433 lines
15 KiB
C++
433 lines
15 KiB
C++
#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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static integer c__1 = 1;
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static doublereal c_b46 = .5;
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int dlatrs_(char *uplo, char *trans, char *diag, char *normin, integer *n, doublereal *a,
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integer *lda, doublereal *x, doublereal *scale, doublereal *cnorm, integer *info,
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ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len, ftnlen normin_len)
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{
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integer a_dim1, a_offset, i__1, i__2, i__3;
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doublereal d__1, d__2, d__3;
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integer i__, j;
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doublereal xj, rec, tjj;
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integer jinc;
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extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *);
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doublereal xbnd;
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integer imax;
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doublereal tmax, tjjs, xmax, grow, sumj, work[1];
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extern int dscal_(integer *, doublereal *, doublereal *, integer *);
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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doublereal tscal, uscal;
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extern doublereal dasum_(integer *, doublereal *, integer *);
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integer jlast;
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extern int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *);
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logical upper;
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extern int dtrsv_(char *, char *, char *, integer *, doublereal *, integer *, doublereal *,
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integer *, ftnlen, ftnlen, ftnlen);
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extern doublereal dlamch_(char *, ftnlen),
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dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *, ftnlen);
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extern integer idamax_(integer *, doublereal *, integer *);
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extern int xerbla_(char *, integer *, ftnlen);
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doublereal bignum;
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logical notran;
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integer jfirst;
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doublereal smlnum;
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logical nounit;
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--x;
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--cnorm;
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*info = 0;
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upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1);
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notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1);
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nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1);
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if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
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*info = -1;
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} else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) &&
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!lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) {
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*info = -2;
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} else if (!nounit && !lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) {
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*info = -3;
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} else if (!lsame_(normin, (char *)"Y", (ftnlen)1, (ftnlen)1) &&
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!lsame_(normin, (char *)"N", (ftnlen)1, (ftnlen)1)) {
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*info = -4;
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} else if (*n < 0) {
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*info = -5;
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} else if (*lda < max(1, *n)) {
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*info = -7;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DLATRS", &i__1, (ftnlen)6);
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return 0;
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}
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*scale = 1.;
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if (*n == 0) {
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return 0;
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}
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smlnum = dlamch_((char *)"Safe minimum", (ftnlen)12) / dlamch_((char *)"Precision", (ftnlen)9);
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bignum = 1. / smlnum;
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if (lsame_(normin, (char *)"N", (ftnlen)1, (ftnlen)1)) {
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if (upper) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j - 1;
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cnorm[j] = dasum_(&i__2, &a[j * a_dim1 + 1], &c__1);
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}
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} else {
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i__1 = *n - 1;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n - j;
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cnorm[j] = dasum_(&i__2, &a[j + 1 + j * a_dim1], &c__1);
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}
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cnorm[*n] = 0.;
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}
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}
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imax = idamax_(n, &cnorm[1], &c__1);
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tmax = cnorm[imax];
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if (tmax <= bignum) {
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tscal = 1.;
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} else {
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if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) {
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tscal = 1. / (smlnum * tmax);
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dscal_(n, &tscal, &cnorm[1], &c__1);
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} else {
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tmax = 0.;
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if (upper) {
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i__1 = *n;
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for (j = 2; j <= i__1; ++j) {
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i__2 = j - 1;
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d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j * a_dim1 + 1], &c__1, work, (ftnlen)1);
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tmax = max(d__1, tmax);
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}
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} else {
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i__1 = *n - 1;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n - j;
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d__1 =
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dlange_((char *)"M", &i__2, &c__1, &a[j + 1 + j * a_dim1], &c__1, work, (ftnlen)1);
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tmax = max(d__1, tmax);
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}
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}
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if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) {
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tscal = 1. / (smlnum * tmax);
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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if (cnorm[j] <= dlamch_((char *)"Overflow", (ftnlen)8)) {
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cnorm[j] *= tscal;
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} else {
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cnorm[j] = 0.;
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if (upper) {
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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cnorm[j] += tscal * (d__1 = a[i__ + j * a_dim1], abs(d__1));
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}
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} else {
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i__2 = *n;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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cnorm[j] += tscal * (d__1 = a[i__ + j * a_dim1], abs(d__1));
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}
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}
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}
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}
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} else {
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dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, (ftnlen)1, (ftnlen)1,
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(ftnlen)1);
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return 0;
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}
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}
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}
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j = idamax_(n, &x[1], &c__1);
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xmax = (d__1 = x[j], abs(d__1));
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xbnd = xmax;
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if (notran) {
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if (upper) {
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jfirst = *n;
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jlast = 1;
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jinc = -1;
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} else {
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jfirst = 1;
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jlast = *n;
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jinc = 1;
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}
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if (tscal != 1.) {
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grow = 0.;
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goto L50;
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}
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if (nounit) {
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grow = 1. / max(xbnd, smlnum);
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xbnd = grow;
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i__1 = jlast;
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i__2 = jinc;
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for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
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if (grow <= smlnum) {
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goto L50;
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}
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tjj = (d__1 = a[j + j * a_dim1], abs(d__1));
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d__1 = xbnd, d__2 = min(1., tjj) * grow;
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xbnd = min(d__1, d__2);
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if (tjj + cnorm[j] >= smlnum) {
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grow *= tjj / (tjj + cnorm[j]);
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} else {
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grow = 0.;
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}
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}
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grow = xbnd;
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} else {
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d__1 = 1., d__2 = 1. / max(xbnd, smlnum);
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grow = min(d__1, d__2);
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i__2 = jlast;
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i__1 = jinc;
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for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
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if (grow <= smlnum) {
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goto L50;
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}
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grow *= 1. / (cnorm[j] + 1.);
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}
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}
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L50:;
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} else {
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if (upper) {
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jfirst = 1;
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jlast = *n;
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jinc = 1;
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} else {
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jfirst = *n;
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jlast = 1;
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jinc = -1;
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}
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if (tscal != 1.) {
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grow = 0.;
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goto L80;
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}
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if (nounit) {
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grow = 1. / max(xbnd, smlnum);
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xbnd = grow;
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i__1 = jlast;
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i__2 = jinc;
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for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
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if (grow <= smlnum) {
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goto L80;
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}
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xj = cnorm[j] + 1.;
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d__1 = grow, d__2 = xbnd / xj;
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grow = min(d__1, d__2);
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tjj = (d__1 = a[j + j * a_dim1], abs(d__1));
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if (xj > tjj) {
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xbnd *= tjj / xj;
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}
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}
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grow = min(grow, xbnd);
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} else {
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d__1 = 1., d__2 = 1. / max(xbnd, smlnum);
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grow = min(d__1, d__2);
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i__2 = jlast;
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i__1 = jinc;
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for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
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if (grow <= smlnum) {
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goto L80;
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}
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xj = cnorm[j] + 1.;
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grow /= xj;
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}
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}
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L80:;
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}
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if (grow * tscal > smlnum) {
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dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, (ftnlen)1, (ftnlen)1,
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(ftnlen)1);
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} else {
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if (xmax > bignum) {
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*scale = bignum / xmax;
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dscal_(n, scale, &x[1], &c__1);
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xmax = bignum;
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}
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if (notran) {
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i__1 = jlast;
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i__2 = jinc;
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for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
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xj = (d__1 = x[j], abs(d__1));
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if (nounit) {
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tjjs = a[j + j * a_dim1] * tscal;
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} else {
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tjjs = tscal;
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if (tscal == 1.) {
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goto L100;
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}
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}
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tjj = abs(tjjs);
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if (tjj > smlnum) {
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if (tjj < 1.) {
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if (xj > tjj * bignum) {
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rec = 1. / xj;
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dscal_(n, &rec, &x[1], &c__1);
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*scale *= rec;
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xmax *= rec;
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}
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}
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x[j] /= tjjs;
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xj = (d__1 = x[j], abs(d__1));
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} else if (tjj > 0.) {
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if (xj > tjj * bignum) {
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rec = tjj * bignum / xj;
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if (cnorm[j] > 1.) {
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rec /= cnorm[j];
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}
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dscal_(n, &rec, &x[1], &c__1);
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*scale *= rec;
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xmax *= rec;
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}
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x[j] /= tjjs;
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xj = (d__1 = x[j], abs(d__1));
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} else {
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i__3 = *n;
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for (i__ = 1; i__ <= i__3; ++i__) {
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x[i__] = 0.;
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}
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x[j] = 1.;
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xj = 1.;
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*scale = 0.;
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xmax = 0.;
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}
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L100:
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if (xj > 1.) {
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rec = 1. / xj;
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if (cnorm[j] > (bignum - xmax) * rec) {
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rec *= .5;
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dscal_(n, &rec, &x[1], &c__1);
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*scale *= rec;
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}
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} else if (xj * cnorm[j] > bignum - xmax) {
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dscal_(n, &c_b46, &x[1], &c__1);
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*scale *= .5;
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}
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if (upper) {
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if (j > 1) {
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i__3 = j - 1;
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d__1 = -x[j] * tscal;
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daxpy_(&i__3, &d__1, &a[j * a_dim1 + 1], &c__1, &x[1], &c__1);
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i__3 = j - 1;
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i__ = idamax_(&i__3, &x[1], &c__1);
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xmax = (d__1 = x[i__], abs(d__1));
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}
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} else {
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if (j < *n) {
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i__3 = *n - j;
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d__1 = -x[j] * tscal;
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daxpy_(&i__3, &d__1, &a[j + 1 + j * a_dim1], &c__1, &x[j + 1], &c__1);
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i__3 = *n - j;
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i__ = j + idamax_(&i__3, &x[j + 1], &c__1);
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xmax = (d__1 = x[i__], abs(d__1));
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}
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}
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}
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} else {
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i__2 = jlast;
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i__1 = jinc;
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for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
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xj = (d__1 = x[j], abs(d__1));
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uscal = tscal;
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rec = 1. / max(xmax, 1.);
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if (cnorm[j] > (bignum - xj) * rec) {
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rec *= .5;
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if (nounit) {
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tjjs = a[j + j * a_dim1] * tscal;
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} else {
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tjjs = tscal;
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}
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tjj = abs(tjjs);
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if (tjj > 1.) {
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d__1 = 1., d__2 = rec * tjj;
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rec = min(d__1, d__2);
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uscal /= tjjs;
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}
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if (rec < 1.) {
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dscal_(n, &rec, &x[1], &c__1);
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*scale *= rec;
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xmax *= rec;
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}
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}
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sumj = 0.;
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if (uscal == 1.) {
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if (upper) {
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i__3 = j - 1;
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sumj = ddot_(&i__3, &a[j * a_dim1 + 1], &c__1, &x[1], &c__1);
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} else if (j < *n) {
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i__3 = *n - j;
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sumj = ddot_(&i__3, &a[j + 1 + j * a_dim1], &c__1, &x[j + 1], &c__1);
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}
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} else {
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if (upper) {
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i__3 = j - 1;
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for (i__ = 1; i__ <= i__3; ++i__) {
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sumj += a[i__ + j * a_dim1] * uscal * x[i__];
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}
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} else if (j < *n) {
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i__3 = *n;
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for (i__ = j + 1; i__ <= i__3; ++i__) {
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sumj += a[i__ + j * a_dim1] * uscal * x[i__];
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}
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}
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}
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if (uscal == tscal) {
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x[j] -= sumj;
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xj = (d__1 = x[j], abs(d__1));
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if (nounit) {
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tjjs = a[j + j * a_dim1] * tscal;
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} else {
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tjjs = tscal;
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if (tscal == 1.) {
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goto L150;
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}
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}
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tjj = abs(tjjs);
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if (tjj > smlnum) {
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if (tjj < 1.) {
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if (xj > tjj * bignum) {
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rec = 1. / xj;
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dscal_(n, &rec, &x[1], &c__1);
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*scale *= rec;
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xmax *= rec;
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}
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}
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x[j] /= tjjs;
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} else if (tjj > 0.) {
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if (xj > tjj * bignum) {
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rec = tjj * bignum / xj;
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dscal_(n, &rec, &x[1], &c__1);
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*scale *= rec;
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xmax *= rec;
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}
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x[j] /= tjjs;
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} else {
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i__3 = *n;
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for (i__ = 1; i__ <= i__3; ++i__) {
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x[i__] = 0.;
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}
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x[j] = 1.;
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*scale = 0.;
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xmax = 0.;
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}
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L150:;
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} else {
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x[j] = x[j] / tjjs - sumj;
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}
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d__2 = xmax, d__3 = (d__1 = x[j], abs(d__1));
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xmax = max(d__2, d__3);
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}
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}
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*scale /= tscal;
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}
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if (tscal != 1.) {
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d__1 = 1. / tscal;
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dscal_(n, &d__1, &cnorm[1], &c__1);
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}
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return 0;
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}
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#ifdef __cplusplus
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}
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#endif
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