/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n,
doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork,
integer *liwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least N + 1.
If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2.
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/output) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK must be at least 1.
If JOBZ = 'N' and N > 1, LRWORK must be at least N.
If JOBZ = 'V' and N > 1, LRWORK must be at least
1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the RWORK array,
returns this value as the first entry of the RWORK array, and
no error message related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK must be at least 1.
If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__0 = 0;
static doublereal c_b13 = 1.;
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer inde;
static doublereal anrm;
static integer imax;
static doublereal rmin, rmax;
static integer lopt;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static doublereal sigma;
extern logical lsame_(char *, char *);
static integer iinfo, lwmin, liopt;
static logical lower;
static integer llrwk, lropt;
static logical wantz;
static integer indwk2, llwrk2;
extern doublereal dlamch_(char *);
static integer iscale;
static doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal bignum;
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *);
static integer indtau;
extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
integer *), zlascl_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, integer *, doublecomplex *, integer *,
integer *), zstedc_(char *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, integer *, integer *, integer *, integer
*);
static integer indrwk, indwrk, liwmin;
extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *,
doublecomplex *, integer *, integer *), zlacpy_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *);
static integer lrwmin, llwork;
static doublereal smlnum;
static logical lquery;
extern /* Subroutine */ int zunmtr_(char *, char *, char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
static doublereal eps;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--w;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lower = lsame_(uplo, "L");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
if (*n <= 1) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
lopt = lwmin;
lropt = lrwmin;
liopt = liwmin;
} else {
if (wantz) {
lwmin = (*n << 1) + *n * *n;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
liwmin = *n * 5 + 3;
} else {
lwmin = *n + 1;
lrwmin = *n;
liwmin = 1;
}
lopt = lwmin;
lropt = lrwmin;
liopt = liwmin;
}
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (lower || lsame_(uplo, "U"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*lwork < lwmin && ! lquery) {
*info = -8;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -10;
} else if (*liwork < liwmin && ! lquery) {
*info = -12;
}
if (*info == 0) {
work[1].r = (doublereal) lopt, work[1].i = 0.;
rwork[1] = (doublereal) lropt;
iwork[1] = liopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHEEVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
i__1 = a_subscr(1, 1);
w[1] = a[i__1].r;
if (wantz) {
i__1 = a_subscr(1, 1);
a[i__1].r = 1., a[i__1].i = 0.;
}
return 0;
}
/* Get machine constants. */
safmin = dlamch_("Safe minimum");
eps = dlamch_("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = zlanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
zlascl_(uplo, &c__0, &c__0, &c_b13, &sigma, n, n, &a[a_offset], lda,
info);
}
/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 1;
indtau = 1;
indwrk = indtau + *n;
indrwk = inde + *n;
indwk2 = indwrk + *n * *n;
llwork = *lwork - indwrk + 1;
llwrk2 = *lwork - indwk2 + 1;
llrwk = *lrwork - indrwk + 1;
zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
work[indwrk], &llwork, &iinfo);
/* Computing MAX */
i__1 = indwrk;
d__1 = (doublereal) lopt, d__2 = (doublereal) (*n) + work[i__1].r;
lopt = (integer) max(d__1,d__2);
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call ZUNMTR to multiply it to the
Householder transformations represented as Householder vectors in
A. */
if (! wantz) {
dsterf_(n, &w[1], &rwork[inde], info);
} else {
zstedc_("I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2],
&llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info);
zunmtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[
indwrk], n, &work[indwk2], &llwrk2, &iinfo);
zlacpy_("A", n, n, &work[indwrk], n, &a[a_offset], lda);
/* Computing MAX
Computing 2nd power */
i__3 = *n;
i__4 = indwk2;
i__1 = lopt, i__2 = *n + i__3 * i__3 + (integer) work[i__4].r;
lopt = max(i__1,i__2);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
dscal_(&imax, &d__1, &w[1], &c__1);
}
work[1].r = (doublereal) lopt, work[1].i = 0.;
rwork[1] = (doublereal) lropt;
iwork[1] = liopt;
return 0;
/* End of ZHEEVD */
} /* zheevd_ */
/* Subroutine */ int zhbgvd_(char *jobz, char *uplo, integer *n, integer *ka,
integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb,
integer *ldbb, doublereal *w, doublecomplex *z__, integer *ldz,
doublecomplex *work, integer *lwork, doublereal *rwork, integer *
lrwork, integer *iwork, integer *liwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1;
/* Local variables */
static integer inde;
static char vect[1];
static integer llwk2;
extern logical lsame_(char *, char *);
static integer iinfo;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwmin;
static logical upper;
static integer llrwk;
static logical wantz;
static integer indwk2;
extern /* Subroutine */ int xerbla_(char *, integer *), dsterf_(
integer *, doublereal *, doublereal *, integer *), zstedc_(char *,
integer *, doublereal *, doublereal *, doublecomplex *, integer *
, doublecomplex *, integer *, doublereal *, integer *, integer *,
integer *, integer *), zhbtrd_(char *, char *, integer *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, doublecomplex *, integer *);
static integer indwrk, liwmin;
extern /* Subroutine */ int zhbgst_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublereal *,
integer *), zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static integer lrwmin;
extern /* Subroutine */ int zpbstf_(char *, integer *, integer *,
doublecomplex *, integer *, integer *);
static logical lquery;
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
and banded, and B is also positive definite. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
KA (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.
KB (input) INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0.
AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first ka+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KA+1.
BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
On entry, the upper or lower triangle of the Hermitian band
matrix B, stored in the first kb+1 rows of the array. The
j-th column of B is stored in the j-th column of the array BB
as follows:
if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization
B = S**H*S, as returned by ZPBSTF.
LDBB (input) INTEGER
The leading dimension of the array BB. LDBB >= KB+1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors, with the i-th column of Z holding the
eigenvector associated with W(i). The eigenvectors are
normalized so that Z**H*B*Z = I.
If JOBZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= N.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO=0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= N.
If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
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/output) DOUBLE PRECISION array, dimension (LRWORK)
On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = 'N' and N > 1, LRWORK >= N.
If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the RWORK array,
returns this value as the first entry of the RWORK array, and
no error message related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of array IWORK.
If JOBZ = 'N' or N <= 1, LIWORK >= 1.
If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
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 algorithm failed to converge:
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Further Details
===============
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
=====================================================================
Test the input parameters.
Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
bb_dim1 = *ldbb;
bb_offset = 1 + bb_dim1 * 1;
bb -= bb_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
if (*n <= 1) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
} else {
if (wantz) {
/* Computing 2nd power */
i__1 = *n;
lwmin = i__1 * i__1 << 1;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
liwmin = *n * 5 + 3;
} else {
lwmin = *n;
lrwmin = *n;
liwmin = 1;
}
}
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ka < 0) {
*info = -4;
} else if (*kb < 0 || *kb > *ka) {
*info = -5;
} else if (*ldab < *ka + 1) {
*info = -7;
} else if (*ldbb < *kb + 1) {
*info = -9;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -12;
} else if (*lwork < lwmin && ! lquery) {
*info = -14;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -16;
} else if (*liwork < liwmin && ! lquery) {
*info = -18;
}
if (*info == 0) {
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHBGVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a split Cholesky factorization of B. */
zpbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem. */
inde = 1;
indwrk = inde + *n;
indwk2 = *n * *n + 1;
llwk2 = *lwork - indwk2 + 2;
llrwk = *lrwork - indwrk + 2;
zhbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb,
&z__[z_offset], ldz, &work[1], &rwork[indwrk], &iinfo);
/* Reduce Hermitian band matrix to tridiagonal form. */
if (wantz) {
*(unsigned char *)vect = 'U';
} else {
*(unsigned char *)vect = 'N';
}
zhbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &rwork[inde], &
z__[z_offset], ldz, &work[1], &iinfo);
/* For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC. */
if (! wantz) {
dsterf_(n, &w[1], &rwork[inde], info);
} else {
zstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], &
llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info);
zgemm_("N", "N", n, n, n, &c_b1, &z__[z_offset], ldz, &work[1], n, &
c_b2, &work[indwk2], n);
zlacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
}
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of ZHBGVD */
} /* zhbgvd_ */
int zheevd_(char *jobz, char *uplo, int *n,
doublecomplex *a, int *lda, double *w, doublecomplex *work,
int *lwork, double *rwork, int *lrwork, int *iwork,
int *liwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2;
double d__1;
/* Builtin functions */
double sqrt(double);
/* Local variables */
double eps;
int inde;
double anrm;
int imax;
double rmin, rmax;
int lopt;
extern int dscal_(int *, double *, double *,
int *);
double sigma;
extern int lsame_(char *, char *);
int iinfo, lwmin, liopt;
int lower;
int llrwk, lropt;
int wantz;
int indwk2, llwrk2;
extern double dlamch_(char *);
int iscale;
double safmin;
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
extern int xerbla_(char *, int *);
double bignum;
extern double zlanhe_(char *, char *, int *, doublecomplex *,
int *, double *);
int indtau;
extern int dsterf_(int *, double *, double *,
int *), zlascl_(char *, int *, int *, double *,
double *, int *, int *, doublecomplex *, int *,
int *), zstedc_(char *, int *, double *,
double *, doublecomplex *, int *, doublecomplex *,
int *, double *, int *, int *, int *, int
*);
int indrwk, indwrk, liwmin;
extern int zhetrd_(char *, int *, doublecomplex *,
int *, double *, double *, doublecomplex *,
doublecomplex *, int *, int *), zlacpy_(char *,
int *, int *, doublecomplex *, int *, doublecomplex *,
int *);
int lrwmin, llwork;
double smlnum;
int lquery;
extern int zunmtr_(char *, char *, char *, int *,
int *, doublecomplex *, int *, doublecomplex *,
doublecomplex *, int *, doublecomplex *, int *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a */
/* complex Hermitian matrix A. If eigenvectors are desired, it uses a */
/* divide and conquer algorithm. */
/* The divide and conquer algorithm makes very mild assumptions about */
/* floating point arithmetic. It will work on machines with a guard */
/* digit in add/subtract, or on those binary machines without guard */
/* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* without guard digits, but we know of none. */
/* Arguments */
/* ========= */
/* JOBZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only; */
/* = 'V': Compute eigenvalues and eigenvectors. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA, N) */
/* On entry, the Hermitian matrix A. If UPLO = 'U', the */
/* leading N-by-N upper triangular part of A contains the */
/* upper triangular part of the matrix A. If UPLO = 'L', */
/* the leading N-by-N lower triangular part of A contains */
/* the lower triangular part of the matrix A. */
/* On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
/* orthonormal eigenvectors of the matrix A. */
/* If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */
/* or the upper triangle (if UPLO='U') of A, including the */
/* diagonal, is destroyed. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* W (output) DOUBLE PRECISION array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length of the array WORK. */
/* If N <= 1, LWORK must be at least 1. */
/* If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. */
/* If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal sizes of the WORK, RWORK and */
/* IWORK arrays, returns these values as the first entries of */
/* the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* RWORK (workspace/output) DOUBLE PRECISION array, */
/* dimension (LRWORK) */
/* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */
/* LRWORK (input) INTEGER */
/* The dimension of the array RWORK. */
/* If N <= 1, LRWORK must be at least 1. */
/* If JOBZ = 'N' and N > 1, LRWORK must be at least N. */
/* If JOBZ = 'V' and N > 1, LRWORK must be at least */
/* 1 + 5*N + 2*N**2. */
/* If LRWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the optimal sizes of the WORK, RWORK */
/* and IWORK arrays, returns these values as the first entries */
/* of the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. */
/* If N <= 1, LIWORK must be at least 1. */
/* If JOBZ = 'N' and N > 1, LIWORK must be at least 1. */
/* If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the optimal sizes of the WORK, RWORK */
/* and IWORK arrays, returns these values as the first entries */
/* of the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i and JOBZ = 'N', then the algorithm failed */
/* to converge; i off-diagonal elements of an intermediate */
/* tridiagonal form did not converge to zero; */
/* if INFO = i and JOBZ = 'V', then the algorithm failed */
/* to compute an eigenvalue while working on the submatrix */
/* lying in rows and columns INFO/(N+1) through */
/* mod(INFO,N+1). */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Jeff Rutter, Computer Science Division, University of California */
/* at Berkeley, USA */
/* Modified description of INFO. Sven, 16 Feb 05. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lower = lsame_(uplo, "L");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (lower || lsame_(uplo, "U"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < MAX(1,*n)) {
*info = -5;
}
if (*info == 0) {
if (*n <= 1) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
lopt = lwmin;
lropt = lrwmin;
liopt = liwmin;
} else {
if (wantz) {
lwmin = (*n << 1) + *n * *n;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
liwmin = *n * 5 + 3;
} else {
lwmin = *n + 1;
lrwmin = *n;
liwmin = 1;
}
/* Computing MAX */
i__1 = lwmin, i__2 = *n + ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1,
&c_n1, &c_n1);
lopt = MAX(i__1,i__2);
lropt = lrwmin;
liopt = liwmin;
}
work[1].r = (double) lopt, work[1].i = 0.;
rwork[1] = (double) lropt;
iwork[1] = liopt;
if (*lwork < lwmin && ! lquery) {
*info = -8;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -10;
} else if (*liwork < liwmin && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHEEVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
i__1 = a_dim1 + 1;
w[1] = a[i__1].r;
if (wantz) {
i__1 = a_dim1 + 1;
a[i__1].r = 1., a[i__1].i = 0.;
}
return 0;
}
/* Get machine constants. */
safmin = dlamch_("Safe minimum");
eps = dlamch_("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = zlanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda,
info);
}
/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 1;
indtau = 1;
indwrk = indtau + *n;
indrwk = inde + *n;
indwk2 = indwrk + *n * *n;
llwork = *lwork - indwrk + 1;
llwrk2 = *lwork - indwk2 + 1;
llrwk = *lrwork - indrwk + 1;
zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
work[indwrk], &llwork, &iinfo);
/* For eigenvalues only, call DSTERF. For eigenvectors, first call */
/* ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */
/* tridiagonal matrix, then call ZUNMTR to multiply it to the */
/* Householder transformations represented as Householder vectors in */
/* A. */
if (! wantz) {
dsterf_(n, &w[1], &rwork[inde], info);
} else {
zstedc_("I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2],
&llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info);
zunmtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[
indwrk], n, &work[indwk2], &llwrk2, &iinfo);
zlacpy_("A", n, n, &work[indwrk], n, &a[a_offset], lda);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
dscal_(&imax, &d__1, &w[1], &c__1);
}
work[1].r = (double) lopt, work[1].i = 0.;
rwork[1] = (double) lropt;
iwork[1] = liopt;
return 0;
/* End of ZHEEVD */
} /* zheevd_ */
/* Subroutine */ int zhpevd_(char *jobz, char *uplo, integer *n,
doublecomplex *ap, doublereal *w, doublecomplex *z__, integer *ldz,
doublecomplex *work, integer *lwork, doublereal *rwork, integer *
lrwork, integer *iwork, integer *liwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least N.
If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
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/output) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of array RWORK.
If N <= 1, LRWORK must be at least 1.
If JOBZ = 'N' and N > 1, LRWORK must be at least N.
If JOBZ = 'V' and N > 1, LRWORK must be at least
1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the RWORK array,
returns this value as the first entry of the RWORK array, and
no error message related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of array IWORK.
If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer z_dim1, z_offset, i__1;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer inde;
static doublereal anrm;
static integer imax;
static doublereal rmin, rmax;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static doublereal sigma;
extern logical lsame_(char *, char *);
static integer iinfo, lwmin, llrwk, llwrk;
static logical wantz;
extern doublereal dlamch_(char *);
static integer iscale;
static doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
integer *, doublereal *, doublecomplex *, integer *);
static doublereal bignum;
static integer indtau;
extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
integer *);
extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *,
doublereal *);
extern /* Subroutine */ int zstedc_(char *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, integer *, integer *, integer *, integer
*);
static integer indrwk, indwrk, liwmin, lrwmin;
static doublereal smlnum;
extern /* Subroutine */ int zhptrd_(char *, integer *, doublecomplex *,
doublereal *, doublereal *, doublecomplex *, integer *);
static logical lquery;
extern /* Subroutine */ int zupmtr_(char *, char *, char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *);
static doublereal eps;
#define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1
#define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)]
--ap;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
if (*n <= 1) {
lwmin = 1;
liwmin = 1;
lrwmin = 1;
} else {
if (wantz) {
lwmin = *n << 1;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
liwmin = *n * 5 + 3;
} else {
lwmin = *n;
lrwmin = *n;
liwmin = 1;
}
}
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (lsame_(uplo, "L") || lsame_(uplo,
"U"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -7;
} else if (*lwork < lwmin && ! lquery) {
*info = -9;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -11;
} else if (*liwork < liwmin && ! lquery) {
*info = -13;
}
if (*info == 0) {
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHPEVD", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
w[1] = ap[1].r;
if (wantz) {
i__1 = z___subscr(1, 1);
z__[i__1].r = 1., z__[i__1].i = 0.;
}
return 0;
}
/* Get machine constants. */
safmin = dlamch_("Safe minimum");
eps = dlamch_("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = zlanhp_("M", uplo, n, &ap[1], &rwork[1]);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
i__1 = *n * (*n + 1) / 2;
zdscal_(&i__1, &sigma, &ap[1], &c__1);
}
/* Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. */
inde = 1;
indtau = 1;
indrwk = inde + *n;
indwrk = indtau + *n;
llwrk = *lwork - indwrk + 1;
llrwk = *lrwork - indrwk + 1;
zhptrd_(uplo, n, &ap[1], &w[1], &rwork[inde], &work[indtau], &iinfo);
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
ZUPGTR to generate the orthogonal matrix, then call ZSTEDC. */
if (! wantz) {
dsterf_(n, &w[1], &rwork[inde], info);
} else {
zstedc_("I", n, &w[1], &rwork[inde], &z__[z_offset], ldz, &work[
indwrk], &llwrk, &rwork[indrwk], &llrwk, &iwork[1], liwork,
info);
zupmtr_("L", uplo, "N", n, n, &ap[1], &work[indtau], &z__[z_offset],
ldz, &work[indwrk], &iinfo);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
dscal_(&imax, &d__1, &w[1], &c__1);
}
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of ZHPEVD */
} /* zhpevd_ */
/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n,
doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork,
integer *liwork, 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
September 30, 1994
Purpose
=======
ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least N + 1.
If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if LRWORK > 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK must be at least 1.
If JOBZ = 'N' and N > 1, LRWORK must be at least N.
If JOBZ = 'V' and N > 1, LRWORK must be at least
1 + 4*N + 2*N*lg N + 3*N**2 ,
where lg( N ) = smallest integer k such
that 2**k >= N .
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK must be at least 1.
If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 1, LIWORK must be at least 2 + 5*N.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
=====================================================================
Test the input parameters.
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__2 = 2;
static integer c__0 = 0;
static doublereal c_b16 = 1.;
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
/* Builtin functions */
double log(doublereal);
integer pow_ii(integer *, integer *);
double sqrt(doublereal);
/* Local variables */
static integer inde;
static doublereal anrm;
static integer imax;
static doublereal rmin, rmax;
static integer lopt;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static doublereal sigma;
extern logical lsame_(char *, char *);
static integer iinfo, lwmin, liopt;
static logical lower;
static integer llrwk, lropt;
static logical wantz;
static integer indwk2, llwrk2;
extern doublereal dlamch_(char *);
static integer iscale;
static doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal bignum;
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *);
static integer indtau;
extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
integer *), zlascl_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, integer *, doublecomplex *, integer *,
integer *), zstedc_(char *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, integer *, integer *, integer *, integer
*);
static integer indrwk, indwrk, liwmin;
extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *,
doublecomplex *, integer *, integer *), zlacpy_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *);
static integer lrwmin, llwork;
static doublereal smlnum;
extern /* Subroutine */ int zunmtr_(char *, char *, char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
static integer lgn;
static doublereal eps;
#define W(I) w[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]
#define IWORK(I) iwork[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
wantz = lsame_(jobz, "V");
lower = lsame_(uplo, "L");
*info = 0;
if (*n <= 1) {
lgn = 0;
lwmin = 1;
lrwmin = 1;
liwmin = 1;
lopt = lwmin;
lropt = lrwmin;
liopt = liwmin;
} else {
lgn = (integer) (log((doublereal) (*n)) / log(2.));
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (wantz) {
lwmin = (*n << 1) + *n * *n;
/* Computing 2nd power */
i__1 = *n;
lrwmin = (*n << 2) + 1 + (*n << 1) * lgn + i__1 * i__1 * 3;
liwmin = *n * 5 + 2;
} else {
lwmin = *n + 1;
lrwmin = *n;
liwmin = 1;
}
lopt = lwmin;
lropt = lrwmin;
liopt = liwmin;
}
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (lower || lsame_(uplo, "U"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*lwork < lwmin) {
*info = -8;
} else if (*lrwork < lrwmin) {
*info = -10;
} else if (*liwork < liwmin) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHEEVD ", &i__1);
goto L10;
}
/* Quick return if possible */
if (*n == 0) {
goto L10;
}
if (*n == 1) {
i__1 = a_dim1 + 1;
W(1) = A(1,1).r;
if (wantz) {
i__1 = a_dim1 + 1;
A(1,1).r = 1., A(1,1).i = 0.;
}
goto L10;
}
/* Get machine constants. */
safmin = dlamch_("Safe minimum");
eps = dlamch_("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = zlanhe_("M", uplo, n, &A(1,1), lda, &RWORK(1));
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
zlascl_(uplo, &c__0, &c__0, &c_b16, &sigma, n, n, &A(1,1), lda,
info);
}
/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 1;
indtau = 1;
indwrk = indtau + *n;
indrwk = inde + *n;
indwk2 = indwrk + *n * *n;
llwork = *lwork - indwrk + 1;
llwrk2 = *lwork - indwk2 + 1;
llrwk = *lrwork - indrwk + 1;
zhetrd_(uplo, n, &A(1,1), lda, &W(1), &RWORK(inde), &WORK(indtau), &
WORK(indwrk), &llwork, &iinfo);
/* Computing MAX */
i__1 = indwrk;
d__1 = (doublereal) lopt, d__2 = (doublereal) (*n) + WORK(indwrk).r;
lopt = (integer) max(d__1,d__2);
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call ZUNMTR to multiply it to the
Householder transformations represented as Householder vectors in
A. */
if (! wantz) {
dsterf_(n, &W(1), &RWORK(inde), info);
} else {
zstedc_("I", n, &W(1), &RWORK(inde), &WORK(indwrk), n, &WORK(indwk2),
&llwrk2, &RWORK(indrwk), &llrwk, &IWORK(1), liwork, info);
zunmtr_("L", uplo, "N", n, n, &A(1,1), lda, &WORK(indtau), &WORK(
indwrk), n, &WORK(indwk2), &llwrk2, &iinfo);
zlacpy_("A", n, n, &WORK(indwrk), n, &A(1,1), lda);
/* Computing MAX
Computing 2nd power */
i__3 = *n;
i__4 = indwk2;
i__1 = lopt, i__2 = *n + i__3 * i__3 + (integer) WORK(indwk2).r;
lopt = max(i__1,i__2);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
dscal_(&imax, &d__1, &W(1), &c__1);
}
L10:
if (*lwork > 0) {
WORK(1).r = (doublereal) lopt, WORK(1).i = 0.;
}
if (*lrwork > 0) {
RWORK(1) = (doublereal) lropt;
}
if (*liwork > 0) {
IWORK(1) = liopt;
}
return 0;
/* End of ZHEEVD */
} /* zheevd_ */
