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nothing more than indentation fixes (using vim '=' command)

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This commit is contained in:
Thomas Capricelli 2009-08-20 23:36:03 +02:00
parent b1e0662785
commit 9e71c2827a
5 changed files with 803 additions and 803 deletions
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330
unsupported/Eigen/src/NonLinear/hybrd.h
View File

@ -1,10 +1,10 @@
template<typename Scalar> template<typename Scalar>
int hybrd_template(minpack_func_nn fcn, void *p, int n, Scalar *x, Scalar * int hybrd_template(minpack_func_nn fcn, void *p, int n, Scalar *x, Scalar *
fvec, Scalar xtol, int maxfev, int ml, int mu, fvec, Scalar xtol, int maxfev, int ml, int mu,
Scalar epsfcn, Scalar *diag, int mode, Scalar factor, int nprint, int *nfev, Scalar * Scalar epsfcn, Scalar *diag, int mode, Scalar factor, int nprint, int *nfev, Scalar *
fjac, int ldfjac, Scalar *r__, int lr, Scalar *qtf, fjac, int ldfjac, Scalar *r__, int lr, Scalar *qtf,
Scalar *wa1, Scalar *wa2, Scalar *wa3, Scalar *wa4) Scalar *wa1, Scalar *wa2, Scalar *wa3, Scalar *wa4)
{ {
/* Initialized data */ /* Initialized data */
@ -50,40 +50,40 @@ int hybrd_template(minpack_func_nn fcn, void *p, int n, Scalar *x, Scalar *
iflag = 0; iflag = 0;
*nfev = 0; *nfev = 0;
/* check the input parameters for errors. */ /* check the input parameters for errors. */
if (n <= 0 || xtol < 0. || maxfev <= 0 || ml < 0 || mu < 0 || if (n <= 0 || xtol < 0. || maxfev <= 0 || ml < 0 || mu < 0 ||
factor <= 0. || ldfjac < n || lr < n * (n + 1) / 2) { factor <= 0. || ldfjac < n || lr < n * (n + 1) / 2) {
goto L300; goto L300;
} }
if (mode != 2) { if (mode != 2) {
goto L20; goto L20;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (diag[j] <= 0.) { if (diag[j] <= 0.) {
goto L300; goto L300;
} }
/* L10: */ /* L10: */
} }
L20: L20:
/* evaluate the function at the starting point */ /* evaluate the function at the starting point */
/* and calculate its norm. */ /* and calculate its norm. */
iflag = (*fcn)(p, n, &x[1], &fvec[1], 1); iflag = (*fcn)(p, n, &x[1], &fvec[1], 1);
*nfev = 1; *nfev = 1;
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
fnorm = ei_enorm<Scalar>(n, &fvec[1]); fnorm = ei_enorm<Scalar>(n, &fvec[1]);
/* determine the number of calls to fcn needed to compute */ /* determine the number of calls to fcn needed to compute */
/* the jacobian matrix. */ /* the jacobian matrix. */
/* Computing MIN */ /* Computing MIN */
msum = min(ml + mu + 1, n); msum = min(ml + mu + 1, n);
/* initialize iteration counter and monitors. */ /* initialize iteration counter and monitors. */
iter = 1; iter = 1;
ncsuc = 0; ncsuc = 0;
@ -91,211 +91,211 @@ L20:
nslow1 = 0; nslow1 = 0;
nslow2 = 0; nslow2 = 0;
/* beginning of the outer loop. */ /* beginning of the outer loop. */
L30: L30:
jeval = TRUE_; jeval = TRUE_;
/* calculate the jacobian matrix. */ /* calculate the jacobian matrix. */
iflag = fdjac1(fcn, p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, iflag = fdjac1(fcn, p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac,
ml, mu, epsfcn, &wa1[1], &wa2[1]); ml, mu, epsfcn, &wa1[1], &wa2[1]);
*nfev += msum; *nfev += msum;
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
/* compute the qr factorization of the jacobian. */ /* compute the qr factorization of the jacobian. */
qrfac(n, n, &fjac[fjac_offset], ldfjac, FALSE_, iwa, 1, &wa1[1], & qrfac(n, n, &fjac[fjac_offset], ldfjac, FALSE_, iwa, 1, &wa1[1], &
wa2[1], &wa3[1]); wa2[1], &wa3[1]);
/* on the first iteration and if mode is 1, scale according */ /* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */ /* to the norms of the columns of the initial jacobian. */
if (iter != 1) { if (iter != 1) {
goto L70; goto L70;
} }
if (mode == 2) { if (mode == 2) {
goto L50; goto L50;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
diag[j] = wa2[j]; diag[j] = wa2[j];
if (wa2[j] == 0.) { if (wa2[j] == 0.) {
diag[j] = 1.; diag[j] = 1.;
} }
/* L40: */ /* L40: */
} }
L50: L50:
/* on the first iteration, calculate the norm of the scaled x */ /* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */ /* and initialize the step bound delta. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa3[j] = diag[j] * x[j]; wa3[j] = diag[j] * x[j];
/* L60: */ /* L60: */
} }
xnorm = ei_enorm<Scalar>(n, &wa3[1]); xnorm = ei_enorm<Scalar>(n, &wa3[1]);
delta = factor * xnorm; delta = factor * xnorm;
if (delta == 0.) { if (delta == 0.) {
delta = factor; delta = factor;
} }
L70: L70:
/* form (q transpose)*fvec and store in qtf. */ /* form (q transpose)*fvec and store in qtf. */
for (i__ = 1; i__ <= n; ++i__) { for (i__ = 1; i__ <= n; ++i__) {
qtf[i__] = fvec[i__]; qtf[i__] = fvec[i__];
/* L80: */ /* L80: */
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (fjac[j + j * fjac_dim1] == 0.) { if (fjac[j + j * fjac_dim1] == 0.) {
goto L110; goto L110;
} }
sum = 0.; sum = 0.;
for (i__ = j; i__ <= n; ++i__) { for (i__ = j; i__ <= n; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * qtf[i__]; sum += fjac[i__ + j * fjac_dim1] * qtf[i__];
/* L90: */ /* L90: */
} }
temp = -sum / fjac[j + j * fjac_dim1]; temp = -sum / fjac[j + j * fjac_dim1];
for (i__ = j; i__ <= n; ++i__) { for (i__ = j; i__ <= n; ++i__) {
qtf[i__] += fjac[i__ + j * fjac_dim1] * temp; qtf[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L100: */ /* L100: */
} }
L110: L110:
/* L120: */ /* L120: */
; ;
} }
/* copy the triangular factor of the qr factorization into r. */ /* copy the triangular factor of the qr factorization into r. */
sing = FALSE_; sing = FALSE_;
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
l = j; l = j;
jm1 = j - 1; jm1 = j - 1;
if (jm1 < 1) { if (jm1 < 1) {
goto L140; goto L140;
} }
for (i__ = 1; i__ <= jm1; ++i__) { for (i__ = 1; i__ <= jm1; ++i__) {
r__[l] = fjac[i__ + j * fjac_dim1]; r__[l] = fjac[i__ + j * fjac_dim1];
l = l + n - i__; l = l + n - i__;
/* L130: */ /* L130: */
} }
L140: L140:
r__[l] = wa1[j]; r__[l] = wa1[j];
if (wa1[j] == 0.) { if (wa1[j] == 0.) {
sing = TRUE_; sing = TRUE_;
} }
/* L150: */ /* L150: */
} }
/* accumulate the orthogonal factor in fjac. */ /* accumulate the orthogonal factor in fjac. */
qform(n, n, &fjac[fjac_offset], ldfjac, &wa1[1]); qform(n, n, &fjac[fjac_offset], ldfjac, &wa1[1]);
/* rescale if necessary. */ /* rescale if necessary. */
if (mode == 2) { if (mode == 2) {
goto L170; goto L170;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
/* Computing MAX */ /* Computing MAX */
d__1 = diag[j], d__2 = wa2[j]; d__1 = diag[j], d__2 = wa2[j];
diag[j] = max(d__1,d__2); diag[j] = max(d__1,d__2);
/* L160: */ /* L160: */
} }
L170: L170:
/* beginning of the inner loop. */ /* beginning of the inner loop. */
L180: L180:
/* if requested, call fcn to enable printing of iterates. */ /* if requested, call fcn to enable printing of iterates. */
if (nprint <= 0) { if (nprint <= 0) {
goto L190; goto L190;
} }
iflag = 0; iflag = 0;
if ((iter - 1) % nprint == 0) { if ((iter - 1) % nprint == 0) {
iflag = (*fcn)(p, n, &x[1], &fvec[1], 0); iflag = (*fcn)(p, n, &x[1], &fvec[1], 0);
} }
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
L190: L190:
/* determine the direction p. */ /* determine the direction p. */
dogleg(n, &r__[1], lr, &diag[1], &qtf[1], delta, &wa1[1], &wa2[1], &wa3[ dogleg(n, &r__[1], lr, &diag[1], &qtf[1], delta, &wa1[1], &wa2[1], &wa3[
1]); 1]);
/* store the direction p and x + p. calculate the norm of p. */ /* store the direction p and x + p. calculate the norm of p. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa1[j] = -wa1[j]; wa1[j] = -wa1[j];
wa2[j] = x[j] + wa1[j]; wa2[j] = x[j] + wa1[j];
wa3[j] = diag[j] * wa1[j]; wa3[j] = diag[j] * wa1[j];
/* L200: */ /* L200: */
} }
pnorm = ei_enorm<Scalar>(n, &wa3[1]); pnorm = ei_enorm<Scalar>(n, &wa3[1]);
/* on the first iteration, adjust the initial step bound. */ /* on the first iteration, adjust the initial step bound. */
if (iter == 1) { if (iter == 1) {
delta = min(delta,pnorm); delta = min(delta,pnorm);
} }
/* evaluate the function at x + p and calculate its norm. */ /* evaluate the function at x + p and calculate its norm. */
iflag = (*fcn)(p, n, &wa2[1], &wa4[1], 1); iflag = (*fcn)(p, n, &wa2[1], &wa4[1], 1);
++(*nfev); ++(*nfev);
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
fnorm1 = ei_enorm<Scalar>(n, &wa4[1]); fnorm1 = ei_enorm<Scalar>(n, &wa4[1]);
/* compute the scaled actual reduction. */ /* compute the scaled actual reduction. */
actred = -1.; actred = -1.;
if (fnorm1 < fnorm) { if (fnorm1 < fnorm) {
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = fnorm1 / fnorm; d__1 = fnorm1 / fnorm;
actred = 1. - d__1 * d__1; actred = 1. - d__1 * d__1;
} }
/* compute the scaled predicted reduction. */ /* compute the scaled predicted reduction. */
l = 1; l = 1;
for (i__ = 1; i__ <= n; ++i__) { for (i__ = 1; i__ <= n; ++i__) {
sum = 0.; sum = 0.;
for (j = i__; j <= n; ++j) { for (j = i__; j <= n; ++j) {
sum += r__[l] * wa1[j]; sum += r__[l] * wa1[j];
++l; ++l;
/* L210: */ /* L210: */
} }
wa3[i__] = qtf[i__] + sum; wa3[i__] = qtf[i__] + sum;
/* L220: */ /* L220: */
} }
temp = ei_enorm<Scalar>(n, &wa3[1]); temp = ei_enorm<Scalar>(n, &wa3[1]);
prered = 0.; prered = 0.;
if (temp < fnorm) { if (temp < fnorm) {
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = temp / fnorm; d__1 = temp / fnorm;
prered = 1. - d__1 * d__1; prered = 1. - d__1 * d__1;
} }
/* compute the ratio of the actual to the predicted */ /* compute the ratio of the actual to the predicted */
/* reduction. */ /* reduction. */
ratio = 0.; ratio = 0.;
if (prered > 0.) { if (prered > 0.) {
ratio = actred / prered; ratio = actred / prered;
} }
/* update the step bound. */ /* update the step bound. */
if (ratio >= p1) { if (ratio >= p1) {
goto L230; goto L230;
} }
ncsuc = 0; ncsuc = 0;
++ncfail; ++ncfail;
@ -305,128 +305,128 @@ L230:
ncfail = 0; ncfail = 0;
++ncsuc; ++ncsuc;
if (ratio >= p5 || ncsuc > 1) { if (ratio >= p5 || ncsuc > 1) {
/* Computing MAX */ /* Computing MAX */
d__1 = delta, d__2 = pnorm / p5; d__1 = delta, d__2 = pnorm / p5;
delta = max(d__1,d__2); delta = max(d__1,d__2);
} }
if (fabs(ratio - 1.) <= p1) { if (fabs(ratio - 1.) <= p1) {
delta = pnorm / p5; delta = pnorm / p5;
} }
L240: L240:
/* test for successful iteration. */ /* test for successful iteration. */
if (ratio < p0001) { if (ratio < p0001) {
goto L260; goto L260;
} }
/* successful iteration. update x, fvec, and their norms. */ /* successful iteration. update x, fvec, and their norms. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
x[j] = wa2[j]; x[j] = wa2[j];
wa2[j] = diag[j] * x[j]; wa2[j] = diag[j] * x[j];
fvec[j] = wa4[j]; fvec[j] = wa4[j];
/* L250: */ /* L250: */
} }
xnorm = ei_enorm<Scalar>(n, &wa2[1]); xnorm = ei_enorm<Scalar>(n, &wa2[1]);
fnorm = fnorm1; fnorm = fnorm1;
++iter; ++iter;
L260: L260:
/* determine the progress of the iteration. */ /* determine the progress of the iteration. */
++nslow1; ++nslow1;
if (actred >= p001) { if (actred >= p001) {
nslow1 = 0; nslow1 = 0;
} }
if (jeval) { if (jeval) {
++nslow2; ++nslow2;
} }
if (actred >= p1) { if (actred >= p1) {
nslow2 = 0; nslow2 = 0;
} }
/* test for convergence. */ /* test for convergence. */
if (delta <= xtol * xnorm || fnorm == 0.) { if (delta <= xtol * xnorm || fnorm == 0.) {
info = 1; info = 1;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* tests for termination and stringent tolerances. */ /* tests for termination and stringent tolerances. */
if (*nfev >= maxfev) { if (*nfev >= maxfev) {
info = 2; info = 2;
} }
/* Computing MAX */ /* Computing MAX */
d__1 = p1 * delta; d__1 = p1 * delta;
if (p1 * max(d__1,pnorm) <= epsilon<Scalar>() * xnorm) { if (p1 * max(d__1,pnorm) <= epsilon<Scalar>() * xnorm) {
info = 3; info = 3;
} }
if (nslow2 == 5) { if (nslow2 == 5) {
info = 4; info = 4;
} }
if (nslow1 == 10) { if (nslow1 == 10) {
info = 5; info = 5;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* criterion for recalculating jacobian approximation */ /* criterion for recalculating jacobian approximation */
/* by forward differences. */ /* by forward differences. */
if (ncfail == 2) { if (ncfail == 2) {
goto L290; goto L290;
} }
/* calculate the rank one modification to the jacobian */ /* calculate the rank one modification to the jacobian */
/* and update qtf if necessary. */ /* and update qtf if necessary. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
sum = 0.; sum = 0.;
for (i__ = 1; i__ <= n; ++i__) { for (i__ = 1; i__ <= n; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * wa4[i__]; sum += fjac[i__ + j * fjac_dim1] * wa4[i__];
/* L270: */ /* L270: */
} }
wa2[j] = (sum - wa3[j]) / pnorm; wa2[j] = (sum - wa3[j]) / pnorm;
wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm); wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm);
if (ratio >= p0001) { if (ratio >= p0001) {
qtf[j] = sum; qtf[j] = sum;
} }
/* L280: */ /* L280: */
} }
/* compute the qr factorization of the updated jacobian. */ /* compute the qr factorization of the updated jacobian. */
r1updt(n, n, &r__[1], lr, &wa1[1], &wa2[1], &wa3[1], &sing); r1updt(n, n, &r__[1], lr, &wa1[1], &wa2[1], &wa3[1], &sing);
r1mpyq(n, n, &fjac[fjac_offset], ldfjac, &wa2[1], &wa3[1]); r1mpyq(n, n, &fjac[fjac_offset], ldfjac, &wa2[1], &wa3[1]);
r1mpyq(1, n, &qtf[1], 1, &wa2[1], &wa3[1]); r1mpyq(1, n, &qtf[1], 1, &wa2[1], &wa3[1]);
/* end of the inner loop. */ /* end of the inner loop. */
jeval = FALSE_; jeval = FALSE_;
goto L180; goto L180;
L290: L290:
/* end of the outer loop. */ /* end of the outer loop. */
goto L30; goto L30;
L300: L300:
/* termination, either normal or user imposed. */ /* termination, either normal or user imposed. */
if (iflag < 0) { if (iflag < 0) {
info = iflag; info = iflag;
} }
if (nprint > 0) { if (nprint > 0) {
(*fcn)(p, n, &x[1], &fvec[1], 0); (*fcn)(p, n, &x[1], &fvec[1], 0);
} }
return info; return info;
/* last card of subroutine hybrd. */ /* last card of subroutine hybrd. */
} /* hybrd_ */ } /* hybrd_ */

322
unsupported/Eigen/src/NonLinear/hybrj.h
View File

@ -1,11 +1,11 @@
template<typename Scalar> template<typename Scalar>
int hybrj_template(minpack_funcder_nn fcn, void *p, int n, Scalar *x, Scalar * int hybrj_template(minpack_funcder_nn fcn, void *p, int n, Scalar *x, Scalar *
fvec, Scalar *fjac, int ldfjac, Scalar xtol, int fvec, Scalar *fjac, int ldfjac, Scalar xtol, int
maxfev, Scalar *diag, int mode, Scalar factor, int maxfev, Scalar *diag, int mode, Scalar factor, int
nprint, int *nfev, int *njev, Scalar *r__, nprint, int *nfev, int *njev, Scalar *r__,
int lr, Scalar *qtf, Scalar *wa1, Scalar *wa2, int lr, Scalar *qtf, Scalar *wa1, Scalar *wa2,
Scalar *wa3, Scalar *wa4) Scalar *wa3, Scalar *wa4)
{ {
/* Initialized data */ /* Initialized data */
@ -52,34 +52,34 @@ int hybrj_template(minpack_funcder_nn fcn, void *p, int n, Scalar *x, Scalar *
*nfev = 0; *nfev = 0;
*njev = 0; *njev = 0;
/* check the input parameters for errors. */ /* check the input parameters for errors. */
if (n <= 0 || ldfjac < n || xtol < 0. || maxfev <= 0 || factor <= if (n <= 0 || ldfjac < n || xtol < 0. || maxfev <= 0 || factor <=
0. || lr < n * (n + 1) / 2) { 0. || lr < n * (n + 1) / 2) {
goto L300; goto L300;
} }
if (mode != 2) { if (mode != 2) {
goto L20; goto L20;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (diag[j] <= 0.) { if (diag[j] <= 0.) {
goto L300; goto L300;
} }
/* L10: */ /* L10: */
} }
L20: L20:
/* evaluate the function at the starting point */ /* evaluate the function at the starting point */
/* and calculate its norm. */ /* and calculate its norm. */
iflag = (*fcn)(p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 1); iflag = (*fcn)(p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 1);
*nfev = 1; *nfev = 1;
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
fnorm = ei_enorm<Scalar>(n, &fvec[1]); fnorm = ei_enorm<Scalar>(n, &fvec[1]);
/* initialize iteration counter and monitors. */ /* initialize iteration counter and monitors. */
iter = 1; iter = 1;
ncsuc = 0; ncsuc = 0;
@ -87,210 +87,210 @@ L20:
nslow1 = 0; nslow1 = 0;
nslow2 = 0; nslow2 = 0;
/* beginning of the outer loop. */ /* beginning of the outer loop. */
L30: L30:
jeval = TRUE_; jeval = TRUE_;
/* calculate the jacobian matrix. */ /* calculate the jacobian matrix. */
iflag = (*fcn)(p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 2); iflag = (*fcn)(p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 2);
++(*njev); ++(*njev);
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
/* compute the qr factorization of the jacobian. */ /* compute the qr factorization of the jacobian. */
qrfac(n, n, &fjac[fjac_offset], ldfjac, FALSE_, iwa, 1, &wa1[1], & qrfac(n, n, &fjac[fjac_offset], ldfjac, FALSE_, iwa, 1, &wa1[1], &
wa2[1], &wa3[1]); wa2[1], &wa3[1]);
/* on the first iteration and if mode is 1, scale according */ /* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */ /* to the norms of the columns of the initial jacobian. */
if (iter != 1) { if (iter != 1) {
goto L70; goto L70;
} }
if (mode == 2) { if (mode == 2) {
goto L50; goto L50;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
diag[j] = wa2[j]; diag[j] = wa2[j];
if (wa2[j] == 0.) { if (wa2[j] == 0.) {
diag[j] = 1.; diag[j] = 1.;
} }
/* L40: */ /* L40: */
} }
L50: L50:
/* on the first iteration, calculate the norm of the scaled x */ /* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */ /* and initialize the step bound delta. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa3[j] = diag[j] * x[j]; wa3[j] = diag[j] * x[j];
/* L60: */ /* L60: */
} }
xnorm = ei_enorm<Scalar>(n, &wa3[1]); xnorm = ei_enorm<Scalar>(n, &wa3[1]);
delta = factor * xnorm; delta = factor * xnorm;
if (delta == 0.) { if (delta == 0.) {
delta = factor; delta = factor;
} }
L70: L70:
/* form (q transpose)*fvec and store in qtf. */ /* form (q transpose)*fvec and store in qtf. */
for (i__ = 1; i__ <= n; ++i__) { for (i__ = 1; i__ <= n; ++i__) {
qtf[i__] = fvec[i__]; qtf[i__] = fvec[i__];
/* L80: */ /* L80: */
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (fjac[j + j * fjac_dim1] == 0.) { if (fjac[j + j * fjac_dim1] == 0.) {
goto L110; goto L110;
} }
sum = 0.; sum = 0.;
for (i__ = j; i__ <= n; ++i__) { for (i__ = j; i__ <= n; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * qtf[i__]; sum += fjac[i__ + j * fjac_dim1] * qtf[i__];
/* L90: */ /* L90: */
} }
temp = -sum / fjac[j + j * fjac_dim1]; temp = -sum / fjac[j + j * fjac_dim1];
for (i__ = j; i__ <= n; ++i__) { for (i__ = j; i__ <= n; ++i__) {
qtf[i__] += fjac[i__ + j * fjac_dim1] * temp; qtf[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L100: */ /* L100: */
} }
L110: L110:
/* L120: */ /* L120: */
; ;
} }
/* copy the triangular factor of the qr factorization into r. */ /* copy the triangular factor of the qr factorization into r. */
sing = FALSE_; sing = FALSE_;
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
l = j; l = j;
jm1 = j - 1; jm1 = j - 1;
if (jm1 < 1) { if (jm1 < 1) {
goto L140; goto L140;
} }
for (i__ = 1; i__ <= jm1; ++i__) { for (i__ = 1; i__ <= jm1; ++i__) {
r__[l] = fjac[i__ + j * fjac_dim1]; r__[l] = fjac[i__ + j * fjac_dim1];
l = l + n - i__; l = l + n - i__;
/* L130: */ /* L130: */
} }
L140: L140:
r__[l] = wa1[j]; r__[l] = wa1[j];
if (wa1[j] == 0.) { if (wa1[j] == 0.) {
sing = TRUE_; sing = TRUE_;
} }
/* L150: */ /* L150: */
} }
/* accumulate the orthogonal factor in fjac. */ /* accumulate the orthogonal factor in fjac. */
qform(n, n, &fjac[fjac_offset], ldfjac, &wa1[1]); qform(n, n, &fjac[fjac_offset], ldfjac, &wa1[1]);
/* rescale if necessary. */ /* rescale if necessary. */
if (mode == 2) { if (mode == 2) {
goto L170; goto L170;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
/* Computing MAX */ /* Computing MAX */
d__1 = diag[j], d__2 = wa2[j]; d__1 = diag[j], d__2 = wa2[j];
diag[j] = max(d__1,d__2); diag[j] = max(d__1,d__2);
/* L160: */ /* L160: */
} }
L170: L170:
/* beginning of the inner loop. */ /* beginning of the inner loop. */
L180: L180:
/* if requested, call fcn to enable printing of iterates. */ /* if requested, call fcn to enable printing of iterates. */
if (nprint <= 0) { if (nprint <= 0) {
goto L190; goto L190;
} }
iflag = 0; iflag = 0;
if ((iter - 1) % nprint == 0) { if ((iter - 1) % nprint == 0) {
iflag = (*fcn)(p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 0); iflag = (*fcn)(p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 0);
} }
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
L190: L190:
/* determine the direction p. */ /* determine the direction p. */
dogleg(n, &r__[1], lr, &diag[1], &qtf[1], delta, &wa1[1], &wa2[1], &wa3[ dogleg(n, &r__[1], lr, &diag[1], &qtf[1], delta, &wa1[1], &wa2[1], &wa3[
1]); 1]);
/* store the direction p and x + p. calculate the norm of p. */ /* store the direction p and x + p. calculate the norm of p. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa1[j] = -wa1[j]; wa1[j] = -wa1[j];
wa2[j] = x[j] + wa1[j]; wa2[j] = x[j] + wa1[j];
wa3[j] = diag[j] * wa1[j]; wa3[j] = diag[j] * wa1[j];
/* L200: */ /* L200: */
} }
pnorm = ei_enorm<Scalar>(n, &wa3[1]); pnorm = ei_enorm<Scalar>(n, &wa3[1]);
/* on the first iteration, adjust the initial step bound. */ /* on the first iteration, adjust the initial step bound. */
if (iter == 1) { if (iter == 1) {
delta = min(delta,pnorm); delta = min(delta,pnorm);
} }
/* evaluate the function at x + p and calculate its norm. */ /* evaluate the function at x + p and calculate its norm. */
iflag = (*fcn)(p, n, &wa2[1], &wa4[1], &fjac[fjac_offset], ldfjac, 1); iflag = (*fcn)(p, n, &wa2[1], &wa4[1], &fjac[fjac_offset], ldfjac, 1);
++(*nfev); ++(*nfev);
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
fnorm1 = ei_enorm<Scalar>(n, &wa4[1]); fnorm1 = ei_enorm<Scalar>(n, &wa4[1]);
/* compute the scaled actual reduction. */ /* compute the scaled actual reduction. */
actred = -1.; actred = -1.;
if (fnorm1 < fnorm) { if (fnorm1 < fnorm) {
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = fnorm1 / fnorm; d__1 = fnorm1 / fnorm;
actred = 1. - d__1 * d__1; actred = 1. - d__1 * d__1;
} }
/* compute the scaled predicted reduction. */ /* compute the scaled predicted reduction. */
l = 1; l = 1;
for (i__ = 1; i__ <= n; ++i__) { for (i__ = 1; i__ <= n; ++i__) {
sum = 0.; sum = 0.;
for (j = i__; j <= n; ++j) { for (j = i__; j <= n; ++j) {
sum += r__[l] * wa1[j]; sum += r__[l] * wa1[j];
++l; ++l;
/* L210: */ /* L210: */
} }
wa3[i__] = qtf[i__] + sum; wa3[i__] = qtf[i__] + sum;
/* L220: */ /* L220: */
} }
temp = ei_enorm<Scalar>(n, &wa3[1]); temp = ei_enorm<Scalar>(n, &wa3[1]);
prered = 0.; prered = 0.;
if (temp < fnorm) { if (temp < fnorm) {
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = temp / fnorm; d__1 = temp / fnorm;
prered = 1. - d__1 * d__1; prered = 1. - d__1 * d__1;
} }
/* compute the ratio of the actual to the predicted */ /* compute the ratio of the actual to the predicted */
/* reduction. */ /* reduction. */
ratio = 0.; ratio = 0.;
if (prered > 0.) { if (prered > 0.) {
ratio = actred / prered; ratio = actred / prered;
} }
/* update the step bound. */ /* update the step bound. */
if (ratio >= p1) { if (ratio >= p1) {
goto L230; goto L230;
} }
ncsuc = 0; ncsuc = 0;
++ncfail; ++ncfail;
@ -300,127 +300,127 @@ L230:
ncfail = 0; ncfail = 0;
++ncsuc; ++ncsuc;
if (ratio >= p5 || ncsuc > 1) { if (ratio >= p5 || ncsuc > 1) {
/* Computing MAX */ /* Computing MAX */
d__1 = delta, d__2 = pnorm / p5; d__1 = delta, d__2 = pnorm / p5;
delta = max(d__1,d__2); delta = max(d__1,d__2);
} }
if (fabs(ratio - 1.) <= p1) { if (fabs(ratio - 1.) <= p1) {
delta = pnorm / p5; delta = pnorm / p5;
} }
L240: L240:
/* test for successful iteration. */ /* test for successful iteration. */
if (ratio < p0001) { if (ratio < p0001) {
goto L260; goto L260;
} }
/* successful iteration. update x, fvec, and their norms. */ /* successful iteration. update x, fvec, and their norms. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
x[j] = wa2[j]; x[j] = wa2[j];
wa2[j] = diag[j] * x[j]; wa2[j] = diag[j] * x[j];
fvec[j] = wa4[j]; fvec[j] = wa4[j];
/* L250: */ /* L250: */
} }
xnorm = ei_enorm<Scalar>(n, &wa2[1]); xnorm = ei_enorm<Scalar>(n, &wa2[1]);
fnorm = fnorm1; fnorm = fnorm1;
++iter; ++iter;
L260: L260:
/* determine the progress of the iteration. */ /* determine the progress of the iteration. */
++nslow1; ++nslow1;
if (actred >= p001) { if (actred >= p001) {
nslow1 = 0; nslow1 = 0;
} }
if (jeval) { if (jeval) {
++nslow2; ++nslow2;
} }
if (actred >= p1) { if (actred >= p1) {
nslow2 = 0; nslow2 = 0;
} }
/* test for convergence. */ /* test for convergence. */
if (delta <= xtol * xnorm || fnorm == 0.) { if (delta <= xtol * xnorm || fnorm == 0.) {
info = 1; info = 1;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* tests for termination and stringent tolerances. */ /* tests for termination and stringent tolerances. */
if (*nfev >= maxfev) { if (*nfev >= maxfev) {
info = 2; info = 2;
} }
/* Computing MAX */ /* Computing MAX */
d__1 = p1 * delta; d__1 = p1 * delta;
if (p1 * max(d__1,pnorm) <= epsilon<Scalar>() * xnorm) { if (p1 * max(d__1,pnorm) <= epsilon<Scalar>() * xnorm) {
info = 3; info = 3;
} }
if (nslow2 == 5) { if (nslow2 == 5) {
info = 4; info = 4;
} }
if (nslow1 == 10) { if (nslow1 == 10) {
info = 5; info = 5;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* criterion for recalculating jacobian. */ /* criterion for recalculating jacobian. */
if (ncfail == 2) { if (ncfail == 2) {
goto L290; goto L290;
} }
/* calculate the rank one modification to the jacobian */ /* calculate the rank one modification to the jacobian */
/* and update qtf if necessary. */ /* and update qtf if necessary. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
sum = 0.; sum = 0.;
for (i__ = 1; i__ <= n; ++i__) { for (i__ = 1; i__ <= n; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * wa4[i__]; sum += fjac[i__ + j * fjac_dim1] * wa4[i__];
/* L270: */ /* L270: */
} }
wa2[j] = (sum - wa3[j]) / pnorm; wa2[j] = (sum - wa3[j]) / pnorm;
wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm); wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm);
if (ratio >= p0001) { if (ratio >= p0001) {
qtf[j] = sum; qtf[j] = sum;
} }
/* L280: */ /* L280: */
} }
/* compute the qr factorization of the updated jacobian. */ /* compute the qr factorization of the updated jacobian. */
r1updt(n, n, &r__[1], lr, &wa1[1], &wa2[1], &wa3[1], &sing); r1updt(n, n, &r__[1], lr, &wa1[1], &wa2[1], &wa3[1], &sing);
r1mpyq(n, n, &fjac[fjac_offset], ldfjac, &wa2[1], &wa3[1]); r1mpyq(n, n, &fjac[fjac_offset], ldfjac, &wa2[1], &wa3[1]);
r1mpyq(1, n, &qtf[1], 1, &wa2[1], &wa3[1]); r1mpyq(1, n, &qtf[1], 1, &wa2[1], &wa3[1]);
/* end of the inner loop. */ /* end of the inner loop. */
jeval = FALSE_; jeval = FALSE_;
goto L180; goto L180;
L290: L290:
/* end of the outer loop. */ /* end of the outer loop. */
goto L30; goto L30;
L300: L300:
/* termination, either normal or user imposed. */ /* termination, either normal or user imposed. */
if (iflag < 0) { if (iflag < 0) {
info = iflag; info = iflag;
} }
if (nprint > 0) { if (nprint > 0) {
iflag = (*fcn)(p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 0); iflag = (*fcn)(p, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 0);
} }
return info; return info;
/* last card of subroutine hybrj. */ /* last card of subroutine hybrj. */
} /* hybrj_ */ } /* hybrj_ */

304
unsupported/Eigen/src/NonLinear/lmder.h
View File

@ -1,11 +1,11 @@
template<typename Scalar> template<typename Scalar>
int lmder_template(minpack_funcder_mn fcn, void *p, int m, int n, Scalar *x, int lmder_template(minpack_funcder_mn fcn, void *p, int m, int n, Scalar *x,
Scalar *fvec, Scalar *fjac, int ldfjac, Scalar ftol, Scalar *fvec, Scalar *fjac, int ldfjac, Scalar ftol,
Scalar xtol, Scalar gtol, int maxfev, Scalar * Scalar xtol, Scalar gtol, int maxfev, Scalar *
diag, int mode, Scalar factor, int nprint, diag, int mode, Scalar factor, int nprint,
int *nfev, int *njev, int *ipvt, Scalar *qtf, int *nfev, int *njev, int *ipvt, Scalar *qtf,
Scalar *wa1, Scalar *wa2, Scalar *wa3, Scalar *wa4) Scalar *wa1, Scalar *wa2, Scalar *wa3, Scalar *wa4)
{ {
/* Initialized data */ /* Initialized data */
@ -45,359 +45,359 @@ int lmder_template(minpack_funcder_mn fcn, void *p, int m, int n, Scalar *x,
*nfev = 0; *nfev = 0;
*njev = 0; *njev = 0;
/* check the input parameters for errors. */ /* check the input parameters for errors. */
if (n <= 0 || m < n || ldfjac < m || ftol < 0. || xtol < 0. || if (n <= 0 || m < n || ldfjac < m || ftol < 0. || xtol < 0. ||
gtol < 0. || maxfev <= 0 || factor <= 0.) { gtol < 0. || maxfev <= 0 || factor <= 0.) {
goto L300; goto L300;
} }
if (mode != 2) { if (mode != 2) {
goto L20; goto L20;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (diag[j] <= 0.) { if (diag[j] <= 0.) {
goto L300; goto L300;
} }
/* L10: */ /* L10: */
} }
L20: L20:
/* evaluate the function at the starting point */ /* evaluate the function at the starting point */
/* and calculate its norm. */ /* and calculate its norm. */
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 1); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 1);
*nfev = 1; *nfev = 1;
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
fnorm = ei_enorm<Scalar>(m, &fvec[1]); fnorm = ei_enorm<Scalar>(m, &fvec[1]);
/* initialize levenberg-marquardt parameter and iteration counter. */ /* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.; par = 0.;
iter = 1; iter = 1;
/* beginning of the outer loop. */ /* beginning of the outer loop. */
L30: L30:
/* calculate the jacobian matrix. */ /* calculate the jacobian matrix. */
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 2); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 2);
++(*njev); ++(*njev);
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
/* if requested, call fcn to enable printing of iterates. */ /* if requested, call fcn to enable printing of iterates. */
if (nprint <= 0) { if (nprint <= 0) {
goto L40; goto L40;
} }
iflag = 0; iflag = 0;
if ((iter - 1) % nprint == 0) { if ((iter - 1) % nprint == 0) {
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 0); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 0);
} }
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
L40: L40:
/* compute the qr factorization of the jacobian. */ /* compute the qr factorization of the jacobian. */
qrfac(m, n, &fjac[fjac_offset], ldfjac, TRUE_, &ipvt[1], n, &wa1[1], & qrfac(m, n, &fjac[fjac_offset], ldfjac, TRUE_, &ipvt[1], n, &wa1[1], &
wa2[1], &wa3[1]); wa2[1], &wa3[1]);
/* on the first iteration and if mode is 1, scale according */ /* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */ /* to the norms of the columns of the initial jacobian. */
if (iter != 1) { if (iter != 1) {
goto L80; goto L80;
} }
if (mode == 2) { if (mode == 2) {
goto L60; goto L60;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
diag[j] = wa2[j]; diag[j] = wa2[j];
if (wa2[j] == 0.) { if (wa2[j] == 0.) {
diag[j] = 1.; diag[j] = 1.;
} }
/* L50: */ /* L50: */
} }
L60: L60:
/* on the first iteration, calculate the norm of the scaled x */ /* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */ /* and initialize the step bound delta. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa3[j] = diag[j] * x[j]; wa3[j] = diag[j] * x[j];
/* L70: */ /* L70: */
} }
xnorm = ei_enorm<Scalar>(n, &wa3[1]); xnorm = ei_enorm<Scalar>(n, &wa3[1]);
delta = factor * xnorm; delta = factor * xnorm;
if (delta == 0.) { if (delta == 0.) {
delta = factor; delta = factor;
} }
L80: L80:
/* form (q transpose)*fvec and store the first n components in */ /* form (q transpose)*fvec and store the first n components in */
/* qtf. */ /* qtf. */
for (i__ = 1; i__ <= m; ++i__) { for (i__ = 1; i__ <= m; ++i__) {
wa4[i__] = fvec[i__]; wa4[i__] = fvec[i__];
/* L90: */ /* L90: */
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (fjac[j + j * fjac_dim1] == 0.) { if (fjac[j + j * fjac_dim1] == 0.) {
goto L120; goto L120;
} }
sum = 0.; sum = 0.;
for (i__ = j; i__ <= m; ++i__) { for (i__ = j; i__ <= m; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * wa4[i__]; sum += fjac[i__ + j * fjac_dim1] * wa4[i__];
/* L100: */ /* L100: */
} }
temp = -sum / fjac[j + j * fjac_dim1]; temp = -sum / fjac[j + j * fjac_dim1];
for (i__ = j; i__ <= m; ++i__) { for (i__ = j; i__ <= m; ++i__) {
wa4[i__] += fjac[i__ + j * fjac_dim1] * temp; wa4[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L110: */ /* L110: */
} }
L120: L120:
fjac[j + j * fjac_dim1] = wa1[j]; fjac[j + j * fjac_dim1] = wa1[j];
qtf[j] = wa4[j]; qtf[j] = wa4[j];
/* L130: */ /* L130: */
} }
/* compute the norm of the scaled gradient. */ /* compute the norm of the scaled gradient. */
gnorm = 0.; gnorm = 0.;
if (fnorm == 0.) { if (fnorm == 0.) {
goto L170; goto L170;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
l = ipvt[j]; l = ipvt[j];
if (wa2[l] == 0.) { if (wa2[l] == 0.) {
goto L150; goto L150;
} }
sum = 0.; sum = 0.;
for (i__ = 1; i__ <= j; ++i__) { for (i__ = 1; i__ <= j; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * (qtf[i__] / fnorm); sum += fjac[i__ + j * fjac_dim1] * (qtf[i__] / fnorm);
/* L140: */ /* L140: */
} }
/* Computing MAX */ /* Computing MAX */
d__2 = gnorm, d__3 = fabs(sum / wa2[l]); d__2 = gnorm, d__3 = fabs(sum / wa2[l]);
gnorm = max(d__2,d__3); gnorm = max(d__2,d__3);
L150: L150:
/* L160: */ /* L160: */
; ;
} }
L170: L170:
/* test for convergence of the gradient norm. */ /* test for convergence of the gradient norm. */
if (gnorm <= gtol) { if (gnorm <= gtol) {
info = 4; info = 4;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* rescale if necessary. */ /* rescale if necessary. */
if (mode == 2) { if (mode == 2) {
goto L190; goto L190;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
/* Computing MAX */ /* Computing MAX */
d__1 = diag[j], d__2 = wa2[j]; d__1 = diag[j], d__2 = wa2[j];
diag[j] = max(d__1,d__2); diag[j] = max(d__1,d__2);
/* L180: */ /* L180: */
} }
L190: L190:
/* beginning of the inner loop. */ /* beginning of the inner loop. */
L200: L200:
/* determine the levenberg-marquardt parameter. */ /* determine the levenberg-marquardt parameter. */
lmpar(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], delta, lmpar(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], delta,
&par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]); &par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]);
/* store the direction p and x + p. calculate the norm of p. */ /* store the direction p and x + p. calculate the norm of p. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa1[j] = -wa1[j]; wa1[j] = -wa1[j];
wa2[j] = x[j] + wa1[j]; wa2[j] = x[j] + wa1[j];
wa3[j] = diag[j] * wa1[j]; wa3[j] = diag[j] * wa1[j];
/* L210: */ /* L210: */
} }
pnorm = ei_enorm<Scalar>(n, &wa3[1]); pnorm = ei_enorm<Scalar>(n, &wa3[1]);
/* on the first iteration, adjust the initial step bound. */ /* on the first iteration, adjust the initial step bound. */
if (iter == 1) { if (iter == 1) {
delta = min(delta,pnorm); delta = min(delta,pnorm);
} }
/* evaluate the function at x + p and calculate its norm. */ /* evaluate the function at x + p and calculate its norm. */
iflag = (*fcn)(p, m, n, &wa2[1], &wa4[1], &fjac[fjac_offset], ldfjac, 1); iflag = (*fcn)(p, m, n, &wa2[1], &wa4[1], &fjac[fjac_offset], ldfjac, 1);
++(*nfev); ++(*nfev);
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
fnorm1 = ei_enorm<Scalar>(m, &wa4[1]); fnorm1 = ei_enorm<Scalar>(m, &wa4[1]);
/* compute the scaled actual reduction. */ /* compute the scaled actual reduction. */
actred = -1.; actred = -1.;
if (p1 * fnorm1 < fnorm) { if (p1 * fnorm1 < fnorm) {
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = fnorm1 / fnorm; d__1 = fnorm1 / fnorm;
actred = 1. - d__1 * d__1; actred = 1. - d__1 * d__1;
} }
/* compute the scaled predicted reduction and */ /* compute the scaled predicted reduction and */
/* the scaled directional derivative. */ /* the scaled directional derivative. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa3[j] = 0.; wa3[j] = 0.;
l = ipvt[j]; l = ipvt[j];
temp = wa1[l]; temp = wa1[l];
for (i__ = 1; i__ <= j; ++i__) { for (i__ = 1; i__ <= j; ++i__) {
wa3[i__] += fjac[i__ + j * fjac_dim1] * temp; wa3[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L220: */ /* L220: */
} }
/* L230: */ /* L230: */
} }
temp1 = ei_enorm<Scalar>(n, &wa3[1]) / fnorm; temp1 = ei_enorm<Scalar>(n, &wa3[1]) / fnorm;
temp2 = sqrt(par) * pnorm / fnorm; temp2 = sqrt(par) * pnorm / fnorm;
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = temp1; d__1 = temp1;
/* Computing 2nd power */ /* Computing 2nd power */
d__2 = temp2; d__2 = temp2;
prered = d__1 * d__1 + d__2 * d__2 / p5; prered = d__1 * d__1 + d__2 * d__2 / p5;
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = temp1; d__1 = temp1;
/* Computing 2nd power */ /* Computing 2nd power */
d__2 = temp2; d__2 = temp2;
dirder = -(d__1 * d__1 + d__2 * d__2); dirder = -(d__1 * d__1 + d__2 * d__2);
/* compute the ratio of the actual to the predicted */ /* compute the ratio of the actual to the predicted */
/* reduction. */ /* reduction. */
ratio = 0.; ratio = 0.;
if (prered != 0.) { if (prered != 0.) {
ratio = actred / prered; ratio = actred / prered;
} }
/* update the step bound. */ /* update the step bound. */
if (ratio > p25) { if (ratio > p25) {
goto L240; goto L240;
} }
if (actred >= 0.) { if (actred >= 0.) {
temp = p5; temp = p5;
} }
if (actred < 0.) { if (actred < 0.) {
temp = p5 * dirder / (dirder + p5 * actred); temp = p5 * dirder / (dirder + p5 * actred);
} }
if (p1 * fnorm1 >= fnorm || temp < p1) { if (p1 * fnorm1 >= fnorm || temp < p1) {
temp = p1; temp = p1;
} }
/* Computing MIN */ /* Computing MIN */
d__1 = delta, d__2 = pnorm / p1; d__1 = delta, d__2 = pnorm / p1;
delta = temp * min(d__1,d__2); delta = temp * min(d__1,d__2);
par /= temp; par /= temp;
goto L260; goto L260;
L240: L240:
if (par != 0. && ratio < p75) { if (par != 0. && ratio < p75) {
goto L250; goto L250;
} }
delta = pnorm / p5; delta = pnorm / p5;
par = p5 * par; par = p5 * par;
L250: L250:
L260: L260:
/* test for successful iteration. */ /* test for successful iteration. */
if (ratio < p0001) { if (ratio < p0001) {
goto L290; goto L290;
} }
/* successful iteration. update x, fvec, and their norms. */ /* successful iteration. update x, fvec, and their norms. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
x[j] = wa2[j]; x[j] = wa2[j];
wa2[j] = diag[j] * x[j]; wa2[j] = diag[j] * x[j];
/* L270: */ /* L270: */
} }
for (i__ = 1; i__ <= m; ++i__) { for (i__ = 1; i__ <= m; ++i__) {
fvec[i__] = wa4[i__]; fvec[i__] = wa4[i__];
/* L280: */ /* L280: */
} }
xnorm = ei_enorm<Scalar>(n, &wa2[1]); xnorm = ei_enorm<Scalar>(n, &wa2[1]);
fnorm = fnorm1; fnorm = fnorm1;
++iter; ++iter;
L290: L290:
/* tests for convergence. */ /* tests for convergence. */
if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1.) { if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1.) {
info = 1; info = 1;
} }
if (delta <= xtol * xnorm) { if (delta <= xtol * xnorm) {
info = 2; info = 2;
} }
if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1. && info if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1. && info
== 2) { == 2) {
info = 3; info = 3;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* tests for termination and stringent tolerances. */ /* tests for termination and stringent tolerances. */
if (*nfev >= maxfev) { if (*nfev >= maxfev) {
info = 5; info = 5;
} }
if (fabs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && p5 * ratio <= 1.) { if (fabs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && p5 * ratio <= 1.) {
info = 6; info = 6;
} }
if (delta <= epsilon<Scalar>() * xnorm) { if (delta <= epsilon<Scalar>() * xnorm) {
info = 7; info = 7;
} }
if (gnorm <= epsilon<Scalar>()) { if (gnorm <= epsilon<Scalar>()) {
info = 8; info = 8;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* end of the inner loop. repeat if iteration unsuccessful. */ /* end of the inner loop. repeat if iteration unsuccessful. */
if (ratio < p0001) { if (ratio < p0001) {
goto L200; goto L200;
} }
/* end of the outer loop. */ /* end of the outer loop. */
goto L30; goto L30;
L300: L300:
/* termination, either normal or user imposed. */ /* termination, either normal or user imposed. */
if (iflag < 0) { if (iflag < 0) {
info = iflag; info = iflag;
} }
iflag = 0; iflag = 0;
if (nprint > 0) { if (nprint > 0) {
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 0); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, 0);
} }
return info; return info;
/* last card of subroutine lmder. */ /* last card of subroutine lmder. */
} /* lmder_ */ } /* lmder_ */

308
unsupported/Eigen/src/NonLinear/lmdif.h
View File

@ -1,12 +1,12 @@
template<typename Scalar> template<typename Scalar>
int lmdif_template(minpack_func_mn fcn, void *p, int m, int n, Scalar *x, int lmdif_template(minpack_func_mn fcn, void *p, int m, int n, Scalar *x,
Scalar *fvec, Scalar ftol, Scalar xtol, Scalar gtol, Scalar *fvec, Scalar ftol, Scalar xtol, Scalar gtol,
int maxfev, Scalar epsfcn, Scalar *diag, int int maxfev, Scalar epsfcn, Scalar *diag, int
mode, Scalar factor, int nprint, int * mode, Scalar factor, int nprint, int *
nfev, Scalar *fjac, int ldfjac, int *ipvt, Scalar * nfev, Scalar *fjac, int ldfjac, int *ipvt, Scalar *
qtf, Scalar *wa1, Scalar *wa2, Scalar *wa3, Scalar * qtf, Scalar *wa1, Scalar *wa2, Scalar *wa3, Scalar *
wa4) wa4)
{ {
/* Initialized data */ /* Initialized data */
@ -46,360 +46,360 @@ int lmdif_template(minpack_func_mn fcn, void *p, int m, int n, Scalar *x,
iflag = 0; iflag = 0;
*nfev = 0; *nfev = 0;
/* check the input parameters for errors. */ /* check the input parameters for errors. */
if (n <= 0 || m < n || ldfjac < m || ftol < 0. || xtol < 0. || if (n <= 0 || m < n || ldfjac < m || ftol < 0. || xtol < 0. ||
gtol < 0. || maxfev <= 0 || factor <= 0.) { gtol < 0. || maxfev <= 0 || factor <= 0.) {
goto L300; goto L300;
} }
if (mode != 2) { if (mode != 2) {
goto L20; goto L20;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (diag[j] <= 0.) { if (diag[j] <= 0.) {
goto L300; goto L300;
} }
/* L10: */ /* L10: */
} }
L20: L20:
/* evaluate the function at the starting point */ /* evaluate the function at the starting point */
/* and calculate its norm. */ /* and calculate its norm. */
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], 1); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], 1);
*nfev = 1; *nfev = 1;
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
fnorm = ei_enorm<Scalar>(m, &fvec[1]); fnorm = ei_enorm<Scalar>(m, &fvec[1]);
/* initialize levenberg-marquardt parameter and iteration counter. */ /* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.; par = 0.;
iter = 1; iter = 1;
/* beginning of the outer loop. */ /* beginning of the outer loop. */
L30: L30:
/* calculate the jacobian matrix. */ /* calculate the jacobian matrix. */
iflag = fdjac2(fcn, p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, iflag = fdjac2(fcn, p, m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac,
epsfcn, &wa4[1]); epsfcn, &wa4[1]);
*nfev += n; *nfev += n;
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
/* if requested, call fcn to enable printing of iterates. */ /* if requested, call fcn to enable printing of iterates. */
if (nprint <= 0) { if (nprint <= 0) {
goto L40; goto L40;
} }
iflag = 0; iflag = 0;
if ((iter - 1) % nprint == 0) { if ((iter - 1) % nprint == 0) {
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], 0); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], 0);
} }
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
L40: L40:
/* compute the qr factorization of the jacobian. */ /* compute the qr factorization of the jacobian. */
qrfac(m, n, &fjac[fjac_offset], ldfjac, TRUE_, &ipvt[1], n, &wa1[1], & qrfac(m, n, &fjac[fjac_offset], ldfjac, TRUE_, &ipvt[1], n, &wa1[1], &
wa2[1], &wa3[1]); wa2[1], &wa3[1]);
/* on the first iteration and if mode is 1, scale according */ /* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */ /* to the norms of the columns of the initial jacobian. */
if (iter != 1) { if (iter != 1) {
goto L80; goto L80;
} }
if (mode == 2) { if (mode == 2) {
goto L60; goto L60;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
diag[j] = wa2[j]; diag[j] = wa2[j];
if (wa2[j] == 0.) { if (wa2[j] == 0.) {
diag[j] = 1.; diag[j] = 1.;
} }
/* L50: */ /* L50: */
} }
L60: L60:
/* on the first iteration, calculate the norm of the scaled x */ /* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */ /* and initialize the step bound delta. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa3[j] = diag[j] * x[j]; wa3[j] = diag[j] * x[j];
/* L70: */ /* L70: */
} }
xnorm = ei_enorm<Scalar>(n, &wa3[1]); xnorm = ei_enorm<Scalar>(n, &wa3[1]);
delta = factor * xnorm; delta = factor * xnorm;
if (delta == 0.) { if (delta == 0.) {
delta = factor; delta = factor;
} }
L80: L80:
/* form (q transpose)*fvec and store the first n components in */ /* form (q transpose)*fvec and store the first n components in */
/* qtf. */ /* qtf. */
for (i__ = 1; i__ <= m; ++i__) { for (i__ = 1; i__ <= m; ++i__) {
wa4[i__] = fvec[i__]; wa4[i__] = fvec[i__];
/* L90: */ /* L90: */
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (fjac[j + j * fjac_dim1] == 0.) { if (fjac[j + j * fjac_dim1] == 0.) {
goto L120; goto L120;
} }
sum = 0.; sum = 0.;
for (i__ = j; i__ <= m; ++i__) { for (i__ = j; i__ <= m; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * wa4[i__]; sum += fjac[i__ + j * fjac_dim1] * wa4[i__];
/* L100: */ /* L100: */
} }
temp = -sum / fjac[j + j * fjac_dim1]; temp = -sum / fjac[j + j * fjac_dim1];
for (i__ = j; i__ <= m; ++i__) { for (i__ = j; i__ <= m; ++i__) {
wa4[i__] += fjac[i__ + j * fjac_dim1] * temp; wa4[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L110: */ /* L110: */
} }
L120: L120:
fjac[j + j * fjac_dim1] = wa1[j]; fjac[j + j * fjac_dim1] = wa1[j];
qtf[j] = wa4[j]; qtf[j] = wa4[j];
/* L130: */ /* L130: */
} }
/* compute the norm of the scaled gradient. */ /* compute the norm of the scaled gradient. */
gnorm = 0.; gnorm = 0.;
if (fnorm == 0.) { if (fnorm == 0.) {
goto L170; goto L170;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
l = ipvt[j]; l = ipvt[j];
if (wa2[l] == 0.) { if (wa2[l] == 0.) {
goto L150; goto L150;
} }
sum = 0.; sum = 0.;
for (i__ = 1; i__ <= j; ++i__) { for (i__ = 1; i__ <= j; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * (qtf[i__] / fnorm); sum += fjac[i__ + j * fjac_dim1] * (qtf[i__] / fnorm);
/* L140: */ /* L140: */
} }
/* Computing MAX */ /* Computing MAX */
d__2 = gnorm, d__3 = fabs(sum / wa2[l]); d__2 = gnorm, d__3 = fabs(sum / wa2[l]);
gnorm = max(d__2,d__3); gnorm = max(d__2,d__3);
L150: L150:
/* L160: */ /* L160: */
; ;
} }
L170: L170:
/* test for convergence of the gradient norm. */ /* test for convergence of the gradient norm. */
if (gnorm <= gtol) { if (gnorm <= gtol) {
info = 4; info = 4;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* rescale if necessary. */ /* rescale if necessary. */
if (mode == 2) { if (mode == 2) {
goto L190; goto L190;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
/* Computing MAX */ /* Computing MAX */
d__1 = diag[j], d__2 = wa2[j]; d__1 = diag[j], d__2 = wa2[j];
diag[j] = max(d__1,d__2); diag[j] = max(d__1,d__2);
/* L180: */ /* L180: */
} }
L190: L190:
/* beginning of the inner loop. */ /* beginning of the inner loop. */
L200: L200:
/* determine the levenberg-marquardt parameter. */ /* determine the levenberg-marquardt parameter. */
lmpar(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], delta, lmpar(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], delta,
&par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]); &par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]);
/* store the direction p and x + p. calculate the norm of p. */ /* store the direction p and x + p. calculate the norm of p. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa1[j] = -wa1[j]; wa1[j] = -wa1[j];
wa2[j] = x[j] + wa1[j]; wa2[j] = x[j] + wa1[j];
wa3[j] = diag[j] * wa1[j]; wa3[j] = diag[j] * wa1[j];
/* L210: */ /* L210: */
} }
pnorm = ei_enorm<Scalar>(n, &wa3[1]); pnorm = ei_enorm<Scalar>(n, &wa3[1]);
/* on the first iteration, adjust the initial step bound. */ /* on the first iteration, adjust the initial step bound. */
if (iter == 1) { if (iter == 1) {
delta = min(delta,pnorm); delta = min(delta,pnorm);
} }
/* evaluate the function at x + p and calculate its norm. */ /* evaluate the function at x + p and calculate its norm. */
iflag = (*fcn)(p, m, n, &wa2[1], &wa4[1], 1); iflag = (*fcn)(p, m, n, &wa2[1], &wa4[1], 1);
++(*nfev); ++(*nfev);
if (iflag < 0) { if (iflag < 0) {
goto L300; goto L300;
} }
fnorm1 = ei_enorm<Scalar>(m, &wa4[1]); fnorm1 = ei_enorm<Scalar>(m, &wa4[1]);
/* compute the scaled actual reduction. */ /* compute the scaled actual reduction. */
actred = -1.; actred = -1.;
if (p1 * fnorm1 < fnorm) { if (p1 * fnorm1 < fnorm) {
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = fnorm1 / fnorm; d__1 = fnorm1 / fnorm;
actred = 1. - d__1 * d__1; actred = 1. - d__1 * d__1;
} }
/* compute the scaled predicted reduction and */ /* compute the scaled predicted reduction and */
/* the scaled directional derivative. */ /* the scaled directional derivative. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa3[j] = 0.; wa3[j] = 0.;
l = ipvt[j]; l = ipvt[j];
temp = wa1[l]; temp = wa1[l];
for (i__ = 1; i__ <= j; ++i__) { for (i__ = 1; i__ <= j; ++i__) {
wa3[i__] += fjac[i__ + j * fjac_dim1] * temp; wa3[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L220: */ /* L220: */
} }
/* L230: */ /* L230: */
} }
temp1 = ei_enorm<Scalar>(n, &wa3[1]) / fnorm; temp1 = ei_enorm<Scalar>(n, &wa3[1]) / fnorm;
temp2 = sqrt(par) * pnorm / fnorm; temp2 = sqrt(par) * pnorm / fnorm;
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = temp1; d__1 = temp1;
/* Computing 2nd power */ /* Computing 2nd power */
d__2 = temp2; d__2 = temp2;
prered = d__1 * d__1 + d__2 * d__2 / p5; prered = d__1 * d__1 + d__2 * d__2 / p5;
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = temp1; d__1 = temp1;
/* Computing 2nd power */ /* Computing 2nd power */
d__2 = temp2; d__2 = temp2;
dirder = -(d__1 * d__1 + d__2 * d__2); dirder = -(d__1 * d__1 + d__2 * d__2);
/* compute the ratio of the actual to the predicted */ /* compute the ratio of the actual to the predicted */
/* reduction. */ /* reduction. */
ratio = 0.; ratio = 0.;
if (prered != 0.) { if (prered != 0.) {
ratio = actred / prered; ratio = actred / prered;
} }
/* update the step bound. */ /* update the step bound. */
if (ratio > p25) { if (ratio > p25) {
goto L240; goto L240;
} }
if (actred >= 0.) { if (actred >= 0.) {
temp = p5; temp = p5;
} }
if (actred < 0.) { if (actred < 0.) {
temp = p5 * dirder / (dirder + p5 * actred); temp = p5 * dirder / (dirder + p5 * actred);
} }
if (p1 * fnorm1 >= fnorm || temp < p1) { if (p1 * fnorm1 >= fnorm || temp < p1) {
temp = p1; temp = p1;
} }
/* Computing MIN */ /* Computing MIN */
d__1 = delta, d__2 = pnorm / p1; d__1 = delta, d__2 = pnorm / p1;
delta = temp * min(d__1,d__2); delta = temp * min(d__1,d__2);
par /= temp; par /= temp;
goto L260; goto L260;
L240: L240:
if (par != 0. && ratio < p75) { if (par != 0. && ratio < p75) {
goto L250; goto L250;
} }
delta = pnorm / p5; delta = pnorm / p5;
par = p5 * par; par = p5 * par;
L250: L250:
L260: L260:
/* test for successful iteration. */ /* test for successful iteration. */
if (ratio < p0001) { if (ratio < p0001) {
goto L290; goto L290;
} }
/* successful iteration. update x, fvec, and their norms. */ /* successful iteration. update x, fvec, and their norms. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
x[j] = wa2[j]; x[j] = wa2[j];
wa2[j] = diag[j] * x[j]; wa2[j] = diag[j] * x[j];
/* L270: */ /* L270: */
} }
for (i__ = 1; i__ <= m; ++i__) { for (i__ = 1; i__ <= m; ++i__) {
fvec[i__] = wa4[i__]; fvec[i__] = wa4[i__];
/* L280: */ /* L280: */
} }
xnorm = ei_enorm<Scalar>(n, &wa2[1]); xnorm = ei_enorm<Scalar>(n, &wa2[1]);
fnorm = fnorm1; fnorm = fnorm1;
++iter; ++iter;
L290: L290:
/* tests for convergence. */ /* tests for convergence. */
if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1.) { if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1.) {
info = 1; info = 1;
} }
if (delta <= xtol * xnorm) { if (delta <= xtol * xnorm) {
info = 2; info = 2;
} }
if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1. && info if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1. && info
== 2) { == 2) {
info = 3; info = 3;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* tests for termination and stringent tolerances. */ /* tests for termination and stringent tolerances. */
if (*nfev >= maxfev) { if (*nfev >= maxfev) {
info = 5; info = 5;
} }
if (fabs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && p5 * ratio <= 1.) { if (fabs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && p5 * ratio <= 1.) {
info = 6; info = 6;
} }
if (delta <= epsilon<Scalar>() * xnorm) { if (delta <= epsilon<Scalar>() * xnorm) {
info = 7; info = 7;
} }
if (gnorm <= epsilon<Scalar>()) { if (gnorm <= epsilon<Scalar>()) {
info = 8; info = 8;
} }
if (info != 0) { if (info != 0) {
goto L300; goto L300;
} }
/* end of the inner loop. repeat if iteration unsuccessful. */ /* end of the inner loop. repeat if iteration unsuccessful. */
if (ratio < p0001) { if (ratio < p0001) {
goto L200; goto L200;
} }
/* end of the outer loop. */ /* end of the outer loop. */
goto L30; goto L30;
L300: L300:
/* termination, either normal or user imposed. */ /* termination, either normal or user imposed. */
if (iflag < 0) { if (iflag < 0) {
info = iflag; info = iflag;
} }
iflag = 0; iflag = 0;
if (nprint > 0) { if (nprint > 0) {
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], 0); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], 0);
} }
return info; return info;
/* last card of subroutine lmdif. */ /* last card of subroutine lmdif. */
} /* lmdif_ */ } /* lmdif_ */

342
unsupported/Eigen/src/NonLinear/lmstr.h
View File

@ -1,11 +1,11 @@
template<typename Scalar> template<typename Scalar>
int lmstr_template(minpack_funcderstr_mn fcn, void *p, int m, int n, Scalar *x, int lmstr_template(minpack_funcderstr_mn fcn, void *p, int m, int n, Scalar *x,
Scalar *fvec, Scalar *fjac, int ldfjac, Scalar ftol, Scalar *fvec, Scalar *fjac, int ldfjac, Scalar ftol,
Scalar xtol, Scalar gtol, int maxfev, Scalar * Scalar xtol, Scalar gtol, int maxfev, Scalar *
diag, int mode, Scalar factor, int nprint, diag, int mode, Scalar factor, int nprint,
int *nfev, int *njev, int *ipvt, Scalar *qtf, int *nfev, int *njev, int *ipvt, Scalar *qtf,
Scalar *wa1, Scalar *wa2, Scalar *wa3, Scalar *wa4) Scalar *wa1, Scalar *wa2, Scalar *wa3, Scalar *wa4)
{ {
/* Initialized data */ /* Initialized data */
@ -46,382 +46,382 @@ int lmstr_template(minpack_funcderstr_mn fcn, void *p, int m, int n, Scalar *x,
*nfev = 0; *nfev = 0;
*njev = 0; *njev = 0;
/* check the input parameters for errors. */ /* check the input parameters for errors. */
if (n <= 0 || m < n || ldfjac < n || ftol < 0. || xtol < 0. || if (n <= 0 || m < n || ldfjac < n || ftol < 0. || xtol < 0. ||
gtol < 0. || maxfev <= 0 || factor <= 0.) { gtol < 0. || maxfev <= 0 || factor <= 0.) {
goto L340; goto L340;
} }
if (mode != 2) { if (mode != 2) {
goto L20; goto L20;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (diag[j] <= 0.) { if (diag[j] <= 0.) {
goto L340; goto L340;
} }
/* L10: */ /* L10: */
} }
L20: L20:
/* evaluate the function at the starting point */ /* evaluate the function at the starting point */
/* and calculate its norm. */ /* and calculate its norm. */
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &wa3[1], 1); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &wa3[1], 1);
*nfev = 1; *nfev = 1;
if (iflag < 0) { if (iflag < 0) {
goto L340; goto L340;
} }
fnorm = ei_enorm<Scalar>(m, &fvec[1]); fnorm = ei_enorm<Scalar>(m, &fvec[1]);
/* initialize levenberg-marquardt parameter and iteration counter. */ /* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.; par = 0.;
iter = 1; iter = 1;
/* beginning of the outer loop. */ /* beginning of the outer loop. */
L30: L30:
/* if requested, call fcn to enable printing of iterates. */ /* if requested, call fcn to enable printing of iterates. */
if (nprint <= 0) { if (nprint <= 0) {
goto L40; goto L40;
} }
iflag = 0; iflag = 0;
if ((iter - 1) % nprint == 0) { if ((iter - 1) % nprint == 0) {
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &wa3[1], 0); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &wa3[1], 0);
} }
if (iflag < 0) { if (iflag < 0) {
goto L340; goto L340;
} }
L40: L40:
/* compute the qr factorization of the jacobian matrix */ /* compute the qr factorization of the jacobian matrix */
/* calculated one row at a time, while simultaneously */ /* calculated one row at a time, while simultaneously */
/* forming (q transpose)*fvec and storing the first */ /* forming (q transpose)*fvec and storing the first */
/* n components in qtf. */ /* n components in qtf. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
qtf[j] = 0.; qtf[j] = 0.;
for (i__ = 1; i__ <= n; ++i__) { for (i__ = 1; i__ <= n; ++i__) {
fjac[i__ + j * fjac_dim1] = 0.; fjac[i__ + j * fjac_dim1] = 0.;
/* L50: */ /* L50: */
} }
/* L60: */ /* L60: */
} }
iflag = 2; iflag = 2;
for (i__ = 1; i__ <= m; ++i__) { for (i__ = 1; i__ <= m; ++i__) {
if ((*fcn)(p, m, n, &x[1], &fvec[1], &wa3[1], iflag) < 0) { if ((*fcn)(p, m, n, &x[1], &fvec[1], &wa3[1], iflag) < 0) {
goto L340; goto L340;
} }
temp = fvec[i__]; temp = fvec[i__];
rwupdt(n, &fjac[fjac_offset], ldfjac, &wa3[1], &qtf[1], &temp, &wa1[ rwupdt(n, &fjac[fjac_offset], ldfjac, &wa3[1], &qtf[1], &temp, &wa1[
1], &wa2[1]); 1], &wa2[1]);
++iflag; ++iflag;
/* L70: */ /* L70: */
} }
++(*njev); ++(*njev);
/* if the jacobian is rank deficient, call qrfac to */ /* if the jacobian is rank deficient, call qrfac to */
/* reorder its columns and update the components of qtf. */ /* reorder its columns and update the components of qtf. */
sing = FALSE_; sing = FALSE_;
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (fjac[j + j * fjac_dim1] == 0.) { if (fjac[j + j * fjac_dim1] == 0.) {
sing = TRUE_; sing = TRUE_;
} }
ipvt[j] = j; ipvt[j] = j;
wa2[j] = ei_enorm<Scalar>(j, &fjac[j * fjac_dim1 + 1]); wa2[j] = ei_enorm<Scalar>(j, &fjac[j * fjac_dim1 + 1]);
/* L80: */ /* L80: */
} }
if (! sing) { if (! sing) {
goto L130; goto L130;
} }
qrfac(n, n, &fjac[fjac_offset], ldfjac, TRUE_, &ipvt[1], n, &wa1[1], & qrfac(n, n, &fjac[fjac_offset], ldfjac, TRUE_, &ipvt[1], n, &wa1[1], &
wa2[1], &wa3[1]); wa2[1], &wa3[1]);
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
if (fjac[j + j * fjac_dim1] == 0.) { if (fjac[j + j * fjac_dim1] == 0.) {
goto L110; goto L110;
} }
sum = 0.; sum = 0.;
for (i__ = j; i__ <= n; ++i__) { for (i__ = j; i__ <= n; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * qtf[i__]; sum += fjac[i__ + j * fjac_dim1] * qtf[i__];
/* L90: */ /* L90: */
} }
temp = -sum / fjac[j + j * fjac_dim1]; temp = -sum / fjac[j + j * fjac_dim1];
for (i__ = j; i__ <= n; ++i__) { for (i__ = j; i__ <= n; ++i__) {
qtf[i__] += fjac[i__ + j * fjac_dim1] * temp; qtf[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L100: */ /* L100: */
} }
L110: L110:
fjac[j + j * fjac_dim1] = wa1[j]; fjac[j + j * fjac_dim1] = wa1[j];
/* L120: */ /* L120: */
} }
L130: L130:
/* on the first iteration and if mode is 1, scale according */ /* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */ /* to the norms of the columns of the initial jacobian. */
if (iter != 1) { if (iter != 1) {
goto L170; goto L170;
} }
if (mode == 2) { if (mode == 2) {
goto L150; goto L150;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
diag[j] = wa2[j]; diag[j] = wa2[j];
if (wa2[j] == 0.) { if (wa2[j] == 0.) {
diag[j] = 1.; diag[j] = 1.;
} }
/* L140: */ /* L140: */
} }
L150: L150:
/* on the first iteration, calculate the norm of the scaled x */ /* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */ /* and initialize the step bound delta. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa3[j] = diag[j] * x[j]; wa3[j] = diag[j] * x[j];
/* L160: */ /* L160: */
} }
xnorm = ei_enorm<Scalar>(n, &wa3[1]); xnorm = ei_enorm<Scalar>(n, &wa3[1]);
delta = factor * xnorm; delta = factor * xnorm;
if (delta == 0.) { if (delta == 0.) {
delta = factor; delta = factor;
} }
L170: L170:
/* compute the norm of the scaled gradient. */ /* compute the norm of the scaled gradient. */
gnorm = 0.; gnorm = 0.;
if (fnorm == 0.) { if (fnorm == 0.) {
goto L210; goto L210;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
l = ipvt[j]; l = ipvt[j];
if (wa2[l] == 0.) { if (wa2[l] == 0.) {
goto L190; goto L190;
} }
sum = 0.; sum = 0.;
for (i__ = 1; i__ <= j; ++i__) { for (i__ = 1; i__ <= j; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * (qtf[i__] / fnorm); sum += fjac[i__ + j * fjac_dim1] * (qtf[i__] / fnorm);
/* L180: */ /* L180: */
} }
/* Computing MAX */ /* Computing MAX */
d__2 = gnorm, d__3 = (d__1 = sum / wa2[l], abs(d__1)); d__2 = gnorm, d__3 = (d__1 = sum / wa2[l], abs(d__1));
gnorm = max(d__2,d__3); gnorm = max(d__2,d__3);
L190: L190:
/* L200: */ /* L200: */
; ;
} }
L210: L210:
/* test for convergence of the gradient norm. */ /* test for convergence of the gradient norm. */
if (gnorm <= gtol) { if (gnorm <= gtol) {
info = 4; info = 4;
} }
if (info != 0) { if (info != 0) {
goto L340; goto L340;
} }
/* rescale if necessary. */ /* rescale if necessary. */
if (mode == 2) { if (mode == 2) {
goto L230; goto L230;
} }
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
/* Computing MAX */ /* Computing MAX */
d__1 = diag[j], d__2 = wa2[j]; d__1 = diag[j], d__2 = wa2[j];
diag[j] = max(d__1,d__2); diag[j] = max(d__1,d__2);
/* L220: */ /* L220: */
} }
L230: L230:
/* beginning of the inner loop. */ /* beginning of the inner loop. */
L240: L240:
/* determine the levenberg-marquardt parameter. */ /* determine the levenberg-marquardt parameter. */
lmpar(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], delta, lmpar(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], delta,
&par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]); &par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]);
/* store the direction p and x + p. calculate the norm of p. */ /* store the direction p and x + p. calculate the norm of p. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa1[j] = -wa1[j]; wa1[j] = -wa1[j];
wa2[j] = x[j] + wa1[j]; wa2[j] = x[j] + wa1[j];
wa3[j] = diag[j] * wa1[j]; wa3[j] = diag[j] * wa1[j];
/* L250: */ /* L250: */
} }
pnorm = ei_enorm<Scalar>(n, &wa3[1]); pnorm = ei_enorm<Scalar>(n, &wa3[1]);
/* on the first iteration, adjust the initial step bound. */ /* on the first iteration, adjust the initial step bound. */
if (iter == 1) { if (iter == 1) {
delta = min(delta,pnorm); delta = min(delta,pnorm);
} }
/* evaluate the function at x + p and calculate its norm. */ /* evaluate the function at x + p and calculate its norm. */
iflag = (*fcn)(p, m, n, &wa2[1], &wa4[1], &wa3[1], 1); iflag = (*fcn)(p, m, n, &wa2[1], &wa4[1], &wa3[1], 1);
++(*nfev); ++(*nfev);
if (iflag < 0) { if (iflag < 0) {
goto L340; goto L340;
} }
fnorm1 = ei_enorm<Scalar>(m, &wa4[1]); fnorm1 = ei_enorm<Scalar>(m, &wa4[1]);
/* compute the scaled actual reduction. */ /* compute the scaled actual reduction. */
actred = -1.; actred = -1.;
if (p1 * fnorm1 < fnorm) { if (p1 * fnorm1 < fnorm) {
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = fnorm1 / fnorm; d__1 = fnorm1 / fnorm;
actred = 1. - d__1 * d__1; actred = 1. - d__1 * d__1;
} }
/* compute the scaled predicted reduction and */ /* compute the scaled predicted reduction and */
/* the scaled directional derivative. */ /* the scaled directional derivative. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
wa3[j] = 0.; wa3[j] = 0.;
l = ipvt[j]; l = ipvt[j];
temp = wa1[l]; temp = wa1[l];
for (i__ = 1; i__ <= j; ++i__) { for (i__ = 1; i__ <= j; ++i__) {
wa3[i__] += fjac[i__ + j * fjac_dim1] * temp; wa3[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L260: */ /* L260: */
} }
/* L270: */ /* L270: */
} }
temp1 = ei_enorm<Scalar>(n, &wa3[1]) / fnorm; temp1 = ei_enorm<Scalar>(n, &wa3[1]) / fnorm;
temp2 = sqrt(par) * pnorm / fnorm; temp2 = sqrt(par) * pnorm / fnorm;
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = temp1; d__1 = temp1;
/* Computing 2nd power */ /* Computing 2nd power */
d__2 = temp2; d__2 = temp2;
prered = d__1 * d__1 + d__2 * d__2 / p5; prered = d__1 * d__1 + d__2 * d__2 / p5;
/* Computing 2nd power */ /* Computing 2nd power */
d__1 = temp1; d__1 = temp1;
/* Computing 2nd power */ /* Computing 2nd power */
d__2 = temp2; d__2 = temp2;
dirder = -(d__1 * d__1 + d__2 * d__2); dirder = -(d__1 * d__1 + d__2 * d__2);
/* compute the ratio of the actual to the predicted */ /* compute the ratio of the actual to the predicted */
/* reduction. */ /* reduction. */
ratio = 0.; ratio = 0.;
if (prered != 0.) { if (prered != 0.) {
ratio = actred / prered; ratio = actred / prered;
} }
/* update the step bound. */ /* update the step bound. */
if (ratio > p25) { if (ratio > p25) {
goto L280; goto L280;
} }
if (actred >= 0.) { if (actred >= 0.) {
temp = p5; temp = p5;
} }
if (actred < 0.) { if (actred < 0.) {
temp = p5 * dirder / (dirder + p5 * actred); temp = p5 * dirder / (dirder + p5 * actred);
} }
if (p1 * fnorm1 >= fnorm || temp < p1) { if (p1 * fnorm1 >= fnorm || temp < p1) {
temp = p1; temp = p1;
} }
/* Computing MIN */ /* Computing MIN */
d__1 = delta, d__2 = pnorm / p1; d__1 = delta, d__2 = pnorm / p1;
delta = temp * min(d__1,d__2); delta = temp * min(d__1,d__2);
par /= temp; par /= temp;
goto L300; goto L300;
L280: L280:
if (par != 0. && ratio < p75) { if (par != 0. && ratio < p75) {
goto L290; goto L290;
} }
delta = pnorm / p5; delta = pnorm / p5;
par = p5 * par; par = p5 * par;
L290: L290:
L300: L300:
/* test for successful iteration. */ /* test for successful iteration. */
if (ratio < p0001) { if (ratio < p0001) {
goto L330; goto L330;
} }
/* successful iteration. update x, fvec, and their norms. */ /* successful iteration. update x, fvec, and their norms. */
for (j = 1; j <= n; ++j) { for (j = 1; j <= n; ++j) {
x[j] = wa2[j]; x[j] = wa2[j];
wa2[j] = diag[j] * x[j]; wa2[j] = diag[j] * x[j];
/* L310: */ /* L310: */
} }
for (i__ = 1; i__ <= m; ++i__) { for (i__ = 1; i__ <= m; ++i__) {
fvec[i__] = wa4[i__]; fvec[i__] = wa4[i__];
/* L320: */ /* L320: */
} }
xnorm = ei_enorm<Scalar>(n, &wa2[1]); xnorm = ei_enorm<Scalar>(n, &wa2[1]);
fnorm = fnorm1; fnorm = fnorm1;
++iter; ++iter;
L330: L330:
/* tests for convergence. */ /* tests for convergence. */
if (abs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1.) { if (abs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1.) {
info = 1; info = 1;
} }
if (delta <= xtol * xnorm) { if (delta <= xtol * xnorm) {
info = 2; info = 2;
} }
if (abs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1. && info if (abs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1. && info
== 2) { == 2) {
info = 3; info = 3;
} }
if (info != 0) { if (info != 0) {
goto L340; goto L340;
} }
/* tests for termination and stringent tolerances. */ /* tests for termination and stringent tolerances. */
if (*nfev >= maxfev) { if (*nfev >= maxfev) {
info = 5; info = 5;
} }
if (abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && p5 * ratio <= 1.) { if (abs(actred) <= epsilon<Scalar>() && prered <= epsilon<Scalar>() && p5 * ratio <= 1.) {
info = 6; info = 6;
} }
if (delta <= epsilon<Scalar>() * xnorm) { if (delta <= epsilon<Scalar>() * xnorm) {
info = 7; info = 7;
} }
if (gnorm <= epsilon<Scalar>()) { if (gnorm <= epsilon<Scalar>()) {
info = 8; info = 8;
} }
if (info != 0) { if (info != 0) {
goto L340; goto L340;
} }
/* end of the inner loop. repeat if iteration unsuccessful. */ /* end of the inner loop. repeat if iteration unsuccessful. */
if (ratio < p0001) { if (ratio < p0001) {
goto L240; goto L240;
} }
/* end of the outer loop. */ /* end of the outer loop. */
goto L30; goto L30;
L340: L340:
/* termination, either normal or user imposed. */ /* termination, either normal or user imposed. */
if (iflag < 0) { if (iflag < 0) {
info = iflag; info = iflag;
} }
iflag = 0; iflag = 0;
if (nprint > 0) { if (nprint > 0) {
iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &wa3[1], 0); iflag = (*fcn)(p, m, n, &x[1], &fvec[1], &wa3[1], 0);
} }
return info; return info;
/* last card of subroutine lmstr. */ /* last card of subroutine lmstr. */
} /* lmstr_ */ } /* lmstr_ */