#define PETSCSNES_DLL /* fnoise/snesdnest.F -- translated by f2c (version 20020314). */ #include "petsc.h" #define FALSE_ 0 #define TRUE_ 1 /* Noise estimation routine, written by Jorge More'. Details are below. */ /* Subroutine */ PetscErrorCode dnest_(PetscInt *nf, double *fval,double *h__,double *fnoise, double *fder2, double *hopt, PetscInt *info, double *eps) { /* Initialized data */ static double const__[15] = { .71,.41,.23,.12,.063,.033,.018,.0089, .0046,.0024,.0012,6.1e-4,3.1e-4,1.6e-4,8e-5 }; /* System generated locals */ PetscInt i__1; double d__1, d__2, d__3, d__4; /* Local variables */ static double emin, emax; static PetscInt dsgn[6]; static double f_max, f_min, stdv; static PetscInt i__, j; static double scale; static PetscInt mh; static PetscInt cancel[6], dnoise; static double err2, est1, est2, est3, est4; /* ********** */ /* Subroutine dnest */ /* This subroutine estimates the noise in a function */ /* and provides estimates of the optimal difference parameter */ /* for a forward-difference approximation. */ /* The user must provide a difference parameter h, and the */ /* function value at nf points centered around the current point. */ /* For example, if nf = 7, the user must provide */ /* f(x-2*h), f(x-h), f(x), f(x+h), f(x+2*h), */ /* in the array fval. The use of nf = 7 function evaluations is */ /* recommended. */ /* The noise in the function is roughly defined as the variance in */ /* the computed value of the function. The noise in the function */ /* provides valuable information. For example, function values */ /* smaller than the noise should be considered to be zero. */ /* This subroutine requires an initial estimate for h. Under estimates */ /* are usually preferred. If noise is not detected, the user should */ /* increase or decrease h according to the ouput value of info. */ /* In most cases, the subroutine detects noise with the initial */ /* value of h. */ /* The subroutine statement is */ /* subroutine dnest(nf,fval,h,hopt,fnoise,info,eps) */ /* where */ /* nf is an int variable. */ /* On entry nf is the number of function values. */ /* On exit nf is unchanged. */ /* f is a double precision array of dimension nf. */ /* On entry f contains the function values. */ /* On exit f is overwritten. */ /* h is a double precision variable. */ /* On entry h is an estimate of the optimal difference parameter. */ /* On exit h is unchanged. */ /* fnoise is a double precision variable. */ /* On entry fnoise need not be specified. */ /* On exit fnoise is set to an estimate of the function noise */ /* if noise is detected; otherwise fnoise is set to zero. */ /* hopt is a double precision variable. */ /* On entry hopt need not be specified. */ /* On exit hopt is set to an estimate of the optimal difference */ /* parameter if noise is detected; otherwise hopt is set to zero. */ /* info is an int variable. */ /* On entry info need not be specified. */ /* On exit info is set as follows: */ /* info = 1 Noise has been detected. */ /* info = 2 Noise has not been detected; h is too small. */ /* Try 100*h for the next value of h. */ /* info = 3 Noise has not been detected; h is too large. */ /* Try h/100 for the next value of h. */ /* info = 4 Noise has been detected but the estimate of hopt */ /* is not reliable; h is too small. */ /* eps is a double precision work array of dimension nf. */ /* MINPACK-2 Project. April 1997. */ /* Argonne National Laboratory. */ /* Jorge J. More'. */ /* ********** */ /* Parameter adjustments */ --eps; --fval; /* Function Body */ *fnoise = 0.; *fder2 = 0.; *hopt = 0.; /* Compute an estimate of the second derivative and */ /* determine a bound on the error. */ mh = (*nf + 1) / 2; est1 = (fval[mh + 1] - fval[mh] * 2 + fval[mh - 1]) / *h__ / *h__; est2 = (fval[mh + 2] - fval[mh] * 2 + fval[mh - 2]) / (*h__ * 2) / (*h__ * 2); est3 = (fval[mh + 3] - fval[mh] * 2 + fval[mh - 3]) / (*h__ * 3) / (*h__ * 3); est4 = (est1 + est2 + est3) / 3; /* Computing MAX */ /* Computing PETSCMAX */ d__3 = PetscMax(est1,est2); /* Computing MIN */ d__4 = PetscMin(est1,est2); d__1 = PetscMax(d__3,est3) - est4, d__2 = est4 - PetscMin(d__4,est3); err2 = PetscMax(d__1,d__2); /* write (2,123) est1, est2, est3 */ /* 123 format ('Second derivative estimates', 3d12.2) */ if (err2 <= PetscAbsScalar(est4) * .1) { *fder2 = est4; } else if (err2 < PetscAbsScalar(est4)) { *fder2 = est3; } else { *fder2 = 0.; } /* Compute the range of function values. */ f_min = fval[1]; f_max = fval[1]; i__1 = *nf; for (i__ = 2; i__ <= i__1; ++i__) { /* Computing MIN */ d__1 = f_min, d__2 = fval[i__]; f_min = PetscMin(d__1,d__2); /* Computing MAX */ d__1 = f_max, d__2 = fval[i__]; f_max = PetscMax(d__1,d__2); } /* Construct the difference table. */ dnoise = FALSE_; for (j = 1; j <= 6; ++j) { dsgn[j - 1] = FALSE_; cancel[j - 1] = FALSE_; scale = 0.; i__1 = *nf - j; for (i__ = 1; i__ <= i__1; ++i__) { fval[i__] = fval[i__ + 1] - fval[i__]; if (fval[i__] == 0.) { cancel[j - 1] = TRUE_; } /* Computing MAX */ d__2 = scale, d__3 = (d__1 = fval[i__], PetscAbsScalar(d__1)); scale = PetscMax(d__2,d__3); } /* Compute the estimates for the noise level. */ if (scale == 0.) { stdv = 0.; } else { stdv = 0.; i__1 = *nf - j; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing 2nd power */ d__1 = fval[i__] / scale; stdv += d__1 * d__1; } stdv = scale * PetscSqrtScalar(stdv / (*nf - j)); } eps[j] = const__[j - 1] * stdv; /* Determine differences in sign. */ i__1 = *nf - j - 1; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MIN */ d__1 = fval[i__], d__2 = fval[i__ + 1]; /* Computing MAX */ d__3 = fval[i__], d__4 = fval[i__ + 1]; if (PetscMin(d__1,d__2) < 0. && PetscMax(d__3,d__4) > 0.) { dsgn[j - 1] = TRUE_; } } } /* First requirement for detection of noise. */ dnoise = dsgn[3]; /* Check for h too small or too large. */ *info = 0; if (f_max == f_min) { *info = 2; } else /* if(complicated condition) */ { /* Computing MIN */ d__1 = PetscAbsScalar(f_max), d__2 = PetscAbsScalar(f_min); if (f_max - f_min > PetscMin(d__1,d__2) * .1) { *info = 3; } } if (*info != 0) { PetscFunctionReturn(0); } /* Determine the noise level. */ /* Computing MIN */ d__1 = PetscMin(eps[4],eps[5]); emin = PetscMin(d__1,eps[6]); /* Computing MAX */ d__1 = PetscMax(eps[4],eps[5]); emax = PetscMax(d__1,eps[6]); if (emax <= emin * 4 && dnoise) { *fnoise = (eps[4] + eps[5] + eps[6]) / 3; if (*fder2 != 0.) { *info = 1; *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68; } else { *info = 4; *hopt = *h__ * 10; } PetscFunctionReturn(0); } /* Computing MIN */ d__1 = PetscMin(eps[3],eps[4]); emin = PetscMin(d__1,eps[5]); /* Computing MAX */ d__1 = PetscMax(eps[3],eps[4]); emax = PetscMax(d__1,eps[5]); if (emax <= emin * 4 && dnoise) { *fnoise = (eps[3] + eps[4] + eps[5]) / 3; if (*fder2 != 0.) { *info = 1; *hopt = PetscSqrtScalar(*fnoise / PetscAbsScalar(*fder2)) * 1.68; } else { *info = 4; *hopt = *h__ * 10; } PetscFunctionReturn(0); } /* Noise not detected; decide if h is too small or too large. */ if (! cancel[3]) { if (dsgn[3]) { *info = 2; } else { *info = 3; } PetscFunctionReturn(0); } if (! cancel[2]) { if (dsgn[2]) { *info = 2; } else { *info = 3; } PetscFunctionReturn(0); } /* If there is cancelllation on the third and fourth column */ /* then h is too small */ *info = 2; PetscFunctionReturn(0); /* if (cancel .or. dsgn(3)) then */ /* info = 2 */ /* else */ /* info = 3 */ /* end if */ } /* dnest_ */