extern "C" magma_int_t
magma_ssygvd_m(magma_int_t nrgpu, magma_int_t itype, char jobz, char uplo, magma_int_t n,
float *a, magma_int_t lda, float *b, magma_int_t ldb,
float *w, float *work, magma_int_t lwork,
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
=======
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-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 symmetric 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
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 symmetric 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**T * B * Z = I;
if ITYPE = 3, Z**T * 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 symmetric 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**T * U or B = L * L**T.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
W (output) REAL 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) REAL 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: SPOTRF or SSYEVD 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 SSYEVD 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};
float d_one = MAGMA_S_ONE;
magma_int_t lower;
char trans[1];
magma_int_t wantz;
magma_int_t lquery;
magma_int_t lwmin;
magma_int_t liwmin;
magma_queue_t stream;
magma_queue_create( &stream );
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
lquery = lwork == -1 || liwork == -1;
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -2;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*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_ssytrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = 1 + 6*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = 2*n + n*nb;
liwmin = 1;
}
work[0] = lwmin * (1. + lapackf77_slamch("Epsilon")); // round up
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -11;
} else if (liwork < liwmin && ! lquery) {
*info = -13;
}
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_ssygvd(&itype, jobz_, uplo_,
&n, a, &lda, b, &ldb,
w, work, &lwork,
iwork, &liwork, info);
return *info;
}
//
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
magma_spotrf_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 spotrf = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
/* Transform problem to standard eigenvalue problem and solve. */
magma_ssygst_m(nrgpu, itype, uplo_[0], n, a, lda, b, ldb, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time ssygst = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
magma_ssyevd_m(nrgpu, jobz_[0], uplo_[0], n, a, lda, w, work, lwork, iwork, liwork, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time ssyevd = %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 = MagmaTrans;
} else {
*(unsigned char *)trans = MagmaNoTrans;
}
magma_strsm_m(nrgpu, MagmaLeft, uplo, *trans, MagmaNonUnit,
n, n, d_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 = MagmaTrans;
}
//magma_strmm(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] = lwmin * (1. + lapackf77_slamch("Epsilon")); // round up
iwork[0] = liwmin;
return *info;
} /* magma_ssygvd_m */
/**
Purpose
-------
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-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 symmetric 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 REAL array, dimension (LDA, N)
On entry, the symmetric 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**T * B * Z = I;
if ITYPE = 3, Z**T * 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 REAL array, dimension (LDB, N)
On entry, the symmetric 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**T * U or B = L * L**T.
@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) REAL 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 >= 2*N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ).
NB can be obtained through magma_get_ssytrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK 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 and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK 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: SPOTRF or SSYEVD 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 SSYEVD 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_ssygv_driver
********************************************************************/
extern "C" magma_int_t
magma_ssygvd_m(
magma_int_t ngpu,
magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n,
float *A, magma_int_t lda,
float *B, magma_int_t ldb,
float *w, float *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 );
float d_one = MAGMA_S_ONE;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz, lquery;
magma_int_t lwmin, liwmin;
magma_queue_t stream;
magma_queue_create( &stream );
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -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_ssytrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n );
liwmin = 3 + 5*n;
}
else {
lwmin = 2*n + n*nb;
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] = lwmin * one_eps;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -11;
} else if (liwork < liwmin && ! lquery) {
*info = -13;
}
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_ssygvd( &itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
iwork, &liwork, info );
return *info;
}
magma_timer_t time=0;
timer_start( time );
magma_spotrf_m( ngpu, uplo, n, B, ldb, info );
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time spotrf = %6.2f\n", time );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_ssygst_m( ngpu, itype, uplo, n, A, lda, B, ldb, info );
timer_stop( time );
timer_printf( "time ssygst = %6.2f\n", time );
timer_start( time );
magma_ssyevd_m( ngpu, jobz, uplo, n, A, lda, w, work, lwork, iwork, liwork, info );
timer_stop( time );
timer_printf( "time ssyevd = %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 = MagmaTrans;
} else {
trans = MagmaNoTrans;
}
magma_strsm_m( ngpu, MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, d_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 = MagmaTrans;
}
printf("--- the multi GPU version is falling back to 1 GPU to perform the last TRMM since there is no TRMM_mgpu --- \n");
float *dA=NULL, *dB=NULL;
magma_int_t ldda = roundup( n, 32 );
magma_int_t lddb = ldda;
if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_smalloc( &dB, n*lddb ) ) {
magma_free( dA );
magma_free( dB );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_ssetmatrix( n, n, B, ldb, dB, lddb );
magma_ssetmatrix( n, n, A, lda, dA, ldda );
magma_strmm( MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, d_one, dB, lddb, dA, ldda );
magma_sgetmatrix( n, n, dA, ldda, A, lda );
magma_free( dA );
magma_free( dB );
}
timer_stop( time );
timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time );
}
work[0] = lwmin * one_eps; // round up
iwork[0] = liwmin;
return *info;
} /* magma_ssygvd_m */
/**
Purpose
-------
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-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 symmetric 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]
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]
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 REAL array, dimension (LDA, N)
On entry, the symmetric 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**T*B*Z = I;
if ITYPE = 3, Z**T*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 REAL array, dimension (LDB, N)
On entry, the symmetric 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**T*U or B = L*L**T.
@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) REAL 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 >= 2*N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ).
NB can be obtained through magma_get_ssytrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message
related to LWORK 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
and IWORK arrays, returns these values as the first entries
of the WORK and IWORK arrays, and no error message
related to LWORK 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: SPOTRF or SSYEVD 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 SSYEVD 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_ssygv_driver
********************************************************************/
extern "C" magma_int_t
magma_ssygvdx_m(
magma_int_t ngpu,
magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
float *A, magma_int_t lda,
float *B, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
float *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)
{
/* Constants */
float c_one = MAGMA_S_ONE;
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
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;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -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_ssytrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n );
liwmin = 3 + 5*n;
}
else {
lwmin = 2*n + n*nb;
liwmin = 1;
}
work[0] = magma_smake_lwork( lwmin );
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (liwork < liwmin && ! lquery) {
*info = -19;
}
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_ssygvd(&itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
iwork, &liwork, info);
*m = n;
return *info;
}
magma_timer_t time=0;
timer_start( time );
magma_spotrf_m(ngpu, uplo, n, B, ldb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time spotrf = %6.2f\n", time );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_ssygst_m(ngpu, itype, uplo, n, A, lda, B, ldb, info);
timer_stop( time );
timer_printf( "time ssygst = %6.2f\n", time );
timer_start( time );
magma_ssyevdx_m(ngpu, jobz, range, uplo, n, A, lda, vl, vu, il, iu, m, w, work, lwork, iwork, liwork, info);
timer_stop( time );
timer_printf( "time ssyevd = %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 = MagmaTrans;
} else {
trans = MagmaNoTrans;
}
magma_strsm_m( ngpu, 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 = MagmaTrans;
}
#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
float *dA=NULL, *dB=NULL;
magma_int_t ldda = magma_roundup( n, 32 );
magma_int_t lddb = ldda;
if (MAGMA_SUCCESS != magma_smalloc( &dA, ldda*(*m) ) ||
MAGMA_SUCCESS != magma_smalloc( &dB, lddb*n ) ) {
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_ssetmatrix( n, n, B, ldb, dB, lddb, queue );
magma_ssetmatrix( n, (*m), A, lda, dA, ldda, queue );
magma_strmm( MagmaLeft, uplo, trans, MagmaNonUnit,
n, (*m), c_one, dB, lddb, dA, ldda, queue );
magma_sgetmatrix( n, (*m), 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_smake_lwork( lwmin );
iwork[0] = liwmin;
return *info;
} /* magma_ssygvd_m */
extern "C" magma_int_t
magma_slobpcg( magma_s_sparse_matrix A, magma_s_solver_par *solver_par ) {
#define residualNorms(i,iter) ( residualNorms + (i) + (iter)*n )
#define magmablas_swap(x, y) { pointer = x; x = y; y = pointer; }
#define hresidualNorms(i,iter) (hresidualNorms + (i) + (iter)*n )
#define gramA( m, n) (gramA + (m) + (n)*ldgram)
#define gramB( m, n) (gramB + (m) + (n)*ldgram)
#define gevectors(m, n) (gevectors + (m) + (n)*ldgram)
#define h_gramB( m, n) (h_gramB + (m) + (n)*ldgram)
#define magma_s_bspmv_tuned(m, n, alpha, A, X, beta, AX) { \
magmablas_stranspose( m, n, X, m, blockW, n ); \
magma_s_vector x, ax; \
x.memory_location = Magma_DEV; x.num_rows = m*n; x.nnz = m*n; x.val = blockW; \
ax.memory_location= Magma_DEV; ax.num_rows = m*n; ax.nnz = m*n; ax.val = AX; \
magma_s_spmv(alpha, A, x, beta, ax ); \
magmablas_stranspose( n, m, blockW, n, X, m ); \
}
//**************************************************************
// Memory allocation for the eigenvectors, eigenvalues, and workspace
solver_par->solver = Magma_LOBPCG;
magma_int_t m = A.num_rows;
magma_int_t n =(solver_par->num_eigenvalues);
float *blockX = solver_par->eigenvectors;
float *evalues = solver_par->eigenvalues;
float *dwork, *hwork;
float *blockP, *blockAP, *blockR, *blockAR, *blockAX, *blockW;
float *gramA, *gramB, *gramM;
float *gevectors, *h_gramB;
float *pointer, *origX = blockX;
float *eval_gpu;
magma_int_t lwork = max( 2*n+n*magma_get_dsytrd_nb(n),
1 + 6*3*n + 2* 3*n* 3*n);
magma_smalloc_pinned( &hwork , lwork );
magma_smalloc( &blockAX , m*n );
magma_smalloc( &blockAR , m*n );
magma_smalloc( &blockAP , m*n );
magma_smalloc( &blockR , m*n );
magma_smalloc( &blockP , m*n );
magma_smalloc( &blockW , m*n );
magma_smalloc( &dwork , m*n );
magma_smalloc( &eval_gpu , 3*n );
//**********************************************************+
magma_int_t verbosity = 1;
magma_int_t *iwork, liwork = 15*n+9;
// === Set solver parameters ===
float residualTolerance = solver_par->epsilon;
magma_int_t maxIterations = solver_par->maxiter;
// === Set some constants & defaults ===
float c_one = MAGMA_S_ONE, c_zero = MAGMA_S_ZERO;
float *residualNorms, *condestGhistory, condestG;
float *gevalues;
magma_int_t *activeMask;
// === Check some parameters for possible quick exit ===
solver_par->info = 0;
if (m < 2)
solver_par->info = -1;
else if (n > m)
solver_par->info = -2;
if (solver_par->info != 0) {
magma_xerbla( __func__, -(solver_par->info) );
return solver_par->info;
}
magma_int_t *info = &(solver_par->info); // local info variable;
// === Allocate GPU memory for the residual norms' history ===
magma_smalloc(&residualNorms, (maxIterations+1) * n);
magma_malloc( (void **)&activeMask, (n+1) * sizeof(magma_int_t) );
// === Allocate CPU work space ===
magma_smalloc_cpu(&condestGhistory, maxIterations+1);
magma_smalloc_cpu(&gevalues, 3 * n);
magma_malloc_cpu((void **)&iwork, liwork * sizeof(magma_int_t));
float *hW;
magma_smalloc_pinned(&hW, n*n);
magma_smalloc_pinned(&gevectors, 9*n*n);
magma_smalloc_pinned(&h_gramB , 9*n*n);
// === Allocate GPU workspace ===
magma_smalloc(&gramM, n * n);
magma_smalloc(&gramA, 9 * n * n);
magma_smalloc(&gramB, 9 * n * n);
#if defined(PRECISION_z) || defined(PRECISION_c)
float *rwork;
magma_int_t lrwork = 1 + 5*(3*n) + 2*(3*n)*(3*n);
magma_smalloc_cpu(&rwork, lrwork);
#endif
// === Set activemask to one ===
for(int k =0; k<n; k++)
iwork[k]=1;
magma_setmatrix(n, 1, sizeof(magma_int_t), iwork, n ,activeMask, n);
magma_int_t gramDim, ldgram = 3*n, ikind = 4;
// === Make the initial vectors orthonormal ===
magma_sgegqr_gpu(ikind, m, n, blockX, m, dwork, hwork, info );
//magma_sorthomgs( m, n, blockX );
magma_s_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX );
// === Compute the Gram matrix = (X, AX) & its eigenstates ===
magma_sgemm(MagmaTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero, gramM, n);
magma_ssyevd_gpu( MagmaVec, MagmaUpper,
n, gramM, n, evalues, hW, n, hwork, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork, info );
// === Update X = X * evectors ===
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockX, m, gramM, n, c_zero, blockW, m);
magmablas_swap(blockW, blockX);
// === Update AX = AX * evectors ===
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockAX, m, gramM, n, c_zero, blockW, m);
magmablas_swap(blockW, blockAX);
condestGhistory[1] = 7.82;
magma_int_t iterationNumber, cBlockSize, restart = 1, iter;
//Chronometry
real_Double_t tempo1, tempo2;
magma_device_sync();
tempo1=magma_wtime();
// === Main LOBPCG loop ============================================================
for(iterationNumber = 1; iterationNumber < maxIterations; iterationNumber++)
{
// === compute the residuals (R = Ax - x evalues )
magmablas_slacpy( MagmaUpperLower, m, n, blockAX, m, blockR, m);
/*
for(int i=0; i<n; i++){
magma_saxpy(m, MAGMA_S_MAKE(-evalues[i],0), blockX+i*m, 1, blockR+i*m, 1);
}
*/
#if defined(PRECISION_z) || defined(PRECISION_d)
magma_dsetmatrix( 3*n, 1, evalues, 3*n, eval_gpu, 3*n );
#else
magma_ssetmatrix( 3*n, 1, evalues, 3*n, eval_gpu, 3*n );
#endif
magma_slobpcg_res( m, n, eval_gpu, blockX, blockR, eval_gpu);
magmablas_snrm2_cols(m, n, blockR, m, residualNorms(0, iterationNumber));
// === remove the residuals corresponding to already converged evectors
magma_scompact(m, n, blockR, m,
residualNorms(0, iterationNumber), residualTolerance,
activeMask, &cBlockSize);
if (cBlockSize == 0)
break;
// === apply a preconditioner P to the active residulas: R_new = P R_old
// === for now set P to be identity (no preconditioner => nothing to be done )
// magmablas_slacpy( MagmaUpperLower, m, cBlockSize, blockR, m, blockW, m);
/*
// === make the preconditioned residuals orthogonal to X
magma_sgemm(MagmaTrans, MagmaNoTrans, n, cBlockSize, m,
c_one, blockX, m, blockR, m, c_zero, gramB(0,0), ldgram);
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n,
c_mone, blockX, m, gramB(0,0), ldgram, c_one, blockR, m);
*/
// === make the active preconditioned residuals orthonormal
magma_sgegqr_gpu(ikind, m, cBlockSize, blockR, m, dwork, hwork, info );
//magma_sorthomgs( m, cBlockSize, blockR );
// === compute AR
magma_s_bspmv_tuned(m, cBlockSize, c_one, A, blockR, c_zero, blockAR );
if (!restart) {
// === compact P & AP as well
magma_scompactActive(m, n, blockP, m, activeMask);
magma_scompactActive(m, n, blockAP, m, activeMask);
/*
// === make P orthogonal to X ?
magma_sgemm(MagmaTrans, MagmaNoTrans, n, cBlockSize, m,
c_one, blockX, m, blockP, m, c_zero, gramB(0,0), ldgram);
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n,
c_mone, blockX, m, gramB(0,0), ldgram, c_one, blockP, m);
// === make P orthogonal to R ?
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockR, m, blockP, m, c_zero, gramB(0,0), ldgram);
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, cBlockSize,
c_mone, blockR, m, gramB(0,0), ldgram, c_one, blockP, m);
*/
// === Make P orthonormal & properly change AP (without multiplication by A)
magma_sgegqr_gpu(ikind, m, cBlockSize, blockP, m, dwork, hwork, info );
//magma_sorthomgs( m, cBlockSize, blockP );
//magma_s_bspmv_tuned(m, cBlockSize, c_one, A, blockP, c_zero, blockAP );
magma_ssetmatrix( cBlockSize, cBlockSize, hwork, cBlockSize, dwork, cBlockSize);
// magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
// m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m);
// replacement according to Stan
#if defined(PRECISION_s) || defined(PRECISION_d)
magmablas_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m);
#else
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m,
cBlockSize, c_one, dwork, cBlockSize, blockAP, m);
#endif
}
iter = max(1,iterationNumber-10- (int)(log(1.*cBlockSize)));
float condestGmean = 0.;
for(int i = 0; i<iterationNumber-iter+1; i++)
condestGmean += condestGhistory[i];
condestGmean = condestGmean / (iterationNumber-iter+1);
if (restart)
gramDim = n+cBlockSize;
else
gramDim = n+2*cBlockSize;
/* --- The Raileight-Ritz method for [X R P] -----------------------
[ X R P ]' [AX AR AP] y = evalues [ X R P ]' [ X R P ], i.e.,
GramA GramB
/ X'AX X'AR X'AP \ / X'X X'R X'P \
| R'AX R'AR R'AP | y = evalues | R'X R'R R'P |
\ P'AX P'AR P'AP / \ P'X P'R P'P /
----------------------------------------------------------------- */
// === assemble GramB; first, set it to I
magmablas_slaset(MagmaFull, ldgram, ldgram, c_zero, c_one, gramB, ldgram); // identity
if (!restart) {
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockP, m, blockX, m, c_zero, gramB(n+cBlockSize,0), ldgram);
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockR, m, c_zero, gramB(n+cBlockSize,n), ldgram);
}
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockR, m, blockX, m, c_zero, gramB(n,0), ldgram);
// === get GramB from the GPU to the CPU and compute its eigenvalues only
magma_sgetmatrix(gramDim, gramDim, gramB, ldgram, h_gramB, ldgram);
lapackf77_ssyev("N", "L", &gramDim, h_gramB, &ldgram, gevalues,
hwork, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork,
#endif
info);
// === check stability criteria if we need to restart
condestG = log10( gevalues[gramDim-1]/gevalues[0] ) + 1.;
if ((condestG/condestGmean>2 && condestG>2) || condestG>8) {
// Steepest descent restart for stability
restart=1;
printf("restart at step #%d\n", (int) iterationNumber);
}
// === assemble GramA; first, set it to I
magmablas_slaset(MagmaFull, ldgram, ldgram, c_zero, c_one, gramA, ldgram); // identity
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockR, m, blockAX, m, c_zero, gramA(n,0), ldgram);
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockR, m, blockAR, m, c_zero, gramA(n,n), ldgram);
if (!restart) {
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockP, m, blockAX, m, c_zero,
gramA(n+cBlockSize,0), ldgram);
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockAR, m, c_zero,
gramA(n+cBlockSize,n), ldgram);
magma_sgemm(MagmaTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockAP, m, c_zero,
gramA(n+cBlockSize,n+cBlockSize), ldgram);
}
/*
// === Compute X' AX or just use the eigenvalues below ?
magma_sgemm(MagmaTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero,
gramA(0,0), ldgram);
*/
if (restart==0) {
magma_sgetmatrix(gramDim, gramDim, gramA, ldgram, gevectors, ldgram);
}
else {
gramDim = n+cBlockSize;
magma_sgetmatrix(gramDim, gramDim, gramA, ldgram, gevectors, ldgram);
}
for(int k=0; k<n; k++)
*gevectors(k,k) = MAGMA_S_MAKE(evalues[k], 0);
// === the previous eigensolver destroyed what is in h_gramB => must copy it again
magma_sgetmatrix(gramDim, gramDim, gramB, ldgram, h_gramB, ldgram);
magma_int_t itype = 1;
lapackf77_ssygvd(&itype, "V", "L", &gramDim,
gevectors, &ldgram, h_gramB, &ldgram,
gevalues, hwork, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork, info);
for(int k =0; k<n; k++)
evalues[k] = gevalues[k];
// === copy back the result to gramA on the GPU and use it for the updates
magma_ssetmatrix(gramDim, gramDim, gevectors, ldgram, gramA, ldgram);
if (restart == 0) {
// === contribution from P to the new X (in new search direction P)
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m);
magmablas_swap(dwork, blockP);
// === contribution from R to the new X (in new search direction P)
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockR, m, gramA(n,0), ldgram, c_one, blockP, m);
// === corresponding contribution from AP to the new AX (in AP)
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockAP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m);
magmablas_swap(dwork, blockAP);
// === corresponding contribution from AR to the new AX (in AP)
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockAR, m, gramA(n,0), ldgram, c_one, blockAP, m);
}
else {
// === contribution from R (only) to the new X
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockR, m, gramA(n,0), ldgram, c_zero, blockP, m);
// === corresponding contribution from AR (only) to the new AX
magma_sgemm(MagmaNoTrans, MagmaNoTrans,m, n, cBlockSize,
c_one, blockAR, m, gramA(n,0), ldgram, c_zero, blockAP, m);
}
// === contribution from old X to the new X + the new search direction P
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockX, m, gramA, ldgram, c_zero, dwork, m);
magmablas_swap(dwork, blockX);
//magma_saxpy(m*n, c_one, blockP, 1, blockX, 1);
magma_slobpcg_maxpy( m, n, blockP, blockX );
// === corresponding contribution from old AX to new AX + AP
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockAX, m, gramA, ldgram, c_zero, dwork, m);
magmablas_swap(dwork, blockAX);
//magma_saxpy(m*n, c_one, blockAP, 1, blockAX, 1);
magma_slobpcg_maxpy( m, n, blockAP, blockAX );
condestGhistory[iterationNumber+1]=condestG;
if (verbosity==1) {
// float res;
// magma_sgetmatrix(1, 1,
// (float*)residualNorms(0, iterationNumber), 1,
// (float*)&res, 1);
//
// printf("Iteration %4d, CBS %4d, Residual: %10.7f\n",
// iterationNumber, cBlockSize, res);
printf("%4d-%2d ", (int) iterationNumber, (int) cBlockSize);
magma_sprint_gpu(1, n, residualNorms(0, iterationNumber), 1);
}
restart = 0;
} // === end for iterationNumber = 1,maxIterations =======================
// fill solver info
magma_device_sync();
tempo2=magma_wtime();
solver_par->runtime = (real_Double_t) tempo2-tempo1;
solver_par->numiter = iterationNumber;
if( solver_par->numiter < solver_par->maxiter) {
solver_par->info = 0;
} else if( solver_par->init_res > solver_par->final_res )
solver_par->info = -2;
else
solver_par->info = -1;
// =============================================================================
// === postprocessing;
// =============================================================================
// === compute the real AX and corresponding eigenvalues
magma_s_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX );
magma_sgemm(MagmaTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero, gramM, n);
magma_ssyevd_gpu( MagmaVec, MagmaUpper,
n, gramM, n, gevalues, dwork, n, hwork, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork, info );
for(int k =0; k<n; k++)
evalues[k] = gevalues[k];
// === update X = X * evectors
magmablas_swap(blockX, dwork);
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, dwork, m, gramM, n, c_zero, blockX, m);
// === update AX = AX * evectors to compute the final residual
magmablas_swap(blockAX, dwork);
magma_sgemm(MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, dwork, m, gramM, n, c_zero, blockAX, m);
// === compute R = AX - evalues X
magmablas_slacpy( MagmaUpperLower, m, n, blockAX, m, blockR, m);
for(int i=0; i<n; i++)
magma_saxpy(m, MAGMA_S_MAKE(-evalues[i], 0), blockX+i*m, 1, blockR+i*m, 1);
// === residualNorms[iterationNumber] = || R ||
magmablas_snrm2_cols(m, n, blockR, m, residualNorms(0, iterationNumber));
// === restore blockX if needed
if (blockX != origX)
magmablas_slacpy( MagmaUpperLower, m, n, blockX, m, origX, m);
printf("Eigenvalues:\n");
for(int i =0; i<n; i++)
printf("%e ", evalues[i]);
printf("\n\n");
printf("Final residuals:\n");
magma_sprint_gpu(1, n, residualNorms(0, iterationNumber), 1);
printf("\n\n");
//=== Print residual history in a file for plotting ====
float *hresidualNorms;
magma_smalloc_cpu(&hresidualNorms, (iterationNumber+1) * n);
magma_sgetmatrix(n, iterationNumber,
(float*)residualNorms, n,
(float*)hresidualNorms, n);
printf("Residuals are stored in file residualNorms\n");
printf("Plot the residuals using: myplot \n");
FILE *residuals_file;
residuals_file = fopen("residualNorms", "w");
for(int i =1; i<iterationNumber; i++) {
for(int j = 0; j<n; j++)
fprintf(residuals_file, "%f ", *hresidualNorms(j,i));
fprintf(residuals_file, "\n");
}
fclose(residuals_file);
magma_free_cpu(hresidualNorms);
// === free work space
magma_free( residualNorms );
magma_free_cpu( condestGhistory );
magma_free_cpu( gevalues );
magma_free_cpu( iwork );
magma_free_pinned( hW );
magma_free_pinned( gevectors );
magma_free_pinned( h_gramB );
magma_free( gramM );
magma_free( gramA );
magma_free( gramB );
magma_free( activeMask );
magma_free( blockAX );
magma_free( blockAR );
magma_free( blockAP );
magma_free( blockR );
magma_free( blockP );
magma_free( blockW );
magma_free( dwork );
magma_free( eval_gpu );
magma_free_pinned( hwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
magma_free_cpu( rwork );
#endif
return MAGMA_SUCCESS;
}
/**
Purpose
-------
SSYGVDX computes selected eigenvalues and, optionally, eigenvectors
of a real generalized symmetric-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 symmetric 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.
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]
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]
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 REAL array, dimension (LDA, N)
On entry, the symmetric 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**T * B * Z = I;
if ITYPE = 3, Z**T * 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 REAL array, dimension (LDB, N)
On entry, the symmetric 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**T * U or B = L * L**T.
@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]
mout INTEGER
The total number of eigenvalues found. 0 <= MOUT <= N.
If RANGE = MagmaRangeAll, MOUT = N, and if RANGE = MagmaRangeI, MOUT = IU-IL+1.
@param[out]
w REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[out]
work (workspace) REAL 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 >= 2*N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ).
NB can be obtained through magma_get_ssytrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK 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 and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK 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: SPOTRF or SSYEVD 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 SSYEVD 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_ssygv_driver
********************************************************************/
extern "C" magma_int_t
magma_ssygvdx(
magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
float *A, magma_int_t lda,
float *B, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *mout, float *w,
float *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 );
float d_one = MAGMA_S_ONE;
float *dA=NULL, *dB=NULL;
magma_int_t ldda = roundup( n, 32 );
magma_int_t lddb = ldda;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz, lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t lwmin, liwmin;
magma_queue_t stream;
magma_queue_create( &stream );
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -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_ssytrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n );
liwmin = 3 + 5*n;
}
else {
lwmin = 2*n + n*nb;
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] = lwmin * one_eps;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (liwork < liwmin && ! lquery) {
*info = -19;
}
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_ssygvd( &itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
iwork, &liwork, info );
*mout = n;
return *info;
}
if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_smalloc( &dB, n*lddb )) {
magma_free( dA );
magma_free( dB );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_ssetmatrix( n, n, B, ldb, dB, lddb );
magma_ssetmatrix_async( n, n,
A, lda,
dA, ldda, stream );
magma_timer_t time=0;
timer_start( time );
magma_spotrf_gpu( uplo, n, dB, lddb, info );
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time spotrf_gpu = %6.2f\n", time );
magma_queue_sync( stream );
magma_sgetmatrix_async( n, n,
dB, lddb,
B, ldb, stream );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_ssygst_gpu( itype, uplo, n, dA, ldda, dB, lddb, info );
timer_stop( time );
timer_printf( "time ssygst_gpu = %6.2f\n", time );
/* simple fix to be able to run bigger size.
* set dB=NULL so we know to re-allocate below
* TODO: have dwork here that will be used as dB and then passed to ssyevd.
*/
if (n > 5000) {
magma_queue_sync( stream );
magma_free( dB ); dB=NULL;
}
timer_start( time );
magma_ssyevdx_gpu( jobz, range, uplo, n, dA, ldda, vl, vu, il, iu, mout, w, A, lda,
work, lwork, iwork, liwork, info );
timer_stop( time );
timer_printf( "time ssyevdx_gpu = %6.2f\n", time );
if (wantz && *info == 0) {
timer_start( time );
/* allocate and copy dB back */
if (dB == NULL) {
if (MAGMA_SUCCESS != magma_smalloc( &dB, n*lddb ) ) {
magma_free( dA ); dA=NULL;
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_ssetmatrix( 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 = MagmaTrans;
} else {
trans = MagmaNoTrans;
}
magma_strsm( MagmaLeft, uplo, trans, MagmaNonUnit,
n, *mout, d_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 = MagmaTrans;
}
magma_strmm( MagmaLeft, uplo, trans, MagmaNonUnit,
n, *mout, d_one, dB, lddb, dA, ldda );
}
magma_sgetmatrix( n, *mout, dA, ldda, A, lda );
timer_stop( time );
timer_printf( "time strsm/mm + getmatrix = %6.2f\n", time );
}
magma_queue_sync( stream );
magma_queue_destroy( stream );
work[0] = lwmin * one_eps; // round up
iwork[0] = liwmin;
magma_free( dA ); dA=NULL;
magma_free( dB ); dB=NULL;
return *info;
} /* magma_ssygvd */
extern "C" magma_int_t
magma_ssygvdx_2stage(magma_int_t itype, char jobz, char range, char uplo, magma_int_t n,
float *a, magma_int_t lda, float *b, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w, float *work, magma_int_t lwork,
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
=======
SSYGVDX_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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 + 2).
If JOBZ = 'V' and N > 1, LWORK >= LQ2 + 1 + 6*N + 2*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.
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};
float d_one = MAGMA_S_ONE;
float *da;
float *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 lwmin;
magma_int_t liwmin;
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 || 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_sbulge_nb(n, threads);
magma_int_t lq2 = magma_sbulge_get_lq2(n, threads);
if (wantz) {
lwmin = lq2 + 1 + 6*n + 2*n*n;
liwmin = 3 + 5*n;
} else {
lwmin = n * (nb + 2);
liwmin = 1;
}
work[0] = lwmin * (1. + lapackf77_slamch("Epsilon"));
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (liwork < liwmin && ! lquery) {
*info = -19;
}
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_ssygvd(&itype, jobz_, uplo_,
&n, a, &lda, b, &ldb,
w, work, &lwork,
iwork, &liwork, info);
*m = n;
return *info;
}
if (MAGMA_SUCCESS != magma_smalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_smalloc( &db, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_ssetmatrix( n, n, b, ldb, db, lddb );
magma_ssetmatrix_async( n, n,
a, lda,
da, ldda, stream );
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
magma_spotrf_gpu(uplo_[0], n, db, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time spotrf_gpu = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_queue_sync( stream );
magma_sgetmatrix_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_ssygst_gpu(itype, uplo, n, da, ldda, db, lddb, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time ssygst_gpu = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_sgetmatrix( 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_ssyevdx_2stage(jobz, range, uplo, n, a, lda, vl, vu, il, iu, m, w, work, lwork, iwork, liwork, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time ssyevdx_2stage = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
if (wantz && *info == 0) {
if (MAGMA_SUCCESS != magma_smalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_smalloc( &db, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
magma_ssetmatrix( n, *m, a, lda, da, ldda );
magma_ssetmatrix( 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_strsm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, d_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_strmm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, d_one, db, lddb, da, ldda);
}
magma_sgetmatrix( n, *m, da, ldda, a, lda );
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time strsm/mm + getmatrix = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_free( da );
magma_free( db );
}
magma_queue_destroy( stream );
work[0] = lwmin * (1. + lapackf77_slamch("Epsilon"));
iwork[0] = liwmin;
return *info;
} /* ssygvdx_2stage */
/**
Purpose
-------
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-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 symmetric 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 REAL array, dimension (LDA, N)
On entry, the symmetric 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**T * B * Z = I;
if ITYPE = 3, Z**T * 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 REAL array, dimension (LDB, N)
On entry, the symmetric 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**T * U or B = L * L**T.
@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) REAL 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 >= 2*N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ).
NB can be obtained through magma_get_ssytrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK 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 and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK 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: SPOTRF or SSYEVD 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 SSYEVD 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_ssygv_driver
********************************************************************/
extern "C" magma_int_t
magma_ssygvd(
magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n,
float *A, magma_int_t lda,
float *B, magma_int_t ldb,
float *w,
float *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 );
float d_one = MAGMA_S_ONE;
float *dA=NULL, *dB=NULL;
magma_int_t ldda = magma_roundup( n, 32 );
magma_int_t lddb = ldda;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz, lquery;
magma_int_t lwmin, liwmin;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -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_ssytrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n );
liwmin = 3 + 5*n;
}
else {
lwmin = 2*n + n*nb;
liwmin = 1;
}
work[0] = magma_smake_lwork( lwmin );
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -11;
} else if (liwork < liwmin && ! lquery) {
*info = -13;
}
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_ssygvd( &itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
iwork, &liwork, info );
return *info;
}
if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_smalloc( &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 );
/* Form a Cholesky factorization of B. */
magma_ssetmatrix( n, n, B, ldb, dB, lddb, queue );
magma_ssetmatrix_async( n, n,
A, lda,
dA, ldda, queue );
magma_timer_t time=0;
timer_start( time );
magma_spotrf_gpu( uplo, n, dB, lddb, info );
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time spotrf_gpu = %6.2f\n", time );
magma_queue_sync( queue );
magma_sgetmatrix_async( n, n,
dB, lddb,
B, ldb, queue );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_ssygst_gpu( itype, uplo, n, dA, ldda, dB, lddb, info );
timer_stop( time );
timer_printf( "time ssygst_gpu = %6.2f\n", time );
/* simple fix to be able to run bigger size.
* set dB=NULL so we know to re-allocate below
* TODO: have dwork here that will be used as dB and then passed to ssyevd.
*/
if (n > 5000) {
magma_queue_sync( queue );
magma_free( dB ); dB=NULL;
}
timer_start( time );
magma_ssyevd_gpu( jobz, uplo, n, dA, ldda, w, A, lda,
work, lwork, iwork, liwork, info );
timer_stop( time );
timer_printf( "time ssyevd_gpu = %6.2f\n", time );
if (wantz && *info == 0) {
timer_start( time );
/* allocate and copy dB back */
if (dB == NULL) {
if (MAGMA_SUCCESS != magma_smalloc( &dB, n*lddb ) ) {
magma_free( dA );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_ssetmatrix( n, n, B, ldb, dB, lddb, queue );
}
/* 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 = MagmaTrans;
} else {
trans = MagmaNoTrans;
}
magma_strsm( MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, d_one, dB, lddb, dA, ldda, queue );
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
trans = MagmaNoTrans;
} else {
trans = MagmaTrans;
}
magma_strmm( MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, d_one, dB, lddb, dA, ldda, queue );
}
magma_sgetmatrix( n, n, dA, ldda, A, lda, queue );
timer_stop( time );
timer_printf( "time strsm/mm + getmatrix = %6.2f\n", time );
}
magma_queue_sync( queue );
magma_queue_destroy( queue );
work[0] = magma_smake_lwork( lwmin );
iwork[0] = liwmin;
magma_free( dA ); dA=NULL;
magma_free( dB ); dB=NULL;
return *info;
} /* magma_ssygvd */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ssygvd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
float *h_A, *h_Ainit, *h_B, *h_Binit, *h_work;
#ifdef COMPLEX
float *rwork;
#endif
float *w1, *w2, result[2]={0, 0};
magma_int_t *iwork;
real_Double_t mgpu_time, gpu_time, cpu_time;
/* Matrix size */
magma_int_t N, n2, nb;
magma_int_t info;
magma_int_t ione = 1;
float c_zero = MAGMA_S_ZERO;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("P");
// checking NoVec requires LAPACK
opts.lapack |= (opts.check && opts.jobz == MagmaNoVec);
printf("using: ngpu = %d, itype = %d, jobz = %s, uplo = %s, check = %d\n",
(int) opts.ngpu, (int) opts.itype,
lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo), (int) opts.check);
printf(" N CPU Time (sec) GPU Time (sec) MGPU Time (sec)\n");
printf("=========================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
// TODO define lda
N = opts.nsize[itest];
n2 = N*N;
nb = magma_get_ssytrd_nb(N);
#ifdef COMPLEX
magma_int_t lwork = max( N + N*nb, 2*N + N*N );
magma_int_t lrwork = 1 + 5*N +2*N*N;
#else
magma_int_t lwork = max( 2*N + N*nb, 1 + 6*N + 2*N*N );
#endif
magma_int_t liwork = 3 + 5*N;
TESTING_MALLOC_PIN( h_A, float, n2 );
TESTING_MALLOC_PIN( h_B, float, n2 );
TESTING_MALLOC_PIN( h_work, float, lwork );
#ifdef COMPLEX
TESTING_MALLOC_PIN( rwork, float, lrwork );
#endif
TESTING_MALLOC_CPU( w1, float, N );
TESTING_MALLOC_CPU( w2, float, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
/* Initialize the matrix */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
lapackf77_slarnv( &ione, ISEED, &n2, h_B );
magma_smake_hpd( N, h_B, N );
magma_smake_symmetric( N, h_A, N );
if ( opts.warmup || opts.check ) {
TESTING_MALLOC_CPU( h_Ainit, float, n2 );
TESTING_MALLOC_CPU( h_Binit, float, n2 );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &N, h_Ainit, &N );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_B, &N, h_Binit, &N );
}
if (opts.warmup) {
// ==================================================================
// Warmup using MAGMA.
// ==================================================================
magma_ssygvd_m( opts.ngpu, opts.itype, opts.jobz, opts.uplo,
N, h_A, N, h_B, N, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info);
lapackf77_slacpy( MagmaFullStr, &N, &N, h_Ainit, &N, h_A, &N );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_Binit, &N, h_B, &N );
}
// ===================================================================
// Performs operation using MAGMA
// ===================================================================
mgpu_time = magma_wtime();
magma_ssygvd_m( opts.ngpu, opts.itype, opts.jobz, opts.uplo,
N, h_A, N, h_B, N, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info);
mgpu_time = magma_wtime() - mgpu_time;
if (info != 0)
printf("magma_ssygvd_m returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.check && opts.jobz != MagmaNoVec ) {
/* =====================================================================
Check the results following the LAPACK's [zc]hegvd routine.
A x = lambda B x is solved
and the following 3 tests computed:
(1) | A Z - B Z D | / ( |A||Z| N ) (itype = 1)
| A B Z - Z D | / ( |A||Z| N ) (itype = 2)
| B A Z - Z D | / ( |A||Z| N ) (itype = 3)
=================================================================== */
#ifdef REAL
float *rwork = h_work + N*N;
#endif
result[0] = 1.;
result[0] /= lapackf77_slansy("1", lapack_uplo_const(opts.uplo), &N, h_Ainit, &N, rwork);
result[0] /= lapackf77_slange("1", &N, &N, h_A, &N, rwork);
if (opts.itype == 1) {
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_Ainit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i < N; ++i)
blasf77_sscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_neg_one, h_Binit, &N, h_A, &N, &c_one, h_work, &N);
result[0] *= lapackf77_slange("1", &N, &N, h_work, &N, rwork)/N;
}
else if (opts.itype == 2) {
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_Binit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i < N; ++i)
blasf77_sscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_Ainit, &N, h_work, &N, &c_neg_one, h_A, &N);
result[0] *= lapackf77_slange("1", &N, &N, h_A, &N, rwork)/N;
}
else if (opts.itype == 3) {
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_Ainit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i < N; ++i)
blasf77_sscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &N, &c_one, h_Binit, &N, h_work, &N, &c_neg_one, h_A, &N);
result[0] *= lapackf77_slange("1", &N, &N, h_A, &N, rwork)/N;
}
}
if ( opts.lapack ) {
lapackf77_slacpy( MagmaFullStr, &N, &N, h_Ainit, &N, h_A, &N );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_Binit, &N, h_B, &N );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_ssygvd(opts.itype, opts.jobz, opts.uplo,
N, h_A, N, h_B, N, w2,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info);
gpu_time = magma_wtime() - gpu_time;
if (info != 0)
printf("magma_ssygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_ssygvd(&opts.itype, lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_Ainit, &N, h_Binit, &N, w2,
h_work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork,
&info);
cpu_time = magma_wtime() - cpu_time;
if (info != 0)
printf("lapackf77_ssygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
float maxw=0, diff=0;
for(int j=0; j < N; j++) {
maxw = max(maxw, fabs(w1[j]));
maxw = max(maxw, fabs(w2[j]));
diff = max(diff, fabs(w1[j] - w2[j]));
}
result[1] = diff / (N*maxw);
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %7.2f %7.2f %7.2f\n",
(int) N, cpu_time, gpu_time, mgpu_time);
}
else {
printf("%5d --- --- %7.2f\n",
(int) N, mgpu_time);
}
if ( opts.check && opts.jobz != MagmaNoVec ) {
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if (opts.itype == 1) {
printf(" | A Z - B Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed") );
}
else if (opts.itype == 2) {
printf(" | A B Z - Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed") );
}
else if (opts.itype == 3) {
printf(" | B A Z - Z D | / (|A| |Z| N) = %8.2e %s\n", result[0], (result[0] < tol ? "ok" : "failed") );
}
status += ! (result[0] < tol);
}
if ( opts.lapack ) {
printf( " | D_mgpu - D_lapack | / |D| = %8.2e %s\n\n", result[1], (result[1] < tolulp ? "ok" : "failed") );
status += ! (result[1] < tolulp);
}
/* Memory clean up */
TESTING_FREE_PIN( h_A );
TESTING_FREE_PIN( h_B );
TESTING_FREE_PIN( h_work );
#ifdef COMPLEX
TESTING_FREE_PIN( rwork );
#endif
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
if ( opts.warmup || opts.check ) {
TESTING_FREE_CPU( h_Ainit );
TESTING_FREE_CPU( h_Binit );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ssygvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT();
/* Constants */
const float c_zero = MAGMA_S_ZERO;
const float c_one = MAGMA_S_ONE;
const float c_neg_one = MAGMA_S_NEG_ONE;
const magma_int_t ione = 1;
/* Local variables */
real_Double_t gpu_time;
float *h_A, *h_R, *h_B, *h_S, *h_work;
#ifdef COMPLEX
float *rwork;
magma_int_t lrwork;
#endif
float *w1, *w2, result[2]={0,0};
magma_int_t *iwork;
magma_int_t N, n2, info, lda, lwork, liwork;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("P");
magma_range_t range = MagmaRangeAll;
if (opts.fraction != 1)
range = MagmaRangeI;
// pass ngpu = -1 to test multi-GPU code using 1 gpu
magma_int_t abs_ngpu = abs( opts.ngpu );
printf("%% itype = %d, jobz = %s, range = %s, uplo = %s, fraction = %6.4f, ngpu = %d\n",
int(opts.itype), lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
opts.fraction, int(abs_ngpu) );
if (opts.itype == 1) {
printf("%% N M GPU Time (sec) |AZ-BZD| |D - D_magma|\n");
}
else if (opts.itype == 2) {
printf("%% N M GPU Time (sec) |ABZ-ZD| |D - D_magma|\n");
}
else if (opts.itype == 3) {
printf("%% N M GPU Time (sec) |BAZ-ZD| |D - D_magma|\n");
}
printf("%%======================================================\n");
magma_int_t threads = magma_get_parallel_numthreads();
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N;
// TODO: test vl-vu range
magma_int_t m1 = 0;
float vl = 0;
float vu = 0;
magma_int_t il = 0;
magma_int_t iu = 0;
if (opts.fraction == 0) {
il = max( 1, magma_int_t(0.1*N) );
iu = max( 1, magma_int_t(0.3*N) );
}
else {
il = 1;
iu = max( 1, magma_int_t(opts.fraction*N) );
}
magma_ssyevdx_getworksize(N, threads, (opts.jobz == MagmaVec),
&lwork,
#ifdef COMPLEX
&lrwork,
#endif
&liwork);
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, float, n2 );
TESTING_MALLOC_CPU( h_B, float, n2 );
TESTING_MALLOC_CPU( w1, float, N );
TESTING_MALLOC_CPU( w2, float, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, float, n2 );
TESTING_MALLOC_PIN( h_S, float, n2 );
TESTING_MALLOC_PIN( h_work, float, max( lwork, N*N )); // check needs N*N
#ifdef COMPLEX
TESTING_MALLOC_PIN( rwork, float, lrwork);
#endif
/* Initialize the matrix */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
lapackf77_slarnv( &ione, ISEED, &n2, h_B );
magma_smake_hpd( N, h_B, lda );
magma_smake_symmetric( N, h_A, lda );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_B, &lda, h_S, &lda );
// ===================================================================
// Performs operation using MAGMA
// ===================================================================
gpu_time = magma_wtime();
if (opts.ngpu == 1) {
magma_ssygvdx_2stage( opts.itype, opts.jobz, range, opts.uplo,
N, h_R, lda, h_S, lda, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
else {
magma_ssygvdx_2stage_m( abs_ngpu, opts.itype, opts.jobz, range, opts.uplo,
N, h_R, lda, h_S, lda, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
gpu_time = magma_wtime() - gpu_time;
if (info != 0) {
printf("magma_ssygvdx_2stage returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
if ( opts.check ) {
/* =====================================================================
Check the results following the LAPACK's [zc]hegvdx routine.
A x = lambda B x is solved
and the following 3 tests computed:
(1) | A Z - B Z D | / ( |A| |Z| N ) (itype = 1)
| A B Z - Z D | / ( |A| |Z| N ) (itype = 2)
| B A Z - Z D | / ( |A| |Z| N ) (itype = 3)
(2) | D(with V, magma) - D(w/o V, lapack) | / | D |
=================================================================== */
#ifdef REAL
float *rwork = h_work + N*N;
#endif
if ( opts.jobz != MagmaNoVec ) {
result[0] = 1.;
result[0] /= safe_lapackf77_slansy("1", lapack_uplo_const(opts.uplo), &N, h_A, &lda, rwork);
result[0] /= lapackf77_slange("1", &N, &m1, h_R, &lda, rwork);
if (opts.itype == 1) {
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &lda, h_R, &lda, &c_zero, h_work, &N);
for (int i=0; i < m1; ++i)
blasf77_sscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_neg_one, h_B, &lda, h_R, &lda, &c_one, h_work, &N);
result[0] *= lapackf77_slange("1", &N, &m1, h_work, &N, rwork)/N;
}
else if (opts.itype == 2) {
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &lda, h_R, &lda, &c_zero, h_work, &N);
for (int i=0; i < m1; ++i)
blasf77_sscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &lda, h_work, &N, &c_neg_one, h_R, &lda);
result[0] *= lapackf77_slange("1", &N, &m1, h_R, &lda, rwork)/N;
}
else if (opts.itype == 3) {
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &lda, h_R, &lda, &c_zero, h_work, &N);
for (int i=0; i < m1; ++i)
blasf77_sscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_ssymm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &lda, h_work, &N, &c_neg_one, h_R, &lda);
result[0] *= lapackf77_slange("1", &N, &m1, h_R, &lda, rwork)/N;
}
}
lapackf77_slacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
lapackf77_slacpy( MagmaFullStr, &N, &N, h_B, &lda, h_S, &lda );
lapackf77_ssygvd( &opts.itype, "N", lapack_uplo_const(opts.uplo), &N,
h_R, &lda, h_S, &lda, w2,
h_work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork,
&info );
if (info != 0) {
printf("lapackf77_ssygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
float maxw=0, diff=0;
for (int j=0; j < m1; j++) {
maxw = max(maxw, fabs(w1[j]));
maxw = max(maxw, fabs(w2[j]));
diff = max(diff, fabs(w1[j] - w2[j]));
}
result[1] = diff / (m1*maxw);
}
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %5d %9.4f ",
(int) N, (int) m1, gpu_time);
if ( opts.check ) {
bool okay = (result[1] < tolulp);
if ( opts.jobz != MagmaNoVec ) {
okay = okay && (result[0] < tol);
printf(" %8.2e", result[0] );
}
else {
printf(" --- ");
}
printf(" %8.2e %s\n", result[1], (okay ? "ok" : "failed"));
status += ! okay;
}
else {
printf(" ---\n");
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_S );
TESTING_FREE_PIN( h_work );
#ifdef COMPLEX
TESTING_FREE_PIN( rwork );
#endif
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-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 symmetric 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]
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]
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 symmetric 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**T*B*Z = I;
if ITYPE = 3, Z**T*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 symmetric 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**T*U or B = L*L**T.
@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_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 >= 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]
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: SPOTRF or SSYEVD 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 SSYEVD 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_ssygv_driver
********************************************************************/
extern "C" magma_int_t
magma_ssygvdx_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,
float *A, magma_int_t lda, float *B, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w, float *work, magma_int_t lwork,
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 );
float c_one = MAGMA_S_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;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -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_ssytrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = 1 + 6*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = 2*n + n*nb;
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] = lwmin * one_eps;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (liwork < liwmin && ! lquery) {
*info = -19;
}
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_ssygvd(&itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
iwork, &liwork, info);
*m = n;
return *info;
}
magma_timer_t time=0;
timer_start( time );
magma_spotrf_m(nrgpu, uplo, n, B, ldb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time spotrf = %6.2f\n", time );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_ssygst_m(nrgpu, itype, uplo, n, A, lda, B, ldb, info);
timer_stop( time );
timer_printf( "time ssygst = %6.2f\n", time );
timer_start( time );
magma_ssyevdx_m(nrgpu, jobz, range, uplo, n, A, lda, vl, vu, il, iu, m, w, work, lwork, iwork, liwork, info);
timer_stop( time );
timer_printf( "time ssyevd = %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 = MagmaTrans;
} else {
trans = MagmaNoTrans;
}
magma_strsm_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 = MagmaTrans;
}
//magma_strmm(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] = lwmin * one_eps; // round up
iwork[0] = liwmin;
return *info;
} /* magma_ssygvd_m */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ssygvd
*/
int main( int argc, char** argv)
{
TESTING_INIT_MGPU();
float *h_A, *h_Ainit, *h_B, *h_Binit, *h_work;
#if defined(PRECISION_z) || defined(PRECISION_c)
float *rwork;
#endif
float *w1, *w2, result;
magma_int_t *iwork;
float mgpu_time, gpu_time, cpu_time;
/* Matrix size */
magma_int_t N=0, n2;
magma_int_t info;
magma_int_t ione = 1;
float c_zero = MAGMA_S_ZERO;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t ISEED[4] = {0,0,0,1};
magma_timestr_t start, end;
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("P");
char jobz = opts.jobz;
int checkres = opts.check;
char uplo = opts.uplo;
magma_int_t itype = opts.itype;
if ( checkres && jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
jobz = MagmaVec;
}
printf("using: nrgpu = %d, itype = %d, jobz = %c, uplo = %c, checkres = %d\n",
(int) opts.ngpu, (int) itype, jobz, uplo, (int) checkres);
printf(" N M nr GPU MGPU Time(s) \n");
printf("====================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
n2 = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
magma_int_t lwork = 2*N + N*N;
magma_int_t lrwork = 1 + 5*N +2*N*N;
// MKL's ssygvd has a bug for small N - it looks like what is returned by a
// query (consistent with LAPACK's number above) is different from a the memory
// requirement ckeck (that returns info -11). The lwork increase below is needed
// to pass this check.
if (N<32)
lwork = 34*32;
#else
magma_int_t lwork = 1 + 6*N + 2*N*N;
#endif
magma_int_t liwork = 3 + 5*N;
TESTING_MALLOC_PIN( h_A, float, n2 );
TESTING_MALLOC_PIN( h_B, float, n2 );
TESTING_MALLOC_PIN( h_work, float, lwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_MALLOC_PIN( rwork, float, lrwork );
#endif
TESTING_MALLOC_CPU( w1, float, N );
TESTING_MALLOC_CPU( w2, float, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
printf(" N CPU Time(s) GPU Time(s) MGPU Time(s) \n");
printf("==================================================\n");
/* Initialize the matrix */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
lapackf77_slarnv( &ione, ISEED, &n2, h_B );
magma_smake_hpd( N, h_B, N );
magma_smake_symmetric( N, h_A, N );
if((opts.warmup)||( checkres )){
TESTING_MALLOC_CPU( h_Ainit, float, n2 );
TESTING_MALLOC_CPU( h_Binit, float, n2 );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_Ainit, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_Binit, &N );
}
if(opts.warmup){
// ==================================================================
// Warmup using MAGMA.
// ==================================================================
magma_ssygvd_m( opts.ngpu, itype, jobz, uplo,
N, h_A, N, h_B, N, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_Ainit, &N, h_A, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_Binit, &N, h_B, &N );
}
// ===================================================================
// Performs operation using MAGMA
// ===================================================================
start = get_current_time();
magma_ssygvd_m( opts.ngpu, itype, jobz, uplo,
N, h_A, N, h_B, N, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
end = get_current_time();
if(info != 0)
printf("magma_ssygvd_m returned error %d: %s.\n",
(int) info, magma_strerror( info ));
mgpu_time = GetTimerValue(start,end)/1000.;
if ( checkres ) {
/* =====================================================================
Check the results following the LAPACK's [zc]hegvd routine.
A x = lambda B x is solved
and the following 3 tests computed:
(1) | A Z - B Z D | / ( |A||Z| N ) (itype = 1)
| A B Z - Z D | / ( |A||Z| N ) (itype = 2)
| B A Z - Z D | / ( |A||Z| N ) (itype = 3)
=================================================================== */
#if defined(PRECISION_d) || defined(PRECISION_s)
float *rwork = h_work + N*N;
#endif
result = 1.;
result /= lapackf77_slansy("1",&uplo, &N, h_Ainit, &N, rwork);
result /= lapackf77_slange("1",&N , &N, h_A, &N, rwork);
if (itype == 1){
blasf77_ssymm("L", &uplo, &N, &N, &c_one, h_Ainit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i<N; ++i)
blasf77_sscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_ssymm("L", &uplo, &N, &N, &c_neg_one, h_Binit, &N, h_A, &N, &c_one, h_work, &N);
result *= lapackf77_slange("1", &N, &N, h_work, &N, rwork)/N;
}
else if (itype == 2){
blasf77_ssymm("L", &uplo, &N, &N, &c_one, h_Binit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i<N; ++i)
blasf77_sscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_ssymm("L", &uplo, &N, &N, &c_one, h_Ainit, &N, h_work, &N, &c_neg_one, h_A, &N);
result *= lapackf77_slange("1", &N, &N, h_A, &N, rwork)/N;
}
else if (itype == 3){
blasf77_ssymm("L", &uplo, &N, &N, &c_one, h_Ainit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i<N; ++i)
blasf77_sscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_ssymm("L", &uplo, &N, &N, &c_one, h_Binit, &N, h_work, &N, &c_neg_one, h_A, &N);
result *= lapackf77_slange("1", &N, &N, h_A, &N, rwork)/N;
}
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_Ainit, &N, h_A, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_Binit, &N, h_B, &N );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
start = get_current_time();
magma_ssygvd(itype, jobz, uplo,
N, h_A, N, h_B, N, w2,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
end = get_current_time();
if(info != 0)
printf("magma_ssygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
gpu_time = GetTimerValue(start,end)/1000.;
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
start = get_current_time();
lapackf77_ssygvd(&itype, &jobz, &uplo,
&N, h_Ainit, &N, h_Binit, &N, w2,
h_work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
&info);
end = get_current_time();
if (info != 0)
printf("lapackf77_ssygvd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
cpu_time = GetTimerValue(start,end)/1000.;
float temp1 = 0;
float temp2 = 0;
for(int j=0; j<N; j++){
temp1 = max(temp1, absv(w1[j]));
temp1 = max(temp1, absv(w2[j]));
temp2 = max(temp2, absv(w1[j]-w2[j]));
}
float result2 = temp2 / (((float)N)*temp1);
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %6.2f %6.2f %6.2f\n",
(int) N, cpu_time, gpu_time, mgpu_time);
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if(itype==1)
printf("(1) | A Z - B Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : " failed") );
else if(itype==2)
printf("(1) | A B Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : " failed") );
else if(itype==3)
printf("(1) | B A Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : " failed") );
printf( "(3) | D(MGPU)-D(LAPACK) |/ |D| = %8.2e%s\n\n", result2, (result2 < tolulp ? "" : " failed") );
}
else {
printf("%5d ------ ------ %6.2f\n",
(int) N, mgpu_time);
}
/* Memory clean up */
TESTING_FREE_PIN( h_A );
TESTING_FREE_PIN( h_B );
TESTING_FREE_PIN( h_work );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_FREE_PIN( rwork );
#endif
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
if((opts.warmup)||( checkres )){
TESTING_FREE_CPU( h_Ainit );
TESTING_FREE_CPU( h_Binit );
}
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
/* Shutdown */
TESTING_FINALIZE_MGPU();
}
