/* Subroutine */ int cgeevx_(char *balanc, char *jobvl, char *jobvr, char *
sense, integer *n, complex *a, integer *lda, complex *w, complex *vl,
integer *ldvl, complex *vr, integer *ldvr, integer *ilo, integer *ihi,
real *scale, real *abnrm, real *rconde, real *rcondv, complex *work,
integer *lwork, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
real r__1, r__2;
complex q__1, q__2;
/* Local variables */
integer i__, k;
char job[1];
real scl, dum[1], eps;
complex tmp;
char side[1];
real anrm;
integer ierr, itau, iwrk, nout;
integer icond;
logical scalea;
real cscale;
logical select[1];
real bignum;
integer minwrk, maxwrk;
logical wantvl, wntsnb;
integer hswork;
logical wntsne;
real smlnum;
logical lquery, wantvr, wntsnn, wntsnv;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the */
/* eigenvalues and, optionally, the left and/or right eigenvectors. */
/* Optionally also, it computes a balancing transformation to improve */
/* the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */
/* SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues */
/* (RCONDE), and reciprocal condition numbers for the right */
/* eigenvectors (RCONDV). */
/* The right eigenvector v(j) of A satisfies */
/* A * v(j) = lambda(j) * v(j) */
/* where lambda(j) is its eigenvalue. */
/* The left eigenvector u(j) of A satisfies */
/* u(j)**H * A = lambda(j) * u(j)**H */
/* where u(j)**H denotes the conjugate transpose of u(j). */
/* The computed eigenvectors are normalized to have Euclidean norm */
/* equal to 1 and largest component real. */
/* Balancing a matrix means permuting the rows and columns to make it */
/* more nearly upper triangular, and applying a diagonal similarity */
/* transformation D * A * D**(-1), where D is a diagonal matrix, to */
/* make its rows and columns closer in norm and the condition numbers */
/* of its eigenvalues and eigenvectors smaller. The computed */
/* reciprocal condition numbers correspond to the balanced matrix. */
/* Permuting rows and columns will not change the condition numbers */
/* (in exact arithmetic) but diagonal scaling will. For further */
/* explanation of balancing, see section 4.10.2 of the LAPACK */
/* Users' Guide. */
/* Arguments */
/* ========= */
/* BALANC (input) CHARACTER*1 */
/* Indicates how the input matrix should be diagonally scaled */
/* and/or permuted to improve the conditioning of its */
/* eigenvalues. */
/* = 'N': Do not diagonally scale or permute; */
/* = 'P': Perform permutations to make the matrix more nearly */
/* upper triangular. Do not diagonally scale; */
/* = 'S': Diagonally scale the matrix, ie. replace A by */
/* D*A*D**(-1), where D is a diagonal matrix chosen */
/* to make the rows and columns of A more equal in */
/* norm. Do not permute; */
/* = 'B': Both diagonally scale and permute A. */
/* Computed reciprocal condition numbers will be for the matrix */
/* after balancing and/or permuting. Permuting does not change */
/* condition numbers (in exact arithmetic), but balancing does. */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': left eigenvectors of A are not computed; */
/* = 'V': left eigenvectors of A are computed. */
/* If SENSE = 'E' or 'B', JOBVL must = 'V'. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': right eigenvectors of A are not computed; */
/* = 'V': right eigenvectors of A are computed. */
/* If SENSE = 'E' or 'B', JOBVR must = 'V'. */
/* SENSE (input) CHARACTER*1 */
/* Determines which reciprocal condition numbers are computed. */
/* = 'N': None are computed; */
/* = 'E': Computed for eigenvalues only; */
/* = 'V': Computed for right eigenvectors only; */
/* = 'B': Computed for eigenvalues and right eigenvectors. */
/* If SENSE = 'E' or 'B', both left and right eigenvectors */
/* must also be computed (JOBVL = 'V' and JOBVR = 'V'). */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A has been overwritten. If JOBVL = 'V' or */
/* JOBVR = 'V', A contains the Schur form of the balanced */
/* version of the matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* W (output) COMPLEX array, dimension (N) */
/* W contains the computed eigenvalues. */
/* VL (output) COMPLEX array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* after another in the columns of VL, in the same order */
/* as their eigenvalues. */
/* If JOBVL = 'N', VL is not referenced. */
/* u(j) = VL(:,j), the j-th column of VL. */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; if */
/* JOBVL = 'V', LDVL >= N. */
/* VR (output) COMPLEX array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* after another in the columns of VR, in the same order */
/* as their eigenvalues. */
/* If JOBVR = 'N', VR is not referenced. */
/* v(j) = VR(:,j), the j-th column of VR. */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1; if */
/* JOBVR = 'V', LDVR >= N. */
/* ILO (output) INTEGER */
/* IHI (output) INTEGER */
/* ILO and IHI are integer values determined when A was */
/* balanced. The balanced A(i,j) = 0 if I > J and */
/* SCALE (output) REAL array, dimension (N) */
/* Details of the permutations and scaling factors applied */
/* when balancing A. If P(j) is the index of the row and column */
/* interchanged with row and column j, and D(j) is the scaling */
/* factor applied to row and column j, then */
/* The order in which the interchanges are made is N to IHI+1, */
/* then 1 to ILO-1. */
/* ABNRM (output) REAL */
/* The one-norm of the balanced matrix (the maximum */
/* of the sum of absolute values of elements of any column). */
/* RCONDE (output) REAL array, dimension (N) */
/* RCONDE(j) is the reciprocal condition number of the j-th */
/* eigenvalue. */
/* RCONDV (output) REAL array, dimension (N) */
/* RCONDV(j) is the reciprocal condition number of the j-th */
/* right eigenvector. */
/* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. If SENSE = 'N' or 'E', */
/* LWORK >= max(1,2*N), and if SENSE = 'V' or 'B', */
/* LWORK >= N*N+2*N. */
/* For good performance, LWORK must generally be larger. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* RWORK (workspace) REAL array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = i, the QR algorithm failed to compute all the */
/* eigenvalues, and no eigenvectors or condition numbers */
/* have been computed; elements 1:ILO-1 and i+1:N of W */
/* contain eigenvalues which have converged. */
/* ===================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--scale;
--rconde;
--rcondv;
--work;
--rwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
wntsnn = lsame_(sense, "N");
wntsne = lsame_(sense, "E");
wntsnv = lsame_(sense, "V");
wntsnb = lsame_(sense, "B");
if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P")
|| lsame_(balanc, "B"))) {
*info = -1;
} else if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -2;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -3;
} else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb)
&& ! (wantvl && wantvr)) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -10;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -12;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* CWorkspace refers to complex workspace, and RWorkspace to real */
/* workspace. NB refers to the optimal block size for the */
/* immediately following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by CHSEQR, as */
/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/* the worst case.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
maxwrk = 1;
} else {
maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
c__0);
if (wantvl) {
chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[1], &c_n1, info);
} else if (wantvr) {
chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[1], &c_n1, info);
} else {
if (wntsnn) {
chseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &
vr[vr_offset], ldvr, &work[1], &c_n1, info);
} else {
chseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &
vr[vr_offset], ldvr, &work[1], &c_n1, info);
}
}
hswork = work[1].r;
if (! wantvl && ! wantvr) {
minwrk = *n << 1;
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + (*n << 1);
minwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,hswork);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
maxwrk = max(i__1,i__2);
}
} else {
minwrk = *n << 1;
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + (*n << 1);
minwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,hswork);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 1;
maxwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,minwrk);
}
work[1].r = (real) maxwrk, work[1].i = 0.f;
if (*lwork < minwrk && ! lquery) {
*info = -20;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEEVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
icond = 0;
anrm = clange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix and compute ABNRM */
cgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
*abnrm = clange_("1", n, n, &a[a_offset], lda, dum);
if (scalea) {
dum[0] = *abnrm;
slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
ierr);
*abnrm = dum[0];
}
/* Reduce to upper Hessenberg form */
/* (CWorkspace: need 2*N, prefer N+N*NB) */
/* (RWorkspace: none) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
cgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, &
ierr);
if (wantvl) {
/* Want left eigenvectors */
/* Copy Householder vectors to VL */
*(unsigned char *)side = 'L';
clacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate unitary matrix in VL */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[iwrk], &i__1, info);
if (wantvr) {
/* Want left and right eigenvectors */
/* Copy Schur vectors to VR */
*(unsigned char *)side = 'B';
clacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
}
} else if (wantvr) {
/* Want right eigenvectors */
/* Copy Householder vectors to VR */
*(unsigned char *)side = 'R';
clacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate unitary matrix in VR */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only */
/* If condition numbers desired, compute Schur form */
if (wntsnn) {
*(unsigned char *)job = 'E';
} else {
*(unsigned char *)job = 'S';
}
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from CHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (CWorkspace: need 2*N) */
/* (RWorkspace: need N) */
ctrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[1], &
ierr);
}
/* Compute condition numbers if desired */
/* (CWorkspace: need N*N+2*N unless SENSE = 'E') */
/* (RWorkspace: need 2*N unless SENSE = 'E') */
if (! wntsnn) {
ctrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout,
&work[iwrk], n, &rwork[1], &icond);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
cgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1.f / scnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
csscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
r__1 = vl[i__3].r;
/* Computing 2nd power */
r__2 = r_imag(&vl[k + i__ * vl_dim1]);
rwork[k] = r__1 * r__1 + r__2 * r__2;
}
k = isamax_(n, &rwork[1], &c__1);
r_cnjg(&q__2, &vl[k + i__ * vl_dim1]);
r__1 = sqrt(rwork[k]);
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
tmp.r = q__1.r, tmp.i = q__1.i;
cscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
r__1 = vl[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
vl[i__2].r = q__1.r, vl[i__2].i = q__1.i;
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
cgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1.f / scnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
csscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
r__1 = vr[i__3].r;
/* Computing 2nd power */
r__2 = r_imag(&vr[k + i__ * vr_dim1]);
rwork[k] = r__1 * r__1 + r__2 * r__2;
}
k = isamax_(n, &rwork[1], &c__1);
r_cnjg(&q__2, &vr[k + i__ * vr_dim1]);
r__1 = sqrt(rwork[k]);
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
tmp.r = q__1.r, tmp.i = q__1.i;
cscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
r__1 = vr[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
vr[i__2].r = q__1.r, vr[i__2].i = q__1.i;
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1]
, &i__2, &ierr);
if (*info == 0) {
if ((wntsnv || wntsnb) && icond == 0) {
slascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[
1], n, &ierr);
}
} else {
i__1 = *ilo - 1;
clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
&ierr);
}
}
work[1].r = (real) maxwrk, work[1].i = 0.f;
return 0;
/* End of CGEEVX */
} /* cgeevx_ */
int cgeev_(char *jobvl, char *jobvr, int *n, complex *a,
int *lda, complex *w, complex *vl, int *ldvl, complex *vr,
int *ldvr, complex *work, int *lwork, float *rwork, int *
info)
{
/* System generated locals */
int a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
float r__1, r__2;
complex q__1, q__2;
/* Builtin functions */
double sqrt(double), r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
int i__, k, ihi;
float scl;
int ilo;
float dum[1], eps;
complex tmp;
int ibal;
char side[1];
float anrm;
int ierr, itau, iwrk, nout;
extern int cscal_(int *, complex *, complex *,
int *);
extern int lsame_(char *, char *);
extern double scnrm2_(int *, complex *, int *);
extern int cgebak_(char *, char *, int *, int *,
int *, float *, int *, complex *, int *, int *), cgebal_(char *, int *, complex *, int *,
int *, int *, float *, int *), slabad_(float *,
float *);
int scalea;
extern double clange_(char *, int *, int *, complex *,
int *, float *);
float cscale;
extern int cgehrd_(int *, int *, int *,
complex *, int *, complex *, complex *, int *, int *),
clascl_(char *, int *, int *, float *, float *, int *,
int *, complex *, int *, int *);
extern double slamch_(char *);
extern int csscal_(int *, float *, complex *, int
*), clacpy_(char *, int *, int *, complex *, int *,
complex *, int *), xerbla_(char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
int select[1];
float bignum;
extern int isamax_(int *, float *, int *);
extern int chseqr_(char *, char *, int *, int *,
int *, complex *, int *, complex *, complex *, int *,
complex *, int *, int *), ctrevc_(char *,
char *, int *, int *, complex *, int *, complex *,
int *, complex *, int *, int *, int *, complex *,
float *, int *), cunghr_(int *, int *,
int *, complex *, int *, complex *, complex *, int *,
int *);
int minwrk, maxwrk;
int wantvl;
float smlnum;
int hswork, irwork;
int lquery, wantvr;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGEEV computes for an N-by-N complex nonsymmetric matrix A, the */
/* eigenvalues and, optionally, the left and/or right eigenvectors. */
/* The right eigenvector v(j) of A satisfies */
/* A * v(j) = lambda(j) * v(j) */
/* where lambda(j) is its eigenvalue. */
/* The left eigenvector u(j) of A satisfies */
/* u(j)**H * A = lambda(j) * u(j)**H */
/* where u(j)**H denotes the conjugate transpose of u(j). */
/* The computed eigenvectors are normalized to have Euclidean norm */
/* equal to 1 and largest component float. */
/* Arguments */
/* ========= */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': left eigenvectors of A are not computed; */
/* = 'V': left eigenvectors of are computed. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': right eigenvectors of A are not computed; */
/* = 'V': right eigenvectors of A are computed. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A has been overwritten. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* W (output) COMPLEX array, dimension (N) */
/* W contains the computed eigenvalues. */
/* VL (output) COMPLEX array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* after another in the columns of VL, in the same order */
/* as their eigenvalues. */
/* If JOBVL = 'N', VL is not referenced. */
/* u(j) = VL(:,j), the j-th column of VL. */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; if */
/* JOBVL = 'V', LDVL >= N. */
/* VR (output) COMPLEX array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* after another in the columns of VR, in the same order */
/* as their eigenvalues. */
/* If JOBVR = 'N', VR is not referenced. */
/* v(j) = VR(:,j), the j-th column of VR. */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1; if */
/* JOBVR = 'V', LDVR >= N. */
/* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= MAX(1,2*N). */
/* For good performance, LWORK must generally be larger. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* RWORK (workspace) REAL array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = i, the QR algorithm failed to compute all the */
/* eigenvalues, and no eigenvectors have been computed; */
/* elements and i+1:N of W contain eigenvalues which have */
/* converged. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
--rwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -1;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < MAX(1,*n)) {
*info = -5;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -8;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -10;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* CWorkspace refers to complex workspace, and RWorkspace to float */
/* workspace. NB refers to the optimal block size for the */
/* immediately following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by CHSEQR, as */
/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/* the worst case.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
maxwrk = 1;
} else {
maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
c__0);
minwrk = *n << 1;
if (wantvl) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1);
maxwrk = MAX(i__1,i__2);
chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[1], &c_n1, info);
} else if (wantvr) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1);
maxwrk = MAX(i__1,i__2);
chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[1], &c_n1, info);
} else {
chseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[1], &c_n1, info);
}
hswork = work[1].r;
/* Computing MAX */
i__1 = MAX(maxwrk,hswork);
maxwrk = MAX(i__1,minwrk);
}
work[1].r = (float) maxwrk, work[1].i = 0.f;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEEV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE;
if (anrm > 0.f && anrm < smlnum) {
scalea = TRUE;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE;
cscale = bignum;
}
if (scalea) {
clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
ibal = 1;
cgebal_("B", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
/* Reduce to upper Hessenberg form */
/* (CWorkspace: need 2*N, prefer N+N*NB) */
/* (RWorkspace: none) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
cgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvl) {
/* Want left eigenvectors */
/* Copy Householder vectors to VL */
*(unsigned char *)side = 'L';
clacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate unitary matrix in VL */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, &ilo, &ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk],
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[iwrk], &i__1, info);
if (wantvr) {
/* Want left and right eigenvectors */
/* Copy Schur vectors to VR */
*(unsigned char *)side = 'B';
clacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
}
} else if (wantvr) {
/* Want right eigenvectors */
/* Copy Householder vectors to VR */
*(unsigned char *)side = 'R';
clacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate unitary matrix in VR */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, &ilo, &ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk],
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("E", "N", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from CHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (CWorkspace: need 2*N) */
/* (RWorkspace: need 2*N) */
irwork = ibal + *n;
ctrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[irwork],
&ierr);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
cgebak_("B", "L", n, &ilo, &ihi, &rwork[ibal], n, &vl[vl_offset],
ldvl, &ierr);
/* Normalize left eigenvectors and make largest component float */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1.f / scnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
csscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
r__1 = vl[i__3].r;
/* Computing 2nd power */
r__2 = r_imag(&vl[k + i__ * vl_dim1]);
rwork[irwork + k - 1] = r__1 * r__1 + r__2 * r__2;
/* L10: */
}
k = isamax_(n, &rwork[irwork], &c__1);
r_cnjg(&q__2, &vl[k + i__ * vl_dim1]);
r__1 = sqrt(rwork[irwork + k - 1]);
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
tmp.r = q__1.r, tmp.i = q__1.i;
cscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
r__1 = vl[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
vl[i__2].r = q__1.r, vl[i__2].i = q__1.i;
/* L20: */
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
cgebak_("B", "R", n, &ilo, &ihi, &rwork[ibal], n, &vr[vr_offset],
ldvr, &ierr);
/* Normalize right eigenvectors and make largest component float */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1.f / scnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
csscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
r__1 = vr[i__3].r;
/* Computing 2nd power */
r__2 = r_imag(&vr[k + i__ * vr_dim1]);
rwork[irwork + k - 1] = r__1 * r__1 + r__2 * r__2;
/* L30: */
}
k = isamax_(n, &rwork[irwork], &c__1);
r_cnjg(&q__2, &vr[k + i__ * vr_dim1]);
r__1 = sqrt(rwork[irwork + k - 1]);
q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
tmp.r = q__1.r, tmp.i = q__1.i;
cscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
r__1 = vr[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
vr[i__2].r = q__1.r, vr[i__2].i = q__1.i;
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = MAX(i__3,1);
clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1]
, &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
&ierr);
}
}
work[1].r = (float) maxwrk, work[1].i = 0.f;
return 0;
/* End of CGEEV */
} /* cgeev_ */
/* Subroutine */ int claqr2_(logical *wantt, logical *wantz, integer *n,
integer *ktop, integer *kbot, integer *nw, complex *h__, integer *ldh,
integer *iloz, integer *ihiz, complex *z__, integer *ldz, integer *
ns, integer *nd, complex *sh, complex *v, integer *ldv, integer *nh,
complex *t, integer *ldt, integer *nv, complex *wv, integer *ldwv,
complex *work, integer *lwork)
{
/* System generated locals */
integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1,
wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4, r__5, r__6;
complex q__1, q__2;
/* Builtin functions */
double r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, j;
complex s;
integer jw;
real foo;
integer kln;
complex tau;
integer knt;
real ulp;
integer lwk1, lwk2;
complex beta;
integer kcol, info, ifst, ilst, ltop, krow;
extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
, integer *, complex *, complex *, integer *, complex *),
cgemm_(char *, char *, integer *, integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, complex *,
integer *), ccopy_(integer *, complex *, integer
*, complex *, integer *);
integer infqr, kwtop;
extern /* Subroutine */ int slabad_(real *, real *), cgehrd_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, integer *), clarfg_(integer *, complex *, complex *,
integer *, complex *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int clahqr_(logical *, logical *, integer *,
integer *, integer *, complex *, integer *, complex *, integer *,
integer *, complex *, integer *, integer *), clacpy_(char *,
integer *, integer *, complex *, integer *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex
*, complex *, integer *);
real safmin, safmax;
extern /* Subroutine */ int ctrexc_(char *, integer *, complex *, integer
*, complex *, integer *, integer *, integer *, integer *),
cunmhr_(char *, char *, integer *, integer *, integer *, integer
*, complex *, integer *, complex *, complex *, integer *, complex
*, integer *, integer *);
real smlnum;
integer lwkopt;
/* -- LAPACK auxiliary routine (version 3.2.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
/* -- April 2009 -- */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* This subroutine is identical to CLAQR3 except that it avoids */
/* recursion by calling CLAHQR instead of CLAQR4. */
/* ****************************************************************** */
/* Aggressive early deflation: */
/* This subroutine accepts as input an upper Hessenberg matrix */
/* H and performs an unitary similarity transformation */
/* designed to detect and deflate fully converged eigenvalues from */
/* a trailing principal submatrix. On output H has been over- */
/* written by a new Hessenberg matrix that is a perturbation of */
/* an unitary similarity transformation of H. It is to be */
/* hoped that the final version of H has many zero subdiagonal */
/* entries. */
/* ****************************************************************** */
/* WANTT (input) LOGICAL */
/* If .TRUE., then the Hessenberg matrix H is fully updated */
/* so that the triangular Schur factor may be */
/* computed (in cooperation with the calling subroutine). */
/* If .FALSE., then only enough of H is updated to preserve */
/* the eigenvalues. */
/* WANTZ (input) LOGICAL */
/* If .TRUE., then the unitary matrix Z is updated so */
/* so that the unitary Schur factor may be computed */
/* (in cooperation with the calling subroutine). */
/* If .FALSE., then Z is not referenced. */
/* N (input) INTEGER */
/* The order of the matrix H and (if WANTZ is .TRUE.) the */
/* order of the unitary matrix Z. */
/* KTOP (input) INTEGER */
/* It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. */
/* KBOT and KTOP together determine an isolated block */
/* along the diagonal of the Hessenberg matrix. */
/* KBOT (input) INTEGER */
/* It is assumed without a check that either */
/* KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together */
/* determine an isolated block along the diagonal of the */
/* Hessenberg matrix. */
/* NW (input) INTEGER */
/* Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1). */
/* H (input/output) COMPLEX array, dimension (LDH,N) */
/* On input the initial N-by-N section of H stores the */
/* Hessenberg matrix undergoing aggressive early deflation. */
/* On output H has been transformed by a unitary */
/* similarity transformation, perturbed, and the returned */
/* to Hessenberg form that (it is to be hoped) has some */
/* zero subdiagonal entries. */
/* LDH (input) integer */
/* Leading dimension of H just as declared in the calling */
/* subroutine. N .LE. LDH */
/* ILOZ (input) INTEGER */
/* IHIZ (input) INTEGER */
/* Specify the rows of Z to which transformations must be */
/* applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N. */
/* Z (input/output) COMPLEX array, dimension (LDZ,N) */
/* IF WANTZ is .TRUE., then on output, the unitary */
/* similarity transformation mentioned above has been */
/* accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right. */
/* If WANTZ is .FALSE., then Z is unreferenced. */
/* LDZ (input) integer */
/* The leading dimension of Z just as declared in the */
/* calling subroutine. 1 .LE. LDZ. */
/* NS (output) integer */
/* The number of unconverged (ie approximate) eigenvalues */
/* returned in SR and SI that may be used as shifts by the */
/* calling subroutine. */
/* ND (output) integer */
/* The number of converged eigenvalues uncovered by this */
/* subroutine. */
/* SH (output) COMPLEX array, dimension KBOT */
/* On output, approximate eigenvalues that may */
/* be used for shifts are stored in SH(KBOT-ND-NS+1) */
/* through SR(KBOT-ND). Converged eigenvalues are */
/* stored in SH(KBOT-ND+1) through SH(KBOT). */
/* V (workspace) COMPLEX array, dimension (LDV,NW) */
/* An NW-by-NW work array. */
/* LDV (input) integer scalar */
/* The leading dimension of V just as declared in the */
/* calling subroutine. NW .LE. LDV */
/* NH (input) integer scalar */
/* The number of columns of T. NH.GE.NW. */
/* T (workspace) COMPLEX array, dimension (LDT,NW) */
/* LDT (input) integer */
/* The leading dimension of T just as declared in the */
/* calling subroutine. NW .LE. LDT */
/* NV (input) integer */
/* The number of rows of work array WV available for */
/* workspace. NV.GE.NW. */
/* WV (workspace) COMPLEX array, dimension (LDWV,NW) */
/* LDWV (input) integer */
/* The leading dimension of W just as declared in the */
/* calling subroutine. NW .LE. LDV */
/* WORK (workspace) COMPLEX array, dimension LWORK. */
/* On exit, WORK(1) is set to an estimate of the optimal value */
/* of LWORK for the given values of N, NW, KTOP and KBOT. */
/* LWORK (input) integer */
/* The dimension of the work array WORK. LWORK = 2*NW */
/* suffices, but greater efficiency may result from larger */
/* values of LWORK. */
/* If LWORK = -1, then a workspace query is assumed; CLAQR2 */
/* only estimates the optimal workspace size for the given */
/* values of N, NW, KTOP and KBOT. The estimate is returned */
/* in WORK(1). No error message related to LWORK is issued */
/* by XERBLA. Neither H nor Z are accessed. */
/* ================================================================ */
/* Based on contributions by */
/* Karen Braman and Ralph Byers, Department of Mathematics, */
/* University of Kansas, USA */
/* ================================================================ */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* ==== Estimate optimal workspace. ==== */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--sh;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
wv_dim1 = *ldwv;
wv_offset = 1 + wv_dim1;
wv -= wv_offset;
--work;
/* Function Body */
/* Computing MIN */
i__1 = *nw, i__2 = *kbot - *ktop + 1;
jw = min(i__1,i__2);
if (jw <= 2) {
lwkopt = 1;
} else {
/* ==== Workspace query call to CGEHRD ==== */
i__1 = jw - 1;
cgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
c_n1, &info);
lwk1 = (integer) work[1].r;
/* ==== Workspace query call to CUNMHR ==== */
i__1 = jw - 1;
cunmhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1],
&v[v_offset], ldv, &work[1], &c_n1, &info);
lwk2 = (integer) work[1].r;
/* ==== Optimal workspace ==== */
lwkopt = jw + max(lwk1,lwk2);
}
/* ==== Quick return in case of workspace query. ==== */
if (*lwork == -1) {
r__1 = (real) lwkopt;
q__1.r = r__1, q__1.i = 0.f;
work[1].r = q__1.r, work[1].i = q__1.i;
return 0;
}
/* ==== Nothing to do ... */
/* ... for an empty active block ... ==== */
*ns = 0;
*nd = 0;
work[1].r = 1.f, work[1].i = 0.f;
if (*ktop > *kbot) {
return 0;
}
/* ... nor for an empty deflation window. ==== */
if (*nw < 1) {
return 0;
}
/* ==== Machine constants ==== */
safmin = slamch_("SAFE MINIMUM");
safmax = 1.f / safmin;
slabad_(&safmin, &safmax);
ulp = slamch_("PRECISION");
smlnum = safmin * ((real) (*n) / ulp);
/* ==== Setup deflation window ==== */
/* Computing MIN */
i__1 = *nw, i__2 = *kbot - *ktop + 1;
jw = min(i__1,i__2);
kwtop = *kbot - jw + 1;
if (kwtop == *ktop) {
s.r = 0.f, s.i = 0.f;
} else {
i__1 = kwtop + (kwtop - 1) * h_dim1;
s.r = h__[i__1].r, s.i = h__[i__1].i;
}
if (*kbot == kwtop) {
/* ==== 1-by-1 deflation window: not much to do ==== */
i__1 = kwtop;
i__2 = kwtop + kwtop * h_dim1;
sh[i__1].r = h__[i__2].r, sh[i__1].i = h__[i__2].i;
*ns = 1;
*nd = 0;
/* Computing MAX */
i__1 = kwtop + kwtop * h_dim1;
r__5 = smlnum, r__6 = ulp * ((r__1 = h__[i__1].r, dabs(r__1)) + (r__2
= r_imag(&h__[kwtop + kwtop * h_dim1]), dabs(r__2)));
if ((r__3 = s.r, dabs(r__3)) + (r__4 = r_imag(&s), dabs(r__4)) <=
dmax(r__5,r__6)) {
*ns = 0;
*nd = 1;
if (kwtop > *ktop) {
i__1 = kwtop + (kwtop - 1) * h_dim1;
h__[i__1].r = 0.f, h__[i__1].i = 0.f;
}
}
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
/* ==== Convert to spike-triangular form. (In case of a */
/* . rare QR failure, this routine continues to do */
/* . aggressive early deflation using that part of */
/* . the deflation window that converged using INFQR */
/* . here and there to keep track.) ==== */
clacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset],
ldt);
i__1 = jw - 1;
i__2 = *ldh + 1;
i__3 = *ldt + 1;
ccopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], &
i__3);
claset_("A", &jw, &jw, &c_b1, &c_b2, &v[v_offset], ldv);
clahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sh[kwtop],
&c__1, &jw, &v[v_offset], ldv, &infqr);
/* ==== Deflation detection loop ==== */
*ns = jw;
ilst = infqr + 1;
i__1 = jw;
for (knt = infqr + 1; knt <= i__1; ++knt) {
/* ==== Small spike tip deflation test ==== */
i__2 = *ns + *ns * t_dim1;
foo = (r__1 = t[i__2].r, dabs(r__1)) + (r__2 = r_imag(&t[*ns + *ns *
t_dim1]), dabs(r__2));
if (foo == 0.f) {
foo = (r__1 = s.r, dabs(r__1)) + (r__2 = r_imag(&s), dabs(r__2));
}
i__2 = *ns * v_dim1 + 1;
/* Computing MAX */
r__5 = smlnum, r__6 = ulp * foo;
if (((r__1 = s.r, dabs(r__1)) + (r__2 = r_imag(&s), dabs(r__2))) * ((
r__3 = v[i__2].r, dabs(r__3)) + (r__4 = r_imag(&v[*ns *
v_dim1 + 1]), dabs(r__4))) <= dmax(r__5,r__6)) {
/* ==== One more converged eigenvalue ==== */
--(*ns);
} else {
/* ==== One undeflatable eigenvalue. Move it up out of the */
/* . way. (CTREXC can not fail in this case.) ==== */
ifst = *ns;
ctrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, &
ilst, &info);
++ilst;
}
/* L10: */
}
/* ==== Return to Hessenberg form ==== */
if (*ns == 0) {
s.r = 0.f, s.i = 0.f;
}
if (*ns < jw) {
/* ==== sorting the diagonal of T improves accuracy for */
/* . graded matrices. ==== */
i__1 = *ns;
for (i__ = infqr + 1; i__ <= i__1; ++i__) {
ifst = i__;
i__2 = *ns;
for (j = i__ + 1; j <= i__2; ++j) {
i__3 = j + j * t_dim1;
i__4 = ifst + ifst * t_dim1;
if ((r__1 = t[i__3].r, dabs(r__1)) + (r__2 = r_imag(&t[j + j *
t_dim1]), dabs(r__2)) > (r__3 = t[i__4].r, dabs(r__3)
) + (r__4 = r_imag(&t[ifst + ifst * t_dim1]), dabs(
r__4))) {
ifst = j;
}
/* L20: */
}
ilst = i__;
if (ifst != ilst) {
ctrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &info);
}
/* L30: */
}
}
/* ==== Restore shift/eigenvalue array from T ==== */
i__1 = jw;
for (i__ = infqr + 1; i__ <= i__1; ++i__) {
i__2 = kwtop + i__ - 1;
i__3 = i__ + i__ * t_dim1;
sh[i__2].r = t[i__3].r, sh[i__2].i = t[i__3].i;
/* L40: */
}
if (*ns < jw || s.r == 0.f && s.i == 0.f) {
if (*ns > 1 && (s.r != 0.f || s.i != 0.f)) {
/* ==== Reflect spike back into lower triangle ==== */
ccopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
i__1 = *ns;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
r_cnjg(&q__1, &work[i__]);
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L50: */
}
beta.r = work[1].r, beta.i = work[1].i;
clarfg_(ns, &beta, &work[2], &c__1, &tau);
work[1].r = 1.f, work[1].i = 0.f;
i__1 = jw - 2;
i__2 = jw - 2;
claset_("L", &i__1, &i__2, &c_b1, &c_b1, &t[t_dim1 + 3], ldt);
r_cnjg(&q__1, &tau);
clarf_("L", ns, &jw, &work[1], &c__1, &q__1, &t[t_offset], ldt, &
work[jw + 1]);
clarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, &
work[jw + 1]);
clarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, &
work[jw + 1]);
i__1 = *lwork - jw;
cgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
, &i__1, &info);
}
/* ==== Copy updated reduced window into place ==== */
if (kwtop > 1) {
i__1 = kwtop + (kwtop - 1) * h_dim1;
r_cnjg(&q__2, &v[v_dim1 + 1]);
q__1.r = s.r * q__2.r - s.i * q__2.i, q__1.i = s.r * q__2.i + s.i
* q__2.r;
h__[i__1].r = q__1.r, h__[i__1].i = q__1.i;
}
clacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1]
, ldh);
i__1 = jw - 1;
i__2 = *ldt + 1;
i__3 = *ldh + 1;
ccopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1],
&i__3);
/* ==== Accumulate orthogonal matrix in order update */
/* . H and Z, if requested. ==== */
if (*ns > 1 && (s.r != 0.f || s.i != 0.f)) {
i__1 = *lwork - jw;
cunmhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1],
&v[v_offset], ldv, &work[jw + 1], &i__1, &info);
}
/* ==== Update vertical slab in H ==== */
if (*wantt) {
ltop = 1;
} else {
ltop = *ktop;
}
i__1 = kwtop - 1;
i__2 = *nv;
for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
i__2) {
/* Computing MIN */
i__3 = *nv, i__4 = kwtop - krow;
kln = min(i__3,i__4);
cgemm_("N", "N", &kln, &jw, &jw, &c_b2, &h__[krow + kwtop *
h_dim1], ldh, &v[v_offset], ldv, &c_b1, &wv[wv_offset],
ldwv);
clacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop *
h_dim1], ldh);
/* L60: */
}
/* ==== Update horizontal slab in H ==== */
if (*wantt) {
i__2 = *n;
i__1 = *nh;
for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2;
kcol += i__1) {
/* Computing MIN */
i__3 = *nh, i__4 = *n - kcol + 1;
kln = min(i__3,i__4);
cgemm_("C", "N", &jw, &kln, &jw, &c_b2, &v[v_offset], ldv, &
h__[kwtop + kcol * h_dim1], ldh, &c_b1, &t[t_offset],
ldt);
clacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol *
h_dim1], ldh);
/* L70: */
}
}
/* ==== Update vertical slab in Z ==== */
if (*wantz) {
i__1 = *ihiz;
i__2 = *nv;
for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
i__2) {
/* Computing MIN */
i__3 = *nv, i__4 = *ihiz - krow + 1;
kln = min(i__3,i__4);
cgemm_("N", "N", &kln, &jw, &jw, &c_b2, &z__[krow + kwtop *
z_dim1], ldz, &v[v_offset], ldv, &c_b1, &wv[wv_offset]
, ldwv);
clacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow +
kwtop * z_dim1], ldz);
/* L80: */
}
}
}
/* ==== Return the number of deflations ... ==== */
*nd = jw - *ns;
/* ==== ... and the number of shifts. (Subtracting */
/* . INFQR from the spike length takes care */
/* . of the case of a rare QR failure while */
/* . calculating eigenvalues of the deflation */
/* . window.) ==== */
*ns -= infqr;
/* ==== Return optimal workspace. ==== */
r__1 = (real) lwkopt;
q__1.r = r__1, q__1.i = 0.f;
work[1].r = q__1.r, work[1].i = q__1.i;
/* ==== End of CLAQR2 ==== */
return 0;
} /* claqr2_ */
/* Subroutine */ int cgeesx_(char *jobvs, char *sort, L_fp select, char *
sense, integer *n, complex *a, integer *lda, integer *sdim, complex *
w, complex *vs, integer *ldvs, real *rconde, real *rcondv, complex *
work, integer *lwork, real *rwork, logical *bwork, integer *info)
{
/* -- LAPACK driver routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
CGEESX computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, the Schur form T, and, optionally, the matrix of Schur
vectors Z. This gives the Schur factorization A = Z*T*(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the
Schur form so that selected eigenvalues are at the top left;
computes a reciprocal condition number for the average of the
selected eigenvalues (RCONDE); and computes a reciprocal condition
number for the right invariant subspace corresponding to the
selected eigenvalues (RCONDV). The leading columns of Z form an
orthonormal basis for this invariant subspace.
For further explanation of the reciprocal condition numbers RCONDE
and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
these quantities are called s and sep respectively).
A complex matrix is in Schur form if it is upper triangular.
Arguments
=========
JOBVS (input) CHARACTER*1
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.
SORT (input) CHARACTER*1
Specifies whether or not to order the eigenvalues on the
diagonal of the Schur form.
= 'N': Eigenvalues are not ordered;
= 'S': Eigenvalues are ordered (see SELECT).
SELECT (input) LOGICAL FUNCTION of one COMPLEX argument
SELECT must be declared EXTERNAL in the calling subroutine.
If SORT = 'S', SELECT is used to select eigenvalues to order
to the top left of the Schur form.
If SORT = 'N', SELECT is not referenced.
An eigenvalue W(j) is selected if SELECT(W(j)) is true.
SENSE (input) CHARACTER*1
Determines which reciprocal condition numbers are computed.
= 'N': None are computed;
= 'E': Computed for average of selected eigenvalues only;
= 'V': Computed for selected right invariant subspace only;
= 'B': Computed for both.
If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA, N)
On entry, the N-by-N matrix A.
On exit, A is overwritten by its Schur form T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
SDIM (output) INTEGER
If SORT = 'N', SDIM = 0.
If SORT = 'S', SDIM = number of eigenvalues for which
SELECT is true.
W (output) COMPLEX array, dimension (N)
W contains the computed eigenvalues, in the same order
that they appear on the diagonal of the output Schur form T.
VS (output) COMPLEX array, dimension (LDVS,N)
If JOBVS = 'V', VS contains the unitary matrix Z of Schur
vectors.
If JOBVS = 'N', VS is not referenced.
LDVS (input) INTEGER
The leading dimension of the array VS. LDVS >= 1, and if
JOBVS = 'V', LDVS >= N.
RCONDE (output) REAL
If SENSE = 'E' or 'B', RCONDE contains the reciprocal
condition number for the average of the selected eigenvalues.
Not referenced if SENSE = 'N' or 'V'.
RCONDV (output) REAL
If SENSE = 'V' or 'B', RCONDV contains the reciprocal
condition number for the selected right invariant subspace.
Not referenced if SENSE = 'N' or 'E'.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,2*N).
Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM),
where SDIM is the number of selected eigenvalues computed by
this routine. Note that 2*SDIM*(N-SDIM) <= N*N/2.
For good performance, LWORK must generally be larger.
RWORK (workspace) REAL array, dimension (N)
BWORK (workspace) LOGICAL array, dimension (N)
Not referenced if SORT = 'N'.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, and i is
<= N: the QR algorithm failed to compute all the
eigenvalues; elements 1:ILO-1 and i+1:N of W
contain those eigenvalues which have converged; if
JOBVS = 'V', VS contains the transformation which
reduces A to its partially converged Schur form.
= N+1: the eigenvalues could not be reordered because some
eigenvalues were too close to separate (the problem
is very ill-conditioned);
= N+2: after reordering, roundoff changed values of some
complex eigenvalues so that leading eigenvalues in
the Schur form no longer satisfy SELECT=.TRUE. This
could also be caused by underflow due to scaling.
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c__0 = 0;
static integer c__8 = 8;
static integer c_n1 = -1;
static integer c__4 = 4;
/* System generated locals */
integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3, i__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer ibal, maxb;
static real anrm;
static integer ierr, itau, iwrk, i, k, icond, ieval;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), cgebak_(char *, char *, integer *, integer
*, integer *, real *, integer *, complex *, integer *, integer *), cgebal_(char *, integer *, complex *, integer *,
integer *, integer *, real *, integer *), slabad_(real *,
real *);
static logical scalea;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
static real cscale;
extern /* Subroutine */ int cgehrd_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *),
clascl_(char *, integer *, integer *, real *, real *, integer *,
integer *, complex *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), xerbla_(char *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *), chseqr_(char *, char *, integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, complex *,
integer *, integer *), cunghr_(integer *, integer
*, integer *, complex *, integer *, complex *, complex *, integer
*, integer *);
static logical wantsb;
extern /* Subroutine */ int ctrsen_(char *, char *, logical *, integer *,
complex *, integer *, complex *, integer *, complex *, integer *,
real *, real *, complex *, integer *, integer *);
static logical wantse;
static integer minwrk, maxwrk;
static logical wantsn;
static real smlnum;
static integer hswork;
static logical wantst, wantsv, wantvs;
static integer ihi, ilo;
static real dum[1], eps;
#define W(I) w[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]
#define BWORK(I) bwork[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define VS(I,J) vs[(I)-1 + ((J)-1)* ( *ldvs)]
*info = 0;
wantvs = lsame_(jobvs, "V");
wantst = lsame_(sort, "S");
wantsn = lsame_(sense, "N");
wantse = lsame_(sense, "E");
wantsv = lsame_(sense, "V");
wantsb = lsame_(sense, "B");
if (! wantvs && ! lsame_(jobvs, "N")) {
*info = -1;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -2;
} else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && !
wantsn) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldvs < 1 || wantvs && *ldvs < *n) {
*info = -11;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of real workspace needed at that point in the
code, as well as the preferred amount for good performance.
CWorkspace refers to complex workspace, and RWorkspace to real
workspace. NB refers to the optimal block size for the
immediately following subroutine, as returned by ILAENV.
HSWORK refers to the workspace preferred by CHSEQR, as
calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
the worst case.
If SENSE = 'E', 'V' or 'B', then the amount of workspace needed
depends on SDIM, which is computed by the routine CTRSEN later
in the code.) */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &c__0,
6L, 1L);
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
minwrk = max(i__1,i__2);
if (! wantvs) {
/* Computing MAX */
i__1 = ilaenv_(&c__8, "CHSEQR", "SN", n, &c__1, n, &c_n1, 6L, 2L);
maxb = max(i__1,2);
/* Computing MIN
Computing MAX */
i__3 = 2, i__4 = ilaenv_(&c__4, "CHSEQR", "SN", n, &c__1, n, &
c_n1, 6L, 2L);
i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
k = min(i__1,i__2);
/* Computing MAX */
i__1 = k * (k + 2), i__2 = *n << 1;
hswork = max(i__1,i__2);
/* Computing MAX */
i__1 = max(maxwrk,hswork);
maxwrk = max(i__1,1);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1, 6L, 1L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = ilaenv_(&c__8, "CHSEQR", "SV", n, &c__1, n, &c_n1, 6L, 2L);
maxb = max(i__1,2);
/* Computing MIN
Computing MAX */
i__3 = 2, i__4 = ilaenv_(&c__4, "CHSEQR", "SV", n, &c__1, n, &
c_n1, 6L, 2L);
i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
k = min(i__1,i__2);
/* Computing MAX */
i__1 = k * (k + 2), i__2 = *n << 1;
hswork = max(i__1,i__2);
/* Computing MAX */
i__1 = max(maxwrk,hswork);
maxwrk = max(i__1,1);
}
WORK(1).r = (real) maxwrk, WORK(1).i = 0.f;
}
if (*lwork < minwrk) {
*info = -15;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEESX", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", n, n, &A(1,1), lda, dum);
scalea = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &A(1,1), lda, &
ierr);
}
/* Permute the matrix to make it more nearly triangular
(CWorkspace: none)
(RWorkspace: need N) */
ibal = 1;
cgebal_("P", n, &A(1,1), lda, &ilo, &ihi, &RWORK(ibal), &ierr);
/* Reduce to upper Hessenberg form
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: none) */
itau = 1;
iwrk = *n + itau;
i__1 = *lwork - iwrk + 1;
cgehrd_(n, &ilo, &ihi, &A(1,1), lda, &WORK(itau), &WORK(iwrk), &i__1,
&ierr);
if (wantvs) {
/* Copy Householder vectors to VS */
clacpy_("L", n, n, &A(1,1), lda, &VS(1,1), ldvs);
/* Generate unitary matrix in VS
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, &ilo, &ihi, &VS(1,1), ldvs, &WORK(itau), &WORK(iwrk),
&i__1, &ierr);
}
*sdim = 0;
/* Perform QR iteration, accumulating Schur vectors in VS if desired
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", jobvs, n, &ilo, &ihi, &A(1,1), lda, &W(1), &VS(1,1), ldvs, &WORK(iwrk), &i__1, &ieval);
if (ieval > 0) {
*info = ieval;
}
/* Sort eigenvalues if desired */
if (wantst && *info == 0) {
if (scalea) {
clascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &W(1), n, &
ierr);
}
i__1 = *n;
for (i = 1; i <= *n; ++i) {
BWORK(i) = (*select)(&W(i));
/* L10: */
}
/* Reorder eigenvalues, transform Schur vectors, and compute
reciprocal condition numbers
(CWorkspace: if SENSE is not 'N', need 2*SDIM*(N-SDIM)
otherwise, need none )
(RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
ctrsen_(sense, jobvs, &BWORK(1), n, &A(1,1), lda, &VS(1,1),
ldvs, &W(1), sdim, rconde, rcondv, &WORK(iwrk), &i__1, &
icond);
if (! wantsn) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
maxwrk = max(i__1,i__2);
}
if (icond == -14) {
/* Not enough complex workspace */
*info = -15;
}
}
if (wantvs) {
/* Undo balancing
(CWorkspace: none)
(RWorkspace: need N) */
cgebak_("P", "R", n, &ilo, &ihi, &RWORK(ibal), n, &VS(1,1),
ldvs, &ierr);
}
if (scalea) {
/* Undo scaling for the Schur form of A */
clascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &A(1,1), lda, &
ierr);
i__1 = *lda + 1;
ccopy_(n, &A(1,1), &i__1, &W(1), &c__1);
if ((wantsv || wantsb) && *info == 0) {
dum[0] = *rcondv;
slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &
c__1, &ierr);
*rcondv = dum[0];
}
}
WORK(1).r = (real) maxwrk, WORK(1).i = 0.f;
return 0;
/* End of CGEESX */
} /* cgeesx_ */
/* Subroutine */ int cchkhs_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, real *thresh, integer *nounit,
complex *a, integer *lda, complex *h__, complex *t1, complex *t2,
complex *u, integer *ldu, complex *z__, complex *uz, complex *w1,
complex *w3, complex *evectl, complex *evectr, complex *evecty,
complex *evectx, complex *uu, complex *tau, complex *work, integer *
nwork, real *rwork, integer *iwork, logical *select, real *result,
integer *info)
{
/* Initialized data */
static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 };
static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 };
static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 };
static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 };
/* Format strings */
static char fmt_9999[] = "(\002 CCHKHS: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 CCHKHS: \002,a,\002 Eigenvectors from"
" \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
"error=\002,0p,g10.3,\002,\002,9x,\002N=\002,i6,\002, JTYPE=\002,"
"i6,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(\002 CCHKHS: Selected \002,a,\002 Eigenvector"
"s from \002,a,\002 do not match other eigenvectors \002,9x,\002N="
"\002,i6,\002, JTYPE=\002,i6,\002, ISEED=(\002,3(i5,\002,\002),i5,"
"\002)\002)";
/* System generated locals */
integer a_dim1, a_offset, evectl_dim1, evectl_offset, evectr_dim1,
evectr_offset, evectx_dim1, evectx_offset, evecty_dim1,
evecty_offset, h_dim1, h_offset, t1_dim1, t1_offset, t2_dim1,
t2_offset, u_dim1, u_offset, uu_dim1, uu_offset, uz_dim1,
uz_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5, i__6;
real r__1, r__2;
complex q__1;
/* Local variables */
integer i__, j, k, n, n1, jj, in, ihi, ilo;
real ulp, cond;
integer jcol, nmax;
real unfl, ovfl, temp1, temp2;
logical badnn;
extern /* Subroutine */ int cget10_(integer *, integer *, complex *,
integer *, complex *, integer *, complex *, real *, real *),
cget22_(char *, char *, char *, integer *, complex *, integer *,
complex *, integer *, complex *, complex *, real *, real *), cgemm_(char *, char *, integer *,
integer *, integer *, complex *, complex *, integer *, complex *,
integer *, complex *, complex *, integer *);
logical match;
integer imode;
extern /* Subroutine */ int chst01_(integer *, integer *, integer *,
complex *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *, real *, real *);
real dumma[4];
integer iinfo;
real conds, aninv, anorm;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
integer nmats, jsize, nerrs, itype, jtype, ntest;
real rtulp;
extern /* Subroutine */ int slabad_(real *, real *), cgehrd_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, integer *), clatme_(integer *, char *, integer *,
complex *, integer *, real *, complex *, char *, char *, char *,
char *, real *, integer *, real *, integer *, integer *, real *,
complex *, integer *, complex *, integer *);
complex cdumma[4];
extern doublereal slamch_(char *);
extern /* Subroutine */ int chsein_(char *, char *, char *, logical *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *, integer *, complex *, real *,
integer *, integer *, integer *), clacpy_(
char *, integer *, integer *, complex *, integer *, complex *,
integer *);
integer idumma[1];
extern /* Subroutine */ int claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *);
integer ioldsd[4];
extern /* Subroutine */ int xerbla_(char *, integer *), clatmr_(
integer *, integer *, char *, integer *, char *, complex *,
integer *, real *, complex *, char *, char *, complex *, integer *
, real *, complex *, integer *, real *, char *, integer *,
integer *, integer *, real *, real *, char *, complex *, integer *
, integer *, integer *), clatms_(integer *, integer *, char *, integer *, char *,
real *, integer *, real *, real *, integer *, integer *, char *,
complex *, integer *, complex *, integer *), chseqr_(char *, char *, integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, complex *,
integer *, integer *), ctrevc_(char *, char *,
logical *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *, integer *, integer *, complex *, real *,
integer *), cunghr_(integer *, integer *, integer
*, complex *, integer *, complex *, complex *, integer *, integer
*), cunmhr_(char *, char *, integer *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *), slafts_(char *,
integer *, integer *, integer *, integer *, real *, integer *,
real *, integer *, integer *), slasum_(char *, integer *,
integer *, integer *);
real rtunfl, rtovfl, rtulpi, ulpinv;
integer mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___35 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___38 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___58 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___59 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___60 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___61 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___62 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___63 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___64 = { 0, 0, 0, fmt_9999, 0 };
/* -- LAPACK test routine (version 3.1.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* February 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CCHKHS checks the nonsymmetric eigenvalue problem routines. */
/* CGEHRD factors A as U H U' , where ' means conjugate */
/* transpose, H is hessenberg, and U is unitary. */
/* CUNGHR generates the unitary matrix U. */
/* CUNMHR multiplies a matrix by the unitary matrix U. */
/* CHSEQR factors H as Z T Z' , where Z is unitary and T */
/* is upper triangular. It also computes the eigenvalues, */
/* w(1), ..., w(n); we define a diagonal matrix W whose */
/* (diagonal) entries are the eigenvalues. */
/* CTREVC computes the left eigenvector matrix L and the */
/* right eigenvector matrix R for the matrix T. The */
/* columns of L are the complex conjugates of the left */
/* eigenvectors of T. The columns of R are the right */
/* eigenvectors of T. L is lower triangular, and R is */
/* upper triangular. */
/* CHSEIN computes the left eigenvector matrix Y and the */
/* right eigenvector matrix X for the matrix H. The */
/* columns of Y are the complex conjugates of the left */
/* eigenvectors of H. The columns of X are the right */
/* eigenvectors of H. Y is lower triangular, and X is */
/* upper triangular. */
/* When CCHKHS is called, a number of matrix "sizes" ("n's") and a */
/* number of matrix "types" are specified. For each size ("n") */
/* and each type of matrix, one matrix will be generated and used */
/* to test the nonsymmetric eigenroutines. For each matrix, 14 */
/* tests will be performed: */
/* (1) | A - U H U**H | / ( |A| n ulp ) */
/* (2) | I - UU**H | / ( n ulp ) */
/* (3) | H - Z T Z**H | / ( |H| n ulp ) */
/* (4) | I - ZZ**H | / ( n ulp ) */
/* (5) | A - UZ H (UZ)**H | / ( |A| n ulp ) */
/* (6) | I - UZ (UZ)**H | / ( n ulp ) */
/* (7) | T(Z computed) - T(Z not computed) | / ( |T| ulp ) */
/* (8) | W(Z computed) - W(Z not computed) | / ( |W| ulp ) */
/* (9) | TR - RW | / ( |T| |R| ulp ) */
/* (10) | L**H T - W**H L | / ( |T| |L| ulp ) */
/* (11) | HX - XW | / ( |H| |X| ulp ) */
/* (12) | Y**H H - W**H Y | / ( |H| |Y| ulp ) */
/* (13) | AX - XW | / ( |A| |X| ulp ) */
/* (14) | Y**H A - W**H Y | / ( |A| |Y| ulp ) */
/* The "sizes" are specified by an array NN(1:NSIZES); the value of */
/* each element NN(j) specifies one size. */
/* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); */
/* if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. */
/* Currently, the list of possible types is: */
/* (1) The zero matrix. */
/* (2) The identity matrix. */
/* (3) A (transposed) Jordan block, with 1's on the diagonal. */
/* (4) A diagonal matrix with evenly spaced entries */
/* 1, ..., ULP and random complex angles. */
/* (ULP = (first number larger than 1) - 1 ) */
/* (5) A diagonal matrix with geometrically spaced entries */
/* 1, ..., ULP and random complex angles. */
/* (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */
/* and random complex angles. */
/* (7) Same as (4), but multiplied by SQRT( overflow threshold ) */
/* (8) Same as (4), but multiplied by SQRT( underflow threshold ) */
/* (9) A matrix of the form U' T U, where U is unitary and */
/* T has evenly spaced entries 1, ..., ULP with random complex */
/* angles on the diagonal and random O(1) entries in the upper */
/* triangle. */
/* (10) A matrix of the form U' T U, where U is unitary and */
/* T has geometrically spaced entries 1, ..., ULP with random */
/* complex angles on the diagonal and random O(1) entries in */
/* the upper triangle. */
/* (11) A matrix of the form U' T U, where U is unitary and */
/* T has "clustered" entries 1, ULP,..., ULP with random */
/* complex angles on the diagonal and random O(1) entries in */
/* the upper triangle. */
/* (12) A matrix of the form U' T U, where U is unitary and */
/* T has complex eigenvalues randomly chosen from */
/* ULP < |z| < 1 and random O(1) entries in the upper */
/* triangle. */
/* (13) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP */
/* with random complex angles on the diagonal and random O(1) */
/* entries in the upper triangle. */
/* (14) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has geometrically spaced entries */
/* 1, ..., ULP with random complex angles on the diagonal */
/* and random O(1) entries in the upper triangle. */
/* (15) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP */
/* with random complex angles on the diagonal and random O(1) */
/* entries in the upper triangle. */
/* (16) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has complex eigenvalues randomly chosen */
/* from ULP < |z| < 1 and random O(1) entries in the upper */
/* triangle. */
/* (17) Same as (16), but multiplied by SQRT( overflow threshold ) */
/* (18) Same as (16), but multiplied by SQRT( underflow threshold ) */
/* (19) Nonsymmetric matrix with random entries chosen from |z| < 1 */
/* (20) Same as (19), but multiplied by SQRT( overflow threshold ) */
/* (21) Same as (19), but multiplied by SQRT( underflow threshold ) */
/* Arguments */
/* ========== */
/* NSIZES - INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* CCHKHS does nothing. It must be at least zero. */
/* Not modified. */
/* NN - INTEGER array, dimension (NSIZES) */
/* An array containing the sizes to be used for the matrices. */
/* Zero values will be skipped. The values must be at least */
/* zero. */
/* Not modified. */
/* NTYPES - INTEGER */
/* The number of elements in DOTYPE. If it is zero, CCHKHS */
/* does nothing. It must be at least zero. If it is MAXTYP+1 */
/* and NSIZES is 1, then an additional type, MAXTYP+1 is */
/* defined, which is to use whatever matrix is in A. This */
/* is only useful if DOTYPE(1:MAXTYP) is .FALSE. and */
/* DOTYPE(MAXTYP+1) is .TRUE. . */
/* Not modified. */
/* DOTYPE - LOGICAL array, dimension (NTYPES) */
/* If DOTYPE(j) is .TRUE., then for each size in NN a */
/* matrix of that size and of type j will be generated. */
/* If NTYPES is smaller than the maximum number of types */
/* defined (PARAMETER MAXTYP), then types NTYPES+1 through */
/* MAXTYP will not be generated. If NTYPES is larger */
/* than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) */
/* will be ignored. */
/* Not modified. */
/* ISEED - INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The array elements should be between 0 and 4095; */
/* if not they will be reduced mod 4096. Also, ISEED(4) must */
/* be odd. The random number generator uses a linear */
/* congruential sequence limited to small integers, and so */
/* should produce machine independent random numbers. The */
/* values of ISEED are changed on exit, and can be used in the */
/* next call to CCHKHS to continue the same random number */
/* sequence. */
/* Modified. */
/* THRESH - REAL */
/* A test will count as "failed" if the "error", computed as */
/* described above, exceeds THRESH. Note that the error */
/* is scaled to be O(1), so THRESH should be a reasonably */
/* small multiple of 1, e.g., 10 or 100. In particular, */
/* it should not depend on the precision (single vs. double) */
/* or the size of the matrix. It must be at least zero. */
/* Not modified. */
/* NOUNIT - INTEGER */
/* The FORTRAN unit number for printing out error messages */
/* (e.g., if a routine returns IINFO not equal to 0.) */
/* Not modified. */
/* A - COMPLEX array, dimension (LDA,max(NN)) */
/* Used to hold the matrix whose eigenvalues are to be */
/* computed. On exit, A contains the last matrix actually */
/* used. */
/* Modified. */
/* LDA - INTEGER */
/* The leading dimension of A, H, T1 and T2. It must be at */
/* least 1 and at least max( NN ). */
/* Not modified. */
/* H - COMPLEX array, dimension (LDA,max(NN)) */
/* The upper hessenberg matrix computed by CGEHRD. On exit, */
/* H contains the Hessenberg form of the matrix in A. */
/* Modified. */
/* T1 - COMPLEX array, dimension (LDA,max(NN)) */
/* The Schur (="quasi-triangular") matrix computed by CHSEQR */
/* if Z is computed. On exit, T1 contains the Schur form of */
/* the matrix in A. */
/* Modified. */
/* T2 - COMPLEX array, dimension (LDA,max(NN)) */
/* The Schur matrix computed by CHSEQR when Z is not computed. */
/* This should be identical to T1. */
/* Modified. */
/* LDU - INTEGER */
/* The leading dimension of U, Z, UZ and UU. It must be at */
/* least 1 and at least max( NN ). */
/* Not modified. */
/* U - COMPLEX array, dimension (LDU,max(NN)) */
/* The unitary matrix computed by CGEHRD. */
/* Modified. */
/* Z - COMPLEX array, dimension (LDU,max(NN)) */
/* The unitary matrix computed by CHSEQR. */
/* Modified. */
/* UZ - COMPLEX array, dimension (LDU,max(NN)) */
/* The product of U times Z. */
/* Modified. */
/* W1 - COMPLEX array, dimension (max(NN)) */
/* The eigenvalues of A, as computed by a full Schur */
/* decomposition H = Z T Z'. On exit, W1 contains the */
/* eigenvalues of the matrix in A. */
/* Modified. */
/* W3 - COMPLEX array, dimension (max(NN)) */
/* The eigenvalues of A, as computed by a partial Schur */
/* decomposition (Z not computed, T only computed as much */
/* as is necessary for determining eigenvalues). On exit, */
/* W3 contains the eigenvalues of the matrix in A, possibly */
/* perturbed by CHSEIN. */
/* Modified. */
/* EVECTL - COMPLEX array, dimension (LDU,max(NN)) */
/* The conjugate transpose of the (upper triangular) left */
/* eigenvector matrix for the matrix in T1. */
/* Modified. */
/* EVECTR - COMPLEX array, dimension (LDU,max(NN)) */
/* The (upper triangular) right eigenvector matrix for the */
/* matrix in T1. */
/* Modified. */
/* EVECTY - COMPLEX array, dimension (LDU,max(NN)) */
/* The conjugate transpose of the left eigenvector matrix */
/* for the matrix in H. */
/* Modified. */
/* EVECTX - COMPLEX array, dimension (LDU,max(NN)) */
/* The right eigenvector matrix for the matrix in H. */
/* Modified. */
/* UU - COMPLEX array, dimension (LDU,max(NN)) */
/* Details of the unitary matrix computed by CGEHRD. */
/* Modified. */
/* TAU - COMPLEX array, dimension (max(NN)) */
/* Further details of the unitary matrix computed by CGEHRD. */
/* Modified. */
/* WORK - COMPLEX array, dimension (NWORK) */
/* Workspace. */
/* Modified. */
/* NWORK - INTEGER */
/* The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2. */
/* RWORK - REAL array, dimension (max(NN)) */
/* Workspace. Could be equivalenced to IWORK, but not SELECT. */
/* Modified. */
/* IWORK - INTEGER array, dimension (max(NN)) */
/* Workspace. */
/* Modified. */
/* SELECT - LOGICAL array, dimension (max(NN)) */
/* Workspace. Could be equivalenced to IWORK, but not RWORK. */
/* Modified. */
/* RESULT - REAL array, dimension (14) */
/* The values computed by the fourteen tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* Modified. */
/* INFO - INTEGER */
/* If 0, then everything ran OK. */
/* -1: NSIZES < 0 */
/* -2: Some NN(j) < 0 */
/* -3: NTYPES < 0 */
/* -6: THRESH < 0 */
/* -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). */
/* -14: LDU < 1 or LDU < NMAX. */
/* -26: NWORK too small. */
/* If CLATMR, CLATMS, or CLATME returns an error code, the */
/* absolute value of it is returned. */
/* If 1, then CHSEQR could not find all the shifts. */
/* If 2, then the EISPACK code (for small blocks) failed. */
/* If >2, then 30*N iterations were not enough to find an */
/* eigenvalue or to decompose the problem. */
/* Modified. */
/* ----------------------------------------------------------------------- */
/* Some Local Variables and Parameters: */
/* ---- ----- --------- --- ---------- */
/* ZERO, ONE Real 0 and 1. */
/* MAXTYP The number of types defined. */
/* MTEST The number of tests defined: care must be taken */
/* that (1) the size of RESULT, (2) the number of */
/* tests actually performed, and (3) MTEST agree. */
/* NTEST The number of tests performed on this matrix */
/* so far. This should be less than MTEST, and */
/* equal to it by the last test. It will be less */
/* if any of the routines being tested indicates */
/* that it could not compute the matrices that */
/* would be tested. */
/* NMAX Largest value in NN. */
/* NMATS The number of matrices generated so far. */
/* NERRS The number of tests which have exceeded THRESH */
/* so far (computed by SLAFTS). */
/* COND, CONDS, */
/* IMODE Values to be passed to the matrix generators. */
/* ANORM Norm of A; passed to matrix generators. */
/* OVFL, UNFL Overflow and underflow thresholds. */
/* ULP, ULPINV Finest relative precision and its inverse. */
/* RTOVFL, RTUNFL, */
/* RTULP, RTULPI Square roots of the previous 4 values. */
/* The following four arrays decode JTYPE: */
/* KTYPE(j) The general type (1-10) for type "j". */
/* KMODE(j) The MODE value to be passed to the matrix */
/* generator for type "j". */
/* KMAGN(j) The order of magnitude ( O(1), */
/* O(overflow^(1/2) ), O(underflow^(1/2) ) */
/* KCONDS(j) Selects whether CONDS is to be 1 or */
/* 1/sqrt(ulp). (0 means irrelevant.) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--dotype;
--iseed;
t2_dim1 = *lda;
t2_offset = 1 + t2_dim1;
t2 -= t2_offset;
t1_dim1 = *lda;
t1_offset = 1 + t1_dim1;
t1 -= t1_offset;
h_dim1 = *lda;
h_offset = 1 + h_dim1;
h__ -= h_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
uu_dim1 = *ldu;
uu_offset = 1 + uu_dim1;
uu -= uu_offset;
evectx_dim1 = *ldu;
evectx_offset = 1 + evectx_dim1;
evectx -= evectx_offset;
evecty_dim1 = *ldu;
evecty_offset = 1 + evecty_dim1;
evecty -= evecty_offset;
evectr_dim1 = *ldu;
evectr_offset = 1 + evectr_dim1;
evectr -= evectr_offset;
evectl_dim1 = *ldu;
evectl_offset = 1 + evectl_dim1;
evectl -= evectl_offset;
uz_dim1 = *ldu;
uz_offset = 1 + uz_dim1;
uz -= uz_offset;
z_dim1 = *ldu;
z_offset = 1 + z_dim1;
z__ -= z_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
--w1;
--w3;
--tau;
--work;
--rwork;
--iwork;
--select;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
ntestt = 0;
*info = 0;
badnn = FALSE_;
nmax = 0;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.f) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -9;
} else if (*ldu <= 1 || *ldu < nmax) {
*info = -14;
} else if ((nmax << 2) * nmax + 2 > *nwork) {
*info = -26;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CCHKHS", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
/* More important constants */
unfl = slamch_("Safe minimum");
ovfl = slamch_("Overflow");
slabad_(&unfl, &ovfl);
ulp = slamch_("Epsilon") * slamch_("Base");
ulpinv = 1.f / ulp;
rtunfl = sqrt(unfl);
rtovfl = sqrt(ovfl);
rtulp = sqrt(ulp);
rtulpi = 1.f / rtulp;
/* Loop over sizes, types */
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
aninv = 1.f / (real) n1;
if (*nsizes != 1) {
mtypes = min(21,*ntypes);
} else {
mtypes = min(22,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L250;
}
++nmats;
ntest = 0;
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Initialize RESULT */
for (j = 1; j <= 14; ++j) {
result[j] = 0.f;
/* L30: */
}
/* Compute "A" */
/* Control parameters: */
/* KMAGN KCONDS KMODE KTYPE */
/* =1 O(1) 1 clustered 1 zero */
/* =2 large large clustered 2 identity */
/* =3 small exponential Jordan */
/* =4 arithmetic diagonal, (w/ eigenvalues) */
/* =5 random log hermitian, w/ eigenvalues */
/* =6 random general, w/ eigenvalues */
/* =7 random diagonal */
/* =8 random hermitian */
/* =9 random general */
/* =10 random triangular */
if (mtypes > 21) {
goto L100;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L40;
case 2: goto L50;
case 3: goto L60;
}
L40:
anorm = 1.f;
goto L70;
L50:
anorm = rtovfl * ulp * aninv;
goto L70;
L60:
anorm = rtunfl * n * ulpinv;
goto L70;
L70:
claset_("Full", lda, &n, &c_b1, &c_b1, &a[a_offset], lda);
iinfo = 0;
cond = ulpinv;
/* Special Matrices */
if (itype == 1) {
/* Zero */
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
i__4 = jcol + jcol * a_dim1;
a[i__4].r = anorm, a[i__4].i = 0.f;
/* L80: */
}
} else if (itype == 3) {
/* Jordan Block */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
i__4 = jcol + jcol * a_dim1;
a[i__4].r = anorm, a[i__4].i = 0.f;
if (jcol > 1) {
i__4 = jcol + (jcol - 1) * a_dim1;
a[i__4].r = 1.f, a[i__4].i = 0.f;
}
/* L90: */
}
} else if (itype == 4) {
/* Diagonal Matrix, [Eigen]values Specified */
clatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &imode, &cond,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &c__0, &
c__0, &c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[
1], &iinfo);
} else if (itype == 5) {
/* Hermitian, eigenvalues specified */
clatms_(&n, &n, "D", &iseed[1], "H", &rwork[1], &imode, &cond,
&anorm, &n, &n, "N", &a[a_offset], lda, &work[1], &
iinfo);
} else if (itype == 6) {
/* General, eigenvalues specified */
if (kconds[jtype - 1] == 1) {
conds = 1.f;
} else if (kconds[jtype - 1] == 2) {
conds = rtulpi;
} else {
conds = 0.f;
}
clatme_(&n, "D", &iseed[1], &work[1], &imode, &cond, &c_b2,
" ", "T", "T", "T", &rwork[1], &c__4, &conds, &n, &n,
&anorm, &a[a_offset], lda, &work[n + 1], &iinfo);
} else if (itype == 7) {
/* Diagonal, random eigenvalues */
clatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &c__0, &
c__0, &c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[
1], &iinfo);
} else if (itype == 8) {
/* Hermitian, random eigenvalues */
clatmr_(&n, &n, "D", &iseed[1], "H", &work[1], &c__6, &c_b27,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &n, &
c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else if (itype == 9) {
/* General, random eigenvalues */
clatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &n, &
c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else if (itype == 10) {
/* Triangular, random eigenvalues */
clatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &c__0, &
c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else {
iinfo = 1;
}
if (iinfo != 0) {
io___35.ciunit = *nounit;
s_wsfe(&io___35);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
return 0;
}
L100:
/* Call CGEHRD to compute H and U, do tests. */
clacpy_(" ", &n, &n, &a[a_offset], lda, &h__[h_offset], lda);
ntest = 1;
ilo = 1;
ihi = n;
i__3 = *nwork - n;
cgehrd_(&n, &ilo, &ihi, &h__[h_offset], lda, &work[1], &work[n +
1], &i__3, &iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
io___38.ciunit = *nounit;
s_wsfe(&io___38);
do_fio(&c__1, "CGEHRD", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
i__3 = n - 1;
for (j = 1; j <= i__3; ++j) {
i__4 = j + 1 + j * uu_dim1;
uu[i__4].r = 0.f, uu[i__4].i = 0.f;
i__4 = n;
for (i__ = j + 2; i__ <= i__4; ++i__) {
i__5 = i__ + j * u_dim1;
i__6 = i__ + j * h_dim1;
u[i__5].r = h__[i__6].r, u[i__5].i = h__[i__6].i;
i__5 = i__ + j * uu_dim1;
i__6 = i__ + j * h_dim1;
uu[i__5].r = h__[i__6].r, uu[i__5].i = h__[i__6].i;
i__5 = i__ + j * h_dim1;
h__[i__5].r = 0.f, h__[i__5].i = 0.f;
/* L110: */
}
/* L120: */
}
i__3 = n - 1;
ccopy_(&i__3, &work[1], &c__1, &tau[1], &c__1);
i__3 = *nwork - n;
cunghr_(&n, &ilo, &ihi, &u[u_offset], ldu, &work[1], &work[n + 1],
&i__3, &iinfo);
ntest = 2;
chst01_(&n, &ilo, &ihi, &a[a_offset], lda, &h__[h_offset], lda, &
u[u_offset], ldu, &work[1], nwork, &rwork[1], &result[1]);
/* Call CHSEQR to compute T1, T2 and Z, do tests. */
/* Eigenvalues only (W3) */
clacpy_(" ", &n, &n, &h__[h_offset], lda, &t2[t2_offset], lda);
ntest = 3;
result[3] = ulpinv;
chseqr_("E", "N", &n, &ilo, &ihi, &t2[t2_offset], lda, &w3[1], &
uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0) {
io___40.ciunit = *nounit;
s_wsfe(&io___40);
do_fio(&c__1, "CHSEQR(E)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
if (iinfo <= n + 2) {
*info = abs(iinfo);
goto L240;
}
}
/* Eigenvalues (W1) and Full Schur Form (T2) */
clacpy_(" ", &n, &n, &h__[h_offset], lda, &t2[t2_offset], lda);
chseqr_("S", "N", &n, &ilo, &ihi, &t2[t2_offset], lda, &w1[1], &
uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0 && iinfo <= n + 2) {
io___41.ciunit = *nounit;
s_wsfe(&io___41);
do_fio(&c__1, "CHSEQR(S)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
/* Eigenvalues (W1), Schur Form (T1), and Schur Vectors (UZ) */
clacpy_(" ", &n, &n, &h__[h_offset], lda, &t1[t1_offset], lda);
clacpy_(" ", &n, &n, &u[u_offset], ldu, &uz[uz_offset], ldu);
chseqr_("S", "V", &n, &ilo, &ihi, &t1[t1_offset], lda, &w1[1], &
uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0 && iinfo <= n + 2) {
io___42.ciunit = *nounit;
s_wsfe(&io___42);
do_fio(&c__1, "CHSEQR(V)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
/* Compute Z = U' UZ */
cgemm_("C", "N", &n, &n, &n, &c_b2, &u[u_offset], ldu, &uz[
uz_offset], ldu, &c_b1, &z__[z_offset], ldu);
ntest = 8;
/* Do Tests 3: | H - Z T Z' | / ( |H| n ulp ) */
/* and 4: | I - Z Z' | / ( n ulp ) */
chst01_(&n, &ilo, &ihi, &h__[h_offset], lda, &t1[t1_offset], lda,
&z__[z_offset], ldu, &work[1], nwork, &rwork[1], &result[
3]);
/* Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp ) */
/* and 6: | I - UZ (UZ)' | / ( n ulp ) */
chst01_(&n, &ilo, &ihi, &a[a_offset], lda, &t1[t1_offset], lda, &
uz[uz_offset], ldu, &work[1], nwork, &rwork[1], &result[5]
);
/* Do Test 7: | T2 - T1 | / ( |T| n ulp ) */
cget10_(&n, &n, &t2[t2_offset], lda, &t1[t1_offset], lda, &work[1]
, &rwork[1], &result[7]);
/* Do Test 8: | W3 - W1 | / ( max(|W1|,|W3|) ulp ) */
temp1 = 0.f;
temp2 = 0.f;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
/* Computing MAX */
r__1 = temp1, r__2 = c_abs(&w1[j]), r__1 = max(r__1,r__2),
r__2 = c_abs(&w3[j]);
temp1 = dmax(r__1,r__2);
/* Computing MAX */
i__4 = j;
i__5 = j;
q__1.r = w1[i__4].r - w3[i__5].r, q__1.i = w1[i__4].i - w3[
i__5].i;
r__1 = temp2, r__2 = c_abs(&q__1);
temp2 = dmax(r__1,r__2);
/* L130: */
}
/* Computing MAX */
r__1 = unfl, r__2 = ulp * dmax(temp1,temp2);
result[8] = temp2 / dmax(r__1,r__2);
/* Compute the Left and Right Eigenvectors of T */
/* Compute the Right eigenvector Matrix: */
ntest = 9;
result[9] = ulpinv;
/* Select every other eigenvector */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
select[j] = FALSE_;
/* L140: */
}
i__3 = n;
for (j = 1; j <= i__3; j += 2) {
select[j] = TRUE_;
/* L150: */
}
ctrevc_("Right", "All", &select[1], &n, &t1[t1_offset], lda,
cdumma, ldu, &evectr[evectr_offset], ldu, &n, &in, &work[
1], &rwork[1], &iinfo);
if (iinfo != 0) {
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "CTREVC(R,A)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
/* Test 9: | TR - RW | / ( |T| |R| ulp ) */
cget22_("N", "N", "N", &n, &t1[t1_offset], lda, &evectr[
evectr_offset], ldu, &w1[1], &work[1], &rwork[1], dumma);
result[9] = dumma[0];
if (dumma[1] > *thresh) {
io___49.ciunit = *nounit;
s_wsfe(&io___49);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "CTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute selected right eigenvectors and confirm that */
/* they agree with previous right eigenvectors */
ctrevc_("Right", "Some", &select[1], &n, &t1[t1_offset], lda,
cdumma, ldu, &evectl[evectl_offset], ldu, &n, &in, &work[
1], &rwork[1], &iinfo);
if (iinfo != 0) {
io___50.ciunit = *nounit;
s_wsfe(&io___50);
do_fio(&c__1, "CTREVC(R,S)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
k = 1;
match = TRUE_;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (select[j]) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
i__5 = jj + j * evectr_dim1;
i__6 = jj + k * evectl_dim1;
if (evectr[i__5].r != evectl[i__6].r || evectr[i__5]
.i != evectl[i__6].i) {
match = FALSE_;
goto L180;
}
/* L160: */
}
++k;
}
/* L170: */
}
L180:
if (! match) {
io___54.ciunit = *nounit;
s_wsfe(&io___54);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "CTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute the Left eigenvector Matrix: */
ntest = 10;
result[10] = ulpinv;
ctrevc_("Left", "All", &select[1], &n, &t1[t1_offset], lda, &
evectl[evectl_offset], ldu, cdumma, ldu, &n, &in, &work[1]
, &rwork[1], &iinfo);
if (iinfo != 0) {
io___55.ciunit = *nounit;
s_wsfe(&io___55);
do_fio(&c__1, "CTREVC(L,A)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
/* Test 10: | LT - WL | / ( |T| |L| ulp ) */
cget22_("C", "N", "C", &n, &t1[t1_offset], lda, &evectl[
evectl_offset], ldu, &w1[1], &work[1], &rwork[1], &dumma[
2]);
result[10] = dumma[2];
if (dumma[3] > *thresh) {
io___56.ciunit = *nounit;
s_wsfe(&io___56);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "CTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[3], (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute selected left eigenvectors and confirm that */
/* they agree with previous left eigenvectors */
ctrevc_("Left", "Some", &select[1], &n, &t1[t1_offset], lda, &
evectr[evectr_offset], ldu, cdumma, ldu, &n, &in, &work[1]
, &rwork[1], &iinfo);
if (iinfo != 0) {
io___57.ciunit = *nounit;
s_wsfe(&io___57);
do_fio(&c__1, "CTREVC(L,S)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
k = 1;
match = TRUE_;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (select[j]) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
i__5 = jj + j * evectl_dim1;
i__6 = jj + k * evectr_dim1;
if (evectl[i__5].r != evectr[i__6].r || evectl[i__5]
.i != evectr[i__6].i) {
match = FALSE_;
goto L210;
}
/* L190: */
}
++k;
}
/* L200: */
}
L210:
if (! match) {
io___58.ciunit = *nounit;
s_wsfe(&io___58);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "CTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Call CHSEIN for Right eigenvectors of H, do test 11 */
ntest = 11;
result[11] = ulpinv;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
select[j] = TRUE_;
/* L220: */
}
chsein_("Right", "Qr", "Ninitv", &select[1], &n, &h__[h_offset],
lda, &w3[1], cdumma, ldu, &evectx[evectx_offset], ldu, &
n1, &in, &work[1], &rwork[1], &iwork[1], &iwork[1], &
iinfo);
if (iinfo != 0) {
io___59.ciunit = *nounit;
s_wsfe(&io___59);
do_fio(&c__1, "CHSEIN(R)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L240;
}
} else {
/* Test 11: | HX - XW | / ( |H| |X| ulp ) */
/* (from inverse iteration) */
cget22_("N", "N", "N", &n, &h__[h_offset], lda, &evectx[
evectx_offset], ldu, &w3[1], &work[1], &rwork[1],
dumma);
if (dumma[0] < ulpinv) {
result[11] = dumma[0] * aninv;
}
if (dumma[1] > *thresh) {
io___60.ciunit = *nounit;
s_wsfe(&io___60);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "CHSEIN", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
}
}
/* Call CHSEIN for Left eigenvectors of H, do test 12 */
ntest = 12;
result[12] = ulpinv;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
select[j] = TRUE_;
/* L230: */
}
chsein_("Left", "Qr", "Ninitv", &select[1], &n, &h__[h_offset],
lda, &w3[1], &evecty[evecty_offset], ldu, cdumma, ldu, &
n1, &in, &work[1], &rwork[1], &iwork[1], &iwork[1], &
iinfo);
if (iinfo != 0) {
io___61.ciunit = *nounit;
s_wsfe(&io___61);
do_fio(&c__1, "CHSEIN(L)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L240;
}
} else {
/* Test 12: | YH - WY | / ( |H| |Y| ulp ) */
/* (from inverse iteration) */
cget22_("C", "N", "C", &n, &h__[h_offset], lda, &evecty[
evecty_offset], ldu, &w3[1], &work[1], &rwork[1], &
dumma[2]);
if (dumma[2] < ulpinv) {
result[12] = dumma[2] * aninv;
}
if (dumma[3] > *thresh) {
io___62.ciunit = *nounit;
s_wsfe(&io___62);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "CHSEIN", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[3], (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
}
}
/* Call CUNMHR for Right eigenvectors of A, do test 13 */
ntest = 13;
result[13] = ulpinv;
cunmhr_("Left", "No transpose", &n, &n, &ilo, &ihi, &uu[uu_offset]
, ldu, &tau[1], &evectx[evectx_offset], ldu, &work[1],
nwork, &iinfo);
if (iinfo != 0) {
io___63.ciunit = *nounit;
s_wsfe(&io___63);
do_fio(&c__1, "CUNMHR(L)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L240;
}
} else {
/* Test 13: | AX - XW | / ( |A| |X| ulp ) */
/* (from inverse iteration) */
cget22_("N", "N", "N", &n, &a[a_offset], lda, &evectx[
evectx_offset], ldu, &w3[1], &work[1], &rwork[1],
dumma);
if (dumma[0] < ulpinv) {
result[13] = dumma[0] * aninv;
}
}
/* Call CUNMHR for Left eigenvectors of A, do test 14 */
ntest = 14;
result[14] = ulpinv;
cunmhr_("Left", "No transpose", &n, &n, &ilo, &ihi, &uu[uu_offset]
, ldu, &tau[1], &evecty[evecty_offset], ldu, &work[1],
nwork, &iinfo);
if (iinfo != 0) {
io___64.ciunit = *nounit;
s_wsfe(&io___64);
do_fio(&c__1, "CUNMHR(L)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L240;
}
} else {
/* Test 14: | YA - WY | / ( |A| |Y| ulp ) */
/* (from inverse iteration) */
cget22_("C", "N", "C", &n, &a[a_offset], lda, &evecty[
evecty_offset], ldu, &w3[1], &work[1], &rwork[1], &
dumma[2]);
if (dumma[2] < ulpinv) {
result[14] = dumma[2] * aninv;
}
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L240:
ntestt += ntest;
slafts_("CHS", &n, &n, &jtype, &ntest, &result[1], ioldsd, thresh,
nounit, &nerrs);
L250:
;
}
/* L260: */
}
/* Summary */
slasum_("CHS", nounit, &nerrs, &ntestt);
return 0;
/* End of CCHKHS */
} /* cchkhs_ */
int main(void)
{
/* Local scalars */
lapack_int n, n_i;
lapack_int ilo, ilo_i;
lapack_int ihi, ihi_i;
lapack_int lda, lda_i;
lapack_int lda_r;
lapack_int lwork, lwork_i;
lapack_int info, info_i;
lapack_int i;
int failed;
/* Local arrays */
lapack_complex_float *a = NULL, *a_i = NULL;
lapack_complex_float *tau = NULL, *tau_i = NULL;
lapack_complex_float *work = NULL, *work_i = NULL;
lapack_complex_float *a_save = NULL;
lapack_complex_float *tau_save = NULL;
lapack_complex_float *a_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_cgehrd( &n, &ilo, &ihi, &lda, &lwork );
lda_r = n+2;
n_i = n;
ilo_i = ilo;
ihi_i = ihi;
lda_i = lda;
lwork_i = lwork;
/* Allocate memory for the LAPACK routine arrays */
a = (lapack_complex_float *)
LAPACKE_malloc( lda*n * sizeof(lapack_complex_float) );
tau = (lapack_complex_float *)
LAPACKE_malloc( (n-1) * sizeof(lapack_complex_float) );
work = (lapack_complex_float *)
LAPACKE_malloc( lwork * sizeof(lapack_complex_float) );
/* Allocate memory for the C interface function arrays */
a_i = (lapack_complex_float *)
LAPACKE_malloc( lda*n * sizeof(lapack_complex_float) );
tau_i = (lapack_complex_float *)
LAPACKE_malloc( (n-1) * sizeof(lapack_complex_float) );
work_i = (lapack_complex_float *)
LAPACKE_malloc( lwork * sizeof(lapack_complex_float) );
/* Allocate memory for the backup arrays */
a_save = (lapack_complex_float *)
LAPACKE_malloc( lda*n * sizeof(lapack_complex_float) );
tau_save = (lapack_complex_float *)
LAPACKE_malloc( (n-1) * sizeof(lapack_complex_float) );
/* Allocate memory for the row-major arrays */
a_r = (lapack_complex_float *)
LAPACKE_malloc( n*(n+2) * sizeof(lapack_complex_float) );
/* Initialize input arrays */
init_a( lda*n, a );
init_tau( (n-1), tau );
init_work( lwork, work );
/* Backup the ouptut arrays */
for( i = 0; i < lda*n; i++ ) {
a_save[i] = a[i];
}
for( i = 0; i < (n-1); i++ ) {
tau_save[i] = tau[i];
}
/* Call the LAPACK routine */
cgehrd_( &n, &ilo, &ihi, a, &lda, tau, work, &lwork, &info );
/* Initialize input data, call the column-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < (n-1); i++ ) {
tau_i[i] = tau_save[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
info_i = LAPACKE_cgehrd_work( LAPACK_COL_MAJOR, n_i, ilo_i, ihi_i, a_i,
lda_i, tau_i, work_i, lwork_i );
failed = compare_cgehrd( a, a_i, tau, tau_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to cgehrd\n" );
} else {
printf( "FAILED: column-major middle-level interface to cgehrd\n" );
}
/* Initialize input data, call the column-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < (n-1); i++ ) {
tau_i[i] = tau_save[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
info_i = LAPACKE_cgehrd( LAPACK_COL_MAJOR, n_i, ilo_i, ihi_i, a_i, lda_i,
tau_i );
failed = compare_cgehrd( a, a_i, tau, tau_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to cgehrd\n" );
} else {
printf( "FAILED: column-major high-level interface to cgehrd\n" );
}
/* Initialize input data, call the row-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < (n-1); i++ ) {
tau_i[i] = tau_save[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
LAPACKE_cge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_cgehrd_work( LAPACK_ROW_MAJOR, n_i, ilo_i, ihi_i, a_r,
lda_r, tau_i, work_i, lwork_i );
LAPACKE_cge_trans( LAPACK_ROW_MAJOR, n, n, a_r, n+2, a_i, lda );
failed = compare_cgehrd( a, a_i, tau, tau_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to cgehrd\n" );
} else {
printf( "FAILED: row-major middle-level interface to cgehrd\n" );
}
/* Initialize input data, call the row-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < (n-1); i++ ) {
tau_i[i] = tau_save[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
/* Init row_major arrays */
LAPACKE_cge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_cgehrd( LAPACK_ROW_MAJOR, n_i, ilo_i, ihi_i, a_r, lda_r,
tau_i );
LAPACKE_cge_trans( LAPACK_ROW_MAJOR, n, n, a_r, n+2, a_i, lda );
failed = compare_cgehrd( a, a_i, tau, tau_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to cgehrd\n" );
} else {
printf( "FAILED: row-major high-level interface to cgehrd\n" );
}
/* Release memory */
if( a != NULL ) {
LAPACKE_free( a );
}
if( a_i != NULL ) {
LAPACKE_free( a_i );
}
if( a_r != NULL ) {
LAPACKE_free( a_r );
}
if( a_save != NULL ) {
LAPACKE_free( a_save );
}
if( tau != NULL ) {
LAPACKE_free( tau );
}
if( tau_i != NULL ) {
LAPACKE_free( tau_i );
}
if( tau_save != NULL ) {
LAPACKE_free( tau_save );
}
if( work != NULL ) {
LAPACKE_free( work );
}
if( work_i != NULL ) {
LAPACKE_free( work_i );
}
return 0;
}
/* Subroutine */ int cgeesx_(char *jobvs, char *sort, L_fp select, char *
sense, integer *n, complex *a, integer *lda, integer *sdim, complex *
w, complex *vs, integer *ldvs, real *rconde, real *rcondv, complex *
work, integer *lwork, real *rwork, logical *bwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, ihi, ilo;
real dum[1], eps;
integer ibal;
real anrm;
integer ierr, itau, iwrk, lwrk, icond, ieval;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), cgebak_(char *, char *, integer *, integer
*, integer *, real *, integer *, complex *, integer *, integer *), cgebal_(char *, integer *, complex *, integer *,
integer *, integer *, real *, integer *), slabad_(real *,
real *);
logical scalea;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
real cscale;
extern /* Subroutine */ int cgehrd_(integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, integer *),
clascl_(char *, integer *, integer *, real *, real *, integer *,
integer *, complex *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), xerbla_(char *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
real bignum;
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *), chseqr_(char *, char *, integer *, integer *, integer *,
complex *, integer *, complex *, complex *, integer *, complex *,
integer *, integer *), cunghr_(integer *, integer
*, integer *, complex *, integer *, complex *, complex *, integer
*, integer *);
logical wantsb;
extern /* Subroutine */ int ctrsen_(char *, char *, logical *, integer *,
complex *, integer *, complex *, integer *, complex *, integer *,
real *, real *, complex *, integer *, integer *);
logical wantse;
integer minwrk, maxwrk;
logical wantsn;
real smlnum;
integer hswork;
logical wantst, wantsv, wantvs;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* .. Function Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGEESX computes for an N-by-N complex nonsymmetric matrix A, the */
/* eigenvalues, the Schur form T, and, optionally, the matrix of Schur */
/* vectors Z. This gives the Schur factorization A = Z*T*(Z**H). */
/* Optionally, it also orders the eigenvalues on the diagonal of the */
/* Schur form so that selected eigenvalues are at the top left; */
/* computes a reciprocal condition number for the average of the */
/* selected eigenvalues (RCONDE); and computes a reciprocal condition */
/* number for the right invariant subspace corresponding to the */
/* selected eigenvalues (RCONDV). The leading columns of Z form an */
/* orthonormal basis for this invariant subspace. */
/* For further explanation of the reciprocal condition numbers RCONDE */
/* and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where */
/* these quantities are called s and sep respectively). */
/* A complex matrix is in Schur form if it is upper triangular. */
/* Arguments */
/* ========= */
/* JOBVS (input) CHARACTER*1 */
/* = 'N': Schur vectors are not computed; */
/* = 'V': Schur vectors are computed. */
/* SORT (input) CHARACTER*1 */
/* Specifies whether or not to order the eigenvalues on the */
/* diagonal of the Schur form. */
/* = 'N': Eigenvalues are not ordered; */
/* = 'S': Eigenvalues are ordered (see SELECT). */
/* SELECT (external procedure) LOGICAL FUNCTION of one COMPLEX argument */
/* SELECT must be declared EXTERNAL in the calling subroutine. */
/* If SORT = 'S', SELECT is used to select eigenvalues to order */
/* to the top left of the Schur form. */
/* If SORT = 'N', SELECT is not referenced. */
/* An eigenvalue W(j) is selected if SELECT(W(j)) is true. */
/* SENSE (input) CHARACTER*1 */
/* Determines which reciprocal condition numbers are computed. */
/* = 'N': None are computed; */
/* = 'E': Computed for average of selected eigenvalues only; */
/* = 'V': Computed for selected right invariant subspace only; */
/* = 'B': Computed for both. */
/* If SENSE = 'E', 'V' or 'B', SORT must equal 'S'. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA, N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A is overwritten by its Schur form T. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* SDIM (output) INTEGER */
/* If SORT = 'N', SDIM = 0. */
/* If SORT = 'S', SDIM = number of eigenvalues for which */
/* SELECT is true. */
/* W (output) COMPLEX array, dimension (N) */
/* W contains the computed eigenvalues, in the same order */
/* that they appear on the diagonal of the output Schur form T. */
/* VS (output) COMPLEX array, dimension (LDVS,N) */
/* If JOBVS = 'V', VS contains the unitary matrix Z of Schur */
/* vectors. */
/* If JOBVS = 'N', VS is not referenced. */
/* LDVS (input) INTEGER */
/* The leading dimension of the array VS. LDVS >= 1, and if */
/* JOBVS = 'V', LDVS >= N. */
/* RCONDE (output) REAL */
/* If SENSE = 'E' or 'B', RCONDE contains the reciprocal */
/* condition number for the average of the selected eigenvalues. */
/* Not referenced if SENSE = 'N' or 'V'. */
/* RCONDV (output) REAL */
/* If SENSE = 'V' or 'B', RCONDV contains the reciprocal */
/* condition number for the selected right invariant subspace. */
/* Not referenced if SENSE = 'N' or 'E'. */
/* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,2*N). */
/* Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM), */
/* where SDIM is the number of selected eigenvalues computed by */
/* this routine. Note that 2*SDIM*(N-SDIM) <= N*N/2. Note also */
/* that an error is only returned if LWORK < max(1,2*N), but if */
/* SENSE = 'E' or 'V' or 'B' this may not be large enough. */
/* For good performance, LWORK must generally be larger. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates upper bound on the optimal size of the */
/* array WORK, returns this value as the first entry of the WORK */
/* array, and no error message related to LWORK is issued by */
/* XERBLA. */
/* RWORK (workspace) REAL array, dimension (N) */
/* BWORK (workspace) LOGICAL array, dimension (N) */
/* Not referenced if SORT = 'N'. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = i, and i is */
/* <= N: the QR algorithm failed to compute all the */
/* eigenvalues; elements 1:ILO-1 and i+1:N of W */
/* contain those eigenvalues which have converged; if */
/* JOBVS = 'V', VS contains the transformation which */
/* reduces A to its partially converged Schur form. */
/* = N+1: the eigenvalues could not be reordered because some */
/* eigenvalues were too close to separate (the problem */
/* is very ill-conditioned); */
/* = N+2: after reordering, roundoff changed values of some */
/* complex eigenvalues so that leading eigenvalues in */
/* the Schur form no longer satisfy SELECT=.TRUE. This */
/* could also be caused by underflow due to scaling. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
vs_dim1 = *ldvs;
vs_offset = 1 + vs_dim1;
vs -= vs_offset;
--work;
--rwork;
--bwork;
/* Function Body */
*info = 0;
wantvs = lsame_(jobvs, "V");
wantst = lsame_(sort, "S");
wantsn = lsame_(sense, "N");
wantse = lsame_(sense, "E");
wantsv = lsame_(sense, "V");
wantsb = lsame_(sense, "B");
if (! wantvs && ! lsame_(jobvs, "N")) {
*info = -1;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -2;
} else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && !
wantsn) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldvs < 1 || wantvs && *ldvs < *n) {
*info = -11;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of real workspace needed at that point in the */
/* code, as well as the preferred amount for good performance. */
/* CWorkspace refers to complex workspace, and RWorkspace to real */
/* workspace. NB refers to the optimal block size for the */
/* immediately following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by CHSEQR, as */
/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/* the worst case. */
/* If SENSE = 'E', 'V' or 'B', then the amount of workspace needed */
/* depends on SDIM, which is computed by the routine CTRSEN later */
/* in the code.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
lwrk = 1;
} else {
maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
c__0);
minwrk = *n << 1;
chseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &w[1], &vs[
vs_offset], ldvs, &work[1], &c_n1, &ieval);
hswork = work[1].r;
if (! wantvs) {
maxwrk = max(maxwrk,hswork);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
" ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,hswork);
}
lwrk = maxwrk;
if (! wantsn) {
/* Computing MAX */
i__1 = lwrk, i__2 = *n * *n / 2;
lwrk = max(i__1,i__2);
}
}
work[1].r = (real) lwrk, work[1].i = 0.f;
if (*lwork < minwrk) {
*info = -15;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEESX", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = slamch_("S");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1.f / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE_;
if (anrm > 0.f && anrm < smlnum) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Permute the matrix to make it more nearly triangular */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
ibal = 1;
cgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
/* Reduce to upper Hessenberg form */
/* (CWorkspace: need 2*N, prefer N+N*NB) */
/* (RWorkspace: none) */
itau = 1;
iwrk = *n + itau;
i__1 = *lwork - iwrk + 1;
cgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvs) {
/* Copy Householder vectors to VS */
clacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
;
/* Generate unitary matrix in VS */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
cunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
&i__1, &ierr);
}
*sdim = 0;
/* Perform QR iteration, accumulating Schur vectors in VS if desired */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
chseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
if (ieval > 0) {
*info = ieval;
}
/* Sort eigenvalues if desired */
if (wantst && *info == 0) {
if (scalea) {
clascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
ierr);
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*select)(&w[i__]);
/* L10: */
}
/* Reorder eigenvalues, transform Schur vectors, and compute */
/* reciprocal condition numbers */
/* (CWorkspace: if SENSE is not 'N', need 2*SDIM*(N-SDIM) */
/* otherwise, need none ) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
ctrsen_(sense, jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
ldvs, &w[1], sdim, rconde, rcondv, &work[iwrk], &i__1, &
icond);
if (! wantsn) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
maxwrk = max(i__1,i__2);
}
if (icond == -14) {
/* Not enough complex workspace */
*info = -15;
}
}
if (wantvs) {
/* Undo balancing */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
cgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset],
ldvs, &ierr);
}
if (scalea) {
/* Undo scaling for the Schur form of A */
clascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
ierr);
i__1 = *lda + 1;
ccopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
if ((wantsv || wantsb) && *info == 0) {
dum[0] = *rcondv;
slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &
c__1, &ierr);
*rcondv = dum[0];
}
}
work[1].r = (real) maxwrk, work[1].i = 0.f;
return 0;
/* End of CGEESX */
} /* cgeesx_ */
