/* Subroutine */
int chbgvd_(char *jobz, char *uplo, integer *n, integer *ka, integer *kb, complex *ab, integer *ldab, complex *bb, integer *ldbb, real *w, complex *z__, integer *ldz, complex *work, integer *lwork, real *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 */
integer inde;
char vect[1];
integer llwk2;
extern /* Subroutine */
int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
integer iinfo, lwmin;
logical upper;
integer llrwk;
logical wantz;
integer indwk2;
extern /* Subroutine */
int cstedc_(char *, integer *, real *, real *, complex *, integer *, complex *, integer *, real *, integer *, integer *, integer *, integer *), chbtrd_(char *, char *, integer *, integer *, complex *, integer *, real *, real *, complex *, integer *, complex *, integer *), chbgst_(char *, char *, integer *, integer *, integer *, complex * , integer *, complex *, integer *, complex *, integer *, complex * , real *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *), cpbstf_(char *, integer *, integer *, complex *, integer *, integer *);
integer indwrk, liwmin;
extern /* Subroutine */
int ssterf_(integer *, real *, real *, integer *);
integer lrwmin;
logical lquery;
/* -- LAPACK driver routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
bb_dim1 = *ldbb;
bb_offset = 1 + bb_dim1;
bb -= bb_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
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 = *n + 1;
lrwmin = *n + 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;
}
if (*info == 0)
{
work[1].r = (real) lwmin;
work[1].i = 0.f; // , expr subst
rwork[1] = (real) lrwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery)
{
*info = -14;
}
else if (*lrwork < lrwmin && ! lquery)
{
*info = -16;
}
else if (*liwork < liwmin && ! lquery)
{
*info = -18;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CHBGVD", &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. */
cpbstf_(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;
chbgst_(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';
}
chbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &rwork[inde], & z__[z_offset], ldz, &work[1], &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEDC. */
if (! wantz)
{
ssterf_(n, &w[1], &rwork[inde], info);
}
else
{
cstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], & llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info);
cgemm_("N", "N", n, n, n, &c_b1, &z__[z_offset], ldz, &work[1], n, & c_b2, &work[indwk2], n);
clacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
}
work[1].r = (real) lwmin;
work[1].i = 0.f; // , expr subst
rwork[1] = (real) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of CHBGVD */
}
/* Subroutine */ int chbgvd_(char *jobz, char *uplo, integer *n, integer *ka,
integer *kb, complex *ab, integer *ldab, complex *bb, integer *ldbb,
real *w, complex *z__, integer *ldz, complex *work, integer *lwork,
real *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 */
integer inde;
char vect[1];
integer llwk2;
integer iinfo, lwmin;
logical upper;
integer llrwk;
logical wantz;
integer indwk2;
integer indwrk, liwmin;
integer lrwmin;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CHBGVD 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 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 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 CPBSTF. */
/* LDBB (input) INTEGER */
/* The leading dimension of the array BB. LDBB >= KB+1. */
/* W (output) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* Z (output) COMPLEX 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 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 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 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) REAL array, dimension (MAX(1,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 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 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 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 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 CPBSTF */
/* 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;
ab -= ab_offset;
bb_dim1 = *ldbb;
bb_offset = 1 + bb_dim1;
bb -= bb_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
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;
}
if (*info == 0) {
work[1].r = (real) lwmin, work[1].i = 0.f;
rwork[1] = (real) lrwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -14;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -16;
} else if (*liwork < liwmin && ! lquery) {
*info = -18;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHBGVD", &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. */
cpbstf_(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;
chbgst_(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';
}
chbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &rwork[inde], &
z__[z_offset], ldz, &work[1], &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEDC. */
if (! wantz) {
ssterf_(n, &w[1], &rwork[inde], info);
} else {
cstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], &
llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info);
cgemm_("N", "N", n, n, n, &c_b1, &z__[z_offset], ldz, &work[1], n, &
c_b2, &work[indwk2], n);
clacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
}
work[1].r = (real) lwmin, work[1].i = 0.f;
rwork[1] = (real) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of CHBGVD */
} /* chbgvd_ */
/* Subroutine */
int chpevd_(char *jobz, char *uplo, integer *n, complex *ap, real *w, complex *z__, integer *ldz, complex *work, integer *lwork, real *rwork, integer *lrwork, integer *iwork, integer *liwork, integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real eps;
integer inde;
real anrm;
integer imax;
real rmin, rmax, sigma;
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */
int sscal_(integer *, real *, real *, integer *);
integer lwmin, llrwk, llwrk;
logical wantz;
integer iscale;
extern real clanhp_(char *, char *, integer *, complex *, real *);
extern /* Subroutine */
int cstedc_(char *, integer *, real *, real *, complex *, integer *, complex *, integer *, real *, integer *, integer *, integer *, integer *);
extern real slamch_(char *);
extern /* Subroutine */
int csscal_(integer *, real *, complex *, integer *);
real safmin;
extern /* Subroutine */
int xerbla_(char *, integer *);
real bignum;
integer indtau;
extern /* Subroutine */
int chptrd_(char *, integer *, complex *, real *, real *, complex *, integer *);
integer indrwk, indwrk, liwmin;
extern /* Subroutine */
int ssterf_(integer *, real *, real *, integer *);
integer lrwmin;
extern /* Subroutine */
int cupmtr_(char *, char *, char *, integer *, integer *, complex *, complex *, complex *, integer *, complex *, integer *);
real smlnum;
logical lquery;
/* -- LAPACK driver routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
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;
}
if (*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;
}
}
work[1].r = (real) lwmin;
work[1].i = 0.f; // , expr subst
rwork[1] = (real) lrwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery)
{
*info = -9;
}
else if (*lrwork < lrwmin && ! lquery)
{
*info = -11;
}
else if (*liwork < liwmin && ! lquery)
{
*info = -13;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CHPEVD", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
return 0;
}
if (*n == 1)
{
w[1] = ap[1].r;
if (wantz)
{
i__1 = z_dim1 + 1;
z__[i__1].r = 1.f;
z__[i__1].i = 0.f; // , expr subst
}
return 0;
}
/* Get machine constants. */
safmin = slamch_("Safe minimum");
eps = slamch_("Precision");
smlnum = safmin / eps;
bignum = 1.f / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = clanhp_("M", uplo, n, &ap[1], &rwork[1]);
iscale = 0;
if (anrm > 0.f && 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;
csscal_(&i__1, &sigma, &ap[1], &c__1);
}
/* Call CHPTRD 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;
chptrd_(uplo, n, &ap[1], &w[1], &rwork[inde], &work[indtau], &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, first call */
/* CUPGTR to generate the orthogonal matrix, then call CSTEDC. */
if (! wantz)
{
ssterf_(n, &w[1], &rwork[inde], info);
}
else
{
cstedc_("I", n, &w[1], &rwork[inde], &z__[z_offset], ldz, &work[ indwrk], &llwrk, &rwork[indrwk], &llrwk, &iwork[1], liwork, info);
cupmtr_("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;
}
r__1 = 1.f / sigma;
sscal_(&imax, &r__1, &w[1], &c__1);
}
work[1].r = (real) lwmin;
work[1].i = 0.f; // , expr subst
rwork[1] = (real) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of CHPEVD */
}
/* Subroutine */ int chpevd_(char *jobz, char *uplo, integer *n, complex *ap,
real *w, complex *z__, integer *ldz, complex *work, integer *lwork,
real *rwork, integer *lrwork, integer *iwork, integer *liwork,
integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real eps;
integer inde;
real anrm;
integer imax;
real rmin, rmax, sigma;
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
integer lwmin, llrwk, llwrk;
logical wantz;
integer iscale;
extern doublereal clanhp_(char *, char *, integer *, complex *, real *);
extern /* Subroutine */ int cstedc_(char *, integer *, real *, real *,
complex *, integer *, complex *, integer *, real *, integer *,
integer *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
integer indtau;
extern /* Subroutine */ int chptrd_(char *, integer *, complex *, real *,
real *, complex *, integer *);
integer indrwk, indwrk, liwmin;
extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
integer lrwmin;
extern /* Subroutine */ int cupmtr_(char *, char *, char *, integer *,
integer *, complex *, complex *, complex *, integer *, complex *,
integer *);
real smlnum;
logical lquery;
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHPEVD 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 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) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* Z (output) COMPLEX 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 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the required 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 required 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) REAL array, dimension (MAX(1,LRWORK)) */
/* On exit, if INFO = 0, RWORK(1) returns the required 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 required 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 required 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 required 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, the algorithm failed to converge; i */
/* off-diagonal elements of an intermediate tridiagonal */
/* form did not converge to zero. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
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;
}
if (*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;
}
}
work[1].r = (real) lwmin, work[1].i = 0.f;
rwork[1] = (real) lrwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -9;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -11;
} else if (*liwork < liwmin && ! lquery) {
*info = -13;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHPEVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
w[1] = ap[1].r;
if (wantz) {
i__1 = z_dim1 + 1;
z__[i__1].r = 1.f, z__[i__1].i = 0.f;
}
return 0;
}
/* Get machine constants. */
safmin = slamch_("Safe minimum");
eps = slamch_("Precision");
smlnum = safmin / eps;
bignum = 1.f / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = clanhp_("M", uplo, n, &ap[1], &rwork[1]);
iscale = 0;
if (anrm > 0.f && 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;
csscal_(&i__1, &sigma, &ap[1], &c__1);
}
/* Call CHPTRD 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;
chptrd_(uplo, n, &ap[1], &w[1], &rwork[inde], &work[indtau], &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, first call */
/* CUPGTR to generate the orthogonal matrix, then call CSTEDC. */
if (! wantz) {
ssterf_(n, &w[1], &rwork[inde], info);
} else {
cstedc_("I", n, &w[1], &rwork[inde], &z__[z_offset], ldz, &work[
indwrk], &llwrk, &rwork[indrwk], &llrwk, &iwork[1], liwork,
info);
cupmtr_("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;
}
r__1 = 1.f / sigma;
sscal_(&imax, &r__1, &w[1], &c__1);
}
work[1].r = (real) lwmin, work[1].i = 0.f;
rwork[1] = (real) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of CHPEVD */
} /* chpevd_ */
/* Subroutine */ int cheevd_(char *jobz, char *uplo, integer *n, complex *a,
integer *lda, real *w, complex *work, integer *lwork, real *rwork,
integer *lrwork, integer *iwork, integer *liwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real eps;
integer inde;
real anrm;
integer imax;
real rmin, rmax;
integer lopt;
real sigma;
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
integer lwmin, liopt;
logical lower;
integer llrwk, lropt;
logical wantz;
integer indwk2, llwrk2;
extern doublereal clanhe_(char *, char *, integer *, complex *, integer *,
real *);
integer iscale;
extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *), cstedc_(char *, integer *, real *, real *, complex *,
integer *, complex *, integer *, real *, integer *, integer *,
integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer
*, real *, real *, complex *, complex *, integer *, integer *), clacpy_(char *, integer *, integer *, complex *, integer
*, complex *, integer *);
real safmin;
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
integer indtau, indrwk, indwrk, liwmin;
extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
integer lrwmin;
extern /* Subroutine */ int cunmtr_(char *, char *, char *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *);
integer llwork;
real smlnum;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHEEVD 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 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) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* WORK (workspace/output) COMPLEX 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) REAL 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, "CHETRD", uplo, n, &c_n1,
&c_n1, &c_n1);
lopt = max(i__1,i__2);
lropt = lrwmin;
liopt = liwmin;
}
work[1].r = (real) lopt, work[1].i = 0.f;
rwork[1] = (real) 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_("CHEEVD", &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.f, a[i__1].i = 0.f;
}
return 0;
}
/* Get machine constants. */
safmin = slamch_("Safe minimum");
eps = slamch_("Precision");
smlnum = safmin / eps;
bignum = 1.f / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = clanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
iscale = 0;
if (anrm > 0.f && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
clascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda,
info);
}
/* Call CHETRD 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;
chetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
work[indwrk], &llwork, &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, first call */
/* CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */
/* tridiagonal matrix, then call CUNMTR to multiply it to the */
/* Householder transformations represented as Householder vectors in */
/* A. */
if (! wantz) {
ssterf_(n, &w[1], &rwork[inde], info);
} else {
cstedc_("I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2],
&llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info);
cunmtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[
indwrk], n, &work[indwk2], &llwrk2, &iinfo);
clacpy_("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;
}
r__1 = 1.f / sigma;
sscal_(&imax, &r__1, &w[1], &c__1);
}
work[1].r = (real) lopt, work[1].i = 0.f;
rwork[1] = (real) lropt;
iwork[1] = liopt;
return 0;
/* End of CHEEVD */
} /* cheevd_ */
int chbevd_(char *jobz, char *uplo, int *n, int *kd,
complex *ab, int *ldab, float *w, complex *z__, int *ldz,
complex *work, int *lwork, float *rwork, int *lrwork, int *
iwork, int *liwork, int *info)
{
/* System generated locals */
int ab_dim1, ab_offset, z_dim1, z_offset, i__1;
float r__1;
/* Builtin functions */
double sqrt(double);
/* Local variables */
float eps;
int inde;
float anrm;
int imax;
float rmin, rmax;
int llwk2;
extern int cgemm_(char *, char *, int *, int *,
int *, complex *, complex *, int *, complex *, int *,
complex *, complex *, int *);
float sigma;
extern int lsame_(char *, char *);
int iinfo;
extern int sscal_(int *, float *, float *, int *);
int lwmin;
int lower;
int llrwk;
int wantz;
int indwk2;
extern double clanhb_(char *, char *, int *, int *, complex *,
int *, float *);
int iscale;
extern int clascl_(char *, int *, int *, float *,
float *, int *, int *, complex *, int *, int *), cstedc_(char *, int *, float *, float *, complex *,
int *, complex *, int *, float *, int *, int *,
int *, int *), chbtrd_(char *, char *, int *,
int *, complex *, int *, float *, float *, complex *,
int *, complex *, int *);
extern double slamch_(char *);
extern int clacpy_(char *, int *, int *, complex
*, int *, complex *, int *);
float safmin;
extern int xerbla_(char *, int *);
float bignum;
int indwrk, liwmin;
extern int ssterf_(int *, float *, float *, int *);
int lrwmin;
float smlnum;
int lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHBEVD computes all the eigenvalues and, optionally, eigenvectors of */
/* a complex Hermitian band 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. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* AB (input/output) COMPLEX array, dimension (LDAB, N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for MAX(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=MIN(n,j+kd). */
/* On exit, AB is overwritten by values generated during the */
/* reduction to tridiagonal form. If UPLO = 'U', the first */
/* superdiagonal and the diagonal of the tridiagonal matrix T */
/* are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */
/* the diagonal and first subdiagonal of T are returned in the */
/* first two rows of AB. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD + 1. */
/* W (output) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* Z (output) COMPLEX 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 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 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**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) REAL 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 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 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 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, the algorithm failed to converge; i */
/* off-diagonal elements of an intermediate tridiagonal */
/* form did not converge to zero. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lower = lsame_(uplo, "L");
lquery = *lwork == -1 || *liwork == -1 || *lrwork == -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 (! (lower || lsame_(uplo, "U"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*kd < 0) {
*info = -4;
} else if (*ldab < *kd + 1) {
*info = -6;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -9;
}
if (*info == 0) {
work[1].r = (float) lwmin, work[1].i = 0.f;
rwork[1] = (float) lrwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -11;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -13;
} else if (*liwork < liwmin && ! lquery) {
*info = -15;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHBEVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
i__1 = ab_dim1 + 1;
w[1] = ab[i__1].r;
if (wantz) {
i__1 = z_dim1 + 1;
z__[i__1].r = 1.f, z__[i__1].i = 0.f;
}
return 0;
}
/* Get machine constants. */
safmin = slamch_("Safe minimum");
eps = slamch_("Precision");
smlnum = safmin / eps;
bignum = 1.f / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = clanhb_("M", uplo, n, kd, &ab[ab_offset], ldab, &rwork[1]);
iscale = 0;
if (anrm > 0.f && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
if (lower) {
clascl_("B", kd, kd, &c_b13, &sigma, n, n, &ab[ab_offset], ldab,
info);
} else {
clascl_("Q", kd, kd, &c_b13, &sigma, n, n, &ab[ab_offset], ldab,
info);
}
}
/* Call CHBTRD to reduce Hermitian band matrix to tridiagonal form. */
inde = 1;
indwrk = inde + *n;
indwk2 = *n * *n + 1;
llwk2 = *lwork - indwk2 + 1;
llrwk = *lrwork - indwrk + 1;
chbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &w[1], &rwork[inde], &
z__[z_offset], ldz, &work[1], &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEDC. */
if (! wantz) {
ssterf_(n, &w[1], &rwork[inde], info);
} else {
cstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], &
llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info);
cgemm_("N", "N", n, n, n, &c_b2, &z__[z_offset], ldz, &work[1], n, &
c_b1, &work[indwk2], n);
clacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *n;
} else {
imax = *info - 1;
}
r__1 = 1.f / sigma;
sscal_(&imax, &r__1, &w[1], &c__1);
}
work[1].r = (float) lwmin, work[1].i = 0.f;
rwork[1] = (float) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of CHBEVD */
} /* chbevd_ */
