next value of h. */

    100: /*            info = 4  Noise has been detected but the estimate of hopt */
    101: /*                      is not reliable; h is too small. */

    103: /*       eps is a double precision work array of dimension nf. */

    105: /*     MINPACK-2 Project. April 1997. */
    106: /*     Argonne National Laboratory. */
    107: /*     Jorge J. More'. */

    109: /*     ********** */
    110:   /* Parameter adjustments */
    111:   --eps;
    112:   --fval;

    114:   /* Function Body */
    115:   *fnoise = 0.;
    116:   *fder2  = 0.;
    117:   *hopt   = 0.;
    118: /*     Compute an estimate of the second derivative and */
    119: /*     determine a bound on the error. */
    120:   mh   = (*nf + 1) / 2;
    121:   est1 = (fval[mh + 1] - fval[mh] * 2 + fval[mh - 1]) / *h__ / *h__;
    122:   est2 = (fval[mh + 2] - fval[mh] * 2 + fval[mh - 2]) / (*h__ * 2) / (*h__ * 2);
    123:   est3 = (fval[mh + 3] - fval[mh] * 2 + fval[mh - 3]) / (*h__ * 3) / (*h__ * 3);
    124:   est4 = (est1 + est2 + est3) / 3;
    125: /* Computing MAX */
    126: /* Computing PETSCMAX */
    127:   d__3 = PetscMax(est1,est2);
    128: /* Computing MIN */
    129:   d__4 = PetscMin(est1,est2);
    130:   d__1 = PetscMax(d__3,est3) - est4, d__2 = est4 - PetscMin(d__4,est3);
    131:   err2 = PetscMax(d__1,d__2);
    132: /*      write (2,123) est1, est2, est3 */
    133: /* 123  format ('Second derivative estimates', 3d12.2) */
    134:   if (err2 <= PetscAbsScalar(est4) * .1) *fder2 = est4;
    135:   else if (err2 < PetscAbsScalar(est4))  *fder2 = est3;
    136:   else *fder2 = 0.;

    138: /*     Compute the range of function values. */
    139:   f_min = fval[1];
    140:   f_max = fval[1];
    141:   i__1  = *nf;
    142:   for (i__ = 2; i__ <= i__1; ++i__) {
    143:     /* Computing MIN */
    144:     d__1 = f_min, d__2 = fval[i__];
    145:     f_min = PetscMin(d__1,d__2);

    147:     /* Computing MAX */
    148:     d__1 = f_max, d__2 = fval[i__];
    149:     f_max = PetscMax(d__1,d__2);
    150:   }
    151: /*     Construct the difference table. */
    152:   dnoise = FALSE_;
    153:   for (j = 1; j <= 6; ++j) {
    154:     dsgn[j - 1]   = FALSE_;
    155:     cancel[j - 1] = FALSE_;
    156:     scale         = 0.;
    157:     i__1          = *nf - j;
    158:     for (i__ = 1; i__ <= i__1; ++i__) {
    159:       fval[i__] = fval[i__ + 1] - fval[i__];
    160:       if (fval[i__] == 0.) cancel[j - 1] = TRUE_;

    162:       /* Computing MAX */
    163:       d__2 = scale, d__3 = (d__1 = fval[i__], PetscAbsScalar(d__1));
    164:       scale = PetscMax(d__2,d__3);
    165:     }

    167:     /*        Compute the estimates for the noise level. */
    168:     if (scale == 0.) stdv = 0.;
    169:     else {
    170:       stdv = 0.;
    171:       i__1 = *nf - j;
    172:       for (i__ = 1; i__ <= i__1; ++i__) {
    173:         /* Computing 2nd power */
    174:         d__1 = fval[i__] / scale;
    175:         stdv += d__1 * d__1;
    176:       }
    177:       stdv = scale * PetscSqrtScalar(stdv / (*nf - j));
    178:     }
    179:     eps[j] = const__[j - 1] * stdv;
    180: /*        Determine differences in sign. */
    181:     i__1 = *nf - j - 1;
    182:     for (i__ = 1; i__ <= i__1; ++i__) {
    183:       /* Computing MIN */
    184:       d__1 = fval[i__], d__2 = fval[i__ + 1];
    185:       /* Computing MAX */
    186:       d__3 = fval[i__], d__4 = fval[i__ + 1];
    187:       if (PetscMin(d__1,d__2) < 0. && PetscMax(d__3,d__4) > 0.) dsgn[j - 1] = TRUE_;
    188:     }
    189:   }
    190:   /*     First requirement for detection of noise. */
    191:   dnoise = dsgn[3];
    192:   /*     Check for h too small or too large. */
    193:   *info = 0;
    194:   if (f_max == f_min) *info = 2;
    195:   else /* if (complicated condition) */ {
    196:     /* Computing MIN */
    197:     d__1 = PetscAbsScalar(f_max), d__2 = PetscAbsScalar(f_min);
    198:     if (f_max - f_min > PetscMin(d__1,d__2) * .1) *info = 3;
    199:   }
    200:   if (*info != 0) return(0);

    202:   /*     Determine the noise level. */
    203:   /* Computing MIN */
    204:   d__1 = PetscMin(eps[4],eps[5]);
    205:   emin = PetscMin(d__1,eps[6]);

    207:   /* Computing MAX */
    208:   d__1 = PetscMax(eps[4],eps[5]);
    209:   emax = PetscMax(d__1,eps[6]);

    211:   if (emax <= emin * 4 && dnoise) {
    212:     *fnoise = (eps[4] + eps[5] + eps[6]) / 3;
    213:     if (*fder2 != 0.) {
    214:       *info = 1;
    215:       *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68;
    216:     } else {
    217:       *info = 4;
    218:       *hopt = *h__ * 10;
    219:     }
    220:     return(0);
    221:   }

    223:   /* Computing MIN */
    224:   d__1 = PetscMin(eps[3],eps[4]);
    225:   emin = PetscMin(d__1,eps[5]);

    227:   /* Computing MAX */
    228:   d__1 = PetscMax(eps[3],eps[4]);
    229:   emax = PetscMax(d__1,eps[5]);

    231:   if (emax <= emin * 4 && dnoise) {
    232:     *fnoise = (eps[3] + eps[4] + eps[5]) / 3;
    233:     if (*fder2 != 0.) {
    234:       *info = 1;
    235:       *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68;
    236:     } else {
    237:       *info = 4;
    238:       *hopt = *h__ * 10;
    239:     }
    240:     return(0);
    241:   }
    242: /*     Noise not detected; decide if h is too small or too large. */
    243:   if (!cancel[3]) {
    244:     if (dsgn[3]) *info = 2;
    245:     else *info = 3;
    246:     return(0);
    247:   }
    248:   if (!cancel[2]) {
    249:     if (dsgn[2]) *info = 2;
    250:     else *info = 3;
    251:     return(0);
    252:   }
    253: /*     If there is cancelllation on the third and fourth column */
    254: /*     then h is too small */
    255:   *info = 2;
    256:   return(0);
    257: /*      if (cancel .or. dsgn(3)) then */
    258: /*         info = 2 */
    259: /*      else */
    260: /*         info = 3 */
    261: /*      end if */
    262: } /* dnest_ */