/* Subroutine */ int dlaqtr_(logical *ltran, logical *lreal, integer *n,
doublereal *t, integer *ldt, doublereal *b, doublereal *w, doublereal
*scale, doublereal *x, doublereal *work, integer *info)
{
/* System generated locals */
integer t_dim1, t_offset, i__1, i__2;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
/* Local variables */
doublereal d__[4] /* was [2][2] */;
integer i__, j, k;
doublereal v[4] /* was [2][2] */, z__;
integer j1, j2, n1, n2;
doublereal si, xj, sr, rec, eps, tjj, tmp;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
integer ierr;
doublereal smin, xmax;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern doublereal dasum_(integer *, doublereal *, integer *);
extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
integer jnext;
doublereal sminw, xnorm;
extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *
, doublereal *, integer *, doublereal *, doublereal *, integer *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern integer idamax_(integer *, doublereal *, integer *);
doublereal scaloc;
extern /* Subroutine */ int dladiv_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *);
doublereal bignum;
logical notran;
doublereal smlnum;
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAQTR solves the real quasi-triangular system */
/* op(T)*p = scale*c, if LREAL = .TRUE. */
/* or the complex quasi-triangular systems */
/* op(T + iB)*(p+iq) = scale*(c+id), if LREAL = .FALSE. */
/* in real arithmetic, where T is upper quasi-triangular. */
/* If LREAL = .FALSE., then the first diagonal block of T must be */
/* 1 by 1, B is the specially structured matrix */
/* B = [ b(1) b(2) ... b(n) ] */
/* [ w ] */
/* [ w ] */
/* [ . ] */
/* [ w ] */
/* op(A) = A or A', A' denotes the conjugate transpose of */
/* matrix A. */
/* On input, X = [ c ]. On output, X = [ p ]. */
/* [ d ] [ q ] */
/* This subroutine is designed for the condition number estimation */
/* in routine DTRSNA. */
/* Arguments */
/* ========= */
/* LTRAN (input) LOGICAL */
/* On entry, LTRAN specifies the option of conjugate transpose: */
/* = .FALSE., op(T+i*B) = T+i*B, */
/* = .TRUE., op(T+i*B) = (T+i*B)'. */
/* LREAL (input) LOGICAL */
/* On entry, LREAL specifies the input matrix structure: */
/* = .FALSE., the input is complex */
/* = .TRUE., the input is real */
/* N (input) INTEGER */
/* On entry, N specifies the order of T+i*B. N >= 0. */
/* T (input) DOUBLE PRECISION array, dimension (LDT,N) */
/* On entry, T contains a matrix in Schur canonical form. */
/* If LREAL = .FALSE., then the first diagonal block of T mu */
/* be 1 by 1. */
/* LDT (input) INTEGER */
/* The leading dimension of the matrix T. LDT >= max(1,N). */
/* B (input) DOUBLE PRECISION array, dimension (N) */
/* On entry, B contains the elements to form the matrix */
/* B as described above. */
/* If LREAL = .TRUE., B is not referenced. */
/* W (input) DOUBLE PRECISION */
/* On entry, W is the diagonal element of the matrix B. */
/* If LREAL = .TRUE., W is not referenced. */
/* SCALE (output) DOUBLE PRECISION */
/* On exit, SCALE is the scale factor. */
/* X (input/output) DOUBLE PRECISION array, dimension (2*N) */
/* On entry, X contains the right hand side of the system. */
/* On exit, X is overwritten by the solution. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* On exit, INFO is set to */
/* 0: successful exit. */
/* 1: the some diagonal 1 by 1 block has been perturbed by */
/* a small number SMIN to keep nonsingularity. */
/* 2: the some diagonal 2 by 2 block has been perturbed by */
/* a small number in DLALN2 to keep nonsingularity. */
/* NOTE: In the interests of speed, this routine does not */
/* check the inputs for errors. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Do not test the input parameters for errors */
/* Parameter adjustments */
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
--b;
--x;
--work;
/* Function Body */
notran = ! (*ltran);
*info = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Set constants to control overflow */
eps = dlamch_("P");
smlnum = dlamch_("S") / eps;
bignum = 1. / smlnum;
xnorm = dlange_("M", n, n, &t[t_offset], ldt, d__);
if (! (*lreal)) {
/* Computing MAX */
d__1 = xnorm, d__2 = abs(*w), d__1 = max(d__1,d__2), d__2 = dlange_(
"M", n, &c__1, &b[1], n, d__);
xnorm = max(d__1,d__2);
}
/* Computing MAX */
d__1 = smlnum, d__2 = eps * xnorm;
smin = max(d__1,d__2);
/* Compute 1-norm of each column of strictly upper triangular */
/* part of T to control overflow in triangular solver. */
work[1] = 0.;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
work[j] = dasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
/* L10: */
}
if (! (*lreal)) {
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
work[i__] += (d__1 = b[i__], abs(d__1));
/* L20: */
}
}
n2 = *n << 1;
n1 = *n;
if (! (*lreal)) {
n1 = n2;
}
k = idamax_(&n1, &x[1], &c__1);
xmax = (d__1 = x[k], abs(d__1));
*scale = 1.;
if (xmax > bignum) {
*scale = bignum / xmax;
dscal_(&n1, scale, &x[1], &c__1);
xmax = bignum;
}
if (*lreal) {
if (notran) {
/* Solve T*p = scale*c */
jnext = *n;
for (j = *n; j >= 1; --j) {
if (j > jnext) {
goto L30;
}
j1 = j;
j2 = j;
jnext = j - 1;
if (j > 1) {
if (t[j + (j - 1) * t_dim1] != 0.) {
j1 = j - 1;
jnext = j - 2;
}
}
if (j1 == j2) {
/* Meet 1 by 1 diagonal block */
/* Scale to avoid overflow when computing */
/* x(j) = b(j)/T(j,j) */
xj = (d__1 = x[j1], abs(d__1));
tjj = (d__1 = t[j1 + j1 * t_dim1], abs(d__1));
tmp = t[j1 + j1 * t_dim1];
if (tjj < smin) {
tmp = smin;
tjj = smin;
*info = 1;
}
if (xj == 0.) {
goto L30;
}
if (tjj < 1.) {
if (xj > bignum * tjj) {
rec = 1. / xj;
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
x[j1] /= tmp;
xj = (d__1 = x[j1], abs(d__1));
/* Scale x if necessary to avoid overflow when adding a */
/* multiple of column j1 of T. */
if (xj > 1.) {
rec = 1. / xj;
if (work[j1] > (bignum - xmax) * rec) {
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
}
if (j1 > 1) {
i__1 = j1 - 1;
d__1 = -x[j1];
daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
k = idamax_(&i__1, &x[1], &c__1);
xmax = (d__1 = x[k], abs(d__1));
}
} else {
/* Meet 2 by 2 diagonal block */
/* Call 2 by 2 linear system solve, to take */
/* care of possible overflow by scaling factor. */
d__[0] = x[j1];
d__[1] = x[j2];
dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b21, &t[j1 + j1
* t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
c_b25, &c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.) {
dscal_(n, &scaloc, &x[1], &c__1);
*scale *= scaloc;
}
x[j1] = v[0];
x[j2] = v[1];
/* Scale V(1,1) (= X(J1)) and/or V(2,1) (=X(J2)) */
/* to avoid overflow in updating right-hand side. */
/* Computing MAX */
d__1 = abs(v[0]), d__2 = abs(v[1]);
xj = max(d__1,d__2);
if (xj > 1.) {
rec = 1. / xj;
/* Computing MAX */
d__1 = work[j1], d__2 = work[j2];
if (max(d__1,d__2) > (bignum - xmax) * rec) {
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
}
/* Update right-hand side */
if (j1 > 1) {
i__1 = j1 - 1;
d__1 = -x[j1];
daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
d__1 = -x[j2];
daxpy_(&i__1, &d__1, &t[j2 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
k = idamax_(&i__1, &x[1], &c__1);
xmax = (d__1 = x[k], abs(d__1));
}
}
L30:
;
}
} else {
/* Solve T'*p = scale*c */
jnext = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < jnext) {
goto L40;
}
j1 = j;
j2 = j;
jnext = j + 1;
if (j < *n) {
if (t[j + 1 + j * t_dim1] != 0.) {
j2 = j + 1;
jnext = j + 2;
}
}
if (j1 == j2) {
/* 1 by 1 diagonal block */
/* Scale if necessary to avoid overflow in forming the */
/* right-hand side element by inner product. */
xj = (d__1 = x[j1], abs(d__1));
if (xmax > 1.) {
rec = 1. / xmax;
if (work[j1] > (bignum - xj) * rec) {
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
x[j1] -= ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &
c__1);
xj = (d__1 = x[j1], abs(d__1));
tjj = (d__1 = t[j1 + j1 * t_dim1], abs(d__1));
tmp = t[j1 + j1 * t_dim1];
if (tjj < smin) {
tmp = smin;
tjj = smin;
*info = 1;
}
if (tjj < 1.) {
if (xj > bignum * tjj) {
rec = 1. / xj;
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
x[j1] /= tmp;
/* Computing MAX */
d__2 = xmax, d__3 = (d__1 = x[j1], abs(d__1));
xmax = max(d__2,d__3);
} else {
/* 2 by 2 diagonal block */
/* Scale if necessary to avoid overflow in forming the */
/* right-hand side elements by inner product. */
/* Computing MAX */
d__3 = (d__1 = x[j1], abs(d__1)), d__4 = (d__2 = x[j2],
abs(d__2));
xj = max(d__3,d__4);
if (xmax > 1.) {
rec = 1. / xmax;
/* Computing MAX */
d__1 = work[j2], d__2 = work[j1];
if (max(d__1,d__2) > (bignum - xj) * rec) {
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
d__[0] = x[j1] - ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d__[1] = x[j2] - ddot_(&i__2, &t[j2 * t_dim1 + 1], &c__1,
&x[1], &c__1);
dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b21, &t[j1 + j1 *
t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &c_b25,
&c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.) {
dscal_(n, &scaloc, &x[1], &c__1);
*scale *= scaloc;
}
x[j1] = v[0];
x[j2] = v[1];
/* Computing MAX */
d__3 = (d__1 = x[j1], abs(d__1)), d__4 = (d__2 = x[j2],
abs(d__2)), d__3 = max(d__3,d__4);
xmax = max(d__3,xmax);
}
L40:
;
}
}
} else {
/* Computing MAX */
d__1 = eps * abs(*w);
sminw = max(d__1,smin);
if (notran) {
/* Solve (T + iB)*(p+iq) = c+id */
jnext = *n;
for (j = *n; j >= 1; --j) {
if (j > jnext) {
goto L70;
}
j1 = j;
j2 = j;
jnext = j - 1;
if (j > 1) {
if (t[j + (j - 1) * t_dim1] != 0.) {
j1 = j - 1;
jnext = j - 2;
}
}
if (j1 == j2) {
/* 1 by 1 diagonal block */
/* Scale if necessary to avoid overflow in division */
z__ = *w;
if (j1 == 1) {
z__ = b[1];
}
xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], abs(
d__2));
tjj = (d__1 = t[j1 + j1 * t_dim1], abs(d__1)) + abs(z__);
tmp = t[j1 + j1 * t_dim1];
if (tjj < sminw) {
tmp = sminw;
tjj = sminw;
*info = 1;
}
if (xj == 0.) {
goto L70;
}
if (tjj < 1.) {
if (xj > bignum * tjj) {
rec = 1. / xj;
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
dladiv_(&x[j1], &x[*n + j1], &tmp, &z__, &sr, &si);
x[j1] = sr;
x[*n + j1] = si;
xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], abs(
d__2));
/* Scale x if necessary to avoid overflow when adding a */
/* multiple of column j1 of T. */
if (xj > 1.) {
rec = 1. / xj;
if (work[j1] > (bignum - xmax) * rec) {
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
}
}
if (j1 > 1) {
i__1 = j1 - 1;
d__1 = -x[j1];
daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
d__1 = -x[*n + j1];
daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[*
n + 1], &c__1);
x[1] += b[j1] * x[*n + j1];
x[*n + 1] -= b[j1] * x[j1];
xmax = 0.;
i__1 = j1 - 1;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
d__3 = xmax, d__4 = (d__1 = x[k], abs(d__1)) + (
d__2 = x[k + *n], abs(d__2));
xmax = max(d__3,d__4);
/* L50: */
}
}
} else {
/* Meet 2 by 2 diagonal block */
d__[0] = x[j1];
d__[1] = x[j2];
d__[2] = x[*n + j1];
d__[3] = x[*n + j2];
d__1 = -(*w);
dlaln2_(&c_false, &c__2, &c__2, &sminw, &c_b21, &t[j1 +
j1 * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
c_b25, &d__1, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.) {
i__1 = *n << 1;
dscal_(&i__1, &scaloc, &x[1], &c__1);
*scale = scaloc * *scale;
}
x[j1] = v[0];
x[j2] = v[1];
x[*n + j1] = v[2];
x[*n + j2] = v[3];
/* Scale X(J1), .... to avoid overflow in */
/* updating right hand side. */
/* Computing MAX */
d__1 = abs(v[0]) + abs(v[2]), d__2 = abs(v[1]) + abs(v[3])
;
xj = max(d__1,d__2);
if (xj > 1.) {
rec = 1. / xj;
/* Computing MAX */
d__1 = work[j1], d__2 = work[j2];
if (max(d__1,d__2) > (bignum - xmax) * rec) {
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
}
}
/* Update the right-hand side. */
if (j1 > 1) {
i__1 = j1 - 1;
d__1 = -x[j1];
daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
d__1 = -x[j2];
daxpy_(&i__1, &d__1, &t[j2 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
d__1 = -x[*n + j1];
daxpy_(&i__1, &d__1, &t[j1 * t_dim1 + 1], &c__1, &x[*
n + 1], &c__1);
i__1 = j1 - 1;
d__1 = -x[*n + j2];
daxpy_(&i__1, &d__1, &t[j2 * t_dim1 + 1], &c__1, &x[*
n + 1], &c__1);
x[1] = x[1] + b[j1] * x[*n + j1] + b[j2] * x[*n + j2];
x[*n + 1] = x[*n + 1] - b[j1] * x[j1] - b[j2] * x[j2];
xmax = 0.;
i__1 = j1 - 1;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
d__3 = (d__1 = x[k], abs(d__1)) + (d__2 = x[k + *
n], abs(d__2));
xmax = max(d__3,xmax);
/* L60: */
}
}
}
L70:
;
}
} else {
/* Solve (T + iB)'*(p+iq) = c+id */
jnext = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < jnext) {
goto L80;
}
j1 = j;
j2 = j;
jnext = j + 1;
if (j < *n) {
if (t[j + 1 + j * t_dim1] != 0.) {
j2 = j + 1;
jnext = j + 2;
}
}
if (j1 == j2) {
/* 1 by 1 diagonal block */
/* Scale if necessary to avoid overflow in forming the */
/* right-hand side element by inner product. */
xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], abs(
d__2));
if (xmax > 1.) {
rec = 1. / xmax;
if (work[j1] > (bignum - xj) * rec) {
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
x[j1] -= ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &
c__1);
i__2 = j1 - 1;
x[*n + j1] -= ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[
*n + 1], &c__1);
if (j1 > 1) {
x[j1] -= b[j1] * x[*n + 1];
x[*n + j1] += b[j1] * x[1];
}
xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], abs(
d__2));
z__ = *w;
if (j1 == 1) {
z__ = b[1];
}
/* Scale if necessary to avoid overflow in */
/* complex division */
tjj = (d__1 = t[j1 + j1 * t_dim1], abs(d__1)) + abs(z__);
tmp = t[j1 + j1 * t_dim1];
if (tjj < sminw) {
tmp = sminw;
tjj = sminw;
*info = 1;
}
if (tjj < 1.) {
if (xj > bignum * tjj) {
rec = 1. / xj;
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
d__1 = -z__;
dladiv_(&x[j1], &x[*n + j1], &tmp, &d__1, &sr, &si);
x[j1] = sr;
x[j1 + *n] = si;
/* Computing MAX */
d__3 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n],
abs(d__2));
xmax = max(d__3,xmax);
} else {
/* 2 by 2 diagonal block */
/* Scale if necessary to avoid overflow in forming the */
/* right-hand side element by inner product. */
/* Computing MAX */
d__5 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1],
abs(d__2)), d__6 = (d__3 = x[j2], abs(d__3)) + (
d__4 = x[*n + j2], abs(d__4));
xj = max(d__5,d__6);
if (xmax > 1.) {
rec = 1. / xmax;
/* Computing MAX */
d__1 = work[j1], d__2 = work[j2];
if (max(d__1,d__2) > (bignum - xj) / xmax) {
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
d__[0] = x[j1] - ddot_(&i__2, &t[j1 * t_dim1 + 1], &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d__[1] = x[j2] - ddot_(&i__2, &t[j2 * t_dim1 + 1], &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d__[2] = x[*n + j1] - ddot_(&i__2, &t[j1 * t_dim1 + 1], &
c__1, &x[*n + 1], &c__1);
i__2 = j1 - 1;
d__[3] = x[*n + j2] - ddot_(&i__2, &t[j2 * t_dim1 + 1], &
c__1, &x[*n + 1], &c__1);
d__[0] -= b[j1] * x[*n + 1];
d__[1] -= b[j2] * x[*n + 1];
d__[2] += b[j1] * x[1];
d__[3] += b[j2] * x[1];
dlaln2_(&c_true, &c__2, &c__2, &sminw, &c_b21, &t[j1 + j1
* t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
c_b25, w, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.) {
dscal_(&n2, &scaloc, &x[1], &c__1);
*scale = scaloc * *scale;
}
x[j1] = v[0];
x[j2] = v[1];
x[*n + j1] = v[2];
x[*n + j2] = v[3];
/* Computing MAX */
d__5 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1],
abs(d__2)), d__6 = (d__3 = x[j2], abs(d__3)) + (
d__4 = x[*n + j2], abs(d__4)), d__5 = max(d__5,
d__6);
xmax = max(d__5,xmax);
}
L80:
;
}
}
}
return 0;
/* End of DLAQTR */
} /* dlaqtr_ */
/* Subroutine */
int dlaein_(logical *rightv, logical *noinit, integer *n, doublereal *h__, integer *ldh, doublereal *wr, doublereal *wi, doublereal *vr, doublereal *vi, doublereal *b, integer *ldb, doublereal *work, doublereal *eps3, doublereal *smlnum, doublereal * bignum, integer *info)
{
/* System generated locals */
integer b_dim1, b_offset, h_dim1, h_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3, d__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j;
doublereal w, x, y;
integer i1, i2, i3;
doublereal w1, ei, ej, xi, xr, rec;
integer its, ierr;
doublereal temp, norm, vmax;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
extern /* Subroutine */
int dscal_(integer *, doublereal *, doublereal *, integer *);
doublereal scale;
extern doublereal dasum_(integer *, doublereal *, integer *);
char trans[1];
doublereal vcrit, rootn, vnorm;
extern doublereal dlapy2_(doublereal *, doublereal *);
doublereal absbii, absbjj;
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */
int dladiv_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), dlatrs_( char *, char *, char *, char *, integer *, doublereal *, integer * , doublereal *, doublereal *, doublereal *, integer *);
char normin[1];
doublereal nrmsml, growto;
/* -- LAPACK auxiliary routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
--vr;
--vi;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
*info = 0;
/* GROWTO is the threshold used in the acceptance test for an */
/* eigenvector. */
rootn = sqrt((doublereal) (*n));
growto = .1 / rootn;
/* Computing MAX */
d__1 = 1.;
d__2 = *eps3 * rootn; // , expr subst
nrmsml = max(d__1,d__2) * *smlnum;
/* Form B = H - (WR,WI)*I (except that the subdiagonal elements and */
/* the imaginary parts of the diagonal elements are not stored). */
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
i__2 = j - 1;
for (i__ = 1;
i__ <= i__2;
++i__)
{
b[i__ + j * b_dim1] = h__[i__ + j * h_dim1];
/* L10: */
}
b[j + j * b_dim1] = h__[j + j * h_dim1] - *wr;
/* L20: */
}
if (*wi == 0.)
{
/* Real eigenvalue. */
if (*noinit)
{
/* Set initial vector. */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
vr[i__] = *eps3;
/* L30: */
}
}
else
{
/* Scale supplied initial vector. */
vnorm = dnrm2_(n, &vr[1], &c__1);
d__1 = *eps3 * rootn / max(vnorm,nrmsml);
dscal_(n, &d__1, &vr[1], &c__1);
}
if (*rightv)
{
/* LU decomposition with partial pivoting of B, replacing zero */
/* pivots by EPS3. */
i__1 = *n - 1;
for (i__ = 1;
i__ <= i__1;
++i__)
{
ei = h__[i__ + 1 + i__ * h_dim1];
if ((d__1 = b[i__ + i__ * b_dim1], abs(d__1)) < abs(ei))
{
/* Interchange rows and eliminate. */
x = b[i__ + i__ * b_dim1] / ei;
b[i__ + i__ * b_dim1] = ei;
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
temp = b[i__ + 1 + j * b_dim1];
b[i__ + 1 + j * b_dim1] = b[i__ + j * b_dim1] - x * temp;
b[i__ + j * b_dim1] = temp;
/* L40: */
}
}
else
{
/* Eliminate without interchange. */
if (b[i__ + i__ * b_dim1] == 0.)
{
b[i__ + i__ * b_dim1] = *eps3;
}
x = ei / b[i__ + i__ * b_dim1];
if (x != 0.)
{
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
b[i__ + 1 + j * b_dim1] -= x * b[i__ + j * b_dim1] ;
/* L50: */
}
}
}
/* L60: */
}
if (b[*n + *n * b_dim1] == 0.)
{
b[*n + *n * b_dim1] = *eps3;
}
*(unsigned char *)trans = 'N';
}
else
{
/* UL decomposition with partial pivoting of B, replacing zero */
/* pivots by EPS3. */
for (j = *n;
j >= 2;
--j)
{
ej = h__[j + (j - 1) * h_dim1];
if ((d__1 = b[j + j * b_dim1], abs(d__1)) < abs(ej))
{
/* Interchange columns and eliminate. */
x = b[j + j * b_dim1] / ej;
b[j + j * b_dim1] = ej;
i__1 = j - 1;
for (i__ = 1;
i__ <= i__1;
++i__)
{
temp = b[i__ + (j - 1) * b_dim1];
b[i__ + (j - 1) * b_dim1] = b[i__ + j * b_dim1] - x * temp;
b[i__ + j * b_dim1] = temp;
/* L70: */
}
}
else
{
/* Eliminate without interchange. */
if (b[j + j * b_dim1] == 0.)
{
b[j + j * b_dim1] = *eps3;
}
x = ej / b[j + j * b_dim1];
if (x != 0.)
{
i__1 = j - 1;
for (i__ = 1;
i__ <= i__1;
++i__)
{
b[i__ + (j - 1) * b_dim1] -= x * b[i__ + j * b_dim1];
/* L80: */
}
}
}
/* L90: */
}
if (b[b_dim1 + 1] == 0.)
{
b[b_dim1 + 1] = *eps3;
}
*(unsigned char *)trans = 'T';
}
*(unsigned char *)normin = 'N';
i__1 = *n;
for (its = 1;
its <= i__1;
++its)
{
/* Solve U*x = scale*v for a right eigenvector */
/* or U**T*x = scale*v for a left eigenvector, */
/* overwriting x on v. */
dlatrs_("Upper", trans, "Nonunit", normin, n, &b[b_offset], ldb, & vr[1], &scale, &work[1], &ierr);
*(unsigned char *)normin = 'Y';
/* Test for sufficient growth in the norm of v. */
vnorm = dasum_(n, &vr[1], &c__1);
if (vnorm >= growto * scale)
{
goto L120;
}
/* Choose new orthogonal starting vector and try again. */
temp = *eps3 / (rootn + 1.);
vr[1] = *eps3;
i__2 = *n;
for (i__ = 2;
i__ <= i__2;
++i__)
{
vr[i__] = temp;
/* L100: */
}
vr[*n - its + 1] -= *eps3 * rootn;
/* L110: */
}
/* Failure to find eigenvector in N iterations. */
*info = 1;
L120: /* Normalize eigenvector. */
i__ = idamax_(n, &vr[1], &c__1);
d__2 = 1. / (d__1 = vr[i__], abs(d__1));
dscal_(n, &d__2, &vr[1], &c__1);
}
else
{
/* Complex eigenvalue. */
if (*noinit)
{
/* Set initial vector. */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
vr[i__] = *eps3;
vi[i__] = 0.;
/* L130: */
}
}
else
{
/* Scale supplied initial vector. */
d__1 = dnrm2_(n, &vr[1], &c__1);
d__2 = dnrm2_(n, &vi[1], &c__1);
norm = dlapy2_(&d__1, &d__2);
rec = *eps3 * rootn / max(norm,nrmsml);
dscal_(n, &rec, &vr[1], &c__1);
dscal_(n, &rec, &vi[1], &c__1);
}
if (*rightv)
{
/* LU decomposition with partial pivoting of B, replacing zero */
/* pivots by EPS3. */
/* The imaginary part of the (i,j)-th element of U is stored in */
/* B(j+1,i). */
b[b_dim1 + 2] = -(*wi);
i__1 = *n;
for (i__ = 2;
i__ <= i__1;
++i__)
{
b[i__ + 1 + b_dim1] = 0.;
/* L140: */
}
i__1 = *n - 1;
for (i__ = 1;
i__ <= i__1;
++i__)
{
absbii = dlapy2_(&b[i__ + i__ * b_dim1], &b[i__ + 1 + i__ * b_dim1]);
ei = h__[i__ + 1 + i__ * h_dim1];
if (absbii < abs(ei))
{
/* Interchange rows and eliminate. */
xr = b[i__ + i__ * b_dim1] / ei;
xi = b[i__ + 1 + i__ * b_dim1] / ei;
b[i__ + i__ * b_dim1] = ei;
b[i__ + 1 + i__ * b_dim1] = 0.;
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
temp = b[i__ + 1 + j * b_dim1];
b[i__ + 1 + j * b_dim1] = b[i__ + j * b_dim1] - xr * temp;
b[j + 1 + (i__ + 1) * b_dim1] = b[j + 1 + i__ * b_dim1] - xi * temp;
b[i__ + j * b_dim1] = temp;
b[j + 1 + i__ * b_dim1] = 0.;
/* L150: */
}
b[i__ + 2 + i__ * b_dim1] = -(*wi);
b[i__ + 1 + (i__ + 1) * b_dim1] -= xi * *wi;
b[i__ + 2 + (i__ + 1) * b_dim1] += xr * *wi;
}
else
{
/* Eliminate without interchanging rows. */
if (absbii == 0.)
{
b[i__ + i__ * b_dim1] = *eps3;
b[i__ + 1 + i__ * b_dim1] = 0.;
absbii = *eps3;
}
ei = ei / absbii / absbii;
xr = b[i__ + i__ * b_dim1] * ei;
xi = -b[i__ + 1 + i__ * b_dim1] * ei;
i__2 = *n;
for (j = i__ + 1;
j <= i__2;
++j)
{
b[i__ + 1 + j * b_dim1] = b[i__ + 1 + j * b_dim1] - xr * b[i__ + j * b_dim1] + xi * b[j + 1 + i__ * b_dim1];
b[j + 1 + (i__ + 1) * b_dim1] = -xr * b[j + 1 + i__ * b_dim1] - xi * b[i__ + j * b_dim1];
/* L160: */
}
b[i__ + 2 + (i__ + 1) * b_dim1] -= *wi;
}
/* Compute 1-norm of offdiagonal elements of i-th row. */
i__2 = *n - i__;
i__3 = *n - i__;
work[i__] = dasum_(&i__2, &b[i__ + (i__ + 1) * b_dim1], ldb) + dasum_(&i__3, &b[i__ + 2 + i__ * b_dim1], &c__1);
/* L170: */
}
if (b[*n + *n * b_dim1] == 0. && b[*n + 1 + *n * b_dim1] == 0.)
{
b[*n + *n * b_dim1] = *eps3;
}
work[*n] = 0.;
i1 = *n;
i2 = 1;
i3 = -1;
}
else
{
/* UL decomposition with partial pivoting of conjg(B), */
/* replacing zero pivots by EPS3. */
/* The imaginary part of the (i,j)-th element of U is stored in */
/* B(j+1,i). */
b[*n + 1 + *n * b_dim1] = *wi;
i__1 = *n - 1;
for (j = 1;
j <= i__1;
++j)
{
b[*n + 1 + j * b_dim1] = 0.;
/* L180: */
}
for (j = *n;
j >= 2;
--j)
{
ej = h__[j + (j - 1) * h_dim1];
absbjj = dlapy2_(&b[j + j * b_dim1], &b[j + 1 + j * b_dim1]);
if (absbjj < abs(ej))
{
/* Interchange columns and eliminate */
xr = b[j + j * b_dim1] / ej;
xi = b[j + 1 + j * b_dim1] / ej;
b[j + j * b_dim1] = ej;
b[j + 1 + j * b_dim1] = 0.;
i__1 = j - 1;
for (i__ = 1;
i__ <= i__1;
++i__)
{
temp = b[i__ + (j - 1) * b_dim1];
b[i__ + (j - 1) * b_dim1] = b[i__ + j * b_dim1] - xr * temp;
b[j + i__ * b_dim1] = b[j + 1 + i__ * b_dim1] - xi * temp;
b[i__ + j * b_dim1] = temp;
b[j + 1 + i__ * b_dim1] = 0.;
/* L190: */
}
b[j + 1 + (j - 1) * b_dim1] = *wi;
b[j - 1 + (j - 1) * b_dim1] += xi * *wi;
b[j + (j - 1) * b_dim1] -= xr * *wi;
}
else
{
/* Eliminate without interchange. */
if (absbjj == 0.)
{
b[j + j * b_dim1] = *eps3;
b[j + 1 + j * b_dim1] = 0.;
absbjj = *eps3;
}
ej = ej / absbjj / absbjj;
xr = b[j + j * b_dim1] * ej;
xi = -b[j + 1 + j * b_dim1] * ej;
i__1 = j - 1;
for (i__ = 1;
i__ <= i__1;
++i__)
{
b[i__ + (j - 1) * b_dim1] = b[i__ + (j - 1) * b_dim1] - xr * b[i__ + j * b_dim1] + xi * b[j + 1 + i__ * b_dim1];
b[j + i__ * b_dim1] = -xr * b[j + 1 + i__ * b_dim1] - xi * b[i__ + j * b_dim1];
/* L200: */
}
b[j + (j - 1) * b_dim1] += *wi;
}
/* Compute 1-norm of offdiagonal elements of j-th column. */
i__1 = j - 1;
i__2 = j - 1;
work[j] = dasum_(&i__1, &b[j * b_dim1 + 1], &c__1) + dasum_(& i__2, &b[j + 1 + b_dim1], ldb);
/* L210: */
}
if (b[b_dim1 + 1] == 0. && b[b_dim1 + 2] == 0.)
{
b[b_dim1 + 1] = *eps3;
}
work[1] = 0.;
i1 = 1;
i2 = *n;
i3 = 1;
}
i__1 = *n;
for (its = 1;
its <= i__1;
++its)
{
scale = 1.;
vmax = 1.;
vcrit = *bignum;
/* Solve U*(xr,xi) = scale*(vr,vi) for a right eigenvector, */
/* or U**T*(xr,xi) = scale*(vr,vi) for a left eigenvector, */
/* overwriting (xr,xi) on (vr,vi). */
i__2 = i2;
i__3 = i3;
for (i__ = i1;
i__3 < 0 ? i__ >= i__2 : i__ <= i__2;
i__ += i__3)
{
if (work[i__] > vcrit)
{
rec = 1. / vmax;
dscal_(n, &rec, &vr[1], &c__1);
dscal_(n, &rec, &vi[1], &c__1);
scale *= rec;
vmax = 1.;
vcrit = *bignum;
}
xr = vr[i__];
xi = vi[i__];
if (*rightv)
{
i__4 = *n;
for (j = i__ + 1;
j <= i__4;
++j)
{
xr = xr - b[i__ + j * b_dim1] * vr[j] + b[j + 1 + i__ * b_dim1] * vi[j];
xi = xi - b[i__ + j * b_dim1] * vi[j] - b[j + 1 + i__ * b_dim1] * vr[j];
/* L220: */
}
}
else
{
i__4 = i__ - 1;
for (j = 1;
j <= i__4;
++j)
{
xr = xr - b[j + i__ * b_dim1] * vr[j] + b[i__ + 1 + j * b_dim1] * vi[j];
xi = xi - b[j + i__ * b_dim1] * vi[j] - b[i__ + 1 + j * b_dim1] * vr[j];
/* L230: */
}
}
w = (d__1 = b[i__ + i__ * b_dim1], abs(d__1)) + (d__2 = b[i__ + 1 + i__ * b_dim1], abs(d__2));
if (w > *smlnum)
{
if (w < 1.)
{
w1 = abs(xr) + abs(xi);
if (w1 > w * *bignum)
{
rec = 1. / w1;
dscal_(n, &rec, &vr[1], &c__1);
dscal_(n, &rec, &vi[1], &c__1);
xr = vr[i__];
xi = vi[i__];
scale *= rec;
vmax *= rec;
}
}
/* Divide by diagonal element of B. */
dladiv_(&xr, &xi, &b[i__ + i__ * b_dim1], &b[i__ + 1 + i__ * b_dim1], &vr[i__], &vi[i__]);
/* Computing MAX */
d__3 = (d__1 = vr[i__], abs(d__1)) + (d__2 = vi[i__], abs( d__2));
vmax = max(d__3,vmax);
vcrit = *bignum / vmax;
}
else
{
i__4 = *n;
for (j = 1;
j <= i__4;
++j)
{
vr[j] = 0.;
vi[j] = 0.;
/* L240: */
}
vr[i__] = 1.;
vi[i__] = 1.;
scale = 0.;
vmax = 1.;
vcrit = *bignum;
}
/* L250: */
}
/* Test for sufficient growth in the norm of (VR,VI). */
vnorm = dasum_(n, &vr[1], &c__1) + dasum_(n, &vi[1], &c__1);
if (vnorm >= growto * scale)
{
goto L280;
}
/* Choose a new orthogonal starting vector and try again. */
y = *eps3 / (rootn + 1.);
vr[1] = *eps3;
vi[1] = 0.;
i__3 = *n;
for (i__ = 2;
i__ <= i__3;
++i__)
{
vr[i__] = y;
vi[i__] = 0.;
/* L260: */
}
vr[*n - its + 1] -= *eps3 * rootn;
/* L270: */
}
/* Failure to find eigenvector in N iterations */
*info = 1;
L280: /* Normalize eigenvector. */
vnorm = 0.;
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
/* Computing MAX */
d__3 = vnorm;
d__4 = (d__1 = vr[i__], abs(d__1)) + (d__2 = vi[i__] , abs(d__2)); // , expr subst
vnorm = max(d__3,d__4);
/* L290: */
}
d__1 = 1. / vnorm;
dscal_(n, &d__1, &vr[1], &c__1);
d__1 = 1. / vnorm;
dscal_(n, &d__1, &vi[1], &c__1);
}
return 0;
/* End of DLAEIN */
}
/* Subroutine */ int dlaln2_(logical *ltrans, integer *na, integer *nw,
doublereal *smin, doublereal *ca, doublereal *a, integer *lda,
doublereal *d1, doublereal *d2, doublereal *b, integer *ldb,
doublereal *wr, doublereal *wi, doublereal *x, integer *ldx,
doublereal *scale, doublereal *xnorm, integer *info)
{
/* Initialized data */
static logical zswap[4] = { FALSE_,FALSE_,TRUE_,TRUE_ };
static logical rswap[4] = { FALSE_,TRUE_,FALSE_,TRUE_ };
static integer ipivot[16] /* was [4][4] */ = { 1,2,3,4,2,1,4,3,3,4,1,2,
4,3,2,1 };
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
static doublereal equiv_0[4], equiv_1[4];
/* Local variables */
static integer j;
#define ci (equiv_0)
#define cr (equiv_1)
static doublereal bi1, bi2, br1, br2, xi1, xi2, xr1, xr2, ci21, ci22,
cr21, cr22, li21, csi, ui11, lr21, ui12, ui22;
#define civ (equiv_0)
static doublereal csr, ur11, ur12, ur22;
#define crv (equiv_1)
static doublereal bbnd, cmax, ui11r, ui12s, temp, ur11r, ur12s, u22abs;
static integer icmax;
static doublereal bnorm, cnorm, smini;
extern doublereal dlamch_(char *, ftnlen);
extern /* Subroutine */ int dladiv_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *);
static doublereal bignum, smlnum;
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* October 31, 1992 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLALN2 solves a system of the form (ca A - w D ) X = s B */
/* or (ca A' - w D) X = s B with possible scaling ("s") and */
/* perturbation of A. (A' means A-transpose.) */
/* A is an NA x NA real matrix, ca is a real scalar, D is an NA x NA */
/* real diagonal matrix, w is a real or complex value, and X and B are */
/* NA x 1 matrices -- real if w is real, complex if w is complex. NA */
/* may be 1 or 2. */
/* If w is complex, X and B are represented as NA x 2 matrices, */
/* the first column of each being the real part and the second */
/* being the imaginary part. */
/* "s" is a scaling factor (.LE. 1), computed by DLALN2, which is */
/* so chosen that X can be computed without overflow. X is further */
/* scaled if necessary to assure that norm(ca A - w D)*norm(X) is less */
/* than overflow. */
/* If both singular values of (ca A - w D) are less than SMIN, */
/* SMIN*identity will be used instead of (ca A - w D). If only one */
/* singular value is less than SMIN, one element of (ca A - w D) will be */
/* perturbed enough to make the smallest singular value roughly SMIN. */
/* If both singular values are at least SMIN, (ca A - w D) will not be */
/* perturbed. In any case, the perturbation will be at most some small */
/* multiple of max( SMIN, ulp*norm(ca A - w D) ). The singular values */
/* are computed by infinity-norm approximations, and thus will only be */
/* correct to a factor of 2 or so. */
/* Note: all input quantities are assumed to be smaller than overflow */
/* by a reasonable factor. (See BIGNUM.) */
/* Arguments */
/* ========== */
/* LTRANS (input) LOGICAL */
/* =.TRUE.: A-transpose will be used. */
/* =.FALSE.: A will be used (not transposed.) */
/* NA (input) INTEGER */
/* The size of the matrix A. It may (only) be 1 or 2. */
/* NW (input) INTEGER */
/* 1 if "w" is real, 2 if "w" is complex. It may only be 1 */
/* or 2. */
/* SMIN (input) DOUBLE PRECISION */
/* The desired lower bound on the singular values of A. This */
/* should be a safe distance away from underflow or overflow, */
/* say, between (underflow/machine precision) and (machine */
/* precision * overflow ). (See BIGNUM and ULP.) */
/* CA (input) DOUBLE PRECISION */
/* The coefficient c, which A is multiplied by. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,NA) */
/* The NA x NA matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of A. It must be at least NA. */
/* D1 (input) DOUBLE PRECISION */
/* The 1,1 element in the diagonal matrix D. */
/* D2 (input) DOUBLE PRECISION */
/* The 2,2 element in the diagonal matrix D. Not used if NW=1. */
/* B (input) DOUBLE PRECISION array, dimension (LDB,NW) */
/* The NA x NW matrix B (right-hand side). If NW=2 ("w" is */
/* complex), column 1 contains the real part of B and column 2 */
/* contains the imaginary part. */
/* LDB (input) INTEGER */
/* The leading dimension of B. It must be at least NA. */
/* WR (input) DOUBLE PRECISION */
/* The real part of the scalar "w". */
/* WI (input) DOUBLE PRECISION */
/* The imaginary part of the scalar "w". Not used if NW=1. */
/* X (output) DOUBLE PRECISION array, dimension (LDX,NW) */
/* The NA x NW matrix X (unknowns), as computed by DLALN2. */
/* If NW=2 ("w" is complex), on exit, column 1 will contain */
/* the real part of X and column 2 will contain the imaginary */
/* part. */
/* LDX (input) INTEGER */
/* The leading dimension of X. It must be at least NA. */
/* SCALE (output) DOUBLE PRECISION */
/* The scale factor that B must be multiplied by to insure */
/* that overflow does not occur when computing X. Thus, */
/* (ca A - w D) X will be SCALE*B, not B (ignoring */
/* perturbations of A.) It will be at most 1. */
/* XNORM (output) DOUBLE PRECISION */
/* The infinity-norm of X, when X is regarded as an NA x NW */
/* real matrix. */
/* INFO (output) INTEGER */
/* An error flag. It will be set to zero if no error occurs, */
/* a negative number if an argument is in error, or a positive */
/* number if ca A - w D had to be perturbed. */
/* The possible values are: */
/* = 0: No error occurred, and (ca A - w D) did not have to be */
/* perturbed. */
/* = 1: (ca A - w D) had to be perturbed to make its smallest */
/* (or only) singular value greater than SMIN. */
/* NOTE: In the interests of speed, this routine does not */
/* check the inputs for errors. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Equivalences .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Compute BIGNUM */
smlnum = 2. * dlamch_("Safe minimum", (ftnlen)12);
bignum = 1. / smlnum;
smini = max(*smin,smlnum);
/* Don't check for input errors */
*info = 0;
/* Standard Initializations */
*scale = 1.;
if (*na == 1) {
/* 1 x 1 (i.e., scalar) system C X = B */
if (*nw == 1) {
/* Real 1x1 system. */
/* C = ca A - w D */
csr = *ca * a[a_dim1 + 1] - *wr * *d1;
cnorm = abs(csr);
/* If | C | < SMINI, use C = SMINI */
if (cnorm < smini) {
csr = smini;
cnorm = smini;
*info = 1;
}
/* Check scaling for X = B / C */
bnorm = (d__1 = b[b_dim1 + 1], abs(d__1));
if (cnorm < 1. && bnorm > 1.) {
if (bnorm > bignum * cnorm) {
*scale = 1. / bnorm;
}
}
/* Compute X */
x[x_dim1 + 1] = b[b_dim1 + 1] * *scale / csr;
*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1));
} else {
/* Complex 1x1 system (w is complex) */
/* C = ca A - w D */
csr = *ca * a[a_dim1 + 1] - *wr * *d1;
csi = -(*wi) * *d1;
cnorm = abs(csr) + abs(csi);
/* If | C | < SMINI, use C = SMINI */
if (cnorm < smini) {
csr = smini;
csi = 0.;
cnorm = smini;
*info = 1;
}
/* Check scaling for X = B / C */
bnorm = (d__1 = b[b_dim1 + 1], abs(d__1)) + (d__2 = b[(b_dim1 <<
1) + 1], abs(d__2));
if (cnorm < 1. && bnorm > 1.) {
if (bnorm > bignum * cnorm) {
*scale = 1. / bnorm;
}
}
/* Compute X */
d__1 = *scale * b[b_dim1 + 1];
d__2 = *scale * b[(b_dim1 << 1) + 1];
dladiv_(&d__1, &d__2, &csr, &csi, &x[x_dim1 + 1], &x[(x_dim1 << 1)
+ 1]);
*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1)) + (d__2 = x[(x_dim1 <<
1) + 1], abs(d__2));
}
} else {
/* 2x2 System */
/* Compute the real part of C = ca A - w D (or ca A' - w D ) */
cr[0] = *ca * a[a_dim1 + 1] - *wr * *d1;
cr[3] = *ca * a[(a_dim1 << 1) + 2] - *wr * *d2;
if (*ltrans) {
cr[2] = *ca * a[a_dim1 + 2];
cr[1] = *ca * a[(a_dim1 << 1) + 1];
} else {
cr[1] = *ca * a[a_dim1 + 2];
cr[2] = *ca * a[(a_dim1 << 1) + 1];
}
if (*nw == 1) {
/* Real 2x2 system (w is real) */
/* Find the largest element in C */
cmax = 0.;
icmax = 0;
for (j = 1; j <= 4; ++j) {
if ((d__1 = crv[j - 1], abs(d__1)) > cmax) {
cmax = (d__1 = crv[j - 1], abs(d__1));
icmax = j;
}
/* L10: */
}
/* If norm(C) < SMINI, use SMINI*identity. */
if (cmax < smini) {
/* Computing MAX */
d__3 = (d__1 = b[b_dim1 + 1], abs(d__1)), d__4 = (d__2 = b[
b_dim1 + 2], abs(d__2));
bnorm = max(d__3,d__4);
if (smini < 1. && bnorm > 1.) {
if (bnorm > bignum * smini) {
*scale = 1. / bnorm;
}
}
temp = *scale / smini;
x[x_dim1 + 1] = temp * b[b_dim1 + 1];
x[x_dim1 + 2] = temp * b[b_dim1 + 2];
*xnorm = temp * bnorm;
*info = 1;
return 0;
}
/* Gaussian elimination with complete pivoting. */
ur11 = crv[icmax - 1];
cr21 = crv[ipivot[(icmax << 2) - 3] - 1];
ur12 = crv[ipivot[(icmax << 2) - 2] - 1];
cr22 = crv[ipivot[(icmax << 2) - 1] - 1];
ur11r = 1. / ur11;
lr21 = ur11r * cr21;
ur22 = cr22 - ur12 * lr21;
/* If smaller pivot < SMINI, use SMINI */
if (abs(ur22) < smini) {
ur22 = smini;
*info = 1;
}
if (rswap[icmax - 1]) {
br1 = b[b_dim1 + 2];
br2 = b[b_dim1 + 1];
} else {
br1 = b[b_dim1 + 1];
br2 = b[b_dim1 + 2];
}
br2 -= lr21 * br1;
/* Computing MAX */
d__2 = (d__1 = br1 * (ur22 * ur11r), abs(d__1)), d__3 = abs(br2);
bbnd = max(d__2,d__3);
if (bbnd > 1. && abs(ur22) < 1.) {
if (bbnd >= bignum * abs(ur22)) {
*scale = 1. / bbnd;
}
}
xr2 = br2 * *scale / ur22;
xr1 = *scale * br1 * ur11r - xr2 * (ur11r * ur12);
if (zswap[icmax - 1]) {
x[x_dim1 + 1] = xr2;
x[x_dim1 + 2] = xr1;
} else {
x[x_dim1 + 1] = xr1;
x[x_dim1 + 2] = xr2;
}
/* Computing MAX */
d__1 = abs(xr1), d__2 = abs(xr2);
*xnorm = max(d__1,d__2);
/* Further scaling if norm(A) norm(X) > overflow */
if (*xnorm > 1. && cmax > 1.) {
if (*xnorm > bignum / cmax) {
temp = cmax / bignum;
x[x_dim1 + 1] = temp * x[x_dim1 + 1];
x[x_dim1 + 2] = temp * x[x_dim1 + 2];
*xnorm = temp * *xnorm;
*scale = temp * *scale;
}
}
} else {
/* Complex 2x2 system (w is complex) */
/* Find the largest element in C */
ci[0] = -(*wi) * *d1;
ci[1] = 0.;
ci[2] = 0.;
ci[3] = -(*wi) * *d2;
cmax = 0.;
icmax = 0;
for (j = 1; j <= 4; ++j) {
if ((d__1 = crv[j - 1], abs(d__1)) + (d__2 = civ[j - 1], abs(
d__2)) > cmax) {
cmax = (d__1 = crv[j - 1], abs(d__1)) + (d__2 = civ[j - 1]
, abs(d__2));
icmax = j;
}
/* L20: */
}
/* If norm(C) < SMINI, use SMINI*identity. */
if (cmax < smini) {
/* Computing MAX */
d__5 = (d__1 = b[b_dim1 + 1], abs(d__1)) + (d__2 = b[(b_dim1
<< 1) + 1], abs(d__2)), d__6 = (d__3 = b[b_dim1 + 2],
abs(d__3)) + (d__4 = b[(b_dim1 << 1) + 2], abs(d__4));
bnorm = max(d__5,d__6);
if (smini < 1. && bnorm > 1.) {
if (bnorm > bignum * smini) {
*scale = 1. / bnorm;
}
}
temp = *scale / smini;
x[x_dim1 + 1] = temp * b[b_dim1 + 1];
x[x_dim1 + 2] = temp * b[b_dim1 + 2];
x[(x_dim1 << 1) + 1] = temp * b[(b_dim1 << 1) + 1];
x[(x_dim1 << 1) + 2] = temp * b[(b_dim1 << 1) + 2];
*xnorm = temp * bnorm;
*info = 1;
return 0;
}
/* Gaussian elimination with complete pivoting. */
ur11 = crv[icmax - 1];
ui11 = civ[icmax - 1];
cr21 = crv[ipivot[(icmax << 2) - 3] - 1];
ci21 = civ[ipivot[(icmax << 2) - 3] - 1];
ur12 = crv[ipivot[(icmax << 2) - 2] - 1];
ui12 = civ[ipivot[(icmax << 2) - 2] - 1];
cr22 = crv[ipivot[(icmax << 2) - 1] - 1];
ci22 = civ[ipivot[(icmax << 2) - 1] - 1];
if (icmax == 1 || icmax == 4) {
/* Code when off-diagonals of pivoted C are real */
if (abs(ur11) > abs(ui11)) {
temp = ui11 / ur11;
/* Computing 2nd power */
d__1 = temp;
ur11r = 1. / (ur11 * (d__1 * d__1 + 1.));
ui11r = -temp * ur11r;
} else {
temp = ur11 / ui11;
/* Computing 2nd power */
d__1 = temp;
ui11r = -1. / (ui11 * (d__1 * d__1 + 1.));
ur11r = -temp * ui11r;
}
lr21 = cr21 * ur11r;
li21 = cr21 * ui11r;
ur12s = ur12 * ur11r;
ui12s = ur12 * ui11r;
ur22 = cr22 - ur12 * lr21;
ui22 = ci22 - ur12 * li21;
} else {
/* Code when diagonals of pivoted C are real */
ur11r = 1. / ur11;
ui11r = 0.;
lr21 = cr21 * ur11r;
li21 = ci21 * ur11r;
ur12s = ur12 * ur11r;
ui12s = ui12 * ur11r;
ur22 = cr22 - ur12 * lr21 + ui12 * li21;
ui22 = -ur12 * li21 - ui12 * lr21;
}
u22abs = abs(ur22) + abs(ui22);
/* If smaller pivot < SMINI, use SMINI */
if (u22abs < smini) {
ur22 = smini;
ui22 = 0.;
*info = 1;
}
if (rswap[icmax - 1]) {
br2 = b[b_dim1 + 1];
br1 = b[b_dim1 + 2];
bi2 = b[(b_dim1 << 1) + 1];
bi1 = b[(b_dim1 << 1) + 2];
} else {
br1 = b[b_dim1 + 1];
br2 = b[b_dim1 + 2];
bi1 = b[(b_dim1 << 1) + 1];
bi2 = b[(b_dim1 << 1) + 2];
}
br2 = br2 - lr21 * br1 + li21 * bi1;
bi2 = bi2 - li21 * br1 - lr21 * bi1;
/* Computing MAX */
d__1 = (abs(br1) + abs(bi1)) * (u22abs * (abs(ur11r) + abs(ui11r))
), d__2 = abs(br2) + abs(bi2);
bbnd = max(d__1,d__2);
if (bbnd > 1. && u22abs < 1.) {
if (bbnd >= bignum * u22abs) {
*scale = 1. / bbnd;
br1 = *scale * br1;
bi1 = *scale * bi1;
br2 = *scale * br2;
bi2 = *scale * bi2;
}
}
dladiv_(&br2, &bi2, &ur22, &ui22, &xr2, &xi2);
xr1 = ur11r * br1 - ui11r * bi1 - ur12s * xr2 + ui12s * xi2;
xi1 = ui11r * br1 + ur11r * bi1 - ui12s * xr2 - ur12s * xi2;
if (zswap[icmax - 1]) {
x[x_dim1 + 1] = xr2;
x[x_dim1 + 2] = xr1;
x[(x_dim1 << 1) + 1] = xi2;
x[(x_dim1 << 1) + 2] = xi1;
} else {
x[x_dim1 + 1] = xr1;
x[x_dim1 + 2] = xr2;
x[(x_dim1 << 1) + 1] = xi1;
x[(x_dim1 << 1) + 2] = xi2;
}
/* Computing MAX */
d__1 = abs(xr1) + abs(xi1), d__2 = abs(xr2) + abs(xi2);
*xnorm = max(d__1,d__2);
/* Further scaling if norm(A) norm(X) > overflow */
if (*xnorm > 1. && cmax > 1.) {
if (*xnorm > bignum / cmax) {
temp = cmax / bignum;
x[x_dim1 + 1] = temp * x[x_dim1 + 1];
x[x_dim1 + 2] = temp * x[x_dim1 + 2];
x[(x_dim1 << 1) + 1] = temp * x[(x_dim1 << 1) + 1];
x[(x_dim1 << 1) + 2] = temp * x[(x_dim1 << 1) + 2];
*xnorm = temp * *xnorm;
*scale = temp * *scale;
}
}
}
}
return 0;
/* End of DLALN2 */
} /* dlaln2_ */
/*< DOUBLE COMPLEX FUNCTION ZLADIV( X, Y ) >*/
/* Double Complex */ VOID zladiv_(doublecomplex * ret_val, doublecomplex *x,
doublecomplex *y)
{
/* System generated locals */
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
doublereal zi, zr;
extern /* Subroutine */ int dladiv_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* October 31, 1992 */
/* .. Scalar Arguments .. */
/*< COMPLEX*16 X, Y >*/
/* .. */
/* Purpose */
/* ======= */
/* ZLADIV := X / Y, where X and Y are complex. The computation of X / Y */
/* will not overflow on an intermediary step unless the results */
/* overflows. */
/* Arguments */
/* ========= */
/* X (input) COMPLEX*16 */
/* Y (input) COMPLEX*16 */
/* The complex scalars X and Y. */
/* ===================================================================== */
/* .. Local Scalars .. */
/*< DOUBLE PRECISION ZI, ZR >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DLADIV >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC DBLE, DCMPLX, DIMAG >*/
/* .. */
/* .. Executable Statements .. */
/*< >*/
d__1 = x->r;
d__2 = d_imag(x);
d__3 = y->r;
d__4 = d_imag(y);
dladiv_(&d__1, &d__2, &d__3, &d__4, &zr, &zi);
/*< ZLADIV = DCMPLX( ZR, ZI ) >*/
z__1.r = zr, z__1.i = zi;
ret_val->r = z__1.r, ret_val->i = z__1.i;
/*< RETURN >*/
return ;
/* End of ZLADIV */
/*< END >*/
} /* zladiv_ */
/* Subroutine */ int dlaqtr_(logical *ltran, logical *lreal, integer *n,
doublereal *t, integer *ldt, doublereal *b, doublereal *w, doublereal
*scale, doublereal *x, doublereal *work, integer *info)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
DLAQTR solves the real quasi-triangular system
op(T)*p = scale*c, if LREAL = .TRUE.
or the complex quasi-triangular systems
op(T + iB)*(p+iq) = scale*(c+id), if LREAL = .FALSE.
in real arithmetic, where T is upper quasi-triangular.
If LREAL = .FALSE., then the first diagonal block of T must be
1 by 1, B is the specially structured matrix
B = [ b(1) b(2) ... b(n) ]
[ w ]
[ w ]
[ . ]
[ w ]
op(A) = A or A', A' denotes the conjugate transpose of
matrix A.
On input, X = [ c ]. On output, X = [ p ].
[ d ] [ q ]
This subroutine is designed for the condition number estimation
in routine DTRSNA.
Arguments
=========
LTRAN (input) LOGICAL
On entry, LTRAN specifies the option of conjugate transpose:
= .FALSE., op(T+i*B) = T+i*B,
= .TRUE., op(T+i*B) = (T+i*B)'.
LREAL (input) LOGICAL
On entry, LREAL specifies the input matrix structure:
= .FALSE., the input is complex
= .TRUE., the input is real
N (input) INTEGER
On entry, N specifies the order of T+i*B. N >= 0.
T (input) DOUBLE PRECISION array, dimension (LDT,N)
On entry, T contains a matrix in Schur canonical form.
If LREAL = .FALSE., then the first diagonal block of T mu
be 1 by 1.
LDT (input) INTEGER
The leading dimension of the matrix T. LDT >= max(1,N).
B (input) DOUBLE PRECISION array, dimension (N)
On entry, B contains the elements to form the matrix
B as described above.
If LREAL = .TRUE., B is not referenced.
W (input) DOUBLE PRECISION
On entry, W is the diagonal element of the matrix B.
If LREAL = .TRUE., W is not referenced.
SCALE (output) DOUBLE PRECISION
On exit, SCALE is the scale factor.
X (input/output) DOUBLE PRECISION array, dimension (2*N)
On entry, X contains the right hand side of the system.
On exit, X is overwritten by the solution.
WORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
On exit, INFO is set to
0: successful exit.
1: the some diagonal 1 by 1 block has been perturbed by
a small number SMIN to keep nonsingularity.
2: the some diagonal 2 by 2 block has been perturbed by
a small number in DLALN2 to keep nonsingularity.
NOTE: In the interests of speed, this routine does not
check the inputs for errors.
=====================================================================
Do not test the input parameters for errors
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static logical c_false = FALSE_;
static integer c__2 = 2;
static doublereal c_b21 = 1.;
static doublereal c_b25 = 0.;
static logical c_true = TRUE_;
/* System generated locals */
integer t_dim1, t_offset, i__1, i__2;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
/* Local variables */
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static integer ierr;
static doublereal smin, xmax, d__[4] /* was [2][2] */;
static integer i__, j, k;
static doublereal v[4] /* was [2][2] */, z__;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern doublereal dasum_(integer *, doublereal *, integer *);
extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
static integer jnext, j1, j2;
static doublereal sminw;
static integer n1, n2;
static doublereal xnorm;
extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *
, doublereal *, integer *, doublereal *, doublereal *, integer *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
static doublereal si, xj;
extern integer idamax_(integer *, doublereal *, integer *);
static doublereal scaloc, sr;
extern /* Subroutine */ int dladiv_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *);
static doublereal bignum;
static logical notran;
static doublereal smlnum, rec, eps, tjj, tmp;
#define d___ref(a_1,a_2) d__[(a_2)*2 + a_1 - 3]
#define t_ref(a_1,a_2) t[(a_2)*t_dim1 + a_1]
#define v_ref(a_1,a_2) v[(a_2)*2 + a_1 - 3]
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
--b;
--x;
--work;
/* Function Body */
notran = ! (*ltran);
*info = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Set constants to control overflow */
eps = dlamch_("P");
smlnum = dlamch_("S") / eps;
bignum = 1. / smlnum;
xnorm = dlange_("M", n, n, &t[t_offset], ldt, d__);
if (! (*lreal)) {
/* Computing MAX */
d__1 = xnorm, d__2 = abs(*w), d__1 = max(d__1,d__2), d__2 = dlange_(
"M", n, &c__1, &b[1], n, d__);
xnorm = max(d__1,d__2);
}
/* Computing MAX */
d__1 = smlnum, d__2 = eps * xnorm;
smin = max(d__1,d__2);
/* Compute 1-norm of each column of strictly upper triangular
part of T to control overflow in triangular solver. */
work[1] = 0.;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
work[j] = dasum_(&i__2, &t_ref(1, j), &c__1);
/* L10: */
}
if (! (*lreal)) {
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
work[i__] += (d__1 = b[i__], abs(d__1));
/* L20: */
}
}
n2 = *n << 1;
n1 = *n;
if (! (*lreal)) {
n1 = n2;
}
k = idamax_(&n1, &x[1], &c__1);
xmax = (d__1 = x[k], abs(d__1));
*scale = 1.;
if (xmax > bignum) {
*scale = bignum / xmax;
dscal_(&n1, scale, &x[1], &c__1);
xmax = bignum;
}
if (*lreal) {
if (notran) {
/* Solve T*p = scale*c */
jnext = *n;
for (j = *n; j >= 1; --j) {
if (j > jnext) {
goto L30;
}
j1 = j;
j2 = j;
jnext = j - 1;
if (j > 1) {
if (t_ref(j, j - 1) != 0.) {
j1 = j - 1;
jnext = j - 2;
}
}
if (j1 == j2) {
/* Meet 1 by 1 diagonal block
Scale to avoid overflow when computing
x(j) = b(j)/T(j,j) */
xj = (d__1 = x[j1], abs(d__1));
tjj = (d__1 = t_ref(j1, j1), abs(d__1));
tmp = t_ref(j1, j1);
if (tjj < smin) {
tmp = smin;
tjj = smin;
*info = 1;
}
if (xj == 0.) {
goto L30;
}
if (tjj < 1.) {
if (xj > bignum * tjj) {
rec = 1. / xj;
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
x[j1] /= tmp;
xj = (d__1 = x[j1], abs(d__1));
/* Scale x if necessary to avoid overflow when adding a
multiple of column j1 of T. */
if (xj > 1.) {
rec = 1. / xj;
if (work[j1] > (bignum - xmax) * rec) {
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
}
if (j1 > 1) {
i__1 = j1 - 1;
d__1 = -x[j1];
daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[1], &
c__1);
i__1 = j1 - 1;
k = idamax_(&i__1, &x[1], &c__1);
xmax = (d__1 = x[k], abs(d__1));
}
} else {
/* Meet 2 by 2 diagonal block
Call 2 by 2 linear system solve, to take
care of possible overflow by scaling factor. */
d___ref(1, 1) = x[j1];
d___ref(2, 1) = x[j2];
dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b21, &t_ref(j1,
j1), ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, &
c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.) {
dscal_(n, &scaloc, &x[1], &c__1);
*scale *= scaloc;
}
x[j1] = v_ref(1, 1);
x[j2] = v_ref(2, 1);
/* Scale V(1,1) (= X(J1)) and/or V(2,1) (=X(J2))
to avoid overflow in updating right-hand side.
Computing MAX */
d__3 = (d__1 = v_ref(1, 1), abs(d__1)), d__4 = (d__2 =
v_ref(2, 1), abs(d__2));
xj = max(d__3,d__4);
if (xj > 1.) {
rec = 1. / xj;
/* Computing MAX */
d__1 = work[j1], d__2 = work[j2];
if (max(d__1,d__2) > (bignum - xmax) * rec) {
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
}
/* Update right-hand side */
if (j1 > 1) {
i__1 = j1 - 1;
d__1 = -x[j1];
daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[1], &
c__1);
i__1 = j1 - 1;
d__1 = -x[j2];
daxpy_(&i__1, &d__1, &t_ref(1, j2), &c__1, &x[1], &
c__1);
i__1 = j1 - 1;
k = idamax_(&i__1, &x[1], &c__1);
xmax = (d__1 = x[k], abs(d__1));
}
}
L30:
;
}
} else {
/* Solve T'*p = scale*c */
jnext = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < jnext) {
goto L40;
}
j1 = j;
j2 = j;
jnext = j + 1;
if (j < *n) {
if (t_ref(j + 1, j) != 0.) {
j2 = j + 1;
jnext = j + 2;
}
}
if (j1 == j2) {
/* 1 by 1 diagonal block
Scale if necessary to avoid overflow in forming the
right-hand side element by inner product. */
xj = (d__1 = x[j1], abs(d__1));
if (xmax > 1.) {
rec = 1. / xmax;
if (work[j1] > (bignum - xj) * rec) {
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
x[j1] -= ddot_(&i__2, &t_ref(1, j1), &c__1, &x[1], &c__1);
xj = (d__1 = x[j1], abs(d__1));
tjj = (d__1 = t_ref(j1, j1), abs(d__1));
tmp = t_ref(j1, j1);
if (tjj < smin) {
tmp = smin;
tjj = smin;
*info = 1;
}
if (tjj < 1.) {
if (xj > bignum * tjj) {
rec = 1. / xj;
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
x[j1] /= tmp;
/* Computing MAX */
d__2 = xmax, d__3 = (d__1 = x[j1], abs(d__1));
xmax = max(d__2,d__3);
} else {
/* 2 by 2 diagonal block
Scale if necessary to avoid overflow in forming the
right-hand side elements by inner product.
Computing MAX */
d__3 = (d__1 = x[j1], abs(d__1)), d__4 = (d__2 = x[j2],
abs(d__2));
xj = max(d__3,d__4);
if (xmax > 1.) {
rec = 1. / xmax;
/* Computing MAX */
d__1 = work[j2], d__2 = work[j1];
if (max(d__1,d__2) > (bignum - xj) * rec) {
dscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
d___ref(1, 1) = x[j1] - ddot_(&i__2, &t_ref(1, j1), &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d___ref(2, 1) = x[j2] - ddot_(&i__2, &t_ref(1, j2), &c__1,
&x[1], &c__1);
dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b21, &t_ref(j1,
j1), ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, &
c_b25, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.) {
dscal_(n, &scaloc, &x[1], &c__1);
*scale *= scaloc;
}
x[j1] = v_ref(1, 1);
x[j2] = v_ref(2, 1);
/* Computing MAX */
d__3 = (d__1 = x[j1], abs(d__1)), d__4 = (d__2 = x[j2],
abs(d__2)), d__3 = max(d__3,d__4);
xmax = max(d__3,xmax);
}
L40:
;
}
}
} else {
/* Computing MAX */
d__1 = eps * abs(*w);
sminw = max(d__1,smin);
if (notran) {
/* Solve (T + iB)*(p+iq) = c+id */
jnext = *n;
for (j = *n; j >= 1; --j) {
if (j > jnext) {
goto L70;
}
j1 = j;
j2 = j;
jnext = j - 1;
if (j > 1) {
if (t_ref(j, j - 1) != 0.) {
j1 = j - 1;
jnext = j - 2;
}
}
if (j1 == j2) {
/* 1 by 1 diagonal block
Scale if necessary to avoid overflow in division */
z__ = *w;
if (j1 == 1) {
z__ = b[1];
}
xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], abs(
d__2));
tjj = (d__1 = t_ref(j1, j1), abs(d__1)) + abs(z__);
tmp = t_ref(j1, j1);
if (tjj < sminw) {
tmp = sminw;
tjj = sminw;
*info = 1;
}
if (xj == 0.) {
goto L70;
}
if (tjj < 1.) {
if (xj > bignum * tjj) {
rec = 1. / xj;
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
dladiv_(&x[j1], &x[*n + j1], &tmp, &z__, &sr, &si);
x[j1] = sr;
x[*n + j1] = si;
xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1], abs(
d__2));
/* Scale x if necessary to avoid overflow when adding a
multiple of column j1 of T. */
if (xj > 1.) {
rec = 1. / xj;
if (work[j1] > (bignum - xmax) * rec) {
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
}
}
if (j1 > 1) {
i__1 = j1 - 1;
d__1 = -x[j1];
daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[1], &
c__1);
i__1 = j1 - 1;
d__1 = -x[*n + j1];
daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[*n + 1],
&c__1);
x[1] += b[j1] * x[*n + j1];
x[*n + 1] -= b[j1] * x[j1];
xmax = 0.;
i__1 = j1 - 1;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
d__3 = xmax, d__4 = (d__1 = x[k], abs(d__1)) + (
d__2 = x[k + *n], abs(d__2));
xmax = max(d__3,d__4);
/* L50: */
}
}
} else {
/* Meet 2 by 2 diagonal block */
d___ref(1, 1) = x[j1];
d___ref(2, 1) = x[j2];
d___ref(1, 2) = x[*n + j1];
d___ref(2, 2) = x[*n + j2];
d__1 = -(*w);
dlaln2_(&c_false, &c__2, &c__2, &sminw, &c_b21, &t_ref(j1,
j1), ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, &
d__1, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.) {
i__1 = *n << 1;
dscal_(&i__1, &scaloc, &x[1], &c__1);
*scale = scaloc * *scale;
}
x[j1] = v_ref(1, 1);
x[j2] = v_ref(2, 1);
x[*n + j1] = v_ref(1, 2);
x[*n + j2] = v_ref(2, 2);
/* Scale X(J1), .... to avoid overflow in
updating right hand side.
Computing MAX */
d__5 = (d__1 = v_ref(1, 1), abs(d__1)) + (d__2 = v_ref(1,
2), abs(d__2)), d__6 = (d__3 = v_ref(2, 1), abs(
d__3)) + (d__4 = v_ref(2, 2), abs(d__4));
xj = max(d__5,d__6);
if (xj > 1.) {
rec = 1. / xj;
/* Computing MAX */
d__1 = work[j1], d__2 = work[j2];
if (max(d__1,d__2) > (bignum - xmax) * rec) {
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
}
}
/* Update the right-hand side. */
if (j1 > 1) {
i__1 = j1 - 1;
d__1 = -x[j1];
daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[1], &
c__1);
i__1 = j1 - 1;
d__1 = -x[j2];
daxpy_(&i__1, &d__1, &t_ref(1, j2), &c__1, &x[1], &
c__1);
i__1 = j1 - 1;
d__1 = -x[*n + j1];
daxpy_(&i__1, &d__1, &t_ref(1, j1), &c__1, &x[*n + 1],
&c__1);
i__1 = j1 - 1;
d__1 = -x[*n + j2];
daxpy_(&i__1, &d__1, &t_ref(1, j2), &c__1, &x[*n + 1],
&c__1);
x[1] = x[1] + b[j1] * x[*n + j1] + b[j2] * x[*n + j2];
x[*n + 1] = x[*n + 1] - b[j1] * x[j1] - b[j2] * x[j2];
xmax = 0.;
i__1 = j1 - 1;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
d__3 = (d__1 = x[k], abs(d__1)) + (d__2 = x[k + *
n], abs(d__2));
xmax = max(d__3,xmax);
/* L60: */
}
}
}
L70:
;
}
} else {
/* Solve (T + iB)'*(p+iq) = c+id */
jnext = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (j < jnext) {
goto L80;
}
j1 = j;
j2 = j;
jnext = j + 1;
if (j < *n) {
if (t_ref(j + 1, j) != 0.) {
j2 = j + 1;
jnext = j + 2;
}
}
if (j1 == j2) {
/* 1 by 1 diagonal block
Scale if necessary to avoid overflow in forming the
right-hand side element by inner product. */
xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], abs(
d__2));
if (xmax > 1.) {
rec = 1. / xmax;
if (work[j1] > (bignum - xj) * rec) {
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
x[j1] -= ddot_(&i__2, &t_ref(1, j1), &c__1, &x[1], &c__1);
i__2 = j1 - 1;
x[*n + j1] -= ddot_(&i__2, &t_ref(1, j1), &c__1, &x[*n +
1], &c__1);
if (j1 > 1) {
x[j1] -= b[j1] * x[*n + 1];
x[*n + j1] += b[j1] * x[1];
}
xj = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n], abs(
d__2));
z__ = *w;
if (j1 == 1) {
z__ = b[1];
}
/* Scale if necessary to avoid overflow in
complex division */
tjj = (d__1 = t_ref(j1, j1), abs(d__1)) + abs(z__);
tmp = t_ref(j1, j1);
if (tjj < sminw) {
tmp = sminw;
tjj = sminw;
*info = 1;
}
if (tjj < 1.) {
if (xj > bignum * tjj) {
rec = 1. / xj;
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
d__1 = -z__;
dladiv_(&x[j1], &x[*n + j1], &tmp, &d__1, &sr, &si);
x[j1] = sr;
x[j1 + *n] = si;
/* Computing MAX */
d__3 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[j1 + *n],
abs(d__2));
xmax = max(d__3,xmax);
} else {
/* 2 by 2 diagonal block
Scale if necessary to avoid overflow in forming the
right-hand side element by inner product.
Computing MAX */
d__5 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1],
abs(d__2)), d__6 = (d__3 = x[j2], abs(d__3)) + (
d__4 = x[*n + j2], abs(d__4));
xj = max(d__5,d__6);
if (xmax > 1.) {
rec = 1. / xmax;
/* Computing MAX */
d__1 = work[j1], d__2 = work[j2];
if (max(d__1,d__2) > (bignum - xj) / xmax) {
dscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
d___ref(1, 1) = x[j1] - ddot_(&i__2, &t_ref(1, j1), &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d___ref(2, 1) = x[j2] - ddot_(&i__2, &t_ref(1, j2), &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d___ref(1, 2) = x[*n + j1] - ddot_(&i__2, &t_ref(1, j1), &
c__1, &x[*n + 1], &c__1);
i__2 = j1 - 1;
d___ref(2, 2) = x[*n + j2] - ddot_(&i__2, &t_ref(1, j2), &
c__1, &x[*n + 1], &c__1);
d___ref(1, 1) = d___ref(1, 1) - b[j1] * x[*n + 1];
d___ref(2, 1) = d___ref(2, 1) - b[j2] * x[*n + 1];
d___ref(1, 2) = d___ref(1, 2) + b[j1] * x[1];
d___ref(2, 2) = d___ref(2, 2) + b[j2] * x[1];
dlaln2_(&c_true, &c__2, &c__2, &sminw, &c_b21, &t_ref(j1,
j1), ldt, &c_b21, &c_b21, d__, &c__2, &c_b25, w,
v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.) {
dscal_(&n2, &scaloc, &x[1], &c__1);
*scale = scaloc * *scale;
}
x[j1] = v_ref(1, 1);
x[j2] = v_ref(2, 1);
x[*n + j1] = v_ref(1, 2);
x[*n + j2] = v_ref(2, 2);
/* Computing MAX */
d__5 = (d__1 = x[j1], abs(d__1)) + (d__2 = x[*n + j1],
abs(d__2)), d__6 = (d__3 = x[j2], abs(d__3)) + (
d__4 = x[*n + j2], abs(d__4)), d__5 = max(d__5,
d__6);
xmax = max(d__5,xmax);
}
L80:
;
}
}
}
return 0;
/* End of DLAQTR */
} /* dlaqtr_ */
