int dgeevx_(char *balanc, char *jobvl, char *jobvr, char *
sense, int *n, double *a, int *lda, double *wr,
double *wi, double *vl, int *ldvl, double *vr,
int *ldvr, int *ilo, int *ihi, double *scale,
double *abnrm, double *rconde, double *rcondv, double
*work, int *lwork, int *iwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
double d__1, d__2;
/* Builtin functions */
double sqrt(double);
/* Local variables */
int i__, k;
double r__, cs, sn;
char job[1];
double scl, dum[1], eps;
char side[1];
double anrm;
int ierr, itau;
extern int drot_(int *, double *, int *,
double *, int *, double *, double *);
int iwrk, nout;
extern double dnrm2_(int *, double *, int *);
extern int dscal_(int *, double *, double *,
int *);
int icond;
extern int lsame_(char *, char *);
extern double dlapy2_(double *, double *);
extern int dlabad_(double *, double *), dgebak_(
char *, char *, int *, int *, int *, double *,
int *, double *, int *, int *),
dgebal_(char *, int *, double *, int *, int *,
int *, double *, int *);
int scalea;
extern double dlamch_(char *);
double cscale;
extern double dlange_(char *, int *, int *, double *,
int *, double *);
extern int dgehrd_(int *, int *, int *,
double *, int *, double *, double *, int *,
int *), dlascl_(char *, int *, int *, double *,
double *, int *, int *, double *, int *,
int *);
extern int idamax_(int *, double *, int *);
extern int dlacpy_(char *, int *, int *,
double *, int *, double *, int *),
dlartg_(double *, double *, double *, double *,
double *), xerbla_(char *, int *);
int select[1];
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
double bignum;
extern int dorghr_(int *, int *, int *,
double *, int *, double *, double *, int *,
int *), dhseqr_(char *, char *, int *, int *, int
*, double *, int *, double *, double *,
double *, int *, double *, int *, int *), dtrevc_(char *, char *, int *, int *,
double *, int *, double *, int *, double *,
int *, int *, int *, double *, int *), dtrsna_(char *, char *, int *, int *, double
*, int *, double *, int *, double *, int *,
double *, double *, int *, int *, double *,
int *, int *, int *);
int minwrk, maxwrk;
int wantvl, wntsnb;
int hswork;
int wntsne;
double smlnum;
int lquery, wantvr, wntsnn, wntsnv;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGEEVX computes for an N-by-N float 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 float. */
/* 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, i.e. 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) DOUBLE PRECISION 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 float Schur form of the balanced */
/* version of the input matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* WR (output) DOUBLE PRECISION array, dimension (N) */
/* WI (output) DOUBLE PRECISION array, dimension (N) */
/* WR and WI contain the float and imaginary parts, */
/* respectively, of the computed eigenvalues. Complex */
/* conjugate pairs of eigenvalues will appear consecutively */
/* with the eigenvalue having the positive imaginary part */
/* first. */
/* VL (output) DOUBLE PRECISION 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. */
/* If the j-th eigenvalue is float, then u(j) = VL(:,j), */
/* the j-th column of VL. */
/* If the j-th and (j+1)-st eigenvalues form a complex */
/* conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and */
/* u(j+1) = VL(:,j) - i*VL(:,j+1). */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; if */
/* JOBVL = 'V', LDVL >= N. */
/* VR (output) DOUBLE PRECISION 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. */
/* If the j-th eigenvalue is float, then v(j) = VR(:,j), */
/* the j-th column of VR. */
/* If the j-th and (j+1)-st eigenvalues form a complex */
/* conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and */
/* v(j+1) = VR(:,j) - i*VR(:,j+1). */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1, and if */
/* JOBVR = 'V', LDVR >= N. */
/* ILO (output) INTEGER */
/* IHI (output) INTEGER */
/* ILO and IHI are int values determined when A was */
/* balanced. The balanced A(i,j) = 0 if I > J and */
/* J = 1,...,ILO-1 or I = IHI+1,...,N. */
/* SCALE (output) DOUBLE PRECISION 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 */
/* SCALE(J) = P(J), for J = 1,...,ILO-1 */
/* = D(J), for J = ILO,...,IHI */
/* = P(J) for J = IHI+1,...,N. */
/* The order in which the interchanges are made is N to IHI+1, */
/* then 1 to ILO-1. */
/* ABNRM (output) DOUBLE PRECISION */
/* The one-norm of the balanced matrix (the maximum */
/* of the sum of absolute values of elements of any column). */
/* RCONDE (output) DOUBLE PRECISION array, dimension (N) */
/* RCONDE(j) is the reciprocal condition number of the j-th */
/* eigenvalue. */
/* RCONDV (output) DOUBLE PRECISION array, dimension (N) */
/* RCONDV(j) is the reciprocal condition number of the j-th */
/* right eigenvector. */
/* WORK (workspace/output) DOUBLE PRECISION 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 JOBVL = 'V' or JOBVR = 'V', */
/* LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6). */
/* 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. */
/* IWORK (workspace) INTEGER array, dimension (2*N-2) */
/* If SENSE = 'N' or 'E', not referenced. */
/* 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 WR */
/* and WI 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;
--wr;
--wi;
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;
--iwork;
/* 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 = -11;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -13;
}
/* 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. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by DHSEQR, 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, "DGEHRD", " ", n, &c__1, n, &
c__0);
if (wantvl) {
dhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vl[vl_offset], ldvl, &work[1], &c_n1, info);
} else if (wantvr) {
dhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vr[vr_offset], ldvr, &work[1], &c_n1, info);
} else {
if (wntsnn) {
dhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &wr[1],
&wi[1], &vr[vr_offset], ldvr, &work[1], &c_n1,
info);
} else {
dhseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &wr[1],
&wi[1], &vr[vr_offset], ldvr, &work[1], &c_n1,
info);
}
}
hswork = (int) work[1];
if (! wantvl && ! wantvr) {
minwrk = *n << 1;
if (! wntsnn) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + *n * 6;
minwrk = MAX(i__1,i__2);
}
maxwrk = MAX(maxwrk,hswork);
if (! wntsnn) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + *n * 6;
maxwrk = MAX(i__1,i__2);
}
} else {
minwrk = *n * 3;
if (! wntsnn && ! wntsne) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + *n * 6;
minwrk = MAX(i__1,i__2);
}
maxwrk = MAX(maxwrk,hswork);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "DORGHR",
" ", 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 * 6;
maxwrk = MAX(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3;
maxwrk = MAX(i__1,i__2);
}
maxwrk = MAX(maxwrk,minwrk);
}
work[1] = (double) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -21;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEEVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = dlamch_("S");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
icond = 0;
anrm = dlange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE;
if (anrm > 0. && anrm < smlnum) {
scalea = TRUE;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE;
cscale = bignum;
}
if (scalea) {
dlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix and compute ABNRM */
dgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
*abnrm = dlange_("1", n, n, &a[a_offset], lda, dum);
if (scalea) {
dum[0] = *abnrm;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
ierr);
*abnrm = dum[0];
}
/* Reduce to upper Hessenberg form */
/* (Workspace: need 2*N, prefer N+N*NB) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
dgehrd_(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';
dlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate orthogonal matrix in VL */
/* (Workspace: need 2*N-1, prefer N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (Workspace: need 1, prefer HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[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';
dlacpy_("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';
dlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate orthogonal matrix in VR */
/* (Workspace: need 2*N-1, prefer N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (Workspace: need 1, prefer HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[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';
}
/* (Workspace: need 1, prefer HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from DHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (Workspace: need 3*N) */
dtrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &ierr);
}
/* Compute condition numbers if desired */
/* (Workspace: need N*N+6*N unless SENSE = 'E') */
if (! wntsnn) {
dtrsna_(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, &iwork[1], &icond);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
dgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component float */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (wi[i__] == 0.) {
scl = 1. / dnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
dscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
} else if (wi[i__] > 0.) {
d__1 = dnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
d__2 = dnrm2_(n, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
scl = 1. / dlapy2_(&d__1, &d__2);
dscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
dscal_(n, &scl, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
d__1 = vl[k + i__ * vl_dim1];
/* Computing 2nd power */
d__2 = vl[k + (i__ + 1) * vl_dim1];
work[k] = d__1 * d__1 + d__2 * d__2;
/* L10: */
}
k = idamax_(n, &work[1], &c__1);
dlartg_(&vl[k + i__ * vl_dim1], &vl[k + (i__ + 1) * vl_dim1],
&cs, &sn, &r__);
drot_(n, &vl[i__ * vl_dim1 + 1], &c__1, &vl[(i__ + 1) *
vl_dim1 + 1], &c__1, &cs, &sn);
vl[k + (i__ + 1) * vl_dim1] = 0.;
}
/* L20: */
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
dgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component float */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (wi[i__] == 0.) {
scl = 1. / dnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
dscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
} else if (wi[i__] > 0.) {
d__1 = dnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
d__2 = dnrm2_(n, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
scl = 1. / dlapy2_(&d__1, &d__2);
dscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
dscal_(n, &scl, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
d__1 = vr[k + i__ * vr_dim1];
/* Computing 2nd power */
d__2 = vr[k + (i__ + 1) * vr_dim1];
work[k] = d__1 * d__1 + d__2 * d__2;
/* L30: */
}
k = idamax_(n, &work[1], &c__1);
dlartg_(&vr[k + i__ * vr_dim1], &vr[k + (i__ + 1) * vr_dim1],
&cs, &sn, &r__);
drot_(n, &vr[i__ * vr_dim1 + 1], &c__1, &vr[(i__ + 1) *
vr_dim1 + 1], &c__1, &cs, &sn);
vr[k + (i__ + 1) * vr_dim1] = 0.;
}
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = MAX(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[*info +
1], &i__2, &ierr);
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = MAX(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[*info +
1], &i__2, &ierr);
if (*info == 0) {
if ((wntsnv || wntsnb) && icond == 0) {
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[
1], n, &ierr);
}
} else {
i__1 = *ilo - 1;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[1],
n, &ierr);
i__1 = *ilo - 1;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[1],
n, &ierr);
}
}
work[1] = (double) maxwrk;
return 0;
/* End of DGEEVX */
} /* dgeevx_ */
/* Subroutine */ int dget37_(doublereal *rmax, integer *lmax, integer *ninfo,
integer *knt, integer *nin)
{
/* System generated locals */
integer i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
integer s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
/* Local variables */
integer i__, j, m, n;
doublereal s[20], t[400] /* was [20][20] */, v, le[400] /* was [20][
20] */, re[400] /* was [20][20] */, wi[20], wr[20], val[3],
dum[1], eps, sep[20], sin__[20], tol, tmp[400] /* was [20][
20] */;
integer ifnd, icmp, iscl, info, lcmp[3], kmin;
doublereal wiin[20], vmax, tnrm, wrin[20], work[1200], vmul, stmp[20];
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal sepin[20];
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal vimin, tolin, vrmin;
integer iwork[40];
doublereal witmp[20], wrtmp[20];
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dlacpy_(char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *);
logical select[20];
doublereal bignum;
extern /* Subroutine */ int dhseqr_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *), dtrevc_(char *, char *, logical *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, doublereal *, integer *), dtrsna_(char *, char *, logical *, integer *, doublereal
*, integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *, integer *);
doublereal septmp[20], smlnum;
/* Fortran I/O blocks */
static cilist io___5 = { 0, 0, 0, 0, 0 };
static cilist io___8 = { 0, 0, 0, 0, 0 };
static cilist io___11 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGET37 tests DTRSNA, a routine for estimating condition numbers of */
/* eigenvalues and/or right eigenvectors of a matrix. */
/* The test matrices are read from a file with logical unit number NIN. */
/* Arguments */
/* ========== */
/* RMAX (output) DOUBLE PRECISION array, dimension (3) */
/* Value of the largest test ratio. */
/* RMAX(1) = largest ratio comparing different calls to DTRSNA */
/* RMAX(2) = largest error in reciprocal condition */
/* numbers taking their conditioning into account */
/* RMAX(3) = largest error in reciprocal condition */
/* numbers not taking their conditioning into */
/* account (may be larger than RMAX(2)) */
/* LMAX (output) INTEGER array, dimension (3) */
/* LMAX(i) is example number where largest test ratio */
/* RMAX(i) is achieved. Also: */
/* If DGEHRD returns INFO nonzero on example i, LMAX(1)=i */
/* If DHSEQR returns INFO nonzero on example i, LMAX(2)=i */
/* If DTRSNA returns INFO nonzero on example i, LMAX(3)=i */
/* NINFO (output) INTEGER array, dimension (3) */
/* NINFO(1) = No. of times DGEHRD returned INFO nonzero */
/* NINFO(2) = No. of times DHSEQR returned INFO nonzero */
/* NINFO(3) = No. of times DTRSNA returned INFO nonzero */
/* KNT (output) INTEGER */
/* Total number of examples tested. */
/* NIN (input) INTEGER */
/* Input logical unit number */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--ninfo;
--lmax;
--rmax;
/* Function Body */
eps = dlamch_("P");
smlnum = dlamch_("S") / eps;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
/* EPSIN = 2**(-24) = precision to which input data computed */
eps = max(eps,5.9605e-8);
rmax[1] = 0.;
rmax[2] = 0.;
rmax[3] = 0.;
lmax[1] = 0;
lmax[2] = 0;
lmax[3] = 0;
*knt = 0;
ninfo[1] = 0;
ninfo[2] = 0;
ninfo[3] = 0;
val[0] = sqrt(smlnum);
val[1] = 1.;
val[2] = sqrt(bignum);
/* Read input data until N=0. Assume input eigenvalues are sorted */
/* lexicographically (increasing by real part, then decreasing by */
/* imaginary part) */
L10:
io___5.ciunit = *nin;
s_rsle(&io___5);
do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer));
e_rsle();
if (n == 0) {
return 0;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___8.ciunit = *nin;
s_rsle(&io___8);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__5, &c__1, (char *)&tmp[i__ + j * 20 - 21], (ftnlen)
sizeof(doublereal));
}
e_rsle();
/* L20: */
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___11.ciunit = *nin;
s_rsle(&io___11);
do_lio(&c__5, &c__1, (char *)&wrin[i__ - 1], (ftnlen)sizeof(
doublereal));
do_lio(&c__5, &c__1, (char *)&wiin[i__ - 1], (ftnlen)sizeof(
doublereal));
do_lio(&c__5, &c__1, (char *)&sin__[i__ - 1], (ftnlen)sizeof(
doublereal));
do_lio(&c__5, &c__1, (char *)&sepin[i__ - 1], (ftnlen)sizeof(
doublereal));
e_rsle();
/* L30: */
}
tnrm = dlange_("M", &n, &n, tmp, &c__20, work);
/* Begin test */
for (iscl = 1; iscl <= 3; ++iscl) {
/* Scale input matrix */
++(*knt);
dlacpy_("F", &n, &n, tmp, &c__20, t, &c__20);
vmul = val[iscl - 1];
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
dscal_(&n, &vmul, &t[i__ * 20 - 20], &c__1);
/* L40: */
}
if (tnrm == 0.) {
vmul = 1.;
}
/* Compute eigenvalues and eigenvectors */
i__1 = 1200 - n;
dgehrd_(&n, &c__1, &n, t, &c__20, work, &work[n], &i__1, &info);
if (info != 0) {
lmax[1] = *knt;
++ninfo[1];
goto L240;
}
i__1 = n - 2;
for (j = 1; j <= i__1; ++j) {
i__2 = n;
for (i__ = j + 2; i__ <= i__2; ++i__) {
t[i__ + j * 20 - 21] = 0.;
/* L50: */
}
/* L60: */
}
/* Compute Schur form */
dhseqr_("S", "N", &n, &c__1, &n, t, &c__20, wr, wi, dum, &c__1, work,
&c__1200, &info);
if (info != 0) {
lmax[2] = *knt;
++ninfo[2];
goto L240;
}
/* Compute eigenvectors */
dtrevc_("Both", "All", select, &n, t, &c__20, le, &c__20, re, &c__20,
&n, &m, work, &info);
/* Compute condition numbers */
dtrsna_("Both", "All", select, &n, t, &c__20, le, &c__20, re, &c__20,
s, sep, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
/* Sort eigenvalues and condition numbers lexicographically */
/* to compare with inputs */
dcopy_(&n, wr, &c__1, wrtmp, &c__1);
dcopy_(&n, wi, &c__1, witmp, &c__1);
dcopy_(&n, s, &c__1, stmp, &c__1);
dcopy_(&n, sep, &c__1, septmp, &c__1);
d__1 = 1. / vmul;
dscal_(&n, &d__1, septmp, &c__1);
i__1 = n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
kmin = i__;
vrmin = wrtmp[i__ - 1];
vimin = witmp[i__ - 1];
i__2 = n;
for (j = i__ + 1; j <= i__2; ++j) {
if (wrtmp[j - 1] < vrmin) {
kmin = j;
vrmin = wrtmp[j - 1];
vimin = witmp[j - 1];
}
/* L70: */
}
wrtmp[kmin - 1] = wrtmp[i__ - 1];
witmp[kmin - 1] = witmp[i__ - 1];
wrtmp[i__ - 1] = vrmin;
witmp[i__ - 1] = vimin;
vrmin = stmp[kmin - 1];
stmp[kmin - 1] = stmp[i__ - 1];
stmp[i__ - 1] = vrmin;
vrmin = septmp[kmin - 1];
septmp[kmin - 1] = septmp[i__ - 1];
septmp[i__ - 1] = vrmin;
/* L80: */
}
/* Compare condition numbers for eigenvalues */
/* taking their condition numbers into account */
/* Computing MAX */
d__1 = (doublereal) n * 2. * eps * tnrm;
v = max(d__1,smlnum);
if (tnrm == 0.) {
v = 1.;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (v > septmp[i__ - 1]) {
tol = 1.;
} else {
tol = v / septmp[i__ - 1];
}
if (v > sepin[i__ - 1]) {
tolin = 1.;
} else {
tolin = v / sepin[i__ - 1];
}
/* Computing MAX */
d__1 = tol, d__2 = smlnum / eps;
tol = max(d__1,d__2);
/* Computing MAX */
d__1 = tolin, d__2 = smlnum / eps;
tolin = max(d__1,d__2);
if (eps * (sin__[i__ - 1] - tolin) > stmp[i__ - 1] + tol) {
vmax = 1. / eps;
} else if (sin__[i__ - 1] - tolin > stmp[i__ - 1] + tol) {
vmax = (sin__[i__ - 1] - tolin) / (stmp[i__ - 1] + tol);
} else if (sin__[i__ - 1] + tolin < eps * (stmp[i__ - 1] - tol)) {
vmax = 1. / eps;
} else if (sin__[i__ - 1] + tolin < stmp[i__ - 1] - tol) {
vmax = (stmp[i__ - 1] - tol) / (sin__[i__ - 1] + tolin);
} else {
vmax = 1.;
}
if (vmax > rmax[2]) {
rmax[2] = vmax;
if (ninfo[2] == 0) {
lmax[2] = *knt;
}
}
/* L90: */
}
/* Compare condition numbers for eigenvectors */
/* taking their condition numbers into account */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (v > septmp[i__ - 1] * stmp[i__ - 1]) {
tol = septmp[i__ - 1];
} else {
tol = v / stmp[i__ - 1];
}
if (v > sepin[i__ - 1] * sin__[i__ - 1]) {
tolin = sepin[i__ - 1];
} else {
tolin = v / sin__[i__ - 1];
}
/* Computing MAX */
d__1 = tol, d__2 = smlnum / eps;
tol = max(d__1,d__2);
/* Computing MAX */
d__1 = tolin, d__2 = smlnum / eps;
tolin = max(d__1,d__2);
if (eps * (sepin[i__ - 1] - tolin) > septmp[i__ - 1] + tol) {
vmax = 1. / eps;
} else if (sepin[i__ - 1] - tolin > septmp[i__ - 1] + tol) {
vmax = (sepin[i__ - 1] - tolin) / (septmp[i__ - 1] + tol);
} else if (sepin[i__ - 1] + tolin < eps * (septmp[i__ - 1] - tol))
{
vmax = 1. / eps;
} else if (sepin[i__ - 1] + tolin < septmp[i__ - 1] - tol) {
vmax = (septmp[i__ - 1] - tol) / (sepin[i__ - 1] + tolin);
} else {
vmax = 1.;
}
if (vmax > rmax[2]) {
rmax[2] = vmax;
if (ninfo[2] == 0) {
lmax[2] = *knt;
}
}
/* L100: */
}
/* Compare condition numbers for eigenvalues */
/* without taking their condition numbers into account */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (sin__[i__ - 1] <= (doublereal) (n << 1) * eps && stmp[i__ - 1]
<= (doublereal) (n << 1) * eps) {
vmax = 1.;
} else if (eps * sin__[i__ - 1] > stmp[i__ - 1]) {
vmax = 1. / eps;
} else if (sin__[i__ - 1] > stmp[i__ - 1]) {
vmax = sin__[i__ - 1] / stmp[i__ - 1];
} else if (sin__[i__ - 1] < eps * stmp[i__ - 1]) {
vmax = 1. / eps;
} else if (sin__[i__ - 1] < stmp[i__ - 1]) {
vmax = stmp[i__ - 1] / sin__[i__ - 1];
} else {
vmax = 1.;
}
if (vmax > rmax[3]) {
rmax[3] = vmax;
if (ninfo[3] == 0) {
lmax[3] = *knt;
}
}
/* L110: */
}
/* Compare condition numbers for eigenvectors */
/* without taking their condition numbers into account */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (sepin[i__ - 1] <= v && septmp[i__ - 1] <= v) {
vmax = 1.;
} else if (eps * sepin[i__ - 1] > septmp[i__ - 1]) {
vmax = 1. / eps;
} else if (sepin[i__ - 1] > septmp[i__ - 1]) {
vmax = sepin[i__ - 1] / septmp[i__ - 1];
} else if (sepin[i__ - 1] < eps * septmp[i__ - 1]) {
vmax = 1. / eps;
} else if (sepin[i__ - 1] < septmp[i__ - 1]) {
vmax = septmp[i__ - 1] / sepin[i__ - 1];
} else {
vmax = 1.;
}
if (vmax > rmax[3]) {
rmax[3] = vmax;
if (ninfo[3] == 0) {
lmax[3] = *knt;
}
}
/* L120: */
}
/* Compute eigenvalue condition numbers only and compare */
vmax = 0.;
dum[0] = -1.;
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Eigcond", "All", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (stmp[i__ - 1] != s[i__ - 1]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
/* L130: */
}
/* Compute eigenvector condition numbers only and compare */
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Veccond", "All", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (stmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != sep[i__ - 1]) {
vmax = 1. / eps;
}
/* L140: */
}
/* Compute all condition numbers using SELECT and compare */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
select[i__ - 1] = TRUE_;
/* L150: */
}
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Bothcond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (septmp[i__ - 1] != sep[i__ - 1]) {
vmax = 1. / eps;
}
if (stmp[i__ - 1] != s[i__ - 1]) {
vmax = 1. / eps;
}
/* L160: */
}
/* Compute eigenvalue condition numbers using SELECT and compare */
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Eigcond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (stmp[i__ - 1] != s[i__ - 1]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
/* L170: */
}
/* Compute eigenvector condition numbers using SELECT and compare */
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Veccond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (stmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != sep[i__ - 1]) {
vmax = 1. / eps;
}
/* L180: */
}
if (vmax > rmax[1]) {
rmax[1] = vmax;
if (ninfo[1] == 0) {
lmax[1] = *knt;
}
}
/* Select first real and first complex eigenvalue */
if (wi[0] == 0.) {
lcmp[0] = 1;
ifnd = 0;
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
if (ifnd == 1 || wi[i__ - 1] == 0.) {
select[i__ - 1] = FALSE_;
} else {
ifnd = 1;
lcmp[1] = i__;
lcmp[2] = i__ + 1;
dcopy_(&n, &re[i__ * 20 - 20], &c__1, &re[20], &c__1);
dcopy_(&n, &re[(i__ + 1) * 20 - 20], &c__1, &re[40], &
c__1);
dcopy_(&n, &le[i__ * 20 - 20], &c__1, &le[20], &c__1);
dcopy_(&n, &le[(i__ + 1) * 20 - 20], &c__1, &le[40], &
c__1);
}
/* L190: */
}
if (ifnd == 0) {
icmp = 1;
} else {
icmp = 3;
}
} else {
lcmp[0] = 1;
lcmp[1] = 2;
ifnd = 0;
i__1 = n;
for (i__ = 3; i__ <= i__1; ++i__) {
if (ifnd == 1 || wi[i__ - 1] != 0.) {
select[i__ - 1] = FALSE_;
} else {
lcmp[2] = i__;
ifnd = 1;
dcopy_(&n, &re[i__ * 20 - 20], &c__1, &re[40], &c__1);
dcopy_(&n, &le[i__ * 20 - 20], &c__1, &le[40], &c__1);
}
/* L200: */
}
if (ifnd == 0) {
icmp = 2;
} else {
icmp = 3;
}
}
/* Compute all selected condition numbers */
dcopy_(&icmp, dum, &c__0, stmp, &c__1);
dcopy_(&icmp, dum, &c__0, septmp, &c__1);
dtrsna_("Bothcond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = icmp;
for (i__ = 1; i__ <= i__1; ++i__) {
j = lcmp[i__ - 1];
if (septmp[i__ - 1] != sep[j - 1]) {
vmax = 1. / eps;
}
if (stmp[i__ - 1] != s[j - 1]) {
vmax = 1. / eps;
}
/* L210: */
}
/* Compute selected eigenvalue condition numbers */
dcopy_(&icmp, dum, &c__0, stmp, &c__1);
dcopy_(&icmp, dum, &c__0, septmp, &c__1);
dtrsna_("Eigcond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = icmp;
for (i__ = 1; i__ <= i__1; ++i__) {
j = lcmp[i__ - 1];
if (stmp[i__ - 1] != s[j - 1]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
/* L220: */
}
/* Compute selected eigenvector condition numbers */
dcopy_(&icmp, dum, &c__0, stmp, &c__1);
dcopy_(&icmp, dum, &c__0, septmp, &c__1);
dtrsna_("Veccond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = icmp;
for (i__ = 1; i__ <= i__1; ++i__) {
j = lcmp[i__ - 1];
if (stmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != sep[j - 1]) {
vmax = 1. / eps;
}
/* L230: */
}
if (vmax > rmax[1]) {
rmax[1] = vmax;
if (ninfo[1] == 0) {
lmax[1] = *knt;
}
}
L240:
;
}
goto L10;
/* End of DGET37 */
} /* dget37_ */
