/* Subroutine */ int slaqtr_(logical *ltran, logical *lreal, integer *n, real
*t, integer *ldt, real *b, real *w, real *scale, real *x, real *work,
integer *info)
{
/* System generated locals */
integer t_dim1, t_offset, i__1, i__2;
real r__1, r__2, r__3, r__4, r__5, r__6;
/* Local variables */
real d__[4] /* was [2][2] */;
integer i__, j, k;
real v[4] /* was [2][2] */, z__;
integer j1, j2, n1, n2;
real si, xj, sr, rec, eps, tjj, tmp;
integer ierr;
real smin;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
real xmax;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
integer jnext;
extern doublereal sasum_(integer *, real *, integer *);
real sminw, xnorm;
extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
real *, integer *), slaln2_(logical *, integer *, integer *, real
*, real *, real *, integer *, real *, real *, real *, integer *,
real *, real *, real *, integer *, real *, real *, integer *);
real scaloc;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
real bignum;
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */ int sladiv_(real *, real *, real *, real *, real *
, real *);
logical notran;
real smlnum;
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAQTR 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 STRSNA. */
/* 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) REAL array, dimension (LDT,N) */
/* On entry, T contains a matrix in Schur canonical form. */
/* If LREAL = .FALSE., then the first diagonal block of T must */
/* be 1 by 1. */
/* LDT (input) INTEGER */
/* The leading dimension of the matrix T. LDT >= max(1,N). */
/* B (input) REAL 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) REAL */
/* On entry, W is the diagonal element of the matrix B. */
/* If LREAL = .TRUE., W is not referenced. */
/* SCALE (output) REAL */
/* On exit, SCALE is the scale factor. */
/* X (input/output) REAL 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) REAL 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 SLALN2 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 = slamch_("P");
smlnum = slamch_("S") / eps;
bignum = 1.f / smlnum;
xnorm = slange_("M", n, n, &t[t_offset], ldt, d__);
if (! (*lreal)) {
/* Computing MAX */
r__1 = xnorm, r__2 = dabs(*w), r__1 = max(r__1,r__2), r__2 = slange_(
"M", n, &c__1, &b[1], n, d__);
xnorm = dmax(r__1,r__2);
}
/* Computing MAX */
r__1 = smlnum, r__2 = eps * xnorm;
smin = dmax(r__1,r__2);
/* Compute 1-norm of each column of strictly upper triangular */
/* part of T to control overflow in triangular solver. */
work[1] = 0.f;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
work[j] = sasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
/* L10: */
}
if (! (*lreal)) {
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
work[i__] += (r__1 = b[i__], dabs(r__1));
/* L20: */
}
}
n2 = *n << 1;
n1 = *n;
if (! (*lreal)) {
n1 = n2;
}
k = isamax_(&n1, &x[1], &c__1);
xmax = (r__1 = x[k], dabs(r__1));
*scale = 1.f;
if (xmax > bignum) {
*scale = bignum / xmax;
sscal_(&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.f) {
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 = (r__1 = x[j1], dabs(r__1));
tjj = (r__1 = t[j1 + j1 * t_dim1], dabs(r__1));
tmp = t[j1 + j1 * t_dim1];
if (tjj < smin) {
tmp = smin;
tjj = smin;
*info = 1;
}
if (xj == 0.f) {
goto L30;
}
if (tjj < 1.f) {
if (xj > bignum * tjj) {
rec = 1.f / xj;
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
x[j1] /= tmp;
xj = (r__1 = x[j1], dabs(r__1));
/* Scale x if necessary to avoid overflow when adding a */
/* multiple of column j1 of T. */
if (xj > 1.f) {
rec = 1.f / xj;
if (work[j1] > (bignum - xmax) * rec) {
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
}
if (j1 > 1) {
i__1 = j1 - 1;
r__1 = -x[j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
k = isamax_(&i__1, &x[1], &c__1);
xmax = (r__1 = x[k], dabs(r__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];
slaln2_(&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.f) {
sscal_(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 */
r__1 = dabs(v[0]), r__2 = dabs(v[1]);
xj = dmax(r__1,r__2);
if (xj > 1.f) {
rec = 1.f / xj;
/* Computing MAX */
r__1 = work[j1], r__2 = work[j2];
if (dmax(r__1,r__2) > (bignum - xmax) * rec) {
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
}
/* Update right-hand side */
if (j1 > 1) {
i__1 = j1 - 1;
r__1 = -x[j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
r__1 = -x[j2];
saxpy_(&i__1, &r__1, &t[j2 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
k = isamax_(&i__1, &x[1], &c__1);
xmax = (r__1 = x[k], dabs(r__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.f) {
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 = (r__1 = x[j1], dabs(r__1));
if (xmax > 1.f) {
rec = 1.f / xmax;
if (work[j1] > (bignum - xj) * rec) {
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
x[j1] -= sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &
c__1);
xj = (r__1 = x[j1], dabs(r__1));
tjj = (r__1 = t[j1 + j1 * t_dim1], dabs(r__1));
tmp = t[j1 + j1 * t_dim1];
if (tjj < smin) {
tmp = smin;
tjj = smin;
*info = 1;
}
if (tjj < 1.f) {
if (xj > bignum * tjj) {
rec = 1.f / xj;
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
x[j1] /= tmp;
/* Computing MAX */
r__2 = xmax, r__3 = (r__1 = x[j1], dabs(r__1));
xmax = dmax(r__2,r__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 */
r__3 = (r__1 = x[j1], dabs(r__1)), r__4 = (r__2 = x[j2],
dabs(r__2));
xj = dmax(r__3,r__4);
if (xmax > 1.f) {
rec = 1.f / xmax;
/* Computing MAX */
r__1 = work[j2], r__2 = work[j1];
if (dmax(r__1,r__2) > (bignum - xj) * rec) {
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
d__[0] = x[j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d__[1] = x[j2] - sdot_(&i__2, &t[j2 * t_dim1 + 1], &c__1,
&x[1], &c__1);
slaln2_(&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.f) {
sscal_(n, &scaloc, &x[1], &c__1);
*scale *= scaloc;
}
x[j1] = v[0];
x[j2] = v[1];
/* Computing MAX */
r__3 = (r__1 = x[j1], dabs(r__1)), r__4 = (r__2 = x[j2],
dabs(r__2)), r__3 = max(r__3,r__4);
xmax = dmax(r__3,xmax);
}
L40:
;
}
}
} else {
/* Computing MAX */
r__1 = eps * dabs(*w);
sminw = dmax(r__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.f) {
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 = (r__1 = x[j1], dabs(r__1)) + (r__2 = x[*n + j1],
dabs(r__2));
tjj = (r__1 = t[j1 + j1 * t_dim1], dabs(r__1)) + dabs(z__)
;
tmp = t[j1 + j1 * t_dim1];
if (tjj < sminw) {
tmp = sminw;
tjj = sminw;
*info = 1;
}
if (xj == 0.f) {
goto L70;
}
if (tjj < 1.f) {
if (xj > bignum * tjj) {
rec = 1.f / xj;
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
sladiv_(&x[j1], &x[*n + j1], &tmp, &z__, &sr, &si);
x[j1] = sr;
x[*n + j1] = si;
xj = (r__1 = x[j1], dabs(r__1)) + (r__2 = x[*n + j1],
dabs(r__2));
/* Scale x if necessary to avoid overflow when adding a */
/* multiple of column j1 of T. */
if (xj > 1.f) {
rec = 1.f / xj;
if (work[j1] > (bignum - xmax) * rec) {
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
}
}
if (j1 > 1) {
i__1 = j1 - 1;
r__1 = -x[j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
r__1 = -x[*n + j1];
saxpy_(&i__1, &r__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.f;
i__1 = j1 - 1;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
r__3 = xmax, r__4 = (r__1 = x[k], dabs(r__1)) + (
r__2 = x[k + *n], dabs(r__2));
xmax = dmax(r__3,r__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];
r__1 = -(*w);
slaln2_(&c_false, &c__2, &c__2, &sminw, &c_b21, &t[j1 +
j1 * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, &
c_b25, &r__1, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0) {
*info = 2;
}
if (scaloc != 1.f) {
i__1 = *n << 1;
sscal_(&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 */
r__1 = dabs(v[0]) + dabs(v[2]), r__2 = dabs(v[1]) + dabs(
v[3]);
xj = dmax(r__1,r__2);
if (xj > 1.f) {
rec = 1.f / xj;
/* Computing MAX */
r__1 = work[j1], r__2 = work[j2];
if (dmax(r__1,r__2) > (bignum - xmax) * rec) {
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
}
}
/* Update the right-hand side. */
if (j1 > 1) {
i__1 = j1 - 1;
r__1 = -x[j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
r__1 = -x[j2];
saxpy_(&i__1, &r__1, &t[j2 * t_dim1 + 1], &c__1, &x[1]
, &c__1);
i__1 = j1 - 1;
r__1 = -x[*n + j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[*
n + 1], &c__1);
i__1 = j1 - 1;
r__1 = -x[*n + j2];
saxpy_(&i__1, &r__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.f;
i__1 = j1 - 1;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
r__3 = (r__1 = x[k], dabs(r__1)) + (r__2 = x[k + *
n], dabs(r__2));
xmax = dmax(r__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.f) {
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 = (r__1 = x[j1], dabs(r__1)) + (r__2 = x[j1 + *n],
dabs(r__2));
if (xmax > 1.f) {
rec = 1.f / xmax;
if (work[j1] > (bignum - xj) * rec) {
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
x[j1] -= sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &
c__1);
i__2 = j1 - 1;
x[*n + j1] -= sdot_(&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 = (r__1 = x[j1], dabs(r__1)) + (r__2 = x[j1 + *n],
dabs(r__2));
z__ = *w;
if (j1 == 1) {
z__ = b[1];
}
/* Scale if necessary to avoid overflow in */
/* complex division */
tjj = (r__1 = t[j1 + j1 * t_dim1], dabs(r__1)) + dabs(z__)
;
tmp = t[j1 + j1 * t_dim1];
if (tjj < sminw) {
tmp = sminw;
tjj = sminw;
*info = 1;
}
if (tjj < 1.f) {
if (xj > bignum * tjj) {
rec = 1.f / xj;
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
r__1 = -z__;
sladiv_(&x[j1], &x[*n + j1], &tmp, &r__1, &sr, &si);
x[j1] = sr;
x[j1 + *n] = si;
/* Computing MAX */
r__3 = (r__1 = x[j1], dabs(r__1)) + (r__2 = x[j1 + *n],
dabs(r__2));
xmax = dmax(r__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 */
r__5 = (r__1 = x[j1], dabs(r__1)) + (r__2 = x[*n + j1],
dabs(r__2)), r__6 = (r__3 = x[j2], dabs(r__3)) + (
r__4 = x[*n + j2], dabs(r__4));
xj = dmax(r__5,r__6);
if (xmax > 1.f) {
rec = 1.f / xmax;
/* Computing MAX */
r__1 = work[j1], r__2 = work[j2];
if (dmax(r__1,r__2) > (bignum - xj) / xmax) {
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
d__[0] = x[j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d__[1] = x[j2] - sdot_(&i__2, &t[j2 * t_dim1 + 1], &c__1,
&x[1], &c__1);
i__2 = j1 - 1;
d__[2] = x[*n + j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], &
c__1, &x[*n + 1], &c__1);
i__2 = j1 - 1;
d__[3] = x[*n + j2] - sdot_(&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];
slaln2_(&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.f) {
sscal_(&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 */
r__5 = (r__1 = x[j1], dabs(r__1)) + (r__2 = x[*n + j1],
dabs(r__2)), r__6 = (r__3 = x[j2], dabs(r__3)) + (
r__4 = x[*n + j2], dabs(r__4)), r__5 = max(r__5,
r__6);
xmax = dmax(r__5,xmax);
}
L80:
;
}
}
}
return 0;
/* End of SLAQTR */
} /* slaqtr_ */
/* Subroutine */ int sget31_(real *rmax, integer *lmax, integer *ninfo,
integer *knt)
{
/* Initialized data */
static logical ltrans[2] = { FALSE_,TRUE_ };
/* System generated locals */
real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8, r__9, r__10, r__11,
r__12, r__13, r__14, r__15, r__16, r__17;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer info;
static real unfl, smin, a[4] /* was [2][2] */, b[4] /* was [2][2]
*/, scale, x[4] /* was [2][2] */;
static integer ismin;
static real d1, d2, vsmin[4], xnorm;
extern /* Subroutine */ int slaln2_(logical *, integer *, integer *, real
*, real *, real *, integer *, real *, real *, real *, integer *,
real *, real *, real *, integer *, real *, real *, integer *);
static real ca;
static integer ia, ib, na;
extern /* Subroutine */ int slabad_(real *, real *);
static real wi;
static integer nw;
extern doublereal slamch_(char *);
static real wr, bignum;
static integer id1, id2, itrans;
static real smlnum;
static integer ica;
static real den, vab[3], vca[5], vdd[4], eps;
static integer iwi;
static real res, tmp;
static integer iwr;
static real vwi[4], vwr[4];
#define a_ref(a_1,a_2) a[(a_2)*2 + a_1 - 3]
#define b_ref(a_1,a_2) b[(a_2)*2 + a_1 - 3]
#define x_ref(a_1,a_2) x[(a_2)*2 + a_1 - 3]
/* -- LAPACK test 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
=======
SGET31 tests SLALN2, a routine for solving
(ca A - w D)X = sB
where A is an NA by NA matrix (NA=1 or 2 only), w is a real (NW=1) or
complex (NW=2) constant, ca is a real constant, D is an NA by NA real
diagonal matrix, and B is an NA by NW matrix (when NW=2 the second
column of B contains the imaginary part of the solution). The code
returns X and s, where s is a scale factor, less than or equal to 1,
which is chosen to avoid overflow in X.
If any singular values of ca A-w D are less than another input
parameter SMIN, they are perturbed up to SMIN.
The test condition is that the scaled residual
norm( (ca A-w D)*X - s*B ) /
( max( ulp*norm(ca A-w D), SMIN )*norm(X) )
should be on the order of 1. Here, ulp is the machine precision.
Also, it is verified that SCALE is less than or equal to 1, and that
XNORM = infinity-norm(X).
Arguments
==========
RMAX (output) REAL
Value of the largest test ratio.
LMAX (output) INTEGER
Example number where largest test ratio achieved.
NINFO (output) INTEGER array, dimension (3)
NINFO(1) = number of examples with INFO less than 0
NINFO(2) = number of examples with INFO greater than 0
KNT (output) INTEGER
Total number of examples tested.
=====================================================================
Parameter adjustments */
--ninfo;
/* Function Body
Get machine parameters */
eps = slamch_("P");
unfl = slamch_("U");
smlnum = slamch_("S") / eps;
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Set up test case parameters */
vsmin[0] = smlnum;
vsmin[1] = eps;
vsmin[2] = .01f;
vsmin[3] = 1.f / eps;
vab[0] = sqrt(smlnum);
vab[1] = 1.f;
vab[2] = sqrt(bignum);
vwr[0] = 0.f;
vwr[1] = .5f;
vwr[2] = 2.f;
vwr[3] = 1.f;
vwi[0] = smlnum;
vwi[1] = eps;
vwi[2] = 1.f;
vwi[3] = 2.f;
vdd[0] = sqrt(smlnum);
vdd[1] = 1.f;
vdd[2] = 2.f;
vdd[3] = sqrt(bignum);
vca[0] = 0.f;
vca[1] = sqrt(smlnum);
vca[2] = eps;
vca[3] = .5f;
vca[4] = 1.f;
*knt = 0;
ninfo[1] = 0;
ninfo[2] = 0;
*lmax = 0;
*rmax = 0.f;
/* Begin test loop */
for (id1 = 1; id1 <= 4; ++id1) {
d1 = vdd[id1 - 1];
for (id2 = 1; id2 <= 4; ++id2) {
d2 = vdd[id2 - 1];
for (ica = 1; ica <= 5; ++ica) {
ca = vca[ica - 1];
for (itrans = 0; itrans <= 1; ++itrans) {
for (ismin = 1; ismin <= 4; ++ismin) {
smin = vsmin[ismin - 1];
na = 1;
nw = 1;
for (ia = 1; ia <= 3; ++ia) {
a_ref(1, 1) = vab[ia - 1];
for (ib = 1; ib <= 3; ++ib) {
b_ref(1, 1) = vab[ib - 1];
for (iwr = 1; iwr <= 4; ++iwr) {
if (d1 == 1.f && d2 == 1.f && ca == 1.f) {
wr = vwr[iwr - 1] * a_ref(1, 1);
} else {
wr = vwr[iwr - 1];
}
wi = 0.f;
slaln2_(<rans[itrans], &na, &nw, &smin,
&ca, a, &c__2, &d1, &d2, b, &c__2,
&wr, &wi, x, &c__2, &scale, &
xnorm, &info);
if (info < 0) {
++ninfo[1];
}
if (info > 0) {
++ninfo[2];
}
res = (r__1 = (ca * a_ref(1, 1) - wr * d1)
* x_ref(1, 1) - scale * b_ref(1,
1), dabs(r__1));
if (info == 0) {
/* Computing MAX */
r__2 = eps * (r__1 = (ca * a_ref(1, 1)
- wr * d1) * x_ref(1, 1),
dabs(r__1));
den = dmax(r__2,smlnum);
} else {
/* Computing MAX */
r__2 = smin * (r__1 = x_ref(1, 1),
dabs(r__1));
den = dmax(r__2,smlnum);
}
res /= den;
if ((r__1 = x_ref(1, 1), dabs(r__1)) <
unfl && (r__3 = b_ref(1, 1), dabs(
r__3)) <= smlnum * (r__2 = ca *
a_ref(1, 1) - wr * d1, dabs(r__2))
) {
res = 0.f;
}
if (scale > 1.f) {
res += 1.f / eps;
}
res += (r__2 = xnorm - (r__1 = x_ref(1, 1)
, dabs(r__1)), dabs(r__2)) / dmax(
smlnum,xnorm) / eps;
if (info != 0 && info != 1) {
res += 1.f / eps;
}
++(*knt);
if (res > *rmax) {
*lmax = *knt;
*rmax = res;
}
/* L10: */
}
/* L20: */
}
/* L30: */
}
na = 1;
nw = 2;
for (ia = 1; ia <= 3; ++ia) {
a_ref(1, 1) = vab[ia - 1];
for (ib = 1; ib <= 3; ++ib) {
b_ref(1, 1) = vab[ib - 1];
b_ref(1, 2) = vab[ib - 1] * -.5f;
for (iwr = 1; iwr <= 4; ++iwr) {
if (d1 == 1.f && d2 == 1.f && ca == 1.f) {
wr = vwr[iwr - 1] * a_ref(1, 1);
} else {
wr = vwr[iwr - 1];
}
for (iwi = 1; iwi <= 4; ++iwi) {
if (d1 == 1.f && d2 == 1.f && ca ==
1.f) {
wi = vwi[iwi - 1] * a_ref(1, 1);
} else {
wi = vwi[iwi - 1];
}
slaln2_(<rans[itrans], &na, &nw, &
smin, &ca, a, &c__2, &d1, &d2,
b, &c__2, &wr, &wi, x, &c__2,
&scale, &xnorm, &info);
if (info < 0) {
++ninfo[1];
}
if (info > 0) {
++ninfo[2];
}
res = (r__1 = (ca * a_ref(1, 1) - wr *
d1) * x_ref(1, 1) + wi * d1 *
x_ref(1, 2) - scale * b_ref(
1, 1), dabs(r__1));
res += (r__1 = -wi * d1 * x_ref(1, 1)
+ (ca * a_ref(1, 1) - wr * d1)
* x_ref(1, 2) - scale *
b_ref(1, 2), dabs(r__1));
if (info == 0) {
/* Computing MAX
Computing MAX */
r__6 = (r__3 = ca * a_ref(1, 1) -
wr * d1, dabs(r__3)),
r__7 = (r__4 = d1 * wi,
dabs(r__4));
r__5 = eps * (dmax(r__6,r__7) * ((
r__1 = x_ref(1, 1), dabs(
r__1)) + (r__2 = x_ref(1,
2), dabs(r__2))));
den = dmax(r__5,smlnum);
} else {
/* Computing MAX */
r__3 = smin * ((r__1 = x_ref(1, 1)
, dabs(r__1)) + (r__2 =
x_ref(1, 2), dabs(r__2)));
den = dmax(r__3,smlnum);
}
res /= den;
if ((r__1 = x_ref(1, 1), dabs(r__1)) <
unfl && (r__2 = x_ref(1, 2),
dabs(r__2)) < unfl && (r__4 =
b_ref(1, 1), dabs(r__4)) <=
smlnum * (r__3 = ca * a_ref(1,
1) - wr * d1, dabs(r__3))) {
res = 0.f;
}
if (scale > 1.f) {
res += 1.f / eps;
}
res += (r__3 = xnorm - (r__1 = x_ref(
1, 1), dabs(r__1)) - (r__2 =
x_ref(1, 2), dabs(r__2)),
dabs(r__3)) / dmax(smlnum,
xnorm) / eps;
if (info != 0 && info != 1) {
res += 1.f / eps;
}
++(*knt);
if (res > *rmax) {
*lmax = *knt;
*rmax = res;
}
/* L40: */
}
/* L50: */
}
/* L60: */
}
/* L70: */
}
na = 2;
nw = 1;
for (ia = 1; ia <= 3; ++ia) {
a_ref(1, 1) = vab[ia - 1];
a_ref(1, 2) = vab[ia - 1] * -3.f;
a_ref(2, 1) = vab[ia - 1] * -7.f;
a_ref(2, 2) = vab[ia - 1] * 21.f;
for (ib = 1; ib <= 3; ++ib) {
b_ref(1, 1) = vab[ib - 1];
b_ref(2, 1) = vab[ib - 1] * -2.f;
for (iwr = 1; iwr <= 4; ++iwr) {
if (d1 == 1.f && d2 == 1.f && ca == 1.f) {
wr = vwr[iwr - 1] * a_ref(1, 1);
} else {
wr = vwr[iwr - 1];
}
wi = 0.f;
slaln2_(<rans[itrans], &na, &nw, &smin,
&ca, a, &c__2, &d1, &d2, b, &c__2,
&wr, &wi, x, &c__2, &scale, &
xnorm, &info);
if (info < 0) {
++ninfo[1];
}
if (info > 0) {
++ninfo[2];
}
if (itrans == 1) {
tmp = a_ref(1, 2);
a_ref(1, 2) = a_ref(2, 1);
a_ref(2, 1) = tmp;
}
res = (r__1 = (ca * a_ref(1, 1) - wr * d1)
* x_ref(1, 1) + ca * a_ref(1, 2)
* x_ref(2, 1) - scale * b_ref(1,
1), dabs(r__1));
res += (r__1 = ca * a_ref(2, 1) * x_ref(1,
1) + (ca * a_ref(2, 2) - wr * d2)
* x_ref(2, 1) - scale * b_ref(2,
1), dabs(r__1));
if (info == 0) {
/* Computing MAX
Computing MAX */
r__8 = (r__1 = ca * a_ref(1, 1) - wr *
d1, dabs(r__1)) + (r__2 = ca
* a_ref(1, 2), dabs(r__2)),
r__9 = (r__3 = ca * a_ref(2,
1), dabs(r__3)) + (r__4 = ca *
a_ref(2, 2) - wr * d2, dabs(
r__4));
/* Computing MAX */
r__10 = (r__5 = x_ref(1, 1), dabs(
r__5)), r__11 = (r__6 = x_ref(
2, 1), dabs(r__6));
r__7 = eps * (dmax(r__8,r__9) * dmax(
r__10,r__11));
den = dmax(r__7,smlnum);
} else {
/* Computing MAX
Computing MAX
Computing MAX */
r__10 = (r__1 = ca * a_ref(1, 1) - wr
* d1, dabs(r__1)) + (r__2 =
ca * a_ref(1, 2), dabs(r__2)),
r__11 = (r__3 = ca * a_ref(2,
1), dabs(r__3)) + (r__4 = ca
* a_ref(2, 2) - wr * d2, dabs(
r__4));
r__8 = smin / eps, r__9 = dmax(r__10,
r__11);
/* Computing MAX */
r__12 = (r__5 = x_ref(1, 1), dabs(
r__5)), r__13 = (r__6 = x_ref(
2, 1), dabs(r__6));
r__7 = eps * (dmax(r__8,r__9) * dmax(
r__12,r__13));
den = dmax(r__7,smlnum);
}
res /= den;
if ((r__1 = x_ref(1, 1), dabs(r__1)) <
unfl && (r__2 = x_ref(2, 1), dabs(
r__2)) < unfl && (r__3 = b_ref(1,
1), dabs(r__3)) + (r__4 = b_ref(2,
1), dabs(r__4)) <= smlnum * ((
r__5 = ca * a_ref(1, 1) - wr * d1,
dabs(r__5)) + (r__6 = ca * a_ref(
1, 2), dabs(r__6)) + (r__7 = ca *
a_ref(2, 1), dabs(r__7)) + (r__8 =
ca * a_ref(2, 2) - wr * d2, dabs(
r__8)))) {
res = 0.f;
}
if (scale > 1.f) {
res += 1.f / eps;
}
/* Computing MAX */
r__4 = (r__1 = x_ref(1, 1), dabs(r__1)),
r__5 = (r__2 = x_ref(2, 1), dabs(
r__2));
res += (r__3 = xnorm - dmax(r__4,r__5),
dabs(r__3)) / dmax(smlnum,xnorm) /
eps;
if (info != 0 && info != 1) {
res += 1.f / eps;
}
++(*knt);
if (res > *rmax) {
*lmax = *knt;
*rmax = res;
}
/* L80: */
}
/* L90: */
}
/* L100: */
}
na = 2;
nw = 2;
for (ia = 1; ia <= 3; ++ia) {
a_ref(1, 1) = vab[ia - 1] * 2.f;
a_ref(1, 2) = vab[ia - 1] * -3.f;
a_ref(2, 1) = vab[ia - 1] * -7.f;
a_ref(2, 2) = vab[ia - 1] * 21.f;
for (ib = 1; ib <= 3; ++ib) {
b_ref(1, 1) = vab[ib - 1];
b_ref(2, 1) = vab[ib - 1] * -2.f;
b_ref(1, 2) = vab[ib - 1] * 4.f;
b_ref(2, 2) = vab[ib - 1] * -7.f;
for (iwr = 1; iwr <= 4; ++iwr) {
if (d1 == 1.f && d2 == 1.f && ca == 1.f) {
wr = vwr[iwr - 1] * a_ref(1, 1);
} else {
wr = vwr[iwr - 1];
}
for (iwi = 1; iwi <= 4; ++iwi) {
if (d1 == 1.f && d2 == 1.f && ca ==
1.f) {
wi = vwi[iwi - 1] * a_ref(1, 1);
} else {
wi = vwi[iwi - 1];
}
slaln2_(<rans[itrans], &na, &nw, &
smin, &ca, a, &c__2, &d1, &d2,
b, &c__2, &wr, &wi, x, &c__2,
&scale, &xnorm, &info);
if (info < 0) {
++ninfo[1];
}
if (info > 0) {
++ninfo[2];
}
if (itrans == 1) {
tmp = a_ref(1, 2);
a_ref(1, 2) = a_ref(2, 1);
a_ref(2, 1) = tmp;
}
res = (r__1 = (ca * a_ref(1, 1) - wr *
d1) * x_ref(1, 1) + ca *
a_ref(1, 2) * x_ref(2, 1) +
wi * d1 * x_ref(1, 2) - scale
* b_ref(1, 1), dabs(r__1));
res += (r__1 = (ca * a_ref(1, 1) - wr
* d1) * x_ref(1, 2) + ca *
a_ref(1, 2) * x_ref(2, 2) -
wi * d1 * x_ref(1, 1) - scale
* b_ref(1, 2), dabs(r__1));
res += (r__1 = ca * a_ref(2, 1) *
x_ref(1, 1) + (ca * a_ref(2,
2) - wr * d2) * x_ref(2, 1) +
wi * d2 * x_ref(2, 2) - scale
* b_ref(2, 1), dabs(r__1));
res += (r__1 = ca * a_ref(2, 1) *
x_ref(1, 2) + (ca * a_ref(2,
2) - wr * d2) * x_ref(2, 2) -
wi * d2 * x_ref(2, 1) - scale
* b_ref(2, 2), dabs(r__1));
if (info == 0) {
/* Computing MAX
Computing MAX */
r__12 = (r__1 = ca * a_ref(1, 1)
- wr * d1, dabs(r__1)) + (
r__2 = ca * a_ref(1, 2),
dabs(r__2)) + (r__3 = wi *
d1, dabs(r__3)), r__13 =
(r__4 = ca * a_ref(2, 1),
dabs(r__4)) + (r__5 = ca *
a_ref(2, 2) - wr * d2,
dabs(r__5)) + (r__6 = wi *
d2, dabs(r__6));
/* Computing MAX */
r__14 = (r__7 = x_ref(1, 1), dabs(
r__7)) + (r__8 = x_ref(2,
1), dabs(r__8)), r__15 = (
r__9 = x_ref(1, 2), dabs(
r__9)) + (r__10 = x_ref(2,
2), dabs(r__10));
r__11 = eps * (dmax(r__12,r__13) *
dmax(r__14,r__15));
den = dmax(r__11,smlnum);
} else {
/* Computing MAX
Computing MAX
Computing MAX */
r__14 = (r__1 = ca * a_ref(1, 1)
- wr * d1, dabs(r__1)) + (
r__2 = ca * a_ref(1, 2),
dabs(r__2)) + (r__3 = wi *
d1, dabs(r__3)), r__15 =
(r__4 = ca * a_ref(2, 1),
dabs(r__4)) + (r__5 = ca *
a_ref(2, 2) - wr * d2,
dabs(r__5)) + (r__6 = wi *
d2, dabs(r__6));
r__12 = smin / eps, r__13 = dmax(
r__14,r__15);
/* Computing MAX */
r__16 = (r__7 = x_ref(1, 1), dabs(
r__7)) + (r__8 = x_ref(2,
1), dabs(r__8)), r__17 = (
r__9 = x_ref(1, 2), dabs(
r__9)) + (r__10 = x_ref(2,
2), dabs(r__10));
r__11 = eps * (dmax(r__12,r__13) *
dmax(r__16,r__17));
den = dmax(r__11,smlnum);
}
res /= den;
if ((r__1 = x_ref(1, 1), dabs(r__1)) <
unfl && (r__2 = x_ref(2, 1),
dabs(r__2)) < unfl && (r__3 =
x_ref(1, 2), dabs(r__3)) <
unfl && (r__4 = x_ref(2, 2),
dabs(r__4)) < unfl && (r__5 =
b_ref(1, 1), dabs(r__5)) + (
r__6 = b_ref(2, 1), dabs(r__6)
) <= smlnum * ((r__7 = ca *
a_ref(1, 1) - wr * d1, dabs(
r__7)) + (r__8 = ca * a_ref(1,
2), dabs(r__8)) + (r__9 = ca
* a_ref(2, 1), dabs(r__9)) + (
r__10 = ca * a_ref(2, 2) - wr
* d2, dabs(r__10)) + (r__11 =
wi * d2, dabs(r__11)) + (
r__12 = wi * d1, dabs(r__12)))
) {
res = 0.f;
}
if (scale > 1.f) {
res += 1.f / eps;
}
/* Computing MAX */
r__6 = (r__1 = x_ref(1, 1), dabs(r__1)
) + (r__2 = x_ref(1, 2), dabs(
r__2)), r__7 = (r__3 = x_ref(
2, 1), dabs(r__3)) + (r__4 =
x_ref(2, 2), dabs(r__4));
res += (r__5 = xnorm - dmax(r__6,r__7)
, dabs(r__5)) / dmax(smlnum,
xnorm) / eps;
if (info != 0 && info != 1) {
res += 1.f / eps;
}
++(*knt);
if (res > *rmax) {
*lmax = *knt;
*rmax = res;
}
/* L110: */
}
/* L120: */
}
/* L130: */
}
/* L140: */
}
/* L150: */
}
/* L160: */
}
/* L170: */
}
/* L180: */
}
/* L190: */
}
return 0;
/* End of SGET31 */
} /* sget31_ */
/* Subroutine */ int stgevc_(char *side, char *howmny, logical *select,
integer *n, real *s, integer *lds, real *p, integer *ldp, real *vl,
integer *ldvl, real *vr, integer *ldvr, integer *mm, integer *m, real
*work, integer *info)
{
/* System generated locals */
integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1,
vr_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4, r__5, r__6;
/* Local variables */
integer i__, j, ja, jc, je, na, im, jr, jw, nw;
real big;
logical lsa, lsb;
real ulp, sum[4] /* was [2][2] */;
integer ibeg, ieig, iend;
real dmin__, temp, xmax, sump[4] /* was [2][2] */, sums[4] /*
was [2][2] */, cim2a, cim2b, cre2a, cre2b;
real temp2, bdiag[2], acoef, scale;
logical ilall;
integer iside;
real sbeta;
logical il2by2;
integer iinfo;
real small;
logical compl;
real anorm, bnorm;
logical compr;
real temp2i, temp2r;
logical ilabad, ilbbad;
real acoefa, bcoefa, cimaga, cimagb;
logical ilback;
real bcoefi, ascale, bscale, creala, crealb, bcoefr;
real salfar, safmin;
real xscale, bignum;
logical ilcomp, ilcplx;
integer ihwmny;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* STGEVC computes some or all of the right and/or left eigenvectors of */
/* a pair of real matrices (S,P), where S is a quasi-triangular matrix */
/* and P is upper triangular. Matrix pairs of this type are produced by */
/* the generalized Schur factorization of a matrix pair (A,B): */
/* A = Q*S*Z**T, B = Q*P*Z**T */
/* as computed by SGGHRD + SHGEQZ. */
/* The right eigenvector x and the left eigenvector y of (S,P) */
/* corresponding to an eigenvalue w are defined by: */
/* S*x = w*P*x, (y**H)*S = w*(y**H)*P, */
/* where y**H denotes the conjugate tranpose of y. */
/* The eigenvalues are not input to this routine, but are computed */
/* directly from the diagonal blocks of S and P. */
/* This routine returns the matrices X and/or Y of right and left */
/* eigenvectors of (S,P), or the products Z*X and/or Q*Y, */
/* where Z and Q are input matrices. */
/* If Q and Z are the orthogonal factors from the generalized Schur */
/* factorization of a matrix pair (A,B), then Z*X and Q*Y */
/* are the matrices of right and left eigenvectors of (A,B). */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'R': compute right eigenvectors only; */
/* = 'L': compute left eigenvectors only; */
/* = 'B': compute both right and left eigenvectors. */
/* HOWMNY (input) CHARACTER*1 */
/* = 'A': compute all right and/or left eigenvectors; */
/* = 'B': compute all right and/or left eigenvectors, */
/* backtransformed by the matrices in VR and/or VL; */
/* = 'S': compute selected right and/or left eigenvectors, */
/* specified by the logical array SELECT. */
/* SELECT (input) LOGICAL array, dimension (N) */
/* If HOWMNY='S', SELECT specifies the eigenvectors to be */
/* computed. If w(j) is a real eigenvalue, the corresponding */
/* If w(j) and w(j+1) are the real and imaginary parts of a */
/* complex eigenvalue, the corresponding complex eigenvector */
/* is computed if either SELECT(j) or SELECT(j+1) is .TRUE., */
/* and on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is */
/* Not referenced if HOWMNY = 'A' or 'B'. */
/* N (input) INTEGER */
/* The order of the matrices S and P. N >= 0. */
/* S (input) REAL array, dimension (LDS,N) */
/* The upper quasi-triangular matrix S from a generalized Schur */
/* factorization, as computed by SHGEQZ. */
/* LDS (input) INTEGER */
/* The leading dimension of array S. LDS >= max(1,N). */
/* P (input) REAL array, dimension (LDP,N) */
/* The upper triangular matrix P from a generalized Schur */
/* factorization, as computed by SHGEQZ. */
/* 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks */
/* of S must be in positive diagonal form. */
/* LDP (input) INTEGER */
/* The leading dimension of array P. LDP >= max(1,N). */
/* VL (input/output) REAL array, dimension (LDVL,MM) */
/* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
/* contain an N-by-N matrix Q (usually the orthogonal matrix Q */
/* of left Schur vectors returned by SHGEQZ). */
/* On exit, if SIDE = 'L' or 'B', VL contains: */
/* if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */
/* if HOWMNY = 'B', the matrix Q*Y; */
/* if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */
/* SELECT, stored consecutively in the columns of */
/* VL, in the same order as their eigenvalues. */
/* A complex eigenvector corresponding to a complex eigenvalue */
/* is stored in two consecutive columns, the first holding the */
/* real part, and the second the imaginary part. */
/* Not referenced if SIDE = 'R'. */
/* LDVL (input) INTEGER */
/* The leading dimension of array VL. LDVL >= 1, and if */
/* SIDE = 'L' or 'B', LDVL >= N. */
/* VR (input/output) REAL array, dimension (LDVR,MM) */
/* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
/* contain an N-by-N matrix Z (usually the orthogonal matrix Z */
/* of right Schur vectors returned by SHGEQZ). */
/* On exit, if SIDE = 'R' or 'B', VR contains: */
/* if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */
/* if HOWMNY = 'B' or 'b', the matrix Z*X; */
/* if HOWMNY = 'S' or 's', the right eigenvectors of (S,P) */
/* specified by SELECT, stored consecutively in the */
/* columns of VR, in the same order as their */
/* eigenvalues. */
/* A complex eigenvector corresponding to a complex eigenvalue */
/* is stored in two consecutive columns, the first holding the */
/* real part and the second the imaginary part. */
/* Not referenced if SIDE = 'L'. */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1, and if */
/* SIDE = 'R' or 'B', LDVR >= N. */
/* MM (input) INTEGER */
/* The number of columns in the arrays VL and/or VR. MM >= M. */
/* M (output) INTEGER */
/* The number of columns in the arrays VL and/or VR actually */
/* used to store the eigenvectors. If HOWMNY = 'A' or 'B', M */
/* is set to N. Each selected real eigenvector occupies one */
/* column and each selected complex eigenvector occupies two */
/* columns. */
/* WORK (workspace) REAL array, dimension (6*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: the 2-by-2 block (INFO:INFO+1) does not have a complex */
/* eigenvalue. */
/* Further Details */
/* =============== */
/* Allocation of workspace: */
/* ---------- -- --------- */
/* WORK( j ) = 1-norm of j-th column of A, above the diagonal */
/* WORK( N+j ) = 1-norm of j-th column of B, above the diagonal */
/* WORK( 2*N+1:3*N ) = real part of eigenvector */
/* WORK( 3*N+1:4*N ) = imaginary part of eigenvector */
/* WORK( 4*N+1:5*N ) = real part of back-transformed eigenvector */
/* WORK( 5*N+1:6*N ) = imaginary part of back-transformed eigenvector */
/* Rowwise vs. columnwise solution methods: */
/* ------- -- ---------- -------- ------- */
/* Finding a generalized eigenvector consists basically of solving the */
/* singular triangular system */
/* (A - w B) x = 0 (for right) or: (A - w B)**H y = 0 (for left) */
/* Consider finding the i-th right eigenvector (assume all eigenvalues */
/* are real). The equation to be solved is: */
/* n i */
/* 0 = sum C(j,k) v(k) = sum C(j,k) v(k) for j = i,. . .,1 */
/* k=j k=j */
/* where C = (A - w B) (The components v(i+1:n) are 0.) */
/* The "rowwise" method is: */
/* (1) v(i) := 1 */
/* for j = i-1,. . .,1: */
/* i */
/* (2) compute s = - sum C(j,k) v(k) and */
/* k=j+1 */
/* (3) v(j) := s / C(j,j) */
/* Step 2 is sometimes called the "dot product" step, since it is an */
/* inner product between the j-th row and the portion of the eigenvector */
/* that has been computed so far. */
/* The "columnwise" method consists basically in doing the sums */
/* for all the rows in parallel. As each v(j) is computed, the */
/* contribution of v(j) times the j-th column of C is added to the */
/* partial sums. Since FORTRAN arrays are stored columnwise, this has */
/* the advantage that at each step, the elements of C that are accessed */
/* are adjacent to one another, whereas with the rowwise method, the */
/* elements accessed at a step are spaced LDS (and LDP) words apart. */
/* When finding left eigenvectors, the matrix in question is the */
/* transpose of the one in storage, so the rowwise method then */
/* actually accesses columns of A and B at each step, and so is the */
/* preferred method. */
/* ===================================================================== */
/* Decode and Test the input parameters */
/* Parameter adjustments */
--select;
s_dim1 = *lds;
s_offset = 1 + s_dim1;
s -= s_offset;
p_dim1 = *ldp;
p_offset = 1 + p_dim1;
p -= p_offset;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
/* Function Body */
if (lsame_(howmny, "A")) {
ihwmny = 1;
ilall = TRUE_;
ilback = FALSE_;
} else if (lsame_(howmny, "S")) {
ihwmny = 2;
ilall = FALSE_;
ilback = FALSE_;
} else if (lsame_(howmny, "B")) {
ihwmny = 3;
ilall = TRUE_;
ilback = TRUE_;
} else {
ihwmny = -1;
ilall = TRUE_;
}
if (lsame_(side, "R")) {
iside = 1;
compl = FALSE_;
compr = TRUE_;
} else if (lsame_(side, "L")) {
iside = 2;
compl = TRUE_;
compr = FALSE_;
} else if (lsame_(side, "B")) {
iside = 3;
compl = TRUE_;
compr = TRUE_;
} else {
iside = -1;
}
*info = 0;
if (iside < 0) {
*info = -1;
} else if (ihwmny < 0) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*lds < max(1,*n)) {
*info = -6;
} else if (*ldp < max(1,*n)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STGEVC", &i__1);
return 0;
}
/* Count the number of eigenvectors to be computed */
if (! ilall) {
im = 0;
ilcplx = FALSE_;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (ilcplx) {
ilcplx = FALSE_;
goto L10;
}
if (j < *n) {
if (s[j + 1 + j * s_dim1] != 0.f) {
ilcplx = TRUE_;
}
}
if (ilcplx) {
if (select[j] || select[j + 1]) {
im += 2;
}
} else {
if (select[j]) {
++im;
}
}
L10:
;
}
} else {
im = *n;
}
/* Check 2-by-2 diagonal blocks of A, B */
ilabad = FALSE_;
ilbbad = FALSE_;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
if (s[j + 1 + j * s_dim1] != 0.f) {
if (p[j + j * p_dim1] == 0.f || p[j + 1 + (j + 1) * p_dim1] ==
0.f || p[j + (j + 1) * p_dim1] != 0.f) {
ilbbad = TRUE_;
}
if (j < *n - 1) {
if (s[j + 2 + (j + 1) * s_dim1] != 0.f) {
ilabad = TRUE_;
}
}
}
}
if (ilabad) {
*info = -5;
} else if (ilbbad) {
*info = -7;
} else if (compl && *ldvl < *n || *ldvl < 1) {
*info = -10;
} else if (compr && *ldvr < *n || *ldvr < 1) {
*info = -12;
} else if (*mm < im) {
*info = -13;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STGEVC", &i__1);
return 0;
}
/* Quick return if possible */
*m = im;
if (*n == 0) {
return 0;
}
/* Machine Constants */
safmin = slamch_("Safe minimum");
big = 1.f / safmin;
slabad_(&safmin, &big);
ulp = slamch_("Epsilon") * slamch_("Base");
small = safmin * *n / ulp;
big = 1.f / small;
bignum = 1.f / (safmin * *n);
/* Compute the 1-norm of each column of the strictly upper triangular */
/* part (i.e., excluding all elements belonging to the diagonal */
/* blocks) of A and B to check for possible overflow in the */
/* triangular solver. */
anorm = (r__1 = s[s_dim1 + 1], dabs(r__1));
if (*n > 1) {
anorm += (r__1 = s[s_dim1 + 2], dabs(r__1));
}
bnorm = (r__1 = p[p_dim1 + 1], dabs(r__1));
work[1] = 0.f;
work[*n + 1] = 0.f;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
temp = 0.f;
temp2 = 0.f;
if (s[j + (j - 1) * s_dim1] == 0.f) {
iend = j - 1;
} else {
iend = j - 2;
}
i__2 = iend;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += (r__1 = s[i__ + j * s_dim1], dabs(r__1));
temp2 += (r__1 = p[i__ + j * p_dim1], dabs(r__1));
}
work[j] = temp;
work[*n + j] = temp2;
/* Computing MIN */
i__3 = j + 1;
i__2 = min(i__3,*n);
for (i__ = iend + 1; i__ <= i__2; ++i__) {
temp += (r__1 = s[i__ + j * s_dim1], dabs(r__1));
temp2 += (r__1 = p[i__ + j * p_dim1], dabs(r__1));
}
anorm = dmax(anorm,temp);
bnorm = dmax(bnorm,temp2);
}
ascale = 1.f / dmax(anorm,safmin);
bscale = 1.f / dmax(bnorm,safmin);
/* Left eigenvectors */
if (compl) {
ieig = 0;
/* Main loop over eigenvalues */
ilcplx = FALSE_;
i__1 = *n;
for (je = 1; je <= i__1; ++je) {
/* Skip this iteration if (a) HOWMNY='S' and SELECT=.FALSE., or */
/* (b) this would be the second of a complex pair. */
/* Check for complex eigenvalue, so as to be sure of which */
/* entry(-ies) of SELECT to look at. */
if (ilcplx) {
ilcplx = FALSE_;
goto L220;
}
nw = 1;
if (je < *n) {
if (s[je + 1 + je * s_dim1] != 0.f) {
ilcplx = TRUE_;
nw = 2;
}
}
if (ilall) {
ilcomp = TRUE_;
} else if (ilcplx) {
ilcomp = select[je] || select[je + 1];
} else {
ilcomp = select[je];
}
if (! ilcomp) {
goto L220;
}
/* Decide if (a) singular pencil, (b) real eigenvalue, or */
/* (c) complex eigenvalue. */
if (! ilcplx) {
if ((r__1 = s[je + je * s_dim1], dabs(r__1)) <= safmin && (
r__2 = p[je + je * p_dim1], dabs(r__2)) <= safmin) {
/* Singular matrix pencil -- return unit eigenvector */
++ieig;
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vl[jr + ieig * vl_dim1] = 0.f;
}
vl[ieig + ieig * vl_dim1] = 1.f;
goto L220;
}
}
/* Clear vector */
i__2 = nw * *n;
for (jr = 1; jr <= i__2; ++jr) {
work[(*n << 1) + jr] = 0.f;
}
/* T */
/* Compute coefficients in ( a A - b B ) y = 0 */
/* a is ACOEF */
/* b is BCOEFR + i*BCOEFI */
if (! ilcplx) {
/* Real eigenvalue */
/* Computing MAX */
r__3 = (r__1 = s[je + je * s_dim1], dabs(r__1)) * ascale,
r__4 = (r__2 = p[je + je * p_dim1], dabs(r__2)) *
bscale, r__3 = max(r__3,r__4);
temp = 1.f / dmax(r__3,safmin);
salfar = temp * s[je + je * s_dim1] * ascale;
sbeta = temp * p[je + je * p_dim1] * bscale;
acoef = sbeta * ascale;
bcoefr = salfar * bscale;
bcoefi = 0.f;
/* Scale to avoid underflow */
scale = 1.f;
lsa = dabs(sbeta) >= safmin && dabs(acoef) < small;
lsb = dabs(salfar) >= safmin && dabs(bcoefr) < small;
if (lsa) {
scale = small / dabs(sbeta) * dmin(anorm,big);
}
if (lsb) {
/* Computing MAX */
r__1 = scale, r__2 = small / dabs(salfar) * dmin(bnorm,
big);
scale = dmax(r__1,r__2);
}
if (lsa || lsb) {
/* Computing MIN */
/* Computing MAX */
r__3 = 1.f, r__4 = dabs(acoef), r__3 = max(r__3,r__4),
r__4 = dabs(bcoefr);
r__1 = scale, r__2 = 1.f / (safmin * dmax(r__3,r__4));
scale = dmin(r__1,r__2);
if (lsa) {
acoef = ascale * (scale * sbeta);
} else {
acoef = scale * acoef;
}
if (lsb) {
bcoefr = bscale * (scale * salfar);
} else {
bcoefr = scale * bcoefr;
}
}
acoefa = dabs(acoef);
bcoefa = dabs(bcoefr);
/* First component is 1 */
work[(*n << 1) + je] = 1.f;
xmax = 1.f;
} else {
/* Complex eigenvalue */
r__1 = safmin * 100.f;
slag2_(&s[je + je * s_dim1], lds, &p[je + je * p_dim1], ldp, &
r__1, &acoef, &temp, &bcoefr, &temp2, &bcoefi);
bcoefi = -bcoefi;
if (bcoefi == 0.f) {
*info = je;
return 0;
}
/* Scale to avoid over/underflow */
acoefa = dabs(acoef);
bcoefa = dabs(bcoefr) + dabs(bcoefi);
scale = 1.f;
if (acoefa * ulp < safmin && acoefa >= safmin) {
scale = safmin / ulp / acoefa;
}
if (bcoefa * ulp < safmin && bcoefa >= safmin) {
/* Computing MAX */
r__1 = scale, r__2 = safmin / ulp / bcoefa;
scale = dmax(r__1,r__2);
}
if (safmin * acoefa > ascale) {
scale = ascale / (safmin * acoefa);
}
if (safmin * bcoefa > bscale) {
/* Computing MIN */
r__1 = scale, r__2 = bscale / (safmin * bcoefa);
scale = dmin(r__1,r__2);
}
if (scale != 1.f) {
acoef = scale * acoef;
acoefa = dabs(acoef);
bcoefr = scale * bcoefr;
bcoefi = scale * bcoefi;
bcoefa = dabs(bcoefr) + dabs(bcoefi);
}
/* Compute first two components of eigenvector */
temp = acoef * s[je + 1 + je * s_dim1];
temp2r = acoef * s[je + je * s_dim1] - bcoefr * p[je + je *
p_dim1];
temp2i = -bcoefi * p[je + je * p_dim1];
if (dabs(temp) > dabs(temp2r) + dabs(temp2i)) {
work[(*n << 1) + je] = 1.f;
work[*n * 3 + je] = 0.f;
work[(*n << 1) + je + 1] = -temp2r / temp;
work[*n * 3 + je + 1] = -temp2i / temp;
} else {
work[(*n << 1) + je + 1] = 1.f;
work[*n * 3 + je + 1] = 0.f;
temp = acoef * s[je + (je + 1) * s_dim1];
work[(*n << 1) + je] = (bcoefr * p[je + 1 + (je + 1) *
p_dim1] - acoef * s[je + 1 + (je + 1) * s_dim1]) /
temp;
work[*n * 3 + je] = bcoefi * p[je + 1 + (je + 1) * p_dim1]
/ temp;
}
/* Computing MAX */
r__5 = (r__1 = work[(*n << 1) + je], dabs(r__1)) + (r__2 =
work[*n * 3 + je], dabs(r__2)), r__6 = (r__3 = work[(*
n << 1) + je + 1], dabs(r__3)) + (r__4 = work[*n * 3
+ je + 1], dabs(r__4));
xmax = dmax(r__5,r__6);
}
/* Computing MAX */
r__1 = ulp * acoefa * anorm, r__2 = ulp * bcoefa * bnorm, r__1 =
max(r__1,r__2);
dmin__ = dmax(r__1,safmin);
/* T */
/* Triangular solve of (a A - b B) y = 0 */
/* T */
/* (rowwise in (a A - b B) , or columnwise in (a A - b B) ) */
il2by2 = FALSE_;
i__2 = *n;
for (j = je + nw; j <= i__2; ++j) {
if (il2by2) {
il2by2 = FALSE_;
goto L160;
}
na = 1;
bdiag[0] = p[j + j * p_dim1];
if (j < *n) {
if (s[j + 1 + j * s_dim1] != 0.f) {
il2by2 = TRUE_;
bdiag[1] = p[j + 1 + (j + 1) * p_dim1];
na = 2;
}
}
/* Check whether scaling is necessary for dot products */
xscale = 1.f / dmax(1.f,xmax);
/* Computing MAX */
r__1 = work[j], r__2 = work[*n + j], r__1 = max(r__1,r__2),
r__2 = acoefa * work[j] + bcoefa * work[*n + j];
temp = dmax(r__1,r__2);
if (il2by2) {
/* Computing MAX */
r__1 = temp, r__2 = work[j + 1], r__1 = max(r__1,r__2),
r__2 = work[*n + j + 1], r__1 = max(r__1,r__2),
r__2 = acoefa * work[j + 1] + bcoefa * work[*n +
j + 1];
temp = dmax(r__1,r__2);
}
if (temp > bignum * xscale) {
i__3 = nw - 1;
for (jw = 0; jw <= i__3; ++jw) {
i__4 = j - 1;
for (jr = je; jr <= i__4; ++jr) {
work[(jw + 2) * *n + jr] = xscale * work[(jw + 2)
* *n + jr];
}
}
xmax *= xscale;
}
/* Compute dot products */
/* j-1 */
/* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */
/* k=je */
/* To reduce the op count, this is done as */
/* _ j-1 _ j-1 */
/* a*conjg( sum S(k,j)*x(k) ) - b*conjg( sum P(k,j)*x(k) ) */
/* k=je k=je */
/* which may cause underflow problems if A or B are close */
/* to underflow. (E.g., less than SMALL.) */
/* A series of compiler directives to defeat vectorization */
/* for the next loop */
/* $PL$ CMCHAR=' ' */
/* DIR$ NEXTSCALAR */
/* $DIR SCALAR */
/* DIR$ NEXT SCALAR */
/* VD$L NOVECTOR */
/* DEC$ NOVECTOR */
/* VD$ NOVECTOR */
/* VDIR NOVECTOR */
/* VOCL LOOP,SCALAR */
/* IBM PREFER SCALAR */
/* $PL$ CMCHAR='*' */
i__3 = nw;
for (jw = 1; jw <= i__3; ++jw) {
/* $PL$ CMCHAR=' ' */
/* DIR$ NEXTSCALAR */
/* $DIR SCALAR */
/* DIR$ NEXT SCALAR */
/* VD$L NOVECTOR */
/* DEC$ NOVECTOR */
/* VD$ NOVECTOR */
/* VDIR NOVECTOR */
/* VOCL LOOP,SCALAR */
/* IBM PREFER SCALAR */
/* $PL$ CMCHAR='*' */
i__4 = na;
for (ja = 1; ja <= i__4; ++ja) {
sums[ja + (jw << 1) - 3] = 0.f;
sump[ja + (jw << 1) - 3] = 0.f;
i__5 = j - 1;
for (jr = je; jr <= i__5; ++jr) {
sums[ja + (jw << 1) - 3] += s[jr + (j + ja - 1) *
s_dim1] * work[(jw + 1) * *n + jr];
sump[ja + (jw << 1) - 3] += p[jr + (j + ja - 1) *
p_dim1] * work[(jw + 1) * *n + jr];
}
}
}
/* $PL$ CMCHAR=' ' */
/* DIR$ NEXTSCALAR */
/* $DIR SCALAR */
/* DIR$ NEXT SCALAR */
/* VD$L NOVECTOR */
/* DEC$ NOVECTOR */
/* VD$ NOVECTOR */
/* VDIR NOVECTOR */
/* VOCL LOOP,SCALAR */
/* IBM PREFER SCALAR */
/* $PL$ CMCHAR='*' */
i__3 = na;
for (ja = 1; ja <= i__3; ++ja) {
if (ilcplx) {
sum[ja - 1] = -acoef * sums[ja - 1] + bcoefr * sump[
ja - 1] - bcoefi * sump[ja + 1];
sum[ja + 1] = -acoef * sums[ja + 1] + bcoefr * sump[
ja + 1] + bcoefi * sump[ja - 1];
} else {
sum[ja - 1] = -acoef * sums[ja - 1] + bcoefr * sump[
ja - 1];
}
}
/* T */
/* Solve ( a A - b B ) y = SUM(,) */
/* with scaling and perturbation of the denominator */
slaln2_(&c_true, &na, &nw, &dmin__, &acoef, &s[j + j * s_dim1]
, lds, bdiag, &bdiag[1], sum, &c__2, &bcoefr, &bcoefi,
&work[(*n << 1) + j], n, &scale, &temp, &iinfo);
if (scale < 1.f) {
i__3 = nw - 1;
for (jw = 0; jw <= i__3; ++jw) {
i__4 = j - 1;
for (jr = je; jr <= i__4; ++jr) {
work[(jw + 2) * *n + jr] = scale * work[(jw + 2) *
*n + jr];
}
}
xmax = scale * xmax;
}
xmax = dmax(xmax,temp);
L160:
;
}
/* Copy eigenvector to VL, back transforming if */
/* HOWMNY='B'. */
++ieig;
if (ilback) {
i__2 = nw - 1;
for (jw = 0; jw <= i__2; ++jw) {
i__3 = *n + 1 - je;
sgemv_("N", n, &i__3, &c_b34, &vl[je * vl_dim1 + 1], ldvl,
&work[(jw + 2) * *n + je], &c__1, &c_b36, &work[(
jw + 4) * *n + 1], &c__1);
}
slacpy_(" ", n, &nw, &work[(*n << 2) + 1], n, &vl[je *
vl_dim1 + 1], ldvl);
ibeg = 1;
} else {
slacpy_(" ", n, &nw, &work[(*n << 1) + 1], n, &vl[ieig *
vl_dim1 + 1], ldvl);
ibeg = je;
}
/* Scale eigenvector */
xmax = 0.f;
if (ilcplx) {
i__2 = *n;
for (j = ibeg; j <= i__2; ++j) {
/* Computing MAX */
r__3 = xmax, r__4 = (r__1 = vl[j + ieig * vl_dim1], dabs(
r__1)) + (r__2 = vl[j + (ieig + 1) * vl_dim1],
dabs(r__2));
xmax = dmax(r__3,r__4);
}
} else {
i__2 = *n;
for (j = ibeg; j <= i__2; ++j) {
/* Computing MAX */
r__2 = xmax, r__3 = (r__1 = vl[j + ieig * vl_dim1], dabs(
r__1));
xmax = dmax(r__2,r__3);
}
}
if (xmax > safmin) {
xscale = 1.f / xmax;
i__2 = nw - 1;
for (jw = 0; jw <= i__2; ++jw) {
i__3 = *n;
for (jr = ibeg; jr <= i__3; ++jr) {
vl[jr + (ieig + jw) * vl_dim1] = xscale * vl[jr + (
ieig + jw) * vl_dim1];
}
}
}
ieig = ieig + nw - 1;
L220:
;
}
}
/* Right eigenvectors */
if (compr) {
ieig = im + 1;
/* Main loop over eigenvalues */
ilcplx = FALSE_;
for (je = *n; je >= 1; --je) {
/* Skip this iteration if (a) HOWMNY='S' and SELECT=.FALSE., or */
/* (b) this would be the second of a complex pair. */
/* Check for complex eigenvalue, so as to be sure of which */
/* entry(-ies) of SELECT to look at -- if complex, SELECT(JE) */
/* or SELECT(JE-1). */
/* If this is a complex pair, the 2-by-2 diagonal block */
/* corresponding to the eigenvalue is in rows/columns JE-1:JE */
if (ilcplx) {
ilcplx = FALSE_;
goto L500;
}
nw = 1;
if (je > 1) {
if (s[je + (je - 1) * s_dim1] != 0.f) {
ilcplx = TRUE_;
nw = 2;
}
}
if (ilall) {
ilcomp = TRUE_;
} else if (ilcplx) {
ilcomp = select[je] || select[je - 1];
} else {
ilcomp = select[je];
}
if (! ilcomp) {
goto L500;
}
/* Decide if (a) singular pencil, (b) real eigenvalue, or */
/* (c) complex eigenvalue. */
if (! ilcplx) {
if ((r__1 = s[je + je * s_dim1], dabs(r__1)) <= safmin && (
r__2 = p[je + je * p_dim1], dabs(r__2)) <= safmin) {
/* Singular matrix pencil -- unit eigenvector */
--ieig;
i__1 = *n;
for (jr = 1; jr <= i__1; ++jr) {
vr[jr + ieig * vr_dim1] = 0.f;
}
vr[ieig + ieig * vr_dim1] = 1.f;
goto L500;
}
}
/* Clear vector */
i__1 = nw - 1;
for (jw = 0; jw <= i__1; ++jw) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
work[(jw + 2) * *n + jr] = 0.f;
}
}
/* Compute coefficients in ( a A - b B ) x = 0 */
/* a is ACOEF */
/* b is BCOEFR + i*BCOEFI */
if (! ilcplx) {
/* Real eigenvalue */
/* Computing MAX */
r__3 = (r__1 = s[je + je * s_dim1], dabs(r__1)) * ascale,
r__4 = (r__2 = p[je + je * p_dim1], dabs(r__2)) *
bscale, r__3 = max(r__3,r__4);
temp = 1.f / dmax(r__3,safmin);
salfar = temp * s[je + je * s_dim1] * ascale;
sbeta = temp * p[je + je * p_dim1] * bscale;
acoef = sbeta * ascale;
bcoefr = salfar * bscale;
bcoefi = 0.f;
/* Scale to avoid underflow */
scale = 1.f;
lsa = dabs(sbeta) >= safmin && dabs(acoef) < small;
lsb = dabs(salfar) >= safmin && dabs(bcoefr) < small;
if (lsa) {
scale = small / dabs(sbeta) * dmin(anorm,big);
}
if (lsb) {
/* Computing MAX */
r__1 = scale, r__2 = small / dabs(salfar) * dmin(bnorm,
big);
scale = dmax(r__1,r__2);
}
if (lsa || lsb) {
/* Computing MIN */
/* Computing MAX */
r__3 = 1.f, r__4 = dabs(acoef), r__3 = max(r__3,r__4),
r__4 = dabs(bcoefr);
r__1 = scale, r__2 = 1.f / (safmin * dmax(r__3,r__4));
scale = dmin(r__1,r__2);
if (lsa) {
acoef = ascale * (scale * sbeta);
} else {
acoef = scale * acoef;
}
if (lsb) {
bcoefr = bscale * (scale * salfar);
} else {
bcoefr = scale * bcoefr;
}
}
acoefa = dabs(acoef);
bcoefa = dabs(bcoefr);
/* First component is 1 */
work[(*n << 1) + je] = 1.f;
xmax = 1.f;
/* Compute contribution from column JE of A and B to sum */
/* (See "Further Details", above.) */
i__1 = je - 1;
for (jr = 1; jr <= i__1; ++jr) {
work[(*n << 1) + jr] = bcoefr * p[jr + je * p_dim1] -
acoef * s[jr + je * s_dim1];
}
} else {
/* Complex eigenvalue */
r__1 = safmin * 100.f;
slag2_(&s[je - 1 + (je - 1) * s_dim1], lds, &p[je - 1 + (je -
1) * p_dim1], ldp, &r__1, &acoef, &temp, &bcoefr, &
temp2, &bcoefi);
if (bcoefi == 0.f) {
*info = je - 1;
return 0;
}
/* Scale to avoid over/underflow */
acoefa = dabs(acoef);
bcoefa = dabs(bcoefr) + dabs(bcoefi);
scale = 1.f;
if (acoefa * ulp < safmin && acoefa >= safmin) {
scale = safmin / ulp / acoefa;
}
if (bcoefa * ulp < safmin && bcoefa >= safmin) {
/* Computing MAX */
r__1 = scale, r__2 = safmin / ulp / bcoefa;
scale = dmax(r__1,r__2);
}
if (safmin * acoefa > ascale) {
scale = ascale / (safmin * acoefa);
}
if (safmin * bcoefa > bscale) {
/* Computing MIN */
r__1 = scale, r__2 = bscale / (safmin * bcoefa);
scale = dmin(r__1,r__2);
}
if (scale != 1.f) {
acoef = scale * acoef;
acoefa = dabs(acoef);
bcoefr = scale * bcoefr;
bcoefi = scale * bcoefi;
bcoefa = dabs(bcoefr) + dabs(bcoefi);
}
/* Compute first two components of eigenvector */
/* and contribution to sums */
temp = acoef * s[je + (je - 1) * s_dim1];
temp2r = acoef * s[je + je * s_dim1] - bcoefr * p[je + je *
p_dim1];
temp2i = -bcoefi * p[je + je * p_dim1];
if (dabs(temp) >= dabs(temp2r) + dabs(temp2i)) {
work[(*n << 1) + je] = 1.f;
work[*n * 3 + je] = 0.f;
work[(*n << 1) + je - 1] = -temp2r / temp;
work[*n * 3 + je - 1] = -temp2i / temp;
} else {
work[(*n << 1) + je - 1] = 1.f;
work[*n * 3 + je - 1] = 0.f;
temp = acoef * s[je - 1 + je * s_dim1];
work[(*n << 1) + je] = (bcoefr * p[je - 1 + (je - 1) *
p_dim1] - acoef * s[je - 1 + (je - 1) * s_dim1]) /
temp;
work[*n * 3 + je] = bcoefi * p[je - 1 + (je - 1) * p_dim1]
/ temp;
}
/* Computing MAX */
r__5 = (r__1 = work[(*n << 1) + je], dabs(r__1)) + (r__2 =
work[*n * 3 + je], dabs(r__2)), r__6 = (r__3 = work[(*
n << 1) + je - 1], dabs(r__3)) + (r__4 = work[*n * 3
+ je - 1], dabs(r__4));
xmax = dmax(r__5,r__6);
/* Compute contribution from columns JE and JE-1 */
/* of A and B to the sums. */
creala = acoef * work[(*n << 1) + je - 1];
cimaga = acoef * work[*n * 3 + je - 1];
crealb = bcoefr * work[(*n << 1) + je - 1] - bcoefi * work[*n
* 3 + je - 1];
cimagb = bcoefi * work[(*n << 1) + je - 1] + bcoefr * work[*n
* 3 + je - 1];
cre2a = acoef * work[(*n << 1) + je];
cim2a = acoef * work[*n * 3 + je];
cre2b = bcoefr * work[(*n << 1) + je] - bcoefi * work[*n * 3
+ je];
cim2b = bcoefi * work[(*n << 1) + je] + bcoefr * work[*n * 3
+ je];
i__1 = je - 2;
for (jr = 1; jr <= i__1; ++jr) {
work[(*n << 1) + jr] = -creala * s[jr + (je - 1) * s_dim1]
+ crealb * p[jr + (je - 1) * p_dim1] - cre2a * s[
jr + je * s_dim1] + cre2b * p[jr + je * p_dim1];
work[*n * 3 + jr] = -cimaga * s[jr + (je - 1) * s_dim1] +
cimagb * p[jr + (je - 1) * p_dim1] - cim2a * s[jr
+ je * s_dim1] + cim2b * p[jr + je * p_dim1];
}
}
/* Computing MAX */
r__1 = ulp * acoefa * anorm, r__2 = ulp * bcoefa * bnorm, r__1 =
max(r__1,r__2);
dmin__ = dmax(r__1,safmin);
/* Columnwise triangular solve of (a A - b B) x = 0 */
il2by2 = FALSE_;
for (j = je - nw; j >= 1; --j) {
/* If a 2-by-2 block, is in position j-1:j, wait until */
/* next iteration to process it (when it will be j:j+1) */
if (! il2by2 && j > 1) {
if (s[j + (j - 1) * s_dim1] != 0.f) {
il2by2 = TRUE_;
goto L370;
}
}
bdiag[0] = p[j + j * p_dim1];
if (il2by2) {
na = 2;
bdiag[1] = p[j + 1 + (j + 1) * p_dim1];
} else {
na = 1;
}
/* Compute x(j) (and x(j+1), if 2-by-2 block) */
slaln2_(&c_false, &na, &nw, &dmin__, &acoef, &s[j + j *
s_dim1], lds, bdiag, &bdiag[1], &work[(*n << 1) + j],
n, &bcoefr, &bcoefi, sum, &c__2, &scale, &temp, &
iinfo);
if (scale < 1.f) {
i__1 = nw - 1;
for (jw = 0; jw <= i__1; ++jw) {
i__2 = je;
for (jr = 1; jr <= i__2; ++jr) {
work[(jw + 2) * *n + jr] = scale * work[(jw + 2) *
*n + jr];
}
}
}
/* Computing MAX */
r__1 = scale * xmax;
xmax = dmax(r__1,temp);
i__1 = nw;
for (jw = 1; jw <= i__1; ++jw) {
i__2 = na;
for (ja = 1; ja <= i__2; ++ja) {
work[(jw + 1) * *n + j + ja - 1] = sum[ja + (jw << 1)
- 3];
}
}
/* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
if (j > 1) {
/* Check whether scaling is necessary for sum. */
xscale = 1.f / dmax(1.f,xmax);
temp = acoefa * work[j] + bcoefa * work[*n + j];
if (il2by2) {
/* Computing MAX */
r__1 = temp, r__2 = acoefa * work[j + 1] + bcoefa *
work[*n + j + 1];
temp = dmax(r__1,r__2);
}
/* Computing MAX */
r__1 = max(temp,acoefa);
temp = dmax(r__1,bcoefa);
if (temp > bignum * xscale) {
i__1 = nw - 1;
for (jw = 0; jw <= i__1; ++jw) {
i__2 = je;
for (jr = 1; jr <= i__2; ++jr) {
work[(jw + 2) * *n + jr] = xscale * work[(jw
+ 2) * *n + jr];
}
}
xmax *= xscale;
}
/* Compute the contributions of the off-diagonals of */
/* column j (and j+1, if 2-by-2 block) of A and B to the */
/* sums. */
i__1 = na;
for (ja = 1; ja <= i__1; ++ja) {
if (ilcplx) {
creala = acoef * work[(*n << 1) + j + ja - 1];
cimaga = acoef * work[*n * 3 + j + ja - 1];
crealb = bcoefr * work[(*n << 1) + j + ja - 1] -
bcoefi * work[*n * 3 + j + ja - 1];
cimagb = bcoefi * work[(*n << 1) + j + ja - 1] +
bcoefr * work[*n * 3 + j + ja - 1];
i__2 = j - 1;
for (jr = 1; jr <= i__2; ++jr) {
work[(*n << 1) + jr] = work[(*n << 1) + jr] -
creala * s[jr + (j + ja - 1) * s_dim1]
+ crealb * p[jr + (j + ja - 1) *
p_dim1];
work[*n * 3 + jr] = work[*n * 3 + jr] -
cimaga * s[jr + (j + ja - 1) * s_dim1]
+ cimagb * p[jr + (j + ja - 1) *
p_dim1];
}
} else {
creala = acoef * work[(*n << 1) + j + ja - 1];
crealb = bcoefr * work[(*n << 1) + j + ja - 1];
i__2 = j - 1;
for (jr = 1; jr <= i__2; ++jr) {
work[(*n << 1) + jr] = work[(*n << 1) + jr] -
creala * s[jr + (j + ja - 1) * s_dim1]
+ crealb * p[jr + (j + ja - 1) *
p_dim1];
}
}
}
}
il2by2 = FALSE_;
L370:
;
}
/* Copy eigenvector to VR, back transforming if */
/* HOWMNY='B'. */
ieig -= nw;
if (ilback) {
i__1 = nw - 1;
for (jw = 0; jw <= i__1; ++jw) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
work[(jw + 4) * *n + jr] = work[(jw + 2) * *n + 1] *
vr[jr + vr_dim1];
}
/* A series of compiler directives to defeat */
/* vectorization for the next loop */
i__2 = je;
for (jc = 2; jc <= i__2; ++jc) {
i__3 = *n;
for (jr = 1; jr <= i__3; ++jr) {
work[(jw + 4) * *n + jr] += work[(jw + 2) * *n +
jc] * vr[jr + jc * vr_dim1];
}
}
}
i__1 = nw - 1;
for (jw = 0; jw <= i__1; ++jw) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + (ieig + jw) * vr_dim1] = work[(jw + 4) * *n +
jr];
}
}
iend = *n;
} else {
i__1 = nw - 1;
for (jw = 0; jw <= i__1; ++jw) {
i__2 = *n;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + (ieig + jw) * vr_dim1] = work[(jw + 2) * *n +
jr];
}
}
iend = je;
}
/* Scale eigenvector */
xmax = 0.f;
if (ilcplx) {
i__1 = iend;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
r__3 = xmax, r__4 = (r__1 = vr[j + ieig * vr_dim1], dabs(
r__1)) + (r__2 = vr[j + (ieig + 1) * vr_dim1],
dabs(r__2));
xmax = dmax(r__3,r__4);
}
} else {
i__1 = iend;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
r__2 = xmax, r__3 = (r__1 = vr[j + ieig * vr_dim1], dabs(
r__1));
xmax = dmax(r__2,r__3);
}
}
if (xmax > safmin) {
xscale = 1.f / xmax;
i__1 = nw - 1;
for (jw = 0; jw <= i__1; ++jw) {
i__2 = iend;
for (jr = 1; jr <= i__2; ++jr) {
vr[jr + (ieig + jw) * vr_dim1] = xscale * vr[jr + (
ieig + jw) * vr_dim1];
}
}
}
L500:
;
}
}
return 0;
/* End of STGEVC */
} /* stgevc_ */
/* Subroutine */
int slaqtr_(logical *ltran, logical *lreal, integer *n, real *t, integer *ldt, real *b, real *w, real *scale, real *x, real *work, integer *info)
{
/* System generated locals */
integer t_dim1, t_offset, i__1, i__2;
real r__1, r__2, r__3, r__4, r__5, r__6;
/* Local variables */
real d__[4] /* was [2][2] */
;
integer i__, j, k;
real v[4] /* was [2][2] */
, z__;
integer j1, j2, n1, n2;
real si, xj, sr, rec, eps, tjj, tmp;
integer ierr;
real smin;
extern real sdot_(integer *, real *, integer *, real *, integer *);
real xmax;
extern /* Subroutine */
int sscal_(integer *, real *, real *, integer *);
integer jnext;
extern real sasum_(integer *, real *, integer *);
real sminw, xnorm;
extern /* Subroutine */
int saxpy_(integer *, real *, real *, integer *, real *, integer *), slaln2_(logical *, integer *, integer *, real *, real *, real *, integer *, real *, real *, real *, integer *, real *, real *, real *, integer *, real *, real *, integer *);
real scaloc;
extern real slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *);
real bignum;
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */
int sladiv_(real *, real *, real *, real *, real * , real *);
logical notran;
real smlnum;
/* -- 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 .. */
/* .. */
/* .. 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 = slamch_("P");
smlnum = slamch_("S") / eps;
bignum = 1.f / smlnum;
xnorm = slange_("M", n, n, &t[t_offset], ldt, d__);
if (! (*lreal))
{
/* Computing MAX */
r__1 = xnorm, r__2 = abs(*w);
r__1 = max(r__1,r__2);
r__2 = slange_( "M", n, &c__1, &b[1], n, d__); // ; expr subst
xnorm = max(r__1,r__2);
}
/* Computing MAX */
r__1 = smlnum;
r__2 = eps * xnorm; // , expr subst
smin = max(r__1,r__2);
/* Compute 1-norm of each column of strictly upper triangular */
/* part of T to control overflow in triangular solver. */
work[1] = 0.f;
i__1 = *n;
for (j = 2;
j <= i__1;
++j)
{
i__2 = j - 1;
work[j] = sasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
/* L10: */
}
if (! (*lreal))
{
i__1 = *n;
for (i__ = 2;
i__ <= i__1;
++i__)
{
work[i__] += (r__1 = b[i__], abs(r__1));
/* L20: */
}
}
n2 = *n << 1;
n1 = *n;
if (! (*lreal))
{
n1 = n2;
}
k = isamax_(&n1, &x[1], &c__1);
xmax = (r__1 = x[k], abs(r__1));
*scale = 1.f;
if (xmax > bignum)
{
*scale = bignum / xmax;
sscal_(&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.f)
{
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 = (r__1 = x[j1], abs(r__1));
tjj = (r__1 = t[j1 + j1 * t_dim1], abs(r__1));
tmp = t[j1 + j1 * t_dim1];
if (tjj < smin)
{
tmp = smin;
tjj = smin;
*info = 1;
}
if (xj == 0.f)
{
goto L30;
}
if (tjj < 1.f)
{
if (xj > bignum * tjj)
{
rec = 1.f / xj;
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
x[j1] /= tmp;
xj = (r__1 = x[j1], abs(r__1));
/* Scale x if necessary to avoid overflow when adding a */
/* multiple of column j1 of T. */
if (xj > 1.f)
{
rec = 1.f / xj;
if (work[j1] > (bignum - xmax) * rec)
{
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
}
if (j1 > 1)
{
i__1 = j1 - 1;
r__1 = -x[j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1] , &c__1);
i__1 = j1 - 1;
k = isamax_(&i__1, &x[1], &c__1);
xmax = (r__1 = x[k], abs(r__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];
slaln2_(&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.f)
{
sscal_(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 */
r__1 = abs(v[0]);
r__2 = abs(v[1]); // , expr subst
xj = max(r__1,r__2);
if (xj > 1.f)
{
rec = 1.f / xj;
/* Computing MAX */
r__1 = work[j1];
r__2 = work[j2]; // , expr subst
if (max(r__1,r__2) > (bignum - xmax) * rec)
{
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
}
/* Update right-hand side */
if (j1 > 1)
{
i__1 = j1 - 1;
r__1 = -x[j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1] , &c__1);
i__1 = j1 - 1;
r__1 = -x[j2];
saxpy_(&i__1, &r__1, &t[j2 * t_dim1 + 1], &c__1, &x[1] , &c__1);
i__1 = j1 - 1;
k = isamax_(&i__1, &x[1], &c__1);
xmax = (r__1 = x[k], abs(r__1));
}
}
L30:
;
}
}
else
{
/* Solve T**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.f)
{
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 = (r__1 = x[j1], abs(r__1));
if (xmax > 1.f)
{
rec = 1.f / xmax;
if (work[j1] > (bignum - xj) * rec)
{
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
x[j1] -= sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], & c__1);
xj = (r__1 = x[j1], abs(r__1));
tjj = (r__1 = t[j1 + j1 * t_dim1], abs(r__1));
tmp = t[j1 + j1 * t_dim1];
if (tjj < smin)
{
tmp = smin;
tjj = smin;
*info = 1;
}
if (tjj < 1.f)
{
if (xj > bignum * tjj)
{
rec = 1.f / xj;
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
x[j1] /= tmp;
/* Computing MAX */
r__2 = xmax;
r__3 = (r__1 = x[j1], abs(r__1)); // , expr subst
xmax = max(r__2,r__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 */
r__3 = (r__1 = x[j1], abs(r__1));
r__4 = (r__2 = x[j2], abs(r__2)); // , expr subst
xj = max(r__3,r__4);
if (xmax > 1.f)
{
rec = 1.f / xmax;
/* Computing MAX */
r__1 = work[j2];
r__2 = work[j1]; // , expr subst
if (max(r__1,r__2) > (bignum - xj) * rec)
{
sscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
d__[0] = x[j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &c__1);
i__2 = j1 - 1;
d__[1] = x[j2] - sdot_(&i__2, &t[j2 * t_dim1 + 1], &c__1, &x[1], &c__1);
slaln2_(&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.f)
{
sscal_(n, &scaloc, &x[1], &c__1);
*scale *= scaloc;
}
x[j1] = v[0];
x[j2] = v[1];
/* Computing MAX */
r__3 = (r__1 = x[j1], abs(r__1));
r__4 = (r__2 = x[j2], abs(r__2));
r__3 = max(r__3,r__4); // ; expr subst
xmax = max(r__3,xmax);
}
L40:
;
}
}
}
else
{
/* Computing MAX */
r__1 = eps * abs(*w);
sminw = max(r__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.f)
{
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 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[*n + j1], abs( r__2));
tjj = (r__1 = t[j1 + j1 * t_dim1], abs(r__1)) + abs(z__);
tmp = t[j1 + j1 * t_dim1];
if (tjj < sminw)
{
tmp = sminw;
tjj = sminw;
*info = 1;
}
if (xj == 0.f)
{
goto L70;
}
if (tjj < 1.f)
{
if (xj > bignum * tjj)
{
rec = 1.f / xj;
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
sladiv_(&x[j1], &x[*n + j1], &tmp, &z__, &sr, &si);
x[j1] = sr;
x[*n + j1] = si;
xj = (r__1 = x[j1], abs(r__1)) + (r__2 = x[*n + j1], abs( r__2));
/* Scale x if necessary to avoid overflow when adding a */
/* multiple of column j1 of T. */
if (xj > 1.f)
{
rec = 1.f / xj;
if (work[j1] > (bignum - xmax) * rec)
{
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
}
}
if (j1 > 1)
{
i__1 = j1 - 1;
r__1 = -x[j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1] , &c__1);
i__1 = j1 - 1;
r__1 = -x[*n + j1];
saxpy_(&i__1, &r__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.f;
i__1 = j1 - 1;
for (k = 1;
k <= i__1;
++k)
{
/* Computing MAX */
r__3 = xmax;
r__4 = (r__1 = x[k], abs(r__1)) + ( r__2 = x[k + *n], abs(r__2)); // , expr subst
xmax = max(r__3,r__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];
r__1 = -(*w);
slaln2_(&c_false, &c__2, &c__2, &sminw, &c_b21, &t[j1 + j1 * t_dim1], ldt, &c_b21, &c_b21, d__, &c__2, & c_b25, &r__1, v, &c__2, &scaloc, &xnorm, &ierr);
if (ierr != 0)
{
*info = 2;
}
if (scaloc != 1.f)
{
i__1 = *n << 1;
sscal_(&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 */
r__1 = abs(v[0]) + abs(v[2]);
r__2 = abs(v[1]) + abs(v[3]) ; // , expr subst
xj = max(r__1,r__2);
if (xj > 1.f)
{
rec = 1.f / xj;
/* Computing MAX */
r__1 = work[j1];
r__2 = work[j2]; // , expr subst
if (max(r__1,r__2) > (bignum - xmax) * rec)
{
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
}
}
/* Update the right-hand side. */
if (j1 > 1)
{
i__1 = j1 - 1;
r__1 = -x[j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[1] , &c__1);
i__1 = j1 - 1;
r__1 = -x[j2];
saxpy_(&i__1, &r__1, &t[j2 * t_dim1 + 1], &c__1, &x[1] , &c__1);
i__1 = j1 - 1;
r__1 = -x[*n + j1];
saxpy_(&i__1, &r__1, &t[j1 * t_dim1 + 1], &c__1, &x[* n + 1], &c__1);
i__1 = j1 - 1;
r__1 = -x[*n + j2];
saxpy_(&i__1, &r__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.f;
i__1 = j1 - 1;
for (k = 1;
k <= i__1;
++k)
{
/* Computing MAX */
r__3 = (r__1 = x[k], abs(r__1)) + (r__2 = x[k + * n], abs(r__2));
xmax = max(r__3,xmax);
/* L60: */
}
}
}
L70:
;
}
}
else
{
/* Solve (T + iB)**T*(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.f)
{
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 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[j1 + *n], abs( r__2));
if (xmax > 1.f)
{
rec = 1.f / xmax;
if (work[j1] > (bignum - xj) * rec)
{
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
x[j1] -= sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], & c__1);
i__2 = j1 - 1;
x[*n + j1] -= sdot_(&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 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[j1 + *n], abs( r__2));
z__ = *w;
if (j1 == 1)
{
z__ = b[1];
}
/* Scale if necessary to avoid overflow in */
/* complex division */
tjj = (r__1 = t[j1 + j1 * t_dim1], abs(r__1)) + abs(z__);
tmp = t[j1 + j1 * t_dim1];
if (tjj < sminw)
{
tmp = sminw;
tjj = sminw;
*info = 1;
}
if (tjj < 1.f)
{
if (xj > bignum * tjj)
{
rec = 1.f / xj;
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
r__1 = -z__;
sladiv_(&x[j1], &x[*n + j1], &tmp, &r__1, &sr, &si);
x[j1] = sr;
x[j1 + *n] = si;
/* Computing MAX */
r__3 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[j1 + *n], abs(r__2));
xmax = max(r__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 */
r__5 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[*n + j1], abs(r__2));
r__6 = (r__3 = x[j2], abs(r__3)) + ( r__4 = x[*n + j2], abs(r__4)); // , expr subst
xj = max(r__5,r__6);
if (xmax > 1.f)
{
rec = 1.f / xmax;
/* Computing MAX */
r__1 = work[j1];
r__2 = work[j2]; // , expr subst
if (max(r__1,r__2) > (bignum - xj) / xmax)
{
sscal_(&n2, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__2 = j1 - 1;
d__[0] = x[j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], &c__1, &x[1], &c__1);
i__2 = j1 - 1;
d__[1] = x[j2] - sdot_(&i__2, &t[j2 * t_dim1 + 1], &c__1, &x[1], &c__1);
i__2 = j1 - 1;
d__[2] = x[*n + j1] - sdot_(&i__2, &t[j1 * t_dim1 + 1], & c__1, &x[*n + 1], &c__1);
i__2 = j1 - 1;
d__[3] = x[*n + j2] - sdot_(&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];
slaln2_(&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.f)
{
sscal_(&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 */
r__5 = (r__1 = x[j1], abs(r__1)) + (r__2 = x[*n + j1], abs(r__2));
r__6 = (r__3 = x[j2], abs(r__3)) + ( r__4 = x[*n + j2], abs(r__4));
r__5 = max(r__5, r__6); // ; expr subst
xmax = max(r__5,xmax);
}
L80:
;
}
}
}
return 0;
/* End of SLAQTR */
}
/* Subroutine */ int strevc_(char *side, char *howmny, logical *select,
integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr,
integer *ldvr, integer *mm, integer *m, real *work, integer *info)
{
/* System generated locals */
integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
real r__1, r__2, r__3, r__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
real x[4] /* was [2][2] */;
integer j1, j2, n2, ii, ki, ip, is;
real wi, wr, rec, ulp, beta, emax;
logical pair, allv;
integer ierr;
real unfl, ovfl, smin;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
logical over;
real vmax;
integer jnxt;
real scale;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
real remax;
logical leftv;
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *);
logical bothv;
real vcrit;
logical somev;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
real xnorm;
extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
real *, integer *), slaln2_(logical *, integer *, integer *, real
*, real *, real *, integer *, real *, real *, real *, integer *,
real *, real *, real *, integer *, real *, real *, integer *),
slabad_(real *, real *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
extern integer isamax_(integer *, real *, integer *);
logical rightv;
real smlnum;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* STREVC computes some or all of the right and/or left eigenvectors of */
/* a real upper quasi-triangular matrix T. */
/* Matrices of this type are produced by the Schur factorization of */
/* a real general matrix: A = Q*T*Q**T, as computed by SHSEQR. */
/* The right eigenvector x and the left eigenvector y of T corresponding */
/* to an eigenvalue w are defined by: */
/* T*x = w*x, (y**H)*T = w*(y**H) */
/* where y**H denotes the conjugate transpose of y. */
/* The eigenvalues are not input to this routine, but are read directly */
/* from the diagonal blocks of T. */
/* This routine returns the matrices X and/or Y of right and left */
/* eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an */
/* input matrix. If Q is the orthogonal factor that reduces a matrix */
/* A to Schur form T, then Q*X and Q*Y are the matrices of right and */
/* left eigenvectors of A. */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'R': compute right eigenvectors only; */
/* = 'L': compute left eigenvectors only; */
/* = 'B': compute both right and left eigenvectors. */
/* HOWMNY (input) CHARACTER*1 */
/* = 'A': compute all right and/or left eigenvectors; */
/* = 'B': compute all right and/or left eigenvectors, */
/* backtransformed by the matrices in VR and/or VL; */
/* = 'S': compute selected right and/or left eigenvectors, */
/* as indicated by the logical array SELECT. */
/* SELECT (input/output) LOGICAL array, dimension (N) */
/* If HOWMNY = 'S', SELECT specifies the eigenvectors to be */
/* computed. */
/* If w(j) is a real eigenvalue, the corresponding real */
/* eigenvector is computed if SELECT(j) is .TRUE.. */
/* If w(j) and w(j+1) are the real and imaginary parts of a */
/* complex eigenvalue, the corresponding complex eigenvector is */
/* computed if either SELECT(j) or SELECT(j+1) is .TRUE., and */
/* on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to */
/* .FALSE.. */
/* Not referenced if HOWMNY = 'A' or 'B'. */
/* N (input) INTEGER */
/* The order of the matrix T. N >= 0. */
/* T (input) REAL array, dimension (LDT,N) */
/* The upper quasi-triangular matrix T in Schur canonical form. */
/* LDT (input) INTEGER */
/* The leading dimension of the array T. LDT >= max(1,N). */
/* VL (input/output) REAL array, dimension (LDVL,MM) */
/* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
/* contain an N-by-N matrix Q (usually the orthogonal matrix Q */
/* of Schur vectors returned by SHSEQR). */
/* On exit, if SIDE = 'L' or 'B', VL contains: */
/* if HOWMNY = 'A', the matrix Y of left eigenvectors of T; */
/* if HOWMNY = 'B', the matrix Q*Y; */
/* if HOWMNY = 'S', the left eigenvectors of T specified by */
/* SELECT, stored consecutively in the columns */
/* of VL, in the same order as their */
/* eigenvalues. */
/* A complex eigenvector corresponding to a complex eigenvalue */
/* is stored in two consecutive columns, the first holding the */
/* real part, and the second the imaginary part. */
/* Not referenced if SIDE = 'R'. */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1, and if */
/* SIDE = 'L' or 'B', LDVL >= N. */
/* VR (input/output) REAL array, dimension (LDVR,MM) */
/* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
/* contain an N-by-N matrix Q (usually the orthogonal matrix Q */
/* of Schur vectors returned by SHSEQR). */
/* On exit, if SIDE = 'R' or 'B', VR contains: */
/* if HOWMNY = 'A', the matrix X of right eigenvectors of T; */
/* if HOWMNY = 'B', the matrix Q*X; */
/* if HOWMNY = 'S', the right eigenvectors of T specified by */
/* SELECT, stored consecutively in the columns */
/* of VR, in the same order as their */
/* eigenvalues. */
/* A complex eigenvector corresponding to a complex eigenvalue */
/* is stored in two consecutive columns, the first holding the */
/* real part and the second the imaginary part. */
/* Not referenced if SIDE = 'L'. */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1, and if */
/* SIDE = 'R' or 'B', LDVR >= N. */
/* MM (input) INTEGER */
/* The number of columns in the arrays VL and/or VR. MM >= M. */
/* M (output) INTEGER */
/* The number of columns in the arrays VL and/or VR actually */
/* used to store the eigenvectors. */
/* If HOWMNY = 'A' or 'B', M is set to N. */
/* Each selected real eigenvector occupies one column and each */
/* selected complex eigenvector occupies two columns. */
/* WORK (workspace) REAL array, dimension (3*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* The algorithm used in this program is basically backward (forward) */
/* substitution, with scaling to make the the code robust against */
/* possible overflow. */
/* Each eigenvector is normalized so that the element of largest */
/* magnitude has magnitude 1; here the magnitude of a complex number */
/* (x,y) is taken to be |x| + |y|. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and test the input parameters */
/* Parameter adjustments */
--select;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
/* Function Body */
bothv = lsame_(side, "B");
rightv = lsame_(side, "R") || bothv;
leftv = lsame_(side, "L") || bothv;
allv = lsame_(howmny, "A");
over = lsame_(howmny, "B");
somev = lsame_(howmny, "S");
*info = 0;
if (! rightv && ! leftv) {
*info = -1;
} else if (! allv && ! over && ! somev) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*ldt < max(1,*n)) {
*info = -6;
} else if (*ldvl < 1 || leftv && *ldvl < *n) {
*info = -8;
} else if (*ldvr < 1 || rightv && *ldvr < *n) {
*info = -10;
} else {
/* Set M to the number of columns required to store the selected */
/* eigenvectors, standardize the array SELECT if necessary, and */
/* test MM. */
if (somev) {
*m = 0;
pair = FALSE_;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (pair) {
pair = FALSE_;
select[j] = FALSE_;
} else {
if (j < *n) {
if (t[j + 1 + j * t_dim1] == 0.f) {
if (select[j]) {
++(*m);
}
} else {
pair = TRUE_;
if (select[j] || select[j + 1]) {
select[j] = TRUE_;
*m += 2;
}
}
} else {
if (select[*n]) {
++(*m);
}
}
}
/* L10: */
}
} else {
*m = *n;
}
if (*mm < *m) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STREVC", &i__1);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
/* Set the constants to control overflow. */
unfl = slamch_("Safe minimum");
ovfl = 1.f / unfl;
slabad_(&unfl, &ovfl);
ulp = slamch_("Precision");
smlnum = unfl * (*n / ulp);
bignum = (1.f - ulp) / smlnum;
/* Compute 1-norm of each column of strictly upper triangular */
/* part of T to control overflow in triangular solver. */
work[1] = 0.f;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
work[j] = 0.f;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
work[j] += (r__1 = t[i__ + j * t_dim1], dabs(r__1));
/* L20: */
}
/* L30: */
}
/* Index IP is used to specify the real or complex eigenvalue: */
/* IP = 0, real eigenvalue, */
/* 1, first of conjugate complex pair: (wr,wi) */
/* -1, second of conjugate complex pair: (wr,wi) */
n2 = *n << 1;
if (rightv) {
/* Compute right eigenvectors. */
ip = 0;
is = *m;
for (ki = *n; ki >= 1; --ki) {
if (ip == 1) {
goto L130;
}
if (ki == 1) {
goto L40;
}
if (t[ki + (ki - 1) * t_dim1] == 0.f) {
goto L40;
}
ip = -1;
L40:
if (somev) {
if (ip == 0) {
if (! select[ki]) {
goto L130;
}
} else {
if (! select[ki - 1]) {
goto L130;
}
}
}
/* Compute the KI-th eigenvalue (WR,WI). */
wr = t[ki + ki * t_dim1];
wi = 0.f;
if (ip != 0) {
wi = sqrt((r__1 = t[ki + (ki - 1) * t_dim1], dabs(r__1))) *
sqrt((r__2 = t[ki - 1 + ki * t_dim1], dabs(r__2)));
}
/* Computing MAX */
r__1 = ulp * (dabs(wr) + dabs(wi));
smin = dmax(r__1,smlnum);
if (ip == 0) {
/* Real right eigenvector */
work[ki + *n] = 1.f;
/* Form right-hand side */
i__1 = ki - 1;
for (k = 1; k <= i__1; ++k) {
work[k + *n] = -t[k + ki * t_dim1];
/* L50: */
}
/* Solve the upper quasi-triangular system: */
/* (T(1:KI-1,1:KI-1) - WR)*X = SCALE*WORK. */
jnxt = ki - 1;
for (j = ki - 1; j >= 1; --j) {
if (j > jnxt) {
goto L60;
}
j1 = j;
j2 = j;
jnxt = j - 1;
if (j > 1) {
if (t[j + (j - 1) * t_dim1] != 0.f) {
j1 = j - 1;
jnxt = j - 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
slaln2_(&c_false, &c__1, &c__1, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm,
&ierr);
/* Scale X(1,1) to avoid overflow when updating */
/* the right-hand side. */
if (xnorm > 1.f) {
if (work[j] > bignum / xnorm) {
x[0] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.f) {
sscal_(&ki, &scale, &work[*n + 1], &c__1);
}
work[j + *n] = x[0];
/* Update right-hand side */
i__1 = j - 1;
r__1 = -x[0];
saxpy_(&i__1, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
*n + 1], &c__1);
} else {
/* 2-by-2 diagonal block */
slaln2_(&c_false, &c__2, &c__1, &smin, &c_b22, &t[j -
1 + (j - 1) * t_dim1], ldt, &c_b22, &c_b22, &
work[j - 1 + *n], n, &wr, &c_b25, x, &c__2, &
scale, &xnorm, &ierr);
/* Scale X(1,1) and X(2,1) to avoid overflow when */
/* updating the right-hand side. */
if (xnorm > 1.f) {
/* Computing MAX */
r__1 = work[j - 1], r__2 = work[j];
beta = dmax(r__1,r__2);
if (beta > bignum / xnorm) {
x[0] /= xnorm;
x[1] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.f) {
sscal_(&ki, &scale, &work[*n + 1], &c__1);
}
work[j - 1 + *n] = x[0];
work[j + *n] = x[1];
/* Update right-hand side */
i__1 = j - 2;
r__1 = -x[0];
saxpy_(&i__1, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[*n + 1], &c__1);
i__1 = j - 2;
r__1 = -x[1];
saxpy_(&i__1, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
*n + 1], &c__1);
}
L60:
;
}
/* Copy the vector x or Q*x to VR and normalize. */
if (! over) {
scopy_(&ki, &work[*n + 1], &c__1, &vr[is * vr_dim1 + 1], &
c__1);
ii = isamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);
remax = 1.f / (r__1 = vr[ii + is * vr_dim1], dabs(r__1));
sscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
i__1 = *n;
for (k = ki + 1; k <= i__1; ++k) {
vr[k + is * vr_dim1] = 0.f;
/* L70: */
}
} else {
if (ki > 1) {
i__1 = ki - 1;
sgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
work[*n + 1], &c__1, &work[ki + *n], &vr[ki *
vr_dim1 + 1], &c__1);
}
ii = isamax_(n, &vr[ki * vr_dim1 + 1], &c__1);
remax = 1.f / (r__1 = vr[ii + ki * vr_dim1], dabs(r__1));
sscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
}
} else {
/* Complex right eigenvector. */
/* Initial solve */
/* [ (T(KI-1,KI-1) T(KI-1,KI) ) - (WR + I* WI)]*X = 0. */
/* [ (T(KI,KI-1) T(KI,KI) ) ] */
if ((r__1 = t[ki - 1 + ki * t_dim1], dabs(r__1)) >= (r__2 = t[
ki + (ki - 1) * t_dim1], dabs(r__2))) {
work[ki - 1 + *n] = 1.f;
work[ki + n2] = wi / t[ki - 1 + ki * t_dim1];
} else {
work[ki - 1 + *n] = -wi / t[ki + (ki - 1) * t_dim1];
work[ki + n2] = 1.f;
}
work[ki + *n] = 0.f;
work[ki - 1 + n2] = 0.f;
/* Form right-hand side */
i__1 = ki - 2;
for (k = 1; k <= i__1; ++k) {
work[k + *n] = -work[ki - 1 + *n] * t[k + (ki - 1) *
t_dim1];
work[k + n2] = -work[ki + n2] * t[k + ki * t_dim1];
/* L80: */
}
/* Solve upper quasi-triangular system: */
/* (T(1:KI-2,1:KI-2) - (WR+i*WI))*X = SCALE*(WORK+i*WORK2) */
jnxt = ki - 2;
for (j = ki - 2; j >= 1; --j) {
if (j > jnxt) {
goto L90;
}
j1 = j;
j2 = j;
jnxt = j - 1;
if (j > 1) {
if (t[j + (j - 1) * t_dim1] != 0.f) {
j1 = j - 1;
jnxt = j - 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
slaln2_(&c_false, &c__1, &c__2, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &wi, x, &c__2, &scale, &xnorm, &
ierr);
/* Scale X(1,1) and X(1,2) to avoid overflow when */
/* updating the right-hand side. */
if (xnorm > 1.f) {
if (work[j] > bignum / xnorm) {
x[0] /= xnorm;
x[2] /= xnorm;
scale /= xnorm;
}
}
/* Scale if necessary */
if (scale != 1.f) {
sscal_(&ki, &scale, &work[*n + 1], &c__1);
sscal_(&ki, &scale, &work[n2 + 1], &c__1);
}
work[j + *n] = x[0];
work[j + n2] = x[2];
/* Update the right-hand side */
i__1 = j - 1;
r__1 = -x[0];
saxpy_(&i__1, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
*n + 1], &c__1);
i__1 = j - 1;
r__1 = -x[2];
saxpy_(&i__1, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
n2 + 1], &c__1);
} else {
/* 2-by-2 diagonal block */
slaln2_(&c_false, &c__2, &c__2, &smin, &c_b22, &t[j -
1 + (j - 1) * t_dim1], ldt, &c_b22, &c_b22, &
work[j - 1 + *n], n, &wr, &wi, x, &c__2, &
scale, &xnorm, &ierr);
/* Scale X to avoid overflow when updating */
/* the right-hand side. */
if (xnorm > 1.f) {
/* Computing MAX */
r__1 = work[j - 1], r__2 = work[j];
beta = dmax(r__1,r__2);
if (beta > bignum / xnorm) {
rec = 1.f / xnorm;
x[0] *= rec;
x[2] *= rec;
x[1] *= rec;
x[3] *= rec;
scale *= rec;
}
}
/* Scale if necessary */
if (scale != 1.f) {
sscal_(&ki, &scale, &work[*n + 1], &c__1);
sscal_(&ki, &scale, &work[n2 + 1], &c__1);
}
work[j - 1 + *n] = x[0];
work[j + *n] = x[1];
work[j - 1 + n2] = x[2];
work[j + n2] = x[3];
/* Update the right-hand side */
i__1 = j - 2;
r__1 = -x[0];
saxpy_(&i__1, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[*n + 1], &c__1);
i__1 = j - 2;
r__1 = -x[1];
saxpy_(&i__1, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
*n + 1], &c__1);
i__1 = j - 2;
r__1 = -x[2];
saxpy_(&i__1, &r__1, &t[(j - 1) * t_dim1 + 1], &c__1,
&work[n2 + 1], &c__1);
i__1 = j - 2;
r__1 = -x[3];
saxpy_(&i__1, &r__1, &t[j * t_dim1 + 1], &c__1, &work[
n2 + 1], &c__1);
}
L90:
;
}
/* Copy the vector x or Q*x to VR and normalize. */
if (! over) {
scopy_(&ki, &work[*n + 1], &c__1, &vr[(is - 1) * vr_dim1
+ 1], &c__1);
scopy_(&ki, &work[n2 + 1], &c__1, &vr[is * vr_dim1 + 1], &
c__1);
emax = 0.f;
i__1 = ki;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = vr[k + (is - 1) * vr_dim1]
, dabs(r__1)) + (r__2 = vr[k + is * vr_dim1],
dabs(r__2));
emax = dmax(r__3,r__4);
/* L100: */
}
remax = 1.f / emax;
sscal_(&ki, &remax, &vr[(is - 1) * vr_dim1 + 1], &c__1);
sscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
i__1 = *n;
for (k = ki + 1; k <= i__1; ++k) {
vr[k + (is - 1) * vr_dim1] = 0.f;
vr[k + is * vr_dim1] = 0.f;
/* L110: */
}
} else {
if (ki > 2) {
i__1 = ki - 2;
sgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
work[*n + 1], &c__1, &work[ki - 1 + *n], &vr[(
ki - 1) * vr_dim1 + 1], &c__1);
i__1 = ki - 2;
sgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &
work[n2 + 1], &c__1, &work[ki + n2], &vr[ki *
vr_dim1 + 1], &c__1);
} else {
sscal_(n, &work[ki - 1 + *n], &vr[(ki - 1) * vr_dim1
+ 1], &c__1);
sscal_(n, &work[ki + n2], &vr[ki * vr_dim1 + 1], &
c__1);
}
emax = 0.f;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = vr[k + (ki - 1) * vr_dim1]
, dabs(r__1)) + (r__2 = vr[k + ki * vr_dim1],
dabs(r__2));
emax = dmax(r__3,r__4);
/* L120: */
}
remax = 1.f / emax;
sscal_(n, &remax, &vr[(ki - 1) * vr_dim1 + 1], &c__1);
sscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
}
}
--is;
if (ip != 0) {
--is;
}
L130:
if (ip == 1) {
ip = 0;
}
if (ip == -1) {
ip = 1;
}
/* L140: */
}
}
if (leftv) {
/* Compute left eigenvectors. */
ip = 0;
is = 1;
i__1 = *n;
for (ki = 1; ki <= i__1; ++ki) {
if (ip == -1) {
goto L250;
}
if (ki == *n) {
goto L150;
}
if (t[ki + 1 + ki * t_dim1] == 0.f) {
goto L150;
}
ip = 1;
L150:
if (somev) {
if (! select[ki]) {
goto L250;
}
}
/* Compute the KI-th eigenvalue (WR,WI). */
wr = t[ki + ki * t_dim1];
wi = 0.f;
if (ip != 0) {
wi = sqrt((r__1 = t[ki + (ki + 1) * t_dim1], dabs(r__1))) *
sqrt((r__2 = t[ki + 1 + ki * t_dim1], dabs(r__2)));
}
/* Computing MAX */
r__1 = ulp * (dabs(wr) + dabs(wi));
smin = dmax(r__1,smlnum);
if (ip == 0) {
/* Real left eigenvector. */
work[ki + *n] = 1.f;
/* Form right-hand side */
i__2 = *n;
for (k = ki + 1; k <= i__2; ++k) {
work[k + *n] = -t[ki + k * t_dim1];
/* L160: */
}
/* Solve the quasi-triangular system: */
/* (T(KI+1:N,KI+1:N) - WR)'*X = SCALE*WORK */
vmax = 1.f;
vcrit = bignum;
jnxt = ki + 1;
i__2 = *n;
for (j = ki + 1; j <= i__2; ++j) {
if (j < jnxt) {
goto L170;
}
j1 = j;
j2 = j;
jnxt = j + 1;
if (j < *n) {
if (t[j + 1 + j * t_dim1] != 0.f) {
j2 = j + 1;
jnxt = j + 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
/* Scale if necessary to avoid overflow when forming */
/* the right-hand side. */
if (work[j] > vcrit) {
rec = 1.f / vmax;
i__3 = *n - ki + 1;
sscal_(&i__3, &rec, &work[ki + *n], &c__1);
vmax = 1.f;
vcrit = bignum;
}
i__3 = j - ki - 1;
work[j + *n] -= sdot_(&i__3, &t[ki + 1 + j * t_dim1],
&c__1, &work[ki + 1 + *n], &c__1);
/* Solve (T(J,J)-WR)'*X = WORK */
slaln2_(&c_false, &c__1, &c__1, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm,
&ierr);
/* Scale if necessary */
if (scale != 1.f) {
i__3 = *n - ki + 1;
sscal_(&i__3, &scale, &work[ki + *n], &c__1);
}
work[j + *n] = x[0];
/* Computing MAX */
r__2 = (r__1 = work[j + *n], dabs(r__1));
vmax = dmax(r__2,vmax);
vcrit = bignum / vmax;
} else {
/* 2-by-2 diagonal block */
/* Scale if necessary to avoid overflow when forming */
/* the right-hand side. */
/* Computing MAX */
r__1 = work[j], r__2 = work[j + 1];
beta = dmax(r__1,r__2);
if (beta > vcrit) {
rec = 1.f / vmax;
i__3 = *n - ki + 1;
sscal_(&i__3, &rec, &work[ki + *n], &c__1);
vmax = 1.f;
vcrit = bignum;
}
i__3 = j - ki - 1;
work[j + *n] -= sdot_(&i__3, &t[ki + 1 + j * t_dim1],
&c__1, &work[ki + 1 + *n], &c__1);
i__3 = j - ki - 1;
work[j + 1 + *n] -= sdot_(&i__3, &t[ki + 1 + (j + 1) *
t_dim1], &c__1, &work[ki + 1 + *n], &c__1);
/* Solve */
/* [T(J,J)-WR T(J,J+1) ]'* X = SCALE*( WORK1 ) */
/* [T(J+1,J) T(J+1,J+1)-WR] ( WORK2 ) */
slaln2_(&c_true, &c__2, &c__1, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm,
&ierr);
/* Scale if necessary */
if (scale != 1.f) {
i__3 = *n - ki + 1;
sscal_(&i__3, &scale, &work[ki + *n], &c__1);
}
work[j + *n] = x[0];
work[j + 1 + *n] = x[1];
/* Computing MAX */
r__3 = (r__1 = work[j + *n], dabs(r__1)), r__4 = (
r__2 = work[j + 1 + *n], dabs(r__2)), r__3 =
max(r__3,r__4);
vmax = dmax(r__3,vmax);
vcrit = bignum / vmax;
}
L170:
;
}
/* Copy the vector x or Q*x to VL and normalize. */
if (! over) {
i__2 = *n - ki + 1;
scopy_(&i__2, &work[ki + *n], &c__1, &vl[ki + is *
vl_dim1], &c__1);
i__2 = *n - ki + 1;
ii = isamax_(&i__2, &vl[ki + is * vl_dim1], &c__1) + ki -
1;
remax = 1.f / (r__1 = vl[ii + is * vl_dim1], dabs(r__1));
i__2 = *n - ki + 1;
sscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);
i__2 = ki - 1;
for (k = 1; k <= i__2; ++k) {
vl[k + is * vl_dim1] = 0.f;
/* L180: */
}
} else {
if (ki < *n) {
i__2 = *n - ki;
sgemv_("N", n, &i__2, &c_b22, &vl[(ki + 1) * vl_dim1
+ 1], ldvl, &work[ki + 1 + *n], &c__1, &work[
ki + *n], &vl[ki * vl_dim1 + 1], &c__1);
}
ii = isamax_(n, &vl[ki * vl_dim1 + 1], &c__1);
remax = 1.f / (r__1 = vl[ii + ki * vl_dim1], dabs(r__1));
sscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
}
} else {
/* Complex left eigenvector. */
/* Initial solve: */
/* ((T(KI,KI) T(KI,KI+1) )' - (WR - I* WI))*X = 0. */
/* ((T(KI+1,KI) T(KI+1,KI+1)) ) */
if ((r__1 = t[ki + (ki + 1) * t_dim1], dabs(r__1)) >= (r__2 =
t[ki + 1 + ki * t_dim1], dabs(r__2))) {
work[ki + *n] = wi / t[ki + (ki + 1) * t_dim1];
work[ki + 1 + n2] = 1.f;
} else {
work[ki + *n] = 1.f;
work[ki + 1 + n2] = -wi / t[ki + 1 + ki * t_dim1];
}
work[ki + 1 + *n] = 0.f;
work[ki + n2] = 0.f;
/* Form right-hand side */
i__2 = *n;
for (k = ki + 2; k <= i__2; ++k) {
work[k + *n] = -work[ki + *n] * t[ki + k * t_dim1];
work[k + n2] = -work[ki + 1 + n2] * t[ki + 1 + k * t_dim1]
;
/* L190: */
}
/* Solve complex quasi-triangular system: */
/* ( T(KI+2,N:KI+2,N) - (WR-i*WI) )*X = WORK1+i*WORK2 */
vmax = 1.f;
vcrit = bignum;
jnxt = ki + 2;
i__2 = *n;
for (j = ki + 2; j <= i__2; ++j) {
if (j < jnxt) {
goto L200;
}
j1 = j;
j2 = j;
jnxt = j + 1;
if (j < *n) {
if (t[j + 1 + j * t_dim1] != 0.f) {
j2 = j + 1;
jnxt = j + 2;
}
}
if (j1 == j2) {
/* 1-by-1 diagonal block */
/* Scale if necessary to avoid overflow when */
/* forming the right-hand side elements. */
if (work[j] > vcrit) {
rec = 1.f / vmax;
i__3 = *n - ki + 1;
sscal_(&i__3, &rec, &work[ki + *n], &c__1);
i__3 = *n - ki + 1;
sscal_(&i__3, &rec, &work[ki + n2], &c__1);
vmax = 1.f;
vcrit = bignum;
}
i__3 = j - ki - 2;
work[j + *n] -= sdot_(&i__3, &t[ki + 2 + j * t_dim1],
&c__1, &work[ki + 2 + *n], &c__1);
i__3 = j - ki - 2;
work[j + n2] -= sdot_(&i__3, &t[ki + 2 + j * t_dim1],
&c__1, &work[ki + 2 + n2], &c__1);
/* Solve (T(J,J)-(WR-i*WI))*(X11+i*X12)= WK+I*WK2 */
r__1 = -wi;
slaln2_(&c_false, &c__1, &c__2, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &r__1, x, &c__2, &scale, &xnorm, &
ierr);
/* Scale if necessary */
if (scale != 1.f) {
i__3 = *n - ki + 1;
sscal_(&i__3, &scale, &work[ki + *n], &c__1);
i__3 = *n - ki + 1;
sscal_(&i__3, &scale, &work[ki + n2], &c__1);
}
work[j + *n] = x[0];
work[j + n2] = x[2];
/* Computing MAX */
r__3 = (r__1 = work[j + *n], dabs(r__1)), r__4 = (
r__2 = work[j + n2], dabs(r__2)), r__3 = max(
r__3,r__4);
vmax = dmax(r__3,vmax);
vcrit = bignum / vmax;
} else {
/* 2-by-2 diagonal block */
/* Scale if necessary to avoid overflow when forming */
/* the right-hand side elements. */
/* Computing MAX */
r__1 = work[j], r__2 = work[j + 1];
beta = dmax(r__1,r__2);
if (beta > vcrit) {
rec = 1.f / vmax;
i__3 = *n - ki + 1;
sscal_(&i__3, &rec, &work[ki + *n], &c__1);
i__3 = *n - ki + 1;
sscal_(&i__3, &rec, &work[ki + n2], &c__1);
vmax = 1.f;
vcrit = bignum;
}
i__3 = j - ki - 2;
work[j + *n] -= sdot_(&i__3, &t[ki + 2 + j * t_dim1],
&c__1, &work[ki + 2 + *n], &c__1);
i__3 = j - ki - 2;
work[j + n2] -= sdot_(&i__3, &t[ki + 2 + j * t_dim1],
&c__1, &work[ki + 2 + n2], &c__1);
i__3 = j - ki - 2;
work[j + 1 + *n] -= sdot_(&i__3, &t[ki + 2 + (j + 1) *
t_dim1], &c__1, &work[ki + 2 + *n], &c__1);
i__3 = j - ki - 2;
work[j + 1 + n2] -= sdot_(&i__3, &t[ki + 2 + (j + 1) *
t_dim1], &c__1, &work[ki + 2 + n2], &c__1);
/* Solve 2-by-2 complex linear equation */
/* ([T(j,j) T(j,j+1) ]'-(wr-i*wi)*I)*X = SCALE*B */
/* ([T(j+1,j) T(j+1,j+1)] ) */
r__1 = -wi;
slaln2_(&c_true, &c__2, &c__2, &smin, &c_b22, &t[j +
j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *
n], n, &wr, &r__1, x, &c__2, &scale, &xnorm, &
ierr);
/* Scale if necessary */
if (scale != 1.f) {
i__3 = *n - ki + 1;
sscal_(&i__3, &scale, &work[ki + *n], &c__1);
i__3 = *n - ki + 1;
sscal_(&i__3, &scale, &work[ki + n2], &c__1);
}
work[j + *n] = x[0];
work[j + n2] = x[2];
work[j + 1 + *n] = x[1];
work[j + 1 + n2] = x[3];
/* Computing MAX */
r__1 = dabs(x[0]), r__2 = dabs(x[2]), r__1 = max(r__1,
r__2), r__2 = dabs(x[1]), r__1 = max(r__1,
r__2), r__2 = dabs(x[3]), r__1 = max(r__1,
r__2);
vmax = dmax(r__1,vmax);
vcrit = bignum / vmax;
}
L200:
;
}
/* Copy the vector x or Q*x to VL and normalize. */
if (! over) {
i__2 = *n - ki + 1;
scopy_(&i__2, &work[ki + *n], &c__1, &vl[ki + is *
vl_dim1], &c__1);
i__2 = *n - ki + 1;
scopy_(&i__2, &work[ki + n2], &c__1, &vl[ki + (is + 1) *
vl_dim1], &c__1);
emax = 0.f;
i__2 = *n;
for (k = ki; k <= i__2; ++k) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = vl[k + is * vl_dim1],
dabs(r__1)) + (r__2 = vl[k + (is + 1) *
vl_dim1], dabs(r__2));
emax = dmax(r__3,r__4);
/* L220: */
}
remax = 1.f / emax;
i__2 = *n - ki + 1;
sscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);
i__2 = *n - ki + 1;
sscal_(&i__2, &remax, &vl[ki + (is + 1) * vl_dim1], &c__1)
;
i__2 = ki - 1;
for (k = 1; k <= i__2; ++k) {
vl[k + is * vl_dim1] = 0.f;
vl[k + (is + 1) * vl_dim1] = 0.f;
/* L230: */
}
} else {
if (ki < *n - 1) {
i__2 = *n - ki - 1;
sgemv_("N", n, &i__2, &c_b22, &vl[(ki + 2) * vl_dim1
+ 1], ldvl, &work[ki + 2 + *n], &c__1, &work[
ki + *n], &vl[ki * vl_dim1 + 1], &c__1);
i__2 = *n - ki - 1;
sgemv_("N", n, &i__2, &c_b22, &vl[(ki + 2) * vl_dim1
+ 1], ldvl, &work[ki + 2 + n2], &c__1, &work[
ki + 1 + n2], &vl[(ki + 1) * vl_dim1 + 1], &
c__1);
} else {
sscal_(n, &work[ki + *n], &vl[ki * vl_dim1 + 1], &
c__1);
sscal_(n, &work[ki + 1 + n2], &vl[(ki + 1) * vl_dim1
+ 1], &c__1);
}
emax = 0.f;
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing MAX */
r__3 = emax, r__4 = (r__1 = vl[k + ki * vl_dim1],
dabs(r__1)) + (r__2 = vl[k + (ki + 1) *
vl_dim1], dabs(r__2));
emax = dmax(r__3,r__4);
/* L240: */
}
remax = 1.f / emax;
sscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
sscal_(n, &remax, &vl[(ki + 1) * vl_dim1 + 1], &c__1);
}
}
++is;
if (ip != 0) {
++is;
}
L250:
if (ip == -1) {
ip = 0;
}
if (ip == 1) {
ip = -1;
}
/* L260: */
}
}
return 0;
/* End of STREVC */
} /* strevc_ */
