/* dtgevc.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static logical c_true = TRUE_;
static integer c__2 = 2;
static doublereal c_b34 = 1.;
static integer c__1 = 1;
static doublereal c_b36 = 0.;
static logical c_false = FALSE_;
/* Subroutine */ int dtgevc_(char *side, char *howmny, logical *select,
integer *n, doublereal *s, integer *lds, doublereal *p, integer *ldp,
doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, integer
*mm, integer *m, doublereal *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;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
/* Local variables */
integer i__, j, ja, jc, je, na, im, jr, jw, nw;
doublereal big;
logical lsa, lsb;
doublereal ulp, sum[4] /* was [2][2] */;
integer ibeg, ieig, iend;
doublereal dmin__, temp, xmax, sump[4] /* was [2][2] */, sums[4]
/* was [2][2] */;
extern /* Subroutine */ int dlag2_(doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *);
doublereal cim2a, cim2b, cre2a, cre2b, temp2, bdiag[2], acoef, scale;
logical ilall;
integer iside;
doublereal sbeta;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *);
logical il2by2;
integer iinfo;
doublereal small;
logical compl;
doublereal anorm, bnorm;
logical compr;
extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *
, doublereal *, integer *, doublereal *, doublereal *, integer *);
doublereal temp2i;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
doublereal temp2r;
logical ilabad, ilbbad;
doublereal acoefa, bcoefa, cimaga, cimagb;
logical ilback;
doublereal bcoefi, ascale, bscale, creala, crealb;
extern doublereal dlamch_(char *);
doublereal bcoefr, salfar, safmin;
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *);
doublereal xscale, bignum;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical ilcomp, ilcplx;
integer ihwmny;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTGEVC 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 DGGHRD + DHGEQZ. */
/* 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 */
/* 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 matrices S and P. N >= 0. */
/* S (input) DOUBLE PRECISION array, dimension (LDS,N) */
/* The upper quasi-triangular matrix S from a generalized Schur */
/* factorization, as computed by DHGEQZ. */
/* LDS (input) INTEGER */
/* The leading dimension of array S. LDS >= max(1,N). */
/* P (input) DOUBLE PRECISION array, dimension (LDP,N) */
/* The upper triangular matrix P from a generalized Schur */
/* factorization, as computed by DHGEQZ. */
/* 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) DOUBLE PRECISION 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 DHGEQZ). */
/* 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) DOUBLE PRECISION 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 DHGEQZ). */
/* 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) DOUBLE PRECISION 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. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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_("DTGEVC", &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.) {
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.) {
if (p[j + j * p_dim1] == 0. || p[j + 1 + (j + 1) * p_dim1] == 0.
|| p[j + (j + 1) * p_dim1] != 0.) {
ilbbad = TRUE_;
}
if (j < *n - 1) {
if (s[j + 2 + (j + 1) * s_dim1] != 0.) {
ilabad = TRUE_;
}
}
}
/* L20: */
}
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_("DTGEVC", &i__1);
return 0;
}
/* Quick return if possible */
*m = im;
if (*n == 0) {
return 0;
}
/* Machine Constants */
safmin = dlamch_("Safe minimum");
big = 1. / safmin;
dlabad_(&safmin, &big);
ulp = dlamch_("Epsilon") * dlamch_("Base");
small = safmin * *n / ulp;
big = 1. / small;
bignum = 1. / (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 = (d__1 = s[s_dim1 + 1], abs(d__1));
if (*n > 1) {
anorm += (d__1 = s[s_dim1 + 2], abs(d__1));
}
bnorm = (d__1 = p[p_dim1 + 1], abs(d__1));
work[1] = 0.;
work[*n + 1] = 0.;
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
temp = 0.;
temp2 = 0.;
if (s[j + (j - 1) * s_dim1] == 0.) {
iend = j - 1;
} else {
iend = j - 2;
}
i__2 = iend;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += (d__1 = s[i__ + j * s_dim1], abs(d__1));
temp2 += (d__1 = p[i__ + j * p_dim1], abs(d__1));
/* L30: */
}
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 += (d__1 = s[i__ + j * s_dim1], abs(d__1));
temp2 += (d__1 = p[i__ + j * p_dim1], abs(d__1));
/* L40: */
}
anorm = max(anorm,temp);
bnorm = max(bnorm,temp2);
/* L50: */
}
ascale = 1. / max(anorm,safmin);
bscale = 1. / max(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.) {
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 ((d__1 = s[je + je * s_dim1], abs(d__1)) <= safmin && (
d__2 = p[je + je * p_dim1], abs(d__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.;
/* L60: */
}
vl[ieig + ieig * vl_dim1] = 1.;
goto L220;
}
}
/* Clear vector */
i__2 = nw * *n;
for (jr = 1; jr <= i__2; ++jr) {
work[(*n << 1) + jr] = 0.;
/* L70: */
}
/* T */
/* Compute coefficients in ( a A - b B ) y = 0 */
/* a is ACOEF */
/* b is BCOEFR + i*BCOEFI */
if (! ilcplx) {
/* Real eigenvalue */
/* Computing MAX */
d__3 = (d__1 = s[je + je * s_dim1], abs(d__1)) * ascale, d__4
= (d__2 = p[je + je * p_dim1], abs(d__2)) * bscale,
d__3 = max(d__3,d__4);
temp = 1. / max(d__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.;
/* Scale to avoid underflow */
scale = 1.;
lsa = abs(sbeta) >= safmin && abs(acoef) < small;
lsb = abs(salfar) >= safmin && abs(bcoefr) < small;
if (lsa) {
scale = small / abs(sbeta) * min(anorm,big);
}
if (lsb) {
/* Computing MAX */
d__1 = scale, d__2 = small / abs(salfar) * min(bnorm,big);
scale = max(d__1,d__2);
}
if (lsa || lsb) {
/* Computing MIN */
/* Computing MAX */
d__3 = 1., d__4 = abs(acoef), d__3 = max(d__3,d__4), d__4
= abs(bcoefr);
d__1 = scale, d__2 = 1. / (safmin * max(d__3,d__4));
scale = min(d__1,d__2);
if (lsa) {
acoef = ascale * (scale * sbeta);
} else {
acoef = scale * acoef;
}
if (lsb) {
bcoefr = bscale * (scale * salfar);
} else {
bcoefr = scale * bcoefr;
}
}
acoefa = abs(acoef);
bcoefa = abs(bcoefr);
/* First component is 1 */
work[(*n << 1) + je] = 1.;
xmax = 1.;
} else {
/* Complex eigenvalue */
d__1 = safmin * 100.;
dlag2_(&s[je + je * s_dim1], lds, &p[je + je * p_dim1], ldp, &
d__1, &acoef, &temp, &bcoefr, &temp2, &bcoefi);
bcoefi = -bcoefi;
if (bcoefi == 0.) {
*info = je;
return 0;
}
/* Scale to avoid over/underflow */
acoefa = abs(acoef);
bcoefa = abs(bcoefr) + abs(bcoefi);
scale = 1.;
if (acoefa * ulp < safmin && acoefa >= safmin) {
scale = safmin / ulp / acoefa;
}
if (bcoefa * ulp < safmin && bcoefa >= safmin) {
/* Computing MAX */
d__1 = scale, d__2 = safmin / ulp / bcoefa;
scale = max(d__1,d__2);
}
if (safmin * acoefa > ascale) {
scale = ascale / (safmin * acoefa);
}
if (safmin * bcoefa > bscale) {
/* Computing MIN */
d__1 = scale, d__2 = bscale / (safmin * bcoefa);
scale = min(d__1,d__2);
}
if (scale != 1.) {
acoef = scale * acoef;
acoefa = abs(acoef);
bcoefr = scale * bcoefr;
bcoefi = scale * bcoefi;
bcoefa = abs(bcoefr) + abs(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 (abs(temp) > abs(temp2r) + abs(temp2i)) {
work[(*n << 1) + je] = 1.;
work[*n * 3 + je] = 0.;
work[(*n << 1) + je + 1] = -temp2r / temp;
work[*n * 3 + je + 1] = -temp2i / temp;
} else {
work[(*n << 1) + je + 1] = 1.;
work[*n * 3 + je + 1] = 0.;
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 */
d__5 = (d__1 = work[(*n << 1) + je], abs(d__1)) + (d__2 =
work[*n * 3 + je], abs(d__2)), d__6 = (d__3 = work[(*
n << 1) + je + 1], abs(d__3)) + (d__4 = work[*n * 3 +
je + 1], abs(d__4));
xmax = max(d__5,d__6);
}
/* Computing MAX */
d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 =
max(d__1,d__2);
dmin__ = max(d__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.) {
il2by2 = TRUE_;
bdiag[1] = p[j + 1 + (j + 1) * p_dim1];
na = 2;
}
}
/* Check whether scaling is necessary for dot products */
xscale = 1. / max(1.,xmax);
/* Computing MAX */
d__1 = work[j], d__2 = work[*n + j], d__1 = max(d__1,d__2),
d__2 = acoefa * work[j] + bcoefa * work[*n + j];
temp = max(d__1,d__2);
if (il2by2) {
/* Computing MAX */
d__1 = temp, d__2 = work[j + 1], d__1 = max(d__1,d__2),
d__2 = work[*n + j + 1], d__1 = max(d__1,d__2),
d__2 = acoefa * work[j + 1] + bcoefa * work[*n +
j + 1];
temp = max(d__1,d__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];
/* L80: */
}
/* L90: */
}
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.;
sump[ja + (jw << 1) - 3] = 0.;
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];
/* L100: */
}
/* L110: */
}
/* L120: */
}
/* $PL$ 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];
}
/* L130: */
}
/* T */
/* Solve ( a A - b B ) y = SUM(,) */
/* with scaling and perturbation of the denominator */
dlaln2_(&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.) {
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];
/* L140: */
}
/* L150: */
}
xmax = scale * xmax;
}
xmax = max(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;
dgemv_("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);
/* L170: */
}
dlacpy_(" ", n, &nw, &work[(*n << 2) + 1], n, &vl[je *
vl_dim1 + 1], ldvl);
ibeg = 1;
} else {
dlacpy_(" ", n, &nw, &work[(*n << 1) + 1], n, &vl[ieig *
vl_dim1 + 1], ldvl);
ibeg = je;
}
/* Scale eigenvector */
xmax = 0.;
if (ilcplx) {
i__2 = *n;
for (j = ibeg; j <= i__2; ++j) {
/* Computing MAX */
d__3 = xmax, d__4 = (d__1 = vl[j + ieig * vl_dim1], abs(
d__1)) + (d__2 = vl[j + (ieig + 1) * vl_dim1],
abs(d__2));
xmax = max(d__3,d__4);
/* L180: */
}
} else {
i__2 = *n;
for (j = ibeg; j <= i__2; ++j) {
/* Computing MAX */
d__2 = xmax, d__3 = (d__1 = vl[j + ieig * vl_dim1], abs(
d__1));
xmax = max(d__2,d__3);
/* L190: */
}
}
if (xmax > safmin) {
xscale = 1. / 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];
/* L200: */
}
/* L210: */
}
}
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.) {
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 ((d__1 = s[je + je * s_dim1], abs(d__1)) <= safmin && (
d__2 = p[je + je * p_dim1], abs(d__2)) <= safmin) {
/* Singular matrix pencil -- unit eigenvector */
--ieig;
i__1 = *n;
for (jr = 1; jr <= i__1; ++jr) {
vr[jr + ieig * vr_dim1] = 0.;
/* L230: */
}
vr[ieig + ieig * vr_dim1] = 1.;
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.;
/* L240: */
}
/* L250: */
}
/* Compute coefficients in ( a A - b B ) x = 0 */
/* a is ACOEF */
/* b is BCOEFR + i*BCOEFI */
if (! ilcplx) {
/* Real eigenvalue */
/* Computing MAX */
d__3 = (d__1 = s[je + je * s_dim1], abs(d__1)) * ascale, d__4
= (d__2 = p[je + je * p_dim1], abs(d__2)) * bscale,
d__3 = max(d__3,d__4);
temp = 1. / max(d__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.;
/* Scale to avoid underflow */
scale = 1.;
lsa = abs(sbeta) >= safmin && abs(acoef) < small;
lsb = abs(salfar) >= safmin && abs(bcoefr) < small;
if (lsa) {
scale = small / abs(sbeta) * min(anorm,big);
}
if (lsb) {
/* Computing MAX */
d__1 = scale, d__2 = small / abs(salfar) * min(bnorm,big);
scale = max(d__1,d__2);
}
if (lsa || lsb) {
/* Computing MIN */
/* Computing MAX */
d__3 = 1., d__4 = abs(acoef), d__3 = max(d__3,d__4), d__4
= abs(bcoefr);
d__1 = scale, d__2 = 1. / (safmin * max(d__3,d__4));
scale = min(d__1,d__2);
if (lsa) {
acoef = ascale * (scale * sbeta);
} else {
acoef = scale * acoef;
}
if (lsb) {
bcoefr = bscale * (scale * salfar);
} else {
bcoefr = scale * bcoefr;
}
}
acoefa = abs(acoef);
bcoefa = abs(bcoefr);
/* First component is 1 */
work[(*n << 1) + je] = 1.;
xmax = 1.;
/* 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];
/* L260: */
}
} else {
/* Complex eigenvalue */
d__1 = safmin * 100.;
dlag2_(&s[je - 1 + (je - 1) * s_dim1], lds, &p[je - 1 + (je -
1) * p_dim1], ldp, &d__1, &acoef, &temp, &bcoefr, &
temp2, &bcoefi);
if (bcoefi == 0.) {
*info = je - 1;
return 0;
}
/* Scale to avoid over/underflow */
acoefa = abs(acoef);
bcoefa = abs(bcoefr) + abs(bcoefi);
scale = 1.;
if (acoefa * ulp < safmin && acoefa >= safmin) {
scale = safmin / ulp / acoefa;
}
if (bcoefa * ulp < safmin && bcoefa >= safmin) {
/* Computing MAX */
d__1 = scale, d__2 = safmin / ulp / bcoefa;
scale = max(d__1,d__2);
}
if (safmin * acoefa > ascale) {
scale = ascale / (safmin * acoefa);
}
if (safmin * bcoefa > bscale) {
/* Computing MIN */
d__1 = scale, d__2 = bscale / (safmin * bcoefa);
scale = min(d__1,d__2);
}
if (scale != 1.) {
acoef = scale * acoef;
acoefa = abs(acoef);
bcoefr = scale * bcoefr;
bcoefi = scale * bcoefi;
bcoefa = abs(bcoefr) + abs(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 (abs(temp) >= abs(temp2r) + abs(temp2i)) {
work[(*n << 1) + je] = 1.;
work[*n * 3 + je] = 0.;
work[(*n << 1) + je - 1] = -temp2r / temp;
work[*n * 3 + je - 1] = -temp2i / temp;
} else {
work[(*n << 1) + je - 1] = 1.;
work[*n * 3 + je - 1] = 0.;
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 */
d__5 = (d__1 = work[(*n << 1) + je], abs(d__1)) + (d__2 =
work[*n * 3 + je], abs(d__2)), d__6 = (d__3 = work[(*
n << 1) + je - 1], abs(d__3)) + (d__4 = work[*n * 3 +
je - 1], abs(d__4));
xmax = max(d__5,d__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];
/* L270: */
}
}
/* Computing MAX */
d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 =
max(d__1,d__2);
dmin__ = max(d__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.) {
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) */
dlaln2_(&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.) {
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];
/* L280: */
}
/* L290: */
}
}
/* Computing MAX */
d__1 = scale * xmax;
xmax = max(d__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];
/* L300: */
}
/* L310: */
}
/* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
if (j > 1) {
/* Check whether scaling is necessary for sum. */
xscale = 1. / max(1.,xmax);
temp = acoefa * work[j] + bcoefa * work[*n + j];
if (il2by2) {
/* Computing MAX */
d__1 = temp, d__2 = acoefa * work[j + 1] + bcoefa *
work[*n + j + 1];
temp = max(d__1,d__2);
}
/* Computing MAX */
d__1 = max(temp,acoefa);
temp = max(d__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];
/* L320: */
}
/* L330: */
}
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];
/* L340: */
}
} 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];
/* L350: */
}
}
/* L360: */
}
}
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];
/* L380: */
}
/* 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];
/* L390: */
}
/* L400: */
}
/* L410: */
}
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];
/* L420: */
}
/* L430: */
}
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];
/* L440: */
}
/* L450: */
}
iend = je;
}
/* Scale eigenvector */
xmax = 0.;
if (ilcplx) {
i__1 = iend;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__3 = xmax, d__4 = (d__1 = vr[j + ieig * vr_dim1], abs(
d__1)) + (d__2 = vr[j + (ieig + 1) * vr_dim1],
abs(d__2));
xmax = max(d__3,d__4);
/* L460: */
}
} else {
i__1 = iend;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__2 = xmax, d__3 = (d__1 = vr[j + ieig * vr_dim1], abs(
d__1));
xmax = max(d__2,d__3);
/* L470: */
}
}
if (xmax > safmin) {
xscale = 1. / 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];
/* L480: */
}
/* L490: */
}
}
L500:
;
}
}
return 0;
/* End of DTGEVC */
} /* dtgevc_ */