/**
Purpose
-------
ZHEGVDX_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
It uses a two-stage algorithm for the tridiagonalization.
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
---------
@param[in]
itype INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
@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 triangles of A and B are stored;
- = MagmaLower: Lower triangles of A and B are stored.
@param[in]
n INTEGER
The order of the matrices A and B. N >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA, 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.
\n
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper)
or the lower triangle (if UPLO=MagmaLower) of A, including the
diagonal, is destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B COMPLEX_16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
\n
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= 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[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)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + N * (NB + 1).
If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store the Q2 matrix
and is returned by magma_bulge_get_lq2.
\n
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.
@param[out]
rwork (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\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.
If N <= 1, LIWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\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[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: ZPOTRF or ZHEEVD returned an error code:
<= N: if INFO = i and JOBZ = MagmaNoVec, 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 = MagmaVec, 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);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of 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
Modified so that no backsubstitution is performed if ZHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.
@ingroup magma_zhegv_driver
********************************************************************/
extern "C" magma_int_t
magma_zhegvdx_2stage(magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *B, magma_int_t ldb,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex *dA;
magmaDoubleComplex *dB;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t lwmin;
magma_int_t liwmin;
magma_int_t lrwmin;
magma_queue_t stream;
magma_queue_create( &stream );
/* determine the number of threads */
magma_int_t parallel_threads = magma_get_parallel_numthreads();
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || (jobz == MagmaNoVec))) {
*info = -3;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_get_zbulge_nb(n, parallel_threads);
magma_int_t lq2 = magma_zbulge_get_lq2(n, parallel_threads);
if (wantz) {
lwmin = lq2 + 2 * n + n * n;
lrwmin = 1 + 5 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_dlamch("Epsilon");
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (lrwork < lrwmin && ! lquery) {
*info = -19;
} else if (liwork < liwmin && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
/* 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
lapackf77_zhegvd(&itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork, info);
*m = n;
return *info;
}
// TODO: fix memory leak
if (MAGMA_SUCCESS != magma_zmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &dB, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_zsetmatrix( n, n, B, ldb, dB, lddb );
magma_zsetmatrix_async( n, n,
A, lda,
dA, ldda, stream );
magma_timer_t time=0;
timer_start( time );
magma_zpotrf_gpu(uplo, n, dB, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time zpotrf_gpu = %6.2f\n", time );
magma_queue_sync( stream );
magma_zgetmatrix_async( n, n,
dB, lddb,
B, ldb, stream );
/* Transform problem to standard eigenvalue problem and solve. */
timer_start( time );
magma_zhegst_gpu(itype, uplo, n, dA, ldda, dB, lddb, info);
timer_stop( time );
timer_printf( "time zhegst_gpu = %6.2f\n", time );
magma_zgetmatrix( n, n, dA, ldda, A, lda );
magma_queue_sync( stream );
magma_free( dA );
magma_free( dB );
timer_start( time );
magma_zheevdx_2stage(jobz, range, uplo, n, A, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info);
timer_stop( time );
timer_printf( "time zheevdx_2stage = %6.2f\n", time );
if (wantz && *info == 0) {
// TODO fix memory leak
if (MAGMA_SUCCESS != magma_zmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &dB, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
timer_start( time );
magma_zsetmatrix( n, *m, A, lda, dA, ldda );
magma_zsetmatrix( n, n, B, ldb, dB, lddb );
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
trans = MagmaConjTrans;
} else {
trans = MagmaNoTrans;
}
magma_ztrsm(MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dA, ldda);
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
trans = MagmaNoTrans;
} else {
trans = MagmaConjTrans;
}
magma_ztrmm(MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dA, ldda);
}
magma_zgetmatrix( n, *m, dA, ldda, A, lda );
timer_stop( time );
timer_printf( "time trsm/mm + getmatrix = %6.2f\n", time );
magma_free( dA );
magma_free( dB );
}
magma_queue_destroy( stream );
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
return *info;
} /* magma_zhegvdx_2stage */
/**
Purpose
-------
ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian 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
---------
@param[in]
itype INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangles of A and B are stored;
- = MagmaLower: Lower triangles of A and B are stored.
@param[in]
n INTEGER
The order of the matrices A and B. N >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA, 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.
\n
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper)
or the lower triangle (if UPLO=MagmaLower) of A, including the
diagonal, is destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B COMPLEX_16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
\n
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[out]
w DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
NB can be obtained through magma_get_zhetrd_nb(N).
\n
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.
@param[out]
rwork (workspace) DOUBLE PRECISION array, dimension (LRWORK)
On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\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[0] returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\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[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: ZPOTRF or ZHEEVD returned an error code:
<= N: if INFO = i and JOBZ = MagmaNoVec, 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 = MagmaVec, 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);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of 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
Modified so that no backsubstitution is performed if ZHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.
@ingroup magma_zhegv_driver
********************************************************************/
extern "C" magma_int_t
magma_zhegvd(magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *B, magma_int_t ldb,
double *w, magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex *da;
magmaDoubleComplex *db;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz;
magma_int_t lquery;
magma_int_t lwmin;
magma_int_t liwmin;
magma_int_t lrwmin;
magma_queue_t stream;
magma_queue_create( &stream );
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (wantz || (jobz == MagmaNoVec))) {
*info = -2;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (lda < max(1,n)) {
*info = -6;
} else if (ldb < max(1,n)) {
*info = -8;
}
magma_int_t nb = magma_get_zhetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( n + n*nb, 2*n + n*n );
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_dlamch("Epsilon");
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -11;
} else if (lrwork < lrwmin && ! lquery) {
*info = -13;
} else if (liwork < liwmin && ! lquery) {
*info = -15;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
/* 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
lapackf77_zhegvd(&itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork, info);
return *info;
}
// TODO fix memory leak
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_zsetmatrix( n, n, B, ldb, db, lddb );
magma_zsetmatrix_async( n, n,
A, lda,
da, ldda, stream );
magma_timer_t time=0;
timer_start( time );
magma_zpotrf_gpu(uplo, n, db, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time zpotrf_gpu = %6.2f\n", time );
magma_queue_sync( stream );
magma_zgetmatrix_async( n, n,
db, lddb,
B, ldb, stream );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_zhegst_gpu(itype, uplo, n, da, ldda, db, lddb, info);
timer_stop( time );
timer_printf( "time zhegst_gpu = %6.2f\n", time );
/* simple fix to be able to run bigger size.
* need to have a dwork here that will be used
* a db and then passed to dsyevd.
* */
if (n > 5000) {
magma_queue_sync( stream );
magma_free( db );
}
timer_start( time );
magma_zheevd_gpu(jobz, uplo, n, da, ldda, w, A, lda,
work, lwork, rwork, lrwork, iwork, liwork, info);
timer_stop( time );
timer_printf( "time zheevd_gpu = %6.2f\n", time );
if (wantz && *info == 0) {
timer_start( time );
/* allocate and copy db back */
if (n > 5000) {
if (MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb ) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zsetmatrix( n, n, B, ldb, db, lddb );
}
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
trans = MagmaConjTrans;
} else {
trans = MagmaNoTrans;
}
magma_ztrsm(MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, c_one, db, lddb, da, ldda);
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
trans = MagmaNoTrans;
} else {
trans = MagmaConjTrans;
}
magma_ztrmm(MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, c_one, db, lddb, da, ldda);
}
magma_zgetmatrix( n, n, da, ldda, A, lda );
/* free db */
if (n > 5000) {
magma_free( db );
}
timer_stop( time );
timer_printf( "time ztrsm/mm + getmatrix = %6.2f\n", time );
}
magma_queue_sync( stream );
magma_queue_destroy( stream );
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
magma_free( da );
if (n <= 5000) {
magma_free( db );
}
return *info;
} /* magma_zhegvd */
extern "C" magma_int_t
magma_zhegvdx_2stage(magma_int_t itype, char jobz, char range, char uplo, magma_int_t n,
magmaDoubleComplex *a, magma_int_t lda,
magmaDoubleComplex *b, magma_int_t ldb,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
ZHEGVDX_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
It uses a two-stage algorithm for the tridiagonalization.
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
=========
ITYPE (input) INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
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.
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.
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
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
or the lower triangle (if UPLO='L') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) COMPLEX_16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = 'U', the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = 'L',
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= 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'.
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)
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 >= 1.
If JOBZ = 'N' and N > 1, LWORK >= LQ2 + N * (NB + 1).
If JOBZ = 'V' and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store
the Q2 matrix and is returned by
MAGMA_BULGE_GET_LQ2.
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 (MAX(1,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 >= 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 the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = 'N' and 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: ZPOTRF or ZHEEVD returned an error code:
<= N: 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);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of 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
Modified so that no backsubstitution is performed if ZHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
char range_[2] = {range, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex *da;
magmaDoubleComplex *db;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lower;
char trans[1];
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
// magma_int_t lopt;
magma_int_t lwmin;
// magma_int_t liopt;
magma_int_t liwmin;
// magma_int_t lropt;
magma_int_t lrwmin;
magma_queue_t stream;
magma_queue_create( &stream );
/* determine the number of threads */
magma_int_t threads = magma_get_numthreads();
magma_setlapack_numthreads(threads);
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
lquery = lwork == -1 || lrwork == -1 || liwork == -1;
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -3;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_get_zbulge_nb(n, threads);
magma_int_t lq2 = magma_zbulge_get_lq2(n, threads);
if (wantz) {
lwmin = lq2 + 2 * n + n * n;
lrwmin = 1 + 5 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
lrwmin = n;
liwmin = 1;
}
work[0] = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (lrwork < lrwmin && ! lquery) {
*info = -19;
} else if (liwork < liwmin && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
/* 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
lapackf77_zhegvd(&itype, jobz_, uplo_,
&n, a, &lda, b, &ldb,
w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork, info);
*m = n;
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_zsetmatrix( n, n, b, ldb, db, lddb );
magma_zsetmatrix_async( n, n,
a, lda,
da, ldda, stream );
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
magma_zpotrf_gpu(uplo_[0], n, db, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zpotrf_gpu = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_queue_sync( stream );
magma_zgetmatrix_async( n, n,
db, lddb,
b, ldb, stream );
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
/* Transform problem to standard eigenvalue problem and solve. */
magma_zhegst_gpu(itype, uplo, n, da, ldda, db, lddb, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zhegst_gpu = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_zgetmatrix( n, n, da, ldda, a, lda );
magma_queue_sync( stream );
magma_free( da );
magma_free( db );
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
magma_zheevdx_2stage(jobz, range, uplo, n, a, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zheevdx_2stage = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
if (wantz && *info == 0) {
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
magma_zsetmatrix( n, *m, a, lda, da, ldda );
magma_zsetmatrix( n, n, b, ldb, db, lddb );
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
*(unsigned char *)trans = MagmaConjTrans;
} else {
*(unsigned char *)trans = MagmaNoTrans;
}
magma_ztrsm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, da, ldda);
} else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
*(unsigned char *)trans = MagmaNoTrans;
} else {
*(unsigned char *)trans = MagmaConjTrans;
}
magma_ztrmm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, da, ldda);
}
magma_zgetmatrix( n, *m, da, ldda, a, lda );
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time trsm/mm + getmatrix = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_free( da );
magma_free( db );
}
magma_queue_destroy( stream );
work[0] = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
iwork[0] = liwmin;
return *info;
} /* zhegvdx_2stage */
extern "C" magma_int_t
magma_zhegvx(magma_int_t itype, char jobz, char range, char uplo, magma_int_t n,
magmaDoubleComplex *a, magma_int_t lda, magmaDoubleComplex *b, magma_int_t ldb,
double vl, double vu, magma_int_t il, magma_int_t iu, double abstol,
magma_int_t *m, double *w, magmaDoubleComplex *z, magma_int_t ldz,
magmaDoubleComplex *work, magma_int_t lwork, double *rwork,
magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZHEGVX computes selected eigenvalues, and optionally, eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
Arguments
=========
ITYPE (input) INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
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 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.
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, 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).
B (input/output) COMPLEX_16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = 'U', the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = 'L',
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= 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').
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)
The first M elements contain the selected
eigenvalues in ascending order.
Z (output) COMPLEX_16 array, dimension (LDZ, max(1,M))
If JOBZ = 'N', then Z is not referenced.
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).
The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = 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.
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.
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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,2*N).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for ZHETRD returned by ILAENV.
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: ZPOTRF or ZHEEVX returned an error code:
<= N: if INFO = i, ZHEEVX failed to converge;
i eigenvectors failed to converge. Their indices
are stored in array IFAIL.
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of 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
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
char range_[2] = {range, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex *da;
magmaDoubleComplex *db;
magmaDoubleComplex *dz;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lddz = n;
magma_int_t lower;
char trans[1];
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t lwmin;
magma_queue_t stream;
magma_queue_create( &stream );
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
lquery = lwork == -1;
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -3;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else if (ldz < 1 || (wantz && ldz < n)) {
*info = -18;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_get_zhetrd_nb(n);
lwmin = n * (nb + 1);
MAGMA_Z_SET2REAL(work[0],(double)lwmin);
if (lwork < lwmin && ! lquery) {
*info = -20;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb ) ||
MAGMA_SUCCESS != magma_zmalloc( &dz, n*lddz )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_zsetmatrix( n, n, b, ldb, db, lddb );
magma_zsetmatrix_async( n, n,
a, lda,
da, ldda, stream );
magma_zpotrf_gpu(uplo_[0], n, db, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
magma_queue_sync( stream );
magma_zgetmatrix_async( n, n,
db, lddb,
b, ldb, stream );
/* Transform problem to standard eigenvalue problem and solve. */
magma_zhegst_gpu(itype, uplo, n, da, ldda, db, lddb, info);
magma_zheevx_gpu(jobz, range, uplo, n, da, ldda, vl, vu, il, iu, abstol, m, w, dz, lddz, a, lda, z, ldz, work, lwork, rwork, iwork, ifail, info);
if (wantz && *info == 0) {
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
*(unsigned char *)trans = MagmaConjTrans;
} else {
*(unsigned char *)trans = MagmaNoTrans;
}
magma_ztrsm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, dz, lddz);
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
*(unsigned char *)trans = MagmaNoTrans;
} else {
*(unsigned char *)trans = MagmaConjTrans;
}
magma_ztrmm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, dz, lddz);
}
magma_zgetmatrix( n, *m, dz, lddz, z, ldz );
}
magma_queue_sync( stream );
magma_queue_destroy( stream );
magma_free( da );
magma_free( db );
magma_free( dz );
return *info;
} /* zhegvx */
