/**
Purpose
-------
ZSTEDX computes some eigenvalues and eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
This code 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. See DLAEX3 for details.
Arguments
---------
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@param[in]
n INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
@param[in]
vl DOUBLE PRECISION
@param[in]
vu DOUBLE PRECISION
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[in,out]
d DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, if INFO = 0, the eigenvalues in ascending order.
@param[in,out]
e DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
@param[out]
Z COMPLEX_16 array, dimension (LDZ,N)
On exit, if INFO = 0, Z contains the orthonormal eigenvectors
of the symmetric tridiagonal matrix.
@param[in]
ldz INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
@param[out]
rwork (workspace) DOUBLE PRECISION array, dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
LRWORK >= 1 + 4*N + 2*N**2.
Note that if N is less than or
equal to the minimum divide size, usually 25, then LRWORK
need only be max(1,2*(N-1)).
\n
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.
@param[out]
iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
LIWORK >= 3 + 5*N .
Note that if N is less than or
equal to the minimum divide size, usually 25, then LIWORK
need only be 1.
\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.
@param
dwork (workspace) DOUBLE PRECISION array, dimension (3*N*N/2+3*N)
@param[out]
info INTEGER
- = 0: successful exit.
- < 0: if INFO = -i, the i-th argument had an illegal value.
- > 0: 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
@ingroup magma_zheev_comp
********************************************************************/
extern "C" magma_int_t
magma_zstedx(magma_range_t range, magma_int_t n, double vl, double vu,
magma_int_t il, magma_int_t iu, double* d, double* e,
magmaDoubleComplex* Z, magma_int_t ldz,
double* rwork, magma_int_t lrwork,
magma_int_t* iwork, magma_int_t liwork,
double* dwork, magma_int_t* info)
{
magma_int_t alleig, indeig, valeig, lquery;
magma_int_t i, j, smlsiz;
magma_int_t liwmin, lrwmin;
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lrwork == -1 || liwork == -1);
*info = 0;
if (! (alleig || valeig || indeig)) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldz < max(1,n)) {
*info = -10;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -4;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -5;
} else if (iu < min(n,il) || iu > n) {
*info = -6;
}
}
}
if (*info == 0) {
// Compute the workspace requirements
smlsiz = magma_get_smlsize_divideconquer();
if ( n <= 1 ) {
lrwmin = 1;
liwmin = 1;
} else {
lrwmin = 1 + 4*n + 2*n*n;
liwmin = 3 + 5*n;
}
rwork[0] = lrwmin;
iwork[0] = liwmin;
if (lrwork < lrwmin && ! lquery) {
*info = -12;
} else if (liwork < liwmin && ! lquery) {
*info = -14;
}
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
// Quick return if possible
if (n == 0)
return *info;
if (n == 1) {
*Z = MAGMA_Z_MAKE( 1, 0 );
return *info;
}
// If N is smaller than the minimum divide size (SMLSIZ+1), then
// solve the problem with another solver.
if (n < smlsiz) {
lapackf77_zsteqr("I", &n, d, e, Z, &ldz, rwork, info);
} else {
// We simply call DSTEDX instead.
magma_dstedx(range, n, vl, vu, il, iu, d, e, rwork, n,
rwork+n*n, lrwork-n*n, iwork, liwork, dwork, info);
for (j=0; j < n; ++j)
for (i=0; i < n; ++i) {
*(Z+i+ldz*j) = MAGMA_Z_MAKE( *(rwork+i+n*j), 0 );
}
}
rwork[0] = lrwmin;
iwork[0] = liwmin;
return *info;
} /* magma_zstedx */
extern "C" magma_int_t
magma_zheevx_gpu(char jobz, char range, char uplo, magma_int_t n,
magmaDoubleComplex *da, magma_int_t ldda, double vl, double vu,
magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m,
double *w, magmaDoubleComplex *dz, magma_int_t lddz,
magmaDoubleComplex *wa, magma_int_t ldwa,
magmaDoubleComplex *wz, magma_int_t ldwz,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
ZHEEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input) CHARACTER*1
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU]
will be found.
= 'I': the IL-th through IU-th eigenvalues will be found.
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.
DA (device input/output) COMPLEX_16 array, dimension (LDDA, 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, the lower triangle (if UPLO='L') or the upper
triangle (if UPLO='U') of A, including the diagonal, is
destroyed.
LDDA (input) INTEGER
The leading dimension of the array DA. LDDA >= max(1,N).
VL (input) DOUBLE PRECISION
VU (input) DOUBLE PRECISION
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
IL (input) INTEGER
IU (input) INTEGER
If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
ABSTOL (input) DOUBLE PRECISION
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABSTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and
Kahan, LAPACK Working Note #3.
M (output) INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (output) DOUBLE PRECISION array, dimension (N)
On normal exit, the first M elements contain the selected
eigenvalues in ascending order.
DZ (device output) COMPLEX_16 array, dimension (LDDZ, max(1,M))
If JOBZ = 'V', then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
If JOBZ = 'N', then Z is not referenced.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used.
********* (workspace) If FAST_HEMV is defined DZ should be (LDDZ, max(1,N)) in both cases.
LDDZ (input) INTEGER
The leading dimension of the array DZ. LDDZ >= 1, and if
JOBZ = 'V', LDDZ >= max(1,N).
WA (workspace) COMPLEX_16 array, dimension (LDWA, N)
LDWA (input) INTEGER
The leading dimension of the array WA. LDWA >= max(1,N).
WZ (workspace) COMPLEX_16 array, dimension (LDWZ, max(1,M))
LDWZ (input) INTEGER
The leading dimension of the array DZ. LDWZ >= 1, and if
JOBZ = 'V', LDWZ >= 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 length of the array WORK. LWORK >= (NB+1)*N,
where NB is the max of the blocksize for ZHETRD.
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) DOUBLE PRECISION array, dimension (7*N)
IWORK (workspace) INTEGER array, dimension (5*N)
IFAIL (output) INTEGER array, dimension (N)
If JOBZ = 'V', then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = 'N', then IFAIL is not referenced.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
char range_[2] = {range, 0};
magma_int_t ione = 1;
char order[1];
magma_int_t indd, inde;
magma_int_t imax;
magma_int_t lopt, itmp1, indee;
magma_int_t lower, wantz;
magma_int_t i, j, jj, i__1;
magma_int_t alleig, valeig, indeig;
magma_int_t iscale, indibl;
magma_int_t indiwk, indisp, indtau;
magma_int_t indrwk, indwrk;
magma_int_t llwork, nsplit;
magma_int_t lquery;
magma_int_t iinfo;
double safmin;
double bignum;
double smlnum;
double eps, tmp1;
double anrm;
double sigma, d__1;
double rmin, rmax;
double *dwork;
/* Function Body */
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
lquery = lwork == -1;
*info = 0;
if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (ldda < max(1,n)) {
*info = -6;
} else if (lddz < 1 || (wantz && lddz < n)) {
*info = -15;
} else if (ldwa < max(1,n)) {
*info = -17;
} else if (ldwz < 1 || (wantz && ldwz < n)) {
*info = -19;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -8;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -9;
} else if (iu < min(n,il) || iu > n) {
*info = -10;
}
}
}
magma_int_t nb = magma_get_zhetrd_nb(n);
lopt = n * (nb + 1);
work[0] = MAGMA_Z_MAKE( lopt, 0 );
if (lwork < lopt && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
*m = 0;
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb);
printf("--------------------------------------------------------------\n");
#endif
magmaDoubleComplex *a = (magmaDoubleComplex *) malloc( n * n * sizeof(magmaDoubleComplex) );
magma_zgetmatrix(n, n, da, ldda, a, n);
lapackf77_zheevx(jobz_, range_, uplo_,
&n, a, &n, &vl, &vu, &il, &iu, &abstol, m,
w, wz, &ldwz, work, &lwork,
rwork, iwork, ifail, info);
magma_zsetmatrix( n, n, a, n, da, ldda);
magma_zsetmatrix( n, *m, wz, ldwz, dz, lddz);
free(a);
return *info;
}
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, n )) {
fprintf (stderr, "!!!! device memory allocation error (magma_zheevx_gpu)\n");
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
--w;
--work;
--rwork;
--iwork;
--ifail;
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = magmablas_zlanhe('M', uplo, n, da, ldda, dwork);
iscale = 0;
sigma = 1;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
d__1 = 1.;
magmablas_zlascl(uplo, 0, 0, 1., sigma, n, n, da,
ldda, info);
if (abstol > 0.) {
abstol *= sigma;
}
if (valeig) {
vl *= sigma;
vu *= sigma;
}
}
/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
indd = 1;
inde = indd + n;
indrwk = inde + n;
indtau = 1;
indwrk = indtau + n;
llwork = lwork - indwrk + 1;
#ifdef FAST_HEMV
magma_zhetrd2_gpu(uplo, n, da, ldda, &rwork[indd], &rwork[inde],
&work[indtau], wa, ldwa, &work[indwrk], llwork, dz, lddz*n, &iinfo);
#else
magma_zhetrd_gpu (uplo, n, da, ldda, &rwork[indd], &rwork[inde],
&work[indtau], wa, ldwa, &work[indwrk], llwork, &iinfo);
#endif
lopt = n + (magma_int_t)MAGMA_Z_REAL(work[indwrk]);
/* If all eigenvalues are desired and ABSTOL is less than or equal to
zero, then call DSTERF or ZUNGTR and ZSTEQR. If this fails for
some eigenvalue, then try DSTEBZ. */
if ((alleig || (indeig && il == 1 && iu == n)) && abstol <= 0.) {
blasf77_dcopy(&n, &rwork[indd], &ione, &w[1], &ione);
indee = indrwk + 2*n;
if (! wantz) {
i__1 = n - 1;
blasf77_dcopy(&i__1, &rwork[inde], &ione, &rwork[indee], &ione);
lapackf77_dsterf(&n, &w[1], &rwork[indee], info);
}
else {
lapackf77_zlacpy("A", &n, &n, wa, &ldwa, wz, &ldwz);
lapackf77_zungtr(uplo_, &n, wz, &ldwz, &work[indtau], &work[indwrk], &llwork, &iinfo);
i__1 = n - 1;
blasf77_dcopy(&i__1, &rwork[inde], &ione, &rwork[indee], &ione);
lapackf77_zsteqr(jobz_, &n, &w[1], &rwork[indee], wz, &ldwz, &rwork[indrwk], info);
if (*info == 0) {
for (i = 1; i <= n; ++i) {
ifail[i] = 0;
}
magma_zsetmatrix( n, n, wz, ldwz, dz, lddz );
}
}
if (*info == 0) {
*m = n;
}
}
/* Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. */
if (*m == 0) {
*info = 0;
if (wantz) {
*(unsigned char *)order = 'B';
} else {
*(unsigned char *)order = 'E';
}
indibl = 1;
indisp = indibl + n;
indiwk = indisp + n;
lapackf77_dstebz(range_, order, &n, &vl, &vu, &il, &iu, &abstol, &rwork[indd], &rwork[inde], m,
&nsplit, &w[1], &iwork[indibl], &iwork[indisp], &rwork[indrwk], &iwork[indiwk], info);
if (wantz) {
lapackf77_zstein(&n, &rwork[indd], &rwork[inde], m, &w[1], &iwork[indibl], &iwork[indisp],
wz, &ldwz, &rwork[indrwk], &iwork[indiwk], &ifail[1], info);
magma_zsetmatrix( n, *m, wz, ldwz, dz, lddz );
/* Apply unitary matrix used in reduction to tridiagonal
form to eigenvectors returned by ZSTEIN. */
magma_zunmtr_gpu(MagmaLeft, uplo, MagmaNoTrans, n, *m, da, ldda, &work[indtau],
dz, lddz, wa, ldwa, &iinfo);
}
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *m;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_dscal(&imax, &d__1, &w[1], &ione);
}
/* If eigenvalues are not in order, then sort them, along with
eigenvectors. */
if (wantz) {
for (j = 1; j <= *m-1; ++j) {
i = 0;
tmp1 = w[j];
for (jj = j + 1; jj <= *m; ++jj) {
if (w[jj] < tmp1) {
i = jj;
tmp1 = w[jj];
}
}
if (i != 0) {
itmp1 = iwork[indibl + i - 1];
w[i] = w[j];
iwork[indibl + i - 1] = iwork[indibl + j - 1];
w[j] = tmp1;
iwork[indibl + j - 1] = itmp1;
magma_zswap(n, dz + (i-1)*lddz, ione, dz + (j-1)*lddz, ione);
if (*info != 0) {
itmp1 = ifail[i];
ifail[i] = ifail[j];
ifail[j] = itmp1;
}
}
}
}
/* Set WORK(1) to optimal complex workspace size. */
work[1] = MAGMA_Z_MAKE( lopt, 0 );
return *info;
} /* magma_zheevx_gpu */
/**
Purpose
-------
ZHEEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
Arguments
---------
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA COMPLEX_16 array, dimension (LDDA, N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, the lower triangle (if UPLO=MagmaLower) or the upper
triangle (if UPLO=MagmaUpper) of A, including the diagonal, is
destroyed.
@param[in]
ldda INTEGER
The leading dimension of the array DA. LDDA >= max(1,N).
@param[in]
vl DOUBLE PRECISION
@param[in]
vu DOUBLE PRECISION
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[in]
abstol DOUBLE PRECISION
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABSTOL + EPS * max( |a|,|b| ),
\n
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.
\n
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO > 0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH('S').
\n
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and
Kahan, LAPACK Working Note #3.
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w DOUBLE PRECISION array, dimension (N)
On normal exit, the first M elements contain the selected
eigenvalues in ascending order.
@param[out]
dZ COMPLEX_16 array, dimension (LDDZ, max(1,M))
If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
If JOBZ = MagmaNoVec, then Z is not referenced.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M
is not known in advance and an upper bound must be used.
********* (workspace) If FAST_HEMV is defined DZ should be (LDDZ, max(1,N)) in both cases.
@param[in]
lddz INTEGER
The leading dimension of the array DZ. LDDZ >= 1, and if
JOBZ = MagmaVec, LDDZ >= max(1,N).
@param
wA (workspace) COMPLEX_16 array, dimension (LDWA, N)
@param[in]
ldwa INTEGER
The leading dimension of the array wA. LDWA >= max(1,N).
@param
wZ (workspace) COMPLEX_16 array, dimension (LDWZ, max(1,M))
@param[in]
ldwz INTEGER
The leading dimension of the array wZ. LDWZ >= 1, and if
JOBZ = MagmaVec, LDWZ >= max(1,N).
@param[out]
work (workspace) COMPLEX_16 array, dimension (LWORK)
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. LWORK >= (NB+1)*N,
where NB is the max of the blocksize for ZHETRD.
\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.
@param
rwork (workspace) DOUBLE PRECISION array, dimension (7*N)
@param
iwork (workspace) INTEGER array, dimension (5*N)
@param[out]
ifail INTEGER array, dimension (N)
If JOBZ = MagmaVec, then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = MagmaNoVec, then IFAIL is not referenced.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.
@ingroup magma_zheev_driver
********************************************************************/
extern "C" magma_int_t
magma_zheevx_gpu(magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex *dA, magma_int_t ldda, double vl, double vu,
magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m,
double *w, magmaDoubleComplex *dZ, magma_int_t lddz,
magmaDoubleComplex *wA, magma_int_t ldwa,
magmaDoubleComplex *wZ, magma_int_t ldwz,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
const char* range_ = lapack_range_const( range );
magma_int_t ione = 1;
const char* order_;
magma_int_t indd, inde;
magma_int_t imax;
magma_int_t lopt, itmp1, indee;
magma_int_t lower, wantz;
magma_int_t i, j, jj, i__1;
magma_int_t alleig, valeig, indeig;
magma_int_t iscale, indibl;
magma_int_t indiwk, indisp, indtau;
magma_int_t indrwk, indwrk;
magma_int_t llwork, nsplit;
magma_int_t lquery;
magma_int_t iinfo;
double safmin;
double bignum;
double smlnum;
double eps, tmp1;
double anrm;
double sigma, d__1;
double rmin, rmax;
double *dwork;
/* Function Body */
lower = (uplo == MagmaLower);
wantz = (jobz == MagmaVec);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1);
*info = 0;
if (! (wantz || (jobz == MagmaNoVec))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (ldda < max(1,n)) {
*info = -6;
} else if (lddz < 1 || (wantz && lddz < n)) {
*info = -15;
} else if (ldwa < max(1,n)) {
*info = -17;
} else if (ldwz < 1 || (wantz && ldwz < n)) {
*info = -19;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -8;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -9;
} else if (iu < min(n,il) || iu > n) {
*info = -10;
}
}
}
magma_int_t nb = magma_get_zhetrd_nb(n);
lopt = n * (nb + 1);
work[0] = MAGMA_Z_MAKE( lopt, 0 );
if (lwork < lopt && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
*m = 0;
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb);
printf("--------------------------------------------------------------\n");
#endif
magmaDoubleComplex *a;
magma_zmalloc_cpu( &a, n*n );
magma_zgetmatrix(n, n, dA, ldda, a, n);
lapackf77_zheevx(jobz_, range_, uplo_,
&n, a, &n, &vl, &vu, &il, &iu, &abstol, m,
w, wZ, &ldwz, work, &lwork,
rwork, iwork, ifail, info);
magma_zsetmatrix( n, n, a, n, dA, ldda);
magma_zsetmatrix( n, *m, wZ, ldwz, dZ, lddz);
magma_free_cpu(a);
return *info;
}
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, n )) {
fprintf (stderr, "!!!! device memory allocation error (magma_zheevx_gpu)\n");
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
--w;
--work;
--rwork;
--iwork;
--ifail;
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = magmablas_zlanhe(MagmaMaxNorm, uplo, n, dA, ldda, dwork);
iscale = 0;
sigma = 1;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
d__1 = 1.;
magmablas_zlascl(uplo, 0, 0, 1., sigma, n, n, dA,
ldda, info);
if (abstol > 0.) {
abstol *= sigma;
}
if (valeig) {
vl *= sigma;
vu *= sigma;
}
}
/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
indd = 1;
inde = indd + n;
indrwk = inde + n;
indtau = 1;
indwrk = indtau + n;
llwork = lwork - indwrk + 1;
#ifdef FAST_HEMV
magma_zhetrd2_gpu(uplo, n, dA, ldda, &rwork[indd], &rwork[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork, dZ, lddz*n, &iinfo);
#else
magma_zhetrd_gpu (uplo, n, dA, ldda, &rwork[indd], &rwork[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork, &iinfo);
#endif
lopt = n + (magma_int_t)MAGMA_Z_REAL(work[indwrk]);
/* If all eigenvalues are desired and ABSTOL is less than or equal to
zero, then call DSTERF or ZUNGTR and ZSTEQR. If this fails for
some eigenvalue, then try DSTEBZ. */
if ((alleig || (indeig && il == 1 && iu == n)) && abstol <= 0.) {
blasf77_dcopy(&n, &rwork[indd], &ione, &w[1], &ione);
indee = indrwk + 2*n;
if (! wantz) {
i__1 = n - 1;
blasf77_dcopy(&i__1, &rwork[inde], &ione, &rwork[indee], &ione);
lapackf77_dsterf(&n, &w[1], &rwork[indee], info);
}
else {
lapackf77_zlacpy("A", &n, &n, wA, &ldwa, wZ, &ldwz);
lapackf77_zungtr(uplo_, &n, wZ, &ldwz, &work[indtau], &work[indwrk], &llwork, &iinfo);
i__1 = n - 1;
blasf77_dcopy(&i__1, &rwork[inde], &ione, &rwork[indee], &ione);
lapackf77_zsteqr(jobz_, &n, &w[1], &rwork[indee], wZ, &ldwz, &rwork[indrwk], info);
if (*info == 0) {
for (i = 1; i <= n; ++i) {
ifail[i] = 0;
}
magma_zsetmatrix( n, n, wZ, ldwz, dZ, lddz );
}
}
if (*info == 0) {
*m = n;
}
}
/* Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. */
if (*m == 0) {
*info = 0;
if (wantz) {
order_ = "B";
} else {
order_ = "E";
}
indibl = 1;
indisp = indibl + n;
indiwk = indisp + n;
lapackf77_dstebz(range_, order_, &n, &vl, &vu, &il, &iu, &abstol, &rwork[indd], &rwork[inde], m,
&nsplit, &w[1], &iwork[indibl], &iwork[indisp], &rwork[indrwk], &iwork[indiwk], info);
if (wantz) {
lapackf77_zstein(&n, &rwork[indd], &rwork[inde], m, &w[1], &iwork[indibl], &iwork[indisp],
wZ, &ldwz, &rwork[indrwk], &iwork[indiwk], &ifail[1], info);
magma_zsetmatrix( n, *m, wZ, ldwz, dZ, lddz );
/* Apply unitary matrix used in reduction to tridiagonal
form to eigenvectors returned by ZSTEIN. */
magma_zunmtr_gpu(MagmaLeft, uplo, MagmaNoTrans, n, *m, dA, ldda, &work[indtau],
dZ, lddz, wA, ldwa, &iinfo);
}
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *m;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_dscal(&imax, &d__1, &w[1], &ione);
}
/* If eigenvalues are not in order, then sort them, along with
eigenvectors. */
if (wantz) {
for (j = 1; j <= *m-1; ++j) {
i = 0;
tmp1 = w[j];
for (jj = j + 1; jj <= *m; ++jj) {
if (w[jj] < tmp1) {
i = jj;
tmp1 = w[jj];
}
}
if (i != 0) {
itmp1 = iwork[indibl + i - 1];
w[i] = w[j];
iwork[indibl + i - 1] = iwork[indibl + j - 1];
w[j] = tmp1;
iwork[indibl + j - 1] = itmp1;
magma_zswap(n, dZ + (i-1)*lddz, ione, dZ + (j-1)*lddz, ione);
if (*info != 0) {
itmp1 = ifail[i];
ifail[i] = ifail[j];
ifail[j] = itmp1;
}
}
}
}
/* Set WORK[0] to optimal complex workspace size. */
work[1] = MAGMA_Z_MAKE( lopt, 0 );
return *info;
} /* magma_zheevx_gpu */
