extern "C" magma_int_t
magma_chegvdx_m(magma_int_t nrgpu, magma_int_t itype, char jobz, char range, char uplo, magma_int_t n,
magmaFloatComplex *a, magma_int_t lda, magmaFloatComplex *b, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork,
float *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CHEGVD 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
=========
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 >= N + 1.
If JOBZ = 'V' and N > 1, LWORK >= 2*N*nb + N**2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
RWORK (workspace/output) DOUBLE PRECISION array, dimension (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: CPOTRF or CHEEVD 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 CHEEVD 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};
magmaFloatComplex c_one = MAGMA_C_ONE;
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_int_t liwmin;
magma_int_t lrwmin;
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_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = 2*n + n*n;
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
work[0] = MAGMA_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_slamch("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_chegvd(&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;
}
//
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
magma_cpotrf_m(nrgpu, uplo_[0], n, b, ldb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time cpotrf = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
/* Transform problem to standard eigenvalue problem and solve. */
magma_chegst_m(nrgpu, itype, uplo_[0], n, a, lda, b, ldb, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time chegst = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
magma_cheevdx_m(nrgpu, 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 cheevd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
if (wantz && *info == 0)
{
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
/* 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_ctrsm_m(nrgpu, MagmaLeft, uplo_[0], *trans, MagmaNonUnit,
n, *m, c_one, b, ldb, a, lda);
}
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_ctrmm(MagmaLeft, uplo_[0], *trans, MagmaNonUnit,
// n, n, c_one, db, lddb, da, ldda);
}
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time setmatrices trsm/mm + getmatrices = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
}
work[0] = MAGMA_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_slamch("Epsilon"));
iwork[0] = liwmin;
return *info;
} /* magma_chegvd_m */
/**
Purpose
-------
CPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix A. This version does not require work
space on the GPU passed as input. GPU memory is allocated in the
routine.
The factorization has the form
A = U**H * U, if uplo = MagmaUpper, or
A = L * L**H, if uplo = MagmaLower,
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
This uses multiple queues to overlap communication and computation.
Arguments
---------
@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]
A COMPLEX 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, and the strictly lower
triangular part of A is not referenced. If uplo = MagmaLower, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H * U or A = L * L**H.
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_cposv_comp
********************************************************************/
extern "C" magma_int_t
magma_cpotrf(
magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
magma_int_t *info )
{
#define A(i_, j_) (A + (i_) + (j_)*lda)
#ifdef HAVE_clBLAS
#define dA(i_, j_) dA, ((i_) + (j_)*ldda)
#else
#define dA(i_, j_) (dA + (i_) + (j_)*ldda)
#endif
/* Constants */
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
const float d_one = 1.0;
const float d_neg_one = -1.0;
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
bool upper = (uplo == MagmaUpper);
magma_int_t j, jb, ldda, nb;
magmaFloatComplex_ptr dA = NULL;
/* Check arguments */
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return */
if ( n == 0 )
return *info;
nb = magma_get_cpotrf_nb( n );
if (nb <= 1 || nb >= n) {
lapackf77_cpotrf( uplo_, &n, A, &lda, info );
}
else {
/* Use hybrid blocked code. */
ldda = magma_roundup( n, 32 );
magma_int_t ngpu = magma_num_gpus();
if ( ngpu > 1 ) {
/* call multi-GPU non-GPU-resident interface */
return magma_cpotrf_m( ngpu, uplo, n, A, lda, info );
}
if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda )) {
/* alloc failed so call the non-GPU-resident version */
return magma_cpotrf_m( ngpu, uplo, n, A, lda, info );
}
magma_queue_t queues[2] = { NULL, NULL };
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
if (upper) {
/* Compute the Cholesky factorization A = U'*U. */
for (j=0; j < n; j += nb) {
/* Update and factorize the current diagonal block and test
for non-positive-definiteness. */
jb = min( nb, n-j );
magma_csetmatrix_async( jb, n-j,
A(j, j), lda,
dA(j, j), ldda, queues[1] );
magma_cherk( MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dA(0, j), ldda,
d_one, dA(j, j), ldda, queues[1] );
magma_queue_sync( queues[1] );
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
A(j, j), lda, queues[0] );
if (j+jb < n) {
magma_cgemm( MagmaConjTrans, MagmaNoTrans,
jb, n-j-jb, j,
c_neg_one, dA(0, j ), ldda,
dA(0, j+jb), ldda,
c_one, dA(j, j+jb), ldda, queues[1] );
}
magma_queue_sync( queues[0] );
// this could be on any queue; it isn't needed until exit.
magma_cgetmatrix_async( j, jb,
dA(0, j), ldda,
A(0, j), lda, queues[0] );
lapackf77_cpotrf( MagmaUpperStr, &jb, A(j, j), &lda, info );
if (*info != 0) {
*info = *info + j;
break;
}
magma_csetmatrix_async( jb, jb,
A(j, j), lda,
dA(j, j), ldda, queues[0] );
magma_queue_sync( queues[0] );
if (j+jb < n) {
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, n-j-jb,
c_one, dA(j, j ), ldda,
dA(j, j+jb), ldda, queues[1] );
}
}
}
else {
//=========================================================
// Compute the Cholesky factorization A = L*L'.
for (j=0; j < n; j += nb) {
// Update and factorize the current diagonal block and test
// for non-positive-definiteness.
jb = min( nb, n-j );
magma_csetmatrix_async( n-j, jb,
A(j, j), lda,
dA(j, j), ldda, queues[1] );
magma_cherk( MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dA(j, 0), ldda,
d_one, dA(j, j), ldda, queues[1] );
magma_queue_sync( queues[1] );
magma_cgetmatrix_async( jb, jb,
dA(j,j), ldda,
A(j,j), lda, queues[0] );
if (j+jb < n) {
magma_cgemm( MagmaNoTrans, MagmaConjTrans,
n-j-jb, jb, j,
c_neg_one, dA(j+jb, 0), ldda,
dA(j, 0), ldda,
c_one, dA(j+jb, j), ldda, queues[1] );
}
magma_queue_sync( queues[0] );
// this could be on any queue; it isn't needed until exit.
magma_cgetmatrix_async( jb, j,
dA(j, 0), ldda,
A(j, 0), lda, queues[0] );
lapackf77_cpotrf( MagmaLowerStr, &jb, A(j, j), &lda, info );
if (*info != 0) {
*info = *info + j;
break;
}
magma_csetmatrix_async( jb, jb,
A(j, j), lda,
dA(j, j), ldda, queues[0] );
magma_queue_sync( queues[0] );
if (j+jb < n) {
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
n-j-jb, jb,
c_one, dA(j, j), ldda,
dA(j+jb, j), ldda, queues[1] );
}
}
}
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
}
return *info;
} /* magma_cpotrf */
/**
Purpose
-------
CHEGVD 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]
nrgpu INTEGER
Number of GPUs to use.
@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 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 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 REAL
@param[in]
vu REAL
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 REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX 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 >= N + 1.
If JOBZ = MagmaVec and N > 1, LWORK >= 2*N*nb + N**2.
\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) REAL 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: CPOTRF or CHEEVD 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 CHEEVD 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_chegv_driver
********************************************************************/
extern "C" magma_int_t
magma_chegvdx_m(magma_int_t nrgpu, magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w, magmaFloatComplex *work, magma_int_t lwork,
float *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 );
magmaFloatComplex c_one = MAGMA_C_ONE;
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;
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_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = 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_slamch("Epsilon");
work[0] = MAGMA_C_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_chegvd(&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;
}
magma_timer_t time=0;
timer_start( time );
magma_cpotrf_m(nrgpu, uplo, n, B, ldb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf("time cpotrf = %6.2f\n", time );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_chegst_m(nrgpu, itype, uplo, n, A, lda, B, ldb, info);
timer_stop( time );
timer_printf( "time chegst = %6.2f\n", time );
timer_start( time );
magma_cheevdx_m(nrgpu, 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 cheevd = %6.2f\n", time );
if (wantz && *info == 0) {
timer_start( time );
/* 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_ctrsm_m(nrgpu, MagmaLeft, uplo, trans, MagmaNonUnit,
n, *m, c_one, B, ldb, A, lda);
}
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_ctrmm(MagmaLeft, uplo, trans, MagmaNonUnit,
// n, n, c_one, db, lddb, da, ldda);
}
timer_stop( time );
timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time );
}
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
return *info;
} /* magma_chegvd_m */
/**
Purpose
-------
CHEGVD 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]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@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 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 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 REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX 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_chetrd_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) REAL array, dimension (MAX(1,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: CPOTRF or CHEEVD 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 CHEEVD 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_chegv_driver
********************************************************************/
extern "C" magma_int_t
magma_chegvd_m(
magma_int_t ngpu,
magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *B, magma_int_t ldb,
float *w, magmaFloatComplex *work, magma_int_t lwork,
#ifdef COMPLEX
float *rwork, magma_int_t lrwork,
#endif
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 );
magmaFloatComplex c_one = MAGMA_C_ONE;
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;
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_chetrd_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;
}
work[0] = magma_cmake_lwork( lwmin );
rwork[0] = magma_smake_lwork( lrwmin );
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;
}
/* If matrix is very small, then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
lapackf77_chegvd( &itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork, info);
return *info;
}
magma_timer_t time=0;
timer_start( time );
magma_cpotrf_m( ngpu, uplo, n, B, ldb, info );
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time cpotrf = %6.2f\n", time );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_chegst_m( ngpu, itype, uplo, n, A, lda, B, ldb, info );
timer_stop( time );
timer_printf( "time chegst = %6.2f\n", time );
timer_start( time );
magma_cheevd_m( ngpu, jobz, uplo, n, A, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info );
timer_stop( time );
timer_printf( "time cheevd = %6.2f\n", time );
if (wantz && *info == 0) {
timer_start( time );
/* 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_ctrsm_m( ngpu, MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, c_one, B, ldb, A, lda );
}
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;
}
#ifdef ENABLE_DEBUG
printf("--- the multi GPU version is falling back to 1 GPU to perform the last TRMM since there is no TRMM_mgpu --- \n");
#endif
magmaFloatComplex *dA=NULL, *dB=NULL;
magma_int_t ldda = magma_roundup( n, 32 );
magma_int_t lddb = ldda;
if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_cmalloc( &dB, n*lddb )) {
magma_free( dA );
magma_free( dB );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
magma_csetmatrix( n, n, B, ldb, dB, lddb, queue );
magma_csetmatrix( n, n, A, lda, dA, ldda, queue );
magma_ctrmm( MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, c_one, dB, lddb, dA, ldda, queue );
magma_cgetmatrix( n, n, dA, ldda, A, lda, queue );
magma_queue_destroy( queue );
magma_free( dA );
magma_free( dB );
}
timer_stop( time );
timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time );
}
work[0] = magma_cmake_lwork( lwmin );
rwork[0] = magma_smake_lwork( lrwmin );
iwork[0] = liwmin;
return *info;
} /* magma_chegvd_m */