lmdif.cpp

L-M法的函数库

/*       minpack-supplied ... dpmpar,enorm,fdjac2,lmpar,qrfac */

/*       fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod */

/*     argonne national laboratory. minpack project. march 1980. */
/*     burton s. garbow, kenneth e. hillstrom, jorge j. more */

/*     ********** */
    /* Parameter adjustments */
    --wa4;
    --wa3;
    --wa2;
    --wa1;
    --qtf;
    --ipvt;
    fjac_dim1 = *ldfjac;
    fjac_offset = fjac_dim1 + 1;
    fjac -= fjac_offset;
    --diag;
    --fvec;
    --x;

    /* Function Body */

/*     epsmch is the machine precision. */

    epsmch = ::dpmpar_(&c__1);

    *info = 0;
    iflag = 0;
    *nfev = 0;

/*     check the input parameters for errors. */

    if (*n <= 0 || *m < *n || *ldfjac < *m || *ftol < zero || *xtol < zero || 
	    *gtol < zero || *maxfev <= 0 || *factor <= zero) {
	goto L300;
    }
    if (*mode != 2) {
	goto L20;
    }
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	if (diag[j] <= zero) {
	    goto L300;
	}
/* L10: */
    }
L20:

/*     evaluate the function at the starting point */
/*     and calculate its norm. */

    iflag = 1;
    (*fcn)(m, n, &x[1], &fvec[1], &iflag);
    *nfev = 1;
    if (iflag < 0) {
	goto L300;
    }
    fnorm = ::enorm_(m, &fvec[1]);

/*     initialize levenberg-marquardt parameter and iteration counter. */

    par = zero;
    iter = 1;

/*     beginning of the outer loop. */

L30:

/*        calculate the jacobian matrix. */

    iflag = 2;
    ::fdjac2_(fcn, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, &iflag, 
	    epsfcn, &wa4[1]);
    *nfev += *n;
    if (iflag < 0) {
	goto L300;
    }

/*        if requested, call fcn to enable printing of iterates. */

    if (*nprint <= 0) {
	goto L40;
    }
    iflag = 0;
    if ((iter - 1) % *nprint == 0) {
	(fcn)(m, n, &x[1], &fvec[1], &iflag);
    }
    if (iflag < 0) {
	goto L300;
    }
L40:

/*        compute the qr factorization of the jacobian. */

    ::qrfac_(m, n, &fjac[fjac_offset], ldfjac, &c__1, &ipvt[1], n, &wa1[1], &
	    wa2[1], &wa3[1]);

/*        on the first iteration and if mode is 1, scale according */
/*        to the norms of the columns of the initial jacobian. */

    if (iter != 1) {
	goto L80;
    }
    if (*mode == 2) {
	goto L60;
    }
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	diag[j] = wa2[j];
	if (wa2[j] == zero) {
	    diag[j] = one;
	}
/* L50: */
    }
L60:

/*        on the first iteration, calculate the norm of the scaled x */
/*        and initialize the step bound delta. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	wa3[j] = diag[j] * x[j];
/* L70: */
    }
    xnorm = ::enorm_(n, &wa3[1]);
    delta = *factor * xnorm;
    if (delta == zero) {
	delta = *factor;
    }
L80:

/*        form (q transpose)*fvec and store the first n components in */
/*        qtf. */

    i__1 = *m;
    for (i = 1; i <= i__1; ++i) {
	wa4[i] = fvec[i];
/* L90: */
    }
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	if (fjac[j + j * fjac_dim1] == zero) {
	    goto L120;
	}
	sum = zero;
	i__2 = *m;
	for (i = j; i <= i__2; ++i) {
	    sum += fjac[i + j * fjac_dim1] * wa4[i];
/* L100: */
	}
	temp = -sum / fjac[j + j * fjac_dim1];
	i__2 = *m;
	for (i = j; i <= i__2; ++i) {
	    wa4[i] += fjac[i + j * fjac_dim1] * temp;
/* L110: */
	}
L120:
	fjac[j + j * fjac_dim1] = wa1[j];
	qtf[j] = wa4[j];
/* L130: */
    }

/*        compute the norm of the scaled gradient. */

    gnorm = zero;
    if (fnorm == zero) {
	goto L170;
    }
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	l = ipvt[j];
	if (wa2[l] == zero) {
	    goto L150;
	}
	sum = zero;
	i__2 = j;
	for (i = 1; i <= i__2; ++i) {
	    sum += fjac[i + j * fjac_dim1] * (qtf[i] / fnorm);
/* L140: */
	}
/* Computing MAX */
	d__2 = gnorm, d__3 = (d__1 = sum / wa2[l], abs(d__1));
	gnorm = xmax(d__2,d__3);
L150:
/* L160: */
	;
    }
L170:

/*        test for convergence of the gradient norm. */

    if (gnorm <= *gtol) {
	*info = 4;
    }
    if (*info != 0) {
	goto L300;
    }

/*        rescale if necessary. */

    if (*mode == 2) {
	goto L190;
    }
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
	d__1 = diag[j], d__2 = wa2[j];
	diag[j] = xmax(d__1,d__2);
/* L180: */
    }
L190:

/*        beginning of the inner loop. */

L200:

/*           determine the levenberg-marquardt parameter. */

    ::lmpar_(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], &delta,
	     &par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]);

/*           store the direction p and x + p. calculate the norm of p. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	wa1[j] = -wa1[j];
	wa2[j] = x[j] + wa1[j];
	wa3[j] = diag[j] * wa1[j];
/* L210: */
    }
    pnorm = ::enorm_(n, &wa3[1]);

/*           on the first iteration, adjust the initial step bound. */

    if (iter == 1) {
	delta = xmin(delta,pnorm);
    }

/*           evaluate the function at x + p and calculate its norm. */

    iflag = 1;
    (*fcn)(m, n, &wa2[1], &wa4[1], &iflag);
    ++(*nfev);
    if (iflag < 0) {
	goto L300;
    }
    fnorm1 = ::enorm_(m, &wa4[1]);

/*           compute the scaled actual reduction. */

    actred = -one;
    if (p1 * fnorm1 < fnorm) {
/* Computing 2nd power */
	d__1 = fnorm1 / fnorm;
	actred = one - d__1 * d__1;
    }

/*           compute the scaled predicted reduction and */
/*           the scaled directional derivative. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	wa3[j] = zero;
	l = ipvt[j];
	temp = wa1[l];
	i__2 = j;
	for (i = 1; i <= i__2; ++i) {
	    wa3[i] += fjac[i + j * fjac_dim1] * temp;
/* L220: */
	}
/* L230: */
    }
    temp1 = ::enorm_(n, &wa3[1]) / fnorm;
    temp2 = ::sqrt(par) * pnorm / fnorm;
/* Computing 2nd power */
    d__1 = temp1;
/* Computing 2nd power */
    d__2 = temp2;
    prered = d__1 * d__1 + d__2 * d__2 / p5;
/* Computing 2nd power */
    d__1 = temp1;
/* Computing 2nd power */
    d__2 = temp2;
    dirder = -(d__1 * d__1 + d__2 * d__2);

/*           compute the ratio of the actual to the predicted */
/*           reduction. */

    ratio = zero;
    if (prered != zero) {
	ratio = actred / prered;
    }

/*           update the step bound. */

    if (ratio > p25) {
	goto L240;
    }
    if (actred >= zero) {
	temp = p5;
    }
    if (actred < zero) {
	temp = p5 * dirder / (dirder + p5 * actred);
    }
    if (p1 * fnorm1 >= fnorm || temp < p1) {
	temp = p1;
    }
/* Computing MIN */
    d__1 = delta, d__2 = pnorm / p1;
    delta = temp * xmin(d__1,d__2);
    par /= temp;
    goto L260;
L240:
    if (par != zero && ratio < p75) {
	goto L250;
    }
    delta = pnorm / p5;
    par = p5 * par;
L250:
L260:

/*           test for successful iteration. */

    if (ratio < p0001) {
	goto L290;
    }

/*           successful iteration. update x, fvec, and their norms. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	x[j] = wa2[j];
	wa2[j] = diag[j] * x[j];
/* L270: */
    }
    i__1 = *m;
    for (i = 1; i <= i__1; ++i) {
	fvec[i] = wa4[i];
/* L280: */
    }
    xnorm = ::enorm_(n, &wa2[1]);
    fnorm = fnorm1;
    ++iter;
L290:

/*           tests for convergence. */

    if (abs(actred) <= *ftol && prered <= *ftol && p5 * ratio <= one) {
	*info = 1;
    }
    if (delta <= *xtol * xnorm) {
	*info = 2;
    }
    if (abs(actred) <= *ftol && prered <= *ftol && p5 * ratio <= one && *info 
	    == 2) {
	*info = 3;
    }
    if (*info != 0) {
	goto L300;
    }

/*           tests for termination and stringent tolerances. */

    if (*nfev >= *maxfev) {
	*info = 5;
    }
    if (abs(actred) <= epsmch && prered <= epsmch && p5 * ratio <= one) {
	*info = 6;
    }
    if (delta <= epsmch * xnorm) {
	*info = 7;
    }
    if (gnorm <= epsmch) {
	*info = 8;
    }
    if (*info != 0) {
	goto L300;
    }

/*           end of the inner loop. repeat if iteration unsuccessful. */

    if (ratio < p0001) {
	goto L200;
    }

/*        end of the outer loop. */

    goto L30;
L300:

/*     termination, either normal or user imposed. */

    if (iflag < 0) {
	*info = iflag;
    }
    iflag = 0;
    if (*nprint > 0) {
	(*fcn)(m, n, &x[1], &fvec[1], &iflag);
    }
    return 0;

/*     last card of subroutine lmdif. */

} /* lmdif_ */