/**
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
-------
SSYEVD computes all eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A 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.
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower)
or the upper triangle (if UPLO=MagmaUpper) of A, including the
diagonal, is destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= 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: 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).
Further Details
---------------
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
@ingroup magma_ssyev_driver
********************************************************************/
extern "C" magma_int_t
magma_ssyevd(magma_vec_t jobz, magma_uplo_t uplo,
magma_int_t n,
float *A, magma_int_t lda,
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 );
magma_int_t ione = 1;
magma_int_t izero = 0;
float d_one = 1.;
float d__1;
float eps;
magma_int_t inde;
float anrm;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indwrk, liwmin;
magma_int_t llwork;
float smlnum;
magma_int_t lquery;
float* dwork;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -1 || liwork == -1);
*info = 0;
if (! (wantz || (jobz == MagmaNoVec))) {
*info = -1;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
}
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 to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
float one_eps = 1. + lapackf77_slamch("Epsilon");
work[0] = lwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -8;
} else if ((liwork < liwmin) && ! lquery) {
*info = -10;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (n == 1) {
w[0] = A[0];
if (wantz) {
A[0] = 1.;
}
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_ssyevd(jobz_, uplo_,
&n, A, &lda,
w, work, &lwork,
iwork, &liwork, info);
return *info;
}
/* Get machine constants. */
safmin = lapackf77_slamch("Safe minimum");
eps = lapackf77_slamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_ssqrt(smlnum);
rmax = magma_ssqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_slansy("M", uplo_, &n, A, &lda, work );
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
lapackf77_slascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A,
&lda, info);
}
/* Call SSYTRD to reduce symmetric matrix to tridiagonal form. */
// ssytrd work: e (n) + tau (n) + llwork (n*nb) ==> 2n + n*nb
// sstedx work: e (n) + tau (n) + z (n*n) + llwrk2 (1 + 4*n + n^2) ==> 1 + 6n + 2n^2
inde = 0;
indtau = inde + n;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
magma_ssytrd(uplo, n, A, lda, w, &work[inde],
&work[indtau], &work[indwrk], llwork, &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call SORMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &work[inde], info);
}
else {
if (MAGMA_SUCCESS != magma_smalloc( &dwork, 3*n*(n/2 + 1) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
// TTT Possible bug for n < 128
magma_sstedx(311, n, 0., 0., 0, 0, w, &work[inde],
&work[indwrk], n, &work[indwk2],
llwrk2, iwork, liwork, dwork, info);
magma_free( dwork );
magma_sormtr(MagmaLeft, uplo, MagmaNoTrans, n, n, A, lda, &work[indtau],
&work[indwrk], n, &work[indwk2], llwrk2, &iinfo);
lapackf77_slacpy("A", &n, &n, &work[indwrk], &n, A, &lda);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
d__1 = 1. / sigma;
blasf77_sscal(&n, &d__1, w, &ione);
}
work[0] = lwmin * one_eps; // round up
iwork[0] = liwmin;
return *info;
} /* magma_ssyevd */
/**
Purpose
-------
SSYTRD reduces a real symmetric matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
Arguments
---------
@param[in]
num_gpus INTEGER
The number of GPUs. num_gpus > 0.
@param[in]
num_streams INTEGER
The number of GPU streams used for update. 10 >= num_streams > 0.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A 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, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
d REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
@param[out]
e REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower.
@param[out]
tau REAL array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@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 dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
@ingroup magma_ssyev_comp
********************************************************************/
extern "C" magma_int_t
magma_ssytrd_mgpu(
magma_int_t num_gpus, magma_int_t num_streams, magma_uplo_t uplo, magma_int_t n,
float *A, magma_int_t lda,
float *d, float *e, float *tau,
float *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define dA(id, i, j) (dA[(id)] + (j)*ldda + (i))
#define dW(id, i, j) (dwork[(id)] + (j)*ldda + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t ln, ldda;
magma_int_t nb = magma_get_ssytrd_nb(n), ib;
float c_neg_one = MAGMA_S_NEG_ONE;
float c_one = MAGMA_S_ONE;
float d_one = MAGMA_D_ONE;
//float mv_time = 0.0;
#ifdef PROFILE_SY2RK
float up_time = 0.0;
#endif
magma_int_t kk, nx;
magma_int_t i = 0, ii, iii, j, did, i_n;
magma_int_t iinfo;
magma_int_t ldwork, lddwork, lwkopt, ldwork2;
magma_int_t lquery;
magma_queue_t stream[MagmaMaxGPUs][10];
float *dx[MagmaMaxGPUs], *dy[MagmaMaxGPUs], *hwork;
float *dwork2[MagmaMaxGPUs];
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < nb*n && ! lquery) {
*info = -9;
} else if ( num_streams > 2 ) {
*info = 2; // TODO fix
}
/* Determine the block size. */
ldwork = lddwork = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_S_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
float *dA[MagmaMaxGPUs];
float *dwork[MagmaMaxGPUs];
float times[11];
for( did=0; did < 11; did++ )
times[did] = 0;
//#define PROFILE_SY2RK
#ifdef PROFILE_SY2RK
magma_event_t start, stop;
float etime;
magma_setdevice(0);
magma_event_create( &start );
magma_event_create( &stop );
#endif
ldda = lda;
ln = ((nb*(1+n/(nb*num_gpus))+31)/32)*32;
ldwork2 = (1+ n / nb + (n % nb != 0)) * ldda;
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
// TODO fix memory leak
if ( MAGMA_SUCCESS != magma_smalloc(&dA[did], ln*ldda+3*lddwork*nb) ||
MAGMA_SUCCESS != magma_smalloc(&dx[did], num_streams*n) ||
MAGMA_SUCCESS != magma_smalloc(&dy[did], num_streams*n) ||
MAGMA_SUCCESS != magma_smalloc(&dwork2[did], ldwork2 ) ) {
for( i=0; i < did; i++ ) {
magma_setdevice(i);
magma_free(dA[i]);
magma_free(dx[i]);
magma_free(dy[i]);
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dwork[did] = dA[did] + ln*ldda;
for( kk=0; kk < num_streams; kk++ )
magma_queue_create(&stream[did][kk]);
}
magma_setdevice(0);
// TODO fix memory leak dwork2
if ( MAGMA_SUCCESS != magma_smalloc_pinned( &hwork, num_streams*num_gpus*n ) ) {
for( i=0; i < num_gpus; i++ ) {
magma_setdevice(i);
magma_free(dA[i]);
magma_free(dx[i]);
magma_free(dy[i]);
}
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if (n < 2048)
nx = n;
else
nx = 512;
if (upper) {
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_shtodhe(num_gpus, uplo, n, nb, A, lda, dA, ldda, stream, &iinfo );
}
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
for (i = nb*((n-1)/nb); i >= nx; i -= nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
/* wait for the next panel */
if (i != nb*((n-1)/nb)) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
magma_slatrd_mgpu(num_gpus, uplo, n, i+ib, ib, nb,
A(0, 0), lda, e, tau,
work, ldwork,
dA, ldda, 0,
dwork, i+ib,
dwork2, ldwork2,
1, dx, dy, hwork,
stream, times);
magma_ssyr2k_mgpu(num_gpus, MagmaUpper, MagmaNoTrans, nb, i, ib,
c_neg_one, dwork, i+ib, 0,
d_one, dA, ldda, 0,
num_streams, stream);
/* get the next panel */
if (i-nb >= nx ) {
ib = min(nb, n-(i-nb));
ii = nb*((i-nb)/(nb*num_gpus));
did = ((i-nb)/nb)%num_gpus;
magma_setdevice(did);
magma_sgetmatrix_async( (i-nb)+ib, ib,
dA(did, 0, ii), ldda,
A(0, i-nb), lda,
stream[did][0] );
}
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j > 0 ) {
*A(j-1,j) = MAGMA_S_MAKE( e[j - 1], 0 );
}
d[j] = MAGMA_S_REAL( *A(j, j) );
}
} /* end of for i=... */
if ( nx > 0 ) {
if (1 <= n-nx) { /* else A is already on CPU */
for (i=0; i < nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
magma_setdevice(did);
magma_sgetmatrix_async( nx, ib,
dA(did, 0, ii), ldda,
A(0, i), lda,
stream[did][0] );
}
}
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
/* Use unblocked code to reduce the last or only block */
lapackf77_ssytd2(uplo_, &nx, A(0, 0), &lda, d, e, tau, &iinfo);
}
}
else {
trace_init( 1, num_gpus, num_streams, (CUstream_st**)stream );
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_shtodhe(num_gpus, uplo, n, nb, A, lda, dA, ldda, stream, &iinfo );
}
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
/* Reduce columns i:i+ib-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != 0) {
magma_setdevice(did);
trace_gpu_start( did, 0, "comm", "get" );
magma_sgetmatrix_async( n-i, ib,
dA(did, i, ii), ldda,
A(i,i), lda,
stream[did][0] );
trace_gpu_end( did, 0 );
magma_queue_sync(stream[did][0]);
magma_setdevice(0);
}
magma_slatrd_mgpu(num_gpus, uplo, n, n-i, ib, nb,
A(i, i), lda, &e[i],
&tau[i], work, ldwork,
dA, ldda, i,
dwork, (n-i),
dwork2, ldwork2,
1, dx, dy, hwork,
stream, times );
#ifdef PROFILE_SY2RK
magma_setdevice(0);
if ( i > 0 ) {
cudaEventElapsedTime(&etime, start, stop);
up_time += (etime/1000.0);
}
magma_event_record(start, 0);
#endif
magma_ssyr2k_mgpu(num_gpus, MagmaLower, MagmaNoTrans, nb, n-i-ib, ib,
c_neg_one, dwork, n-i, ib,
d_one, dA, ldda, i+ib, num_streams, stream);
#ifdef PROFILE_SY2RK
magma_setdevice(0);
magma_event_record(stop, 0);
#endif
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j+1 < n ) {
*A(j+1,j) = MAGMA_S_MAKE( e[j], 0 );
}
d[j] = MAGMA_S_REAL( *A(j, j) );
}
} /* for i=... */
/* Use unblocked code to reduce the last or only block */
if ( i < n ) {
iii = i;
i_n = n-i;
if ( i > 0 ) {
for (; i < n; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
magma_setdevice(did);
magma_sgetmatrix_async( i_n, ib,
dA(did, iii, ii), ldda,
A(iii, i), lda,
stream[did][0] );
}
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
}
lapackf77_ssytrd(uplo_, &i_n, A(iii, iii), &lda, &d[iii], &e[iii],
&tau[iii], work, &lwork, &iinfo);
}
}
#ifdef PROFILE_SY2RK
magma_setdevice(0);
if ( n > nx ) {
cudaEventElapsedTime(&etime, start, stop);
up_time += (etime/1000.0);
}
magma_event_destroy( start );
magma_event_destroy( stop );
#endif
trace_finalize( "ssytrd.svg", "trace.css" );
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
for( kk=0; kk < num_streams; kk++ )
magma_queue_sync(stream[did][kk]);
for( kk=0; kk < num_streams; kk++ )
magma_queue_destroy(stream[did][kk]);
magma_free(dA[did]);
magma_free(dx[did]);
magma_free(dy[did]);
magma_free(dwork2[did]);
}
magma_free_pinned(hwork);
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
work[0] = MAGMA_S_MAKE( lwkopt, 0 );
#ifdef PROFILE_SY2RK
printf( " n=%d nb=%d\n", n, nb );
printf( " Time in SLARFG: %.2e seconds\n", times[0] );
//printf( " Time in SSYMV : %.2e seconds\n", mv_time );
printf( " Time in SSYR2K: %.2e seconds\n", up_time );
#endif
return *info;
} /* magma_ssytrd */
/**
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_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 */
extern "C" magma_err_t
magma_ssytrd(char uplo, magma_int_t n,
float *a, magma_int_t lda,
float *d, float *e, float *tau,
float *work, magma_int_t lwork,
magma_int_t *info, magma_queue_t queue)
{
/* -- clMAGMA (version 1.0.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
April 2012
Purpose
=======
SSYTRD reduces a real symmetric matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**T * A * Q = T.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) REAL 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, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = 'U', the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
D (output) REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
E (output) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
TAU (output) REAL array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
===================================================================== */
char uplo_[2] = {uplo, 0};
magma_int_t ldda = lda;
magma_int_t nb = magma_get_ssytrd_nb(n);
float c_neg_one = MAGMA_S_NEG_ONE;
float c_one = MAGMA_S_ONE;
float d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldwork, lddwork, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = lapackf77_lsame(uplo_, "U");
lquery = lwork == -1;
if (! upper && ! lapackf77_lsame(uplo_, "L")) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < nb*n && ! lquery) {
*info = -9;
}
if (*info == 0) {
/* Determine the block size. */
ldwork = lddwork = n;
lwkopt = n * nb;
// ACD
// MAGMA_S_SET2REAL( work[0], lwkopt );
MAGMA_S_SET2REAL( work[0], (float) lwkopt );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
magmaFloat_ptr da;
size_t da_offset = 0;
if (MAGMA_SUCCESS != magma_malloc( &da, (n*ldda + 2*n*nb )*sizeof(float))) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmaFloat_ptr dwork = da;
size_t dwork_offset = da_offset + (n)*ldda;
if (n < 2048)
nx = n;
else
nx = 512;
if (upper) {
/* Copy the matrix to the GPU */
magma_ssetmatrix( n, n, A(0, 0), 0, lda, dA(0, 0), ldda, queue );
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb)
{
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i!=n-nb)
magma_sgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), 0, lda, queue );
magma_slatrd(uplo, i+nb, nb, A(0, 0), lda, e, tau,
work, ldwork, dA(0, 0), ldda, dwork, dwork_offset, lddwork, queue);
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_ssetmatrix( i + nb, nb, work, 0, ldwork, dwork, dwork_offset, lddwork, queue );
magma_ssyr2k(magma_uplo_const(uplo), MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork, dwork_offset,
lddwork, d_one, dA(0, 0), ldda, queue);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
MAGMA_S_SET2REAL( *A(j-1, j), e[j - 1] );
d[j] = MAGMA_S_REAL( *A(j, j) );
}
}
magma_sgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), 0, lda, queue );
/* Use unblocked code to reduce the last or only block */
lapackf77_ssytd2(uplo_, &kk, A(0, 0), &lda, d, e, tau, &iinfo);
}
else
{
/* Copy the matrix to the GPU */
if (1<=n-nx)
magma_ssetmatrix( n, n, A(0,0), 0, lda, dA(0,0), ldda, queue );
#ifdef FAST_SYMV
// TODO this leaks memory from da, above
magmaFloat_ptr dwork2;
if (MAGMA_SUCCESS != magma_malloc( &dwork2, (n*n)*sizeof(float) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
size_t dwork2_offset = 0;
#endif
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb)
{
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i!=0)
magma_sgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), 0, lda, queue );
#ifdef FAST_SYMV
// unported
magma_slatrd2(uplo, n-i, nb, A(i, i), lda, &e[i],
&tau[i], work, ldwork,
dA(i, i), ldda,
dwork, lddwork, dwork2, n*n);
#else
magma_slatrd(uplo, n-i, nb, A(i, i), lda, &e[i],
&tau[i], work, ldwork,
dA(i, i), ldda,
dwork, dwork_offset, lddwork, queue);
#endif
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_ssetmatrix( n-i, nb, work, 0, ldwork, dwork, dwork_offset, lddwork, queue );
magma_ssyr2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda,
dwork, (dwork_offset+nb), lddwork, d_one,
dA(i+nb, i+nb), ldda, queue);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
MAGMA_S_SET2REAL( *A(j+1, j), e[j] );
d[j] = MAGMA_S_REAL( *A(j, j) );
}
}
#ifdef FAST_SYMV
magma_free( dwork2 );
#endif
/* Use unblocked code to reduce the last or only block */
if (1<=n-nx)
magma_sgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), 0, lda, queue );
i_n = n-i;
lapackf77_ssytrd(uplo_, &i_n, A(i, i), &lda, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo);
}
magma_free( da );
// ACD
// MAGMA_S_SET2REAL( work[0], lwkopt );
MAGMA_S_SET2REAL( work[0], (float) lwkopt );
return *info;
} /* magma_ssytrd */
/**
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 */
extern "C" magma_int_t
magma_ssyevd_gpu(char jobz, char uplo,
magma_int_t n,
float *da, magma_int_t ldda,
float *w,
float *wa, magma_int_t ldwa,
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
=======
SSYEVD_GPU computes all eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
DA (device input/output) REAL array on the GPU,
dimension (LDDA, 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
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDDA (input) INTEGER
The leading dimension of the array DA. LDDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WA (workspace) DOUBLE PRECISION array, dimension (LDWA, N)
LDWA (input) INTEGER
The leading dimension of the array WA. LDWA >= max(1,N).
WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] 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 >= 2*N + N*NB.
If JOBZ = 'V' 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).
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.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK[0] 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 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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i and JOBZ = 'N', then the algorithm failed
to converge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
if INFO = i and JOBZ = 'V', then the algorithm failed
to compute an eigenvalue while working on the submatrix
lying in rows and columns INFO/(N+1) through
mod(INFO,N+1).
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
magma_int_t ione = 1;
float d__1;
float eps;
magma_int_t inde;
float anrm;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indwrk, liwmin;
magma_int_t llwork;
float smlnum;
magma_int_t lquery;
float *dwork;
magma_int_t lddc = ldda;
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
lquery = lwork == -1 || liwork == -1;
*info = 0;
if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -1;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
}
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 to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
work[0] = lwmin * (1. + lapackf77_slamch("Epsilon"));
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -10;
} else if ((liwork < liwmin) && ! lquery) {
*info = -12;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
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
char jobz_[2] = {jobz, 0}, uplo_[2] = {uplo, 0};
float *a = (float *) malloc( n * n * sizeof(float) );
magma_sgetmatrix(n, n, da, ldda, a, n);
lapackf77_ssyevd(jobz_, uplo_,
&n, a, &n,
w, work, &lwork,
iwork, &liwork, info);
magma_ssetmatrix( n, n, a, n, da, ldda);
free(a);
return *info;
}
magma_queue_t stream;
magma_queue_create( &stream );
// n*lddc for ssytrd2_gpu
// n for slansy
magma_int_t ldwork = n*lddc;
if ( wantz ) {
// need 3n^2/2 for sstedx
ldwork = max( ldwork, 3*n*(n/2 + 1));
}
if (MAGMA_SUCCESS != magma_smalloc( &dwork, ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Get machine constants. */
safmin = lapackf77_slamch("Safe minimum");
eps = lapackf77_slamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_ssqrt(smlnum);
rmax = magma_ssqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = magmablas_slansy('M', uplo, n, da, ldda, dwork);
iscale = 0;
sigma = 1;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
magmablas_slascl(uplo, 0, 0, 1., sigma, n, n, da, ldda, info);
}
/* Call SSYTRD to reduce symmetric matrix to tridiagonal form. */
// ssytrd work: e (n) + tau (n) + llwork (n*nb) ==> 2n + n*nb
// sstedx work: e (n) + tau (n) + z (n*n) + llwrk2 (1 + 4*n + n^2) ==> 1 + 6n + 2n^2
inde = 0;
indtau = inde + n;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
//
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
#ifdef FAST_SYMV
magma_ssytrd2_gpu(uplo, n, da, ldda, w, &work[inde],
&work[indtau], wa, ldwa, &work[indwrk], llwork,
dwork, n*lddc, &iinfo);
#else
magma_ssytrd_gpu(uplo, n, da, ldda, w, &work[inde],
&work[indtau], wa, ldwa, &work[indwrk], llwork,
&iinfo);
#endif
#ifdef ENABLE_TIMER
end = get_current_time();
#ifdef FAST_SYMV
printf("time ssytrd2 = %6.2f\n", GetTimerValue(start,end)/1000.);
#else
printf("time ssytrd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
#endif
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call SORMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &work[inde], info);
} else {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
magma_sstedx('A', n, 0., 0., 0, 0, w, &work[inde],
&work[indwrk], n, &work[indwk2],
llwrk2, iwork, liwork, dwork, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time sstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_ssetmatrix( n, n, &work[indwrk], n, dwork, lddc );
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
magma_sormtr_gpu(MagmaLeft, uplo, MagmaNoTrans, n, n, da, ldda, &work[indtau],
dwork, lddc, wa, ldwa, &iinfo);
magma_scopymatrix( n, n, dwork, lddc, da, ldda );
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time sormtr + copy = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
d__1 = 1. / sigma;
blasf77_sscal(&n, &d__1, w, &ione);
}
work[0] = lwmin * (1. + lapackf77_slamch("Epsilon")); // round up
iwork[0] = liwmin;
magma_queue_destroy( stream );
magma_free( dwork );
return *info;
} /* magma_ssyevd_gpu */
/**
Purpose
-------
SSYTRD2_GPU reduces a real symmetric matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version passes a workspace that is used in an optimized
GPU matrix-vector product.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA 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, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
d REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
@param[out]
e REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower.
@param[out]
tau REAL array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
wA (workspace) REAL array, dimension (LDA,N)
On exit the diagonal, the upper part (UPLO=MagmaUpper)
or the lower part (UPLO=MagmaLower) are copies of DA
@param[in]
ldwa INTEGER
The leading dimension of the array wA. LDWA >= max(1,N).
@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 dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
dwork (workspace) REAL array on the GPU, dim (MAX(1,LDWORK))
@param[in]
ldwork INTEGER
The dimension of the array DWORK.
LDWORK >= (n*n+64-1)/64 + 2*n*nb, where nb = magma_get_ssytrd_nb(n)
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
@ingroup magma_ssyev_comp
********************************************************************/
extern "C" magma_int_t
magma_ssytrd2_gpu(
magma_uplo_t uplo, magma_int_t n,
magmaFloat_ptr dA, magma_int_t ldda,
float *d, float *e, float *tau,
float *wA, magma_int_t ldwa,
float *work, magma_int_t lwork,
magmaFloat_ptr dwork, magma_int_t ldwork,
magma_int_t *info)
{
#define A(i, j) (wA + (j)*ldwa + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t nb = magma_get_ssytrd_nb(n);
float c_neg_one = MAGMA_S_NEG_ONE;
float c_one = MAGMA_S_ONE;
float d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldw, lddw, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
} else if (ldwa < max(1,n)) {
*info = -9;
} else if (lwork < 1 && ! lquery) {
*info = -11;
}
/* Determine the block size. */
ldw = lddw = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_S_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
if (n < 1024)
nx = n;
else
nx = 300;
if (ldwork < (ldw*n+64-1)/64 + 2*ldw*nb) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_sgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), ldwa );
magma_slatrd2(uplo, i+nb, nb, A(0, 0), ldwa, e, tau,
work, ldw, dA(0, 0), ldda, dwork, lddw, dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_ssetmatrix( i + nb, nb, work, ldw, dwork, lddw );
magma_ssyr2k(uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork,
lddw, d_one, dA(0, 0), ldda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j-1,j) = MAGMA_S_MAKE( e[j - 1], 0 );
d[j] = MAGMA_S_REAL( *A(j, j) );
}
}
magma_sgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), ldwa );
/* Use CPU code to reduce the last or only block */
lapackf77_ssytrd(uplo_, &kk, A(0, 0), &ldwa, d, e, tau, work, &lwork, &iinfo);
magma_ssetmatrix( kk, kk, A(0, 0), ldwa, dA(0, 0), ldda );
}
else {
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_sgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), ldwa );
magma_slatrd2(uplo, n-i, nb, A(i, i), ldwa, &e[i],
&tau[i], work, ldw,
dA(i, i), ldda,
dwork, lddw,
dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_ssetmatrix( n-i, nb, work, ldw, dwork, lddw );
magma_ssyr2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda,
&dwork[nb], lddw, d_one,
dA(i+nb, i+nb), ldda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j+1,j) = MAGMA_S_MAKE( e[j], 0 );
d[j] = MAGMA_S_REAL( *A(j, j) );
}
}
/* Use unblocked code to reduce the last or only block */
magma_sgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), ldwa );
i_n = n-i;
lapackf77_ssytrd(uplo_, &i_n, A(i, i), &ldwa, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo);
magma_ssetmatrix( n-i, n-i, A(i, i), ldwa, dA(i, i), ldda );
}
work[0] = MAGMA_S_MAKE( lwkopt, 0 );
return *info;
} /* magma_ssytrd2_gpu */
/**
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 */
/**
Purpose
-------
SSYTRD reduces a real symmetric matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A 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, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
d REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
@param[out]
e REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower.
@param[out]
tau REAL array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@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 dimension of the array WORK. LWORK >= N*NB, where NB is the
optimal blocksize given by magma_get_ssytrd_nb().
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
@ingroup magma_ssyev_comp
********************************************************************/
extern "C" magma_int_t
magma_ssytrd(magma_uplo_t uplo, magma_int_t n,
float *A, magma_int_t lda,
float *d, float *e, float *tau,
float *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) ( A + (j)*lda + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t ldda = lda;
magma_int_t nb = magma_get_ssytrd_nb(n);
float c_neg_one = MAGMA_S_NEG_ONE;
float c_one = MAGMA_S_ONE;
float d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldwork, lddwork, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < nb*n && ! lquery) {
*info = -9;
}
/* Determine the block size. */
ldwork = lddwork = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_S_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
float *dA;
if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda + 2*n*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
float *dwork = dA + n*ldda;
if (n < 2048)
nx = n;
else
nx = 512;
if (upper) {
/* Copy the matrix to the GPU */
magma_ssetmatrix( n, n, A(0, 0), lda, dA(0, 0), ldda );
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != n-nb)
magma_sgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), lda );
magma_slatrd(uplo, i+nb, nb, A(0, 0), lda, e, tau,
work, ldwork, dA(0, 0), ldda, dwork, lddwork);
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_ssetmatrix( i + nb, nb, work, ldwork, dwork, lddwork );
magma_ssyr2k(uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork,
lddwork, d_one, dA(0, 0), ldda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j-1,j) = MAGMA_S_MAKE( e[j - 1], 0 );
d[j] = MAGMA_S_REAL( *A(j, j) );
}
}
magma_sgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), lda );
/* Use unblocked code to reduce the last or only block */
lapackf77_ssytd2(uplo_, &kk, A(0, 0), &lda, d, e, tau, &iinfo);
}
else {
/* Copy the matrix to the GPU */
if (1 <= n-nx)
magma_ssetmatrix( n, n, A(0,0), lda, dA(0,0), ldda );
#ifdef FAST_HEMV
// TODO this leaks memory from dA, above
float *dwork2;
if (MAGMA_SUCCESS != magma_smalloc( &dwork2, n*n )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#endif
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != 0)
magma_sgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), lda );
#ifdef FAST_HEMV
magma_slatrd2(uplo, n-i, nb, A(i, i), lda, &e[i],
&tau[i], work, ldwork,
dA(i, i), ldda,
dwork, lddwork, dwork2, n*n);
#else
magma_slatrd(uplo, n-i, nb, A(i, i), lda, &e[i],
&tau[i], work, ldwork,
dA(i, i), ldda,
dwork, lddwork);
#endif
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_ssetmatrix( n-i, nb, work, ldwork, dwork, lddwork );
magma_ssyr2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda,
&dwork[nb], lddwork, d_one,
dA(i+nb, i+nb), ldda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j+1,j) = MAGMA_S_MAKE( e[j], 0 );
d[j] = MAGMA_S_REAL( *A(j, j) );
}
}
#ifdef FAST_HEMV
magma_free( dwork2 );
#endif
/* Use unblocked code to reduce the last or only block */
if (1 <= n-nx)
magma_sgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), lda );
i_n = n-i;
lapackf77_ssytrd(uplo_, &i_n, A(i, i), &lda, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo);
}
magma_free( dA );
work[0] = MAGMA_S_MAKE( lwkopt, 0 );
return *info;
} /* magma_ssytrd */
magma_int_t magmaf_get_ssytrd_nb( magma_int_t *m )
{
return magma_get_ssytrd_nb( *m );
}
/* ////////////////////////////////////////////////////////////////////////////
-- 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;
}
extern "C" magma_int_t
magma_ssyevd(magma_vec_t jobz, magma_vec_t uplo,
magma_int_t n,
float *a, magma_int_t lda,
float *w,
float *work, magma_int_t lwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info, magma_queue_t queue)
{
/* -- MAGMA (version 1.0.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
September 2012
Purpose
=======
SSYEVD computes all eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) REAL 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
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least 2*N + N*NB.
If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2.
NB can be obtained through magma_get_ssytrd_nb(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.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK must be at least 1.
If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK 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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i and JOBZ = 'N', then the algorithm failed
to converge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
if INFO = i and JOBZ = 'V', then the algorithm failed
to compute an eigenvalue while working on the submatrix
lying in rows and columns INFO/(N+1) through
mod(INFO,N+1).
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
===================================================================== */
magma_uplo_t uplo_ = uplo;
magma_vec_t jobz_ = jobz;
magma_int_t ione = 1;
magma_int_t izero = 0;
float d_one = 1.;
float d__1;
float eps;
magma_int_t inde;
float anrm;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indwrk, liwmin;
magma_int_t llwork;
float smlnum;
magma_int_t lquery;
//magmaFloat_ptr dwork;
wantz = lapackf77_lsame(lapack_const(jobz_), MagmaVectorsStr);
lower = lapackf77_lsame(lapack_const(uplo_), MagmaLowerStr);
lquery = lwork == -1 || liwork == -1;
*info = 0;
if (! (wantz || lapackf77_lsame(lapack_const(jobz_), MagmaNoVectorsStr))) {
*info = -1;
} else if (! (lower || lapackf77_lsame(lapack_const(uplo_), MagmaUpperStr))) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
}
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 to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
// ACD
// work[0] = lwmin * (1. + lapackf77_slamch("Epsilon"));
work[0] = (float)( lwmin * (1. + lapackf77_slamch("Epsilon")) );
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -8;
} else if ((liwork < liwmin) && ! lquery) {
*info = -10;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (n == 1) {
w[0] = a[0];
if (wantz) {
a[0] = 1.;
}
return *info;
}
/* Get machine constants. */
safmin = lapackf77_slamch("Safe minimum");
eps = lapackf77_slamch("Precision");
smlnum = safmin / eps;
// ACD
// bignum = 1. / smlnum;
bignum = 1.F / smlnum;
rmin = magma_ssqrt(smlnum);
rmax = magma_ssqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_slansy("M", lapack_const(uplo_), &n, a, &lda, work );
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
lapackf77_slascl(lapack_const(uplo_), &izero, &izero, &d_one, &sigma, &n, &n, a,
&lda, info);
}
/* Call SSYTRD to reduce symmetric matrix to tridiagonal form. */
// ssytrd work: e (n) + tau (n) + llwork (n*nb) ==> 2n + n*nb
// sstedx work: e (n) + tau (n) + z (n*n) + llwrk2 (1 + 4*n + n^2) ==> 1 + 6n + 2n^2
inde = 0;
indtau = inde + n;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
//#define ENABLE_TIMER
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
//char _uplo_[2] = { lapack_const(uplo)[0], 0 };
//lapackf77_ssytrd(_uplo_, &n, a, &lda, w, &work[inde],
// &work[indtau], &work[indwrk], &llwork, &iinfo);
magma_ssytrd(lapack_const(uplo)[0], n, a, lda, w, &work[inde],
&work[indtau], &work[indwrk], llwork, &iinfo, queue);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time ssytrd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call SORMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &work[inde], info);
} else {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
//if (MAGMA_SUCCESS != magma_malloc( &dwork, 3*n*(n/2 + 1)*sizeof(float) )) {
// *info = MAGMA_ERR_DEVICE_ALLOC;
// return *info;
//}
//magma_sstedx(MagmaAllVec, n, 0., 0., 0, 0, w, &work[inde],
// &work[indwrk], n, &work[indwk2],
// llwrk2, iwork, liwork, dwork, info, queue);
lapackf77_sstevd(V_char, &n, w, &work[inde],
&work[indwrk], &n, &work[indwk2],
&llwrk2, iwork, &liwork, info
);
//magma_free( dwork );
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time sstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
lapackf77_sormtr(L_char, lapack_const(uplo), N_char, &n, &n, a, &lda, &work[indtau],
&work[indwrk], &n, &work[indwk2], &llwrk2, &iinfo);
//magma_sormtr(MagmaLeft, uplo, MagmaNoTrans, n, n, a, lda, &work[indtau],
// &work[indwrk], n, &work[indwk2], llwrk2, &iinfo, queue);
lapackf77_slacpy("A", &n, &n, &work[indwrk], &n, a, &lda);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time sormtr + copy = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
// ACD
// d__1 = 1. / sigma;
d__1 = 1.F / sigma;
blasf77_sscal(&n, &d__1, w, &ione);
}
// ACD
// work[0] = lwmin * (1. + lapackf77_slamch("Epsilon")); // round up
work[0] = (float)( lwmin * (1. + lapackf77_slamch("Epsilon")) ); // round up
iwork[0] = liwmin;
return *info;
} /* magma_ssyevd */
extern "C" magma_int_t
magma_ssygvd(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 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
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) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= 2*N*nb + 1.
If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N*nb + 2*N**2.
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.
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
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.
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;
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, lquery;
magma_int_t lopt, lwmin, liopt, liwmin;
cudaStream_t stream;
magma_queue_create( &stream );
wantz = lapackf77_lsame(jobz_, MagmaVectorsStr);
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_, MagmaNoVectorsStr))) {
*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) {
liwmin = 1;
lwmin = 1;
} else if (wantz) {
lwmin = 1 + 6 * n * nb + 2* n * n;
liwmin = 5 * n + 3;
} else {
lwmin = 2 * n * nb + 1;
liwmin = 1;
}
lopt = lwmin;
liopt = liwmin;
work[ 0] = lopt;
iwork[0] = liopt;
if (lwork < lwmin && ! lquery) {
*info = -11;
} else if (liwork < liwmin && ! lquery) {
*info = -13;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return MAGMA_ERR_ILLEGAL_VALUE;
}
else if (lquery) {
return MAGMA_SUCCESS;
}
/* Quick return if possible */
if (n == 0) {
return 0;
}
if (MAGMA_SUCCESS != magma_smalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_smalloc( &db, n*lddb )) {
*info = -17;
return MAGMA_ERR_DEVICE_ALLOC;
}
/* 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_spotrf_gpu(uplo_[0], n, db, lddb, info);
if (*info != 0) {
*info = n + *info;
return 0;
}
magma_queue_sync( stream );
magma_sgetmatrix_async( n, n,
db, lddb,
b, ldb, stream );
/* Transform problem to standard eigenvalue problem and solve. */
magma_ssygst_gpu(itype, uplo_[0], n, da, ldda, db, lddb, info);
magma_ssyevd_gpu(jobz_[0], uplo_[0], n, da, ldda, w, a, lda,
work, lwork, iwork, liwork, info);
lopt = max( lopt, (magma_int_t) work[0]);
liopt = max(liopt, iwork[0]);
if (wantz && *info == 0)
{
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2)
{
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
*(unsigned char *)trans = MagmaTrans;
} else {
*(unsigned char *)trans = MagmaNoTrans;
}
magma_strsm(MagmaLeft, uplo_[0], *trans, MagmaNonUnit,
n, n, 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 = MagmaTrans;
}
magma_strmm(MagmaLeft, uplo_[0], *trans, MagmaNonUnit,
n, n, d_one, db, lddb, da, ldda);
}
magma_sgetmatrix( n, n, da, ldda, a, lda );
}
magma_queue_sync( stream );
magma_queue_destroy( stream );
work[0] = (float) lopt;
iwork[0] = liopt;
magma_free( da );
magma_free( db );
return MAGMA_SUCCESS;
} /* magma_ssygvd */
/**
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 */
/**
Purpose
-------
SSYEVDX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A. 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]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA REAL array on the GPU,
dimension (LDDA, 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.
On exit, if JOBZ = MagmaVec, then if INFO = 0, the first m columns
of A contains the required
orthonormal eigenvectors of the matrix A.
If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower)
or the upper triangle (if UPLO=MagmaUpper) of A, including the
diagonal, is destroyed.
@param[in]
ldda INTEGER
The leading dimension of the array DA. LDDA >= max(1,N).
@param[in]
vl 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 required m eigenvalues in ascending order.
@param
wA (workspace) REAL array, dimension (LDWA, N)
@param[in]
ldwa INTEGER
The leading dimension of the array wA. LDWA >= max(1,N).
@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: 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).
Further Details
---------------
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
@ingroup magma_ssyev_driver
********************************************************************/
extern "C" magma_int_t
magma_ssyevdx_gpu(magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
magma_int_t n,
float *dA, magma_int_t ldda,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
float *wA, magma_int_t ldwa,
float *work, magma_int_t lwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
magma_int_t ione = 1;
float d__1;
float eps;
magma_int_t inde;
float anrm;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indwrk, liwmin;
magma_int_t llwork;
float smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
float *dwork;
magma_int_t lddc = ldda;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1 || liwork == -1);
*info = 0;
if (! (wantz || (jobz == MagmaNoVec))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (ldda < max(1,n)) {
*info = -6;
} else if (ldwa < max(1,n)) {
*info = -14;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -8;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -9;
} else if (iu < min(n,il) || iu > n) {
*info = -10;
}
}
}
magma_int_t nb = magma_get_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 = -16;
} else if ((liwork < liwmin) && ! lquery) {
*info = -18;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
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
const char* jobz_ = lapack_vec_const( jobz );
const char* uplo_ = lapack_uplo_const( uplo );
float *A;
magma_smalloc_cpu( &A, n*n );
magma_sgetmatrix(n, n, dA, ldda, A, n);
lapackf77_ssyevd(jobz_, uplo_,
&n, A, &n,
w, work, &lwork,
iwork, &liwork, info);
magma_ssetmatrix( n, n, A, n, dA, ldda);
magma_free_cpu(A);
return *info;
}
magma_queue_t stream;
magma_queue_create( &stream );
// n*lddc for ssytrd2_gpu
// n for slansy
magma_int_t ldwork = n*lddc;
if ( wantz ) {
// need 3n^2/2 for sstedx
ldwork = max( ldwork, 3*n*(n/2 + 1));
}
if (MAGMA_SUCCESS != magma_smalloc( &dwork, ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Get machine constants. */
safmin = lapackf77_slamch("Safe minimum");
eps = lapackf77_slamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_ssqrt(smlnum);
rmax = magma_ssqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = magmablas_slansy(MagmaMaxNorm, uplo, n, dA, ldda, dwork);
iscale = 0;
sigma = 1;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
magmablas_slascl(uplo, 0, 0, 1., sigma, n, n, dA, ldda, info);
}
/* Call SSYTRD to reduce symmetric matrix to tridiagonal form. */
// ssytrd work: e (n) + tau (n) + llwork (n*nb) ==> 2n + n*nb
// sstedx work: e (n) + tau (n) + z (n*n) + llwrk2 (1 + 4*n + n^2) ==> 1 + 6n + 2n^2
inde = 0;
indtau = inde + n;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
magma_timer_t time=0;
timer_start( time );
#ifdef FAST_SYMV
magma_ssytrd2_gpu(uplo, n, dA, ldda, w, &work[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork,
dwork, n*lddc, &iinfo);
#else
magma_ssytrd_gpu(uplo, n, dA, ldda, w, &work[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork,
&iinfo);
#endif
timer_stop( time );
timer_printf( "time ssytrd = %6.2f\n", time );
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call SORMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &work[inde], info);
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
}
else {
timer_start( time );
magma_sstedx(range, n, vl, vu, il, iu, w, &work[inde],
&work[indwrk], n, &work[indwk2],
llwrk2, iwork, liwork, dwork, info);
timer_stop( time );
timer_printf( "time sstedx = %6.2f\n", time );
timer_start( time );
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
magma_ssetmatrix( n, *m, &work[indwrk + n* (il-1) ], n, dwork, lddc );
magma_sormtr_gpu(MagmaLeft, uplo, MagmaNoTrans, n, *m, dA, ldda, &work[indtau],
dwork, lddc, wA, ldwa, &iinfo);
magma_scopymatrix( n, *m, dwork, lddc, dA, ldda );
timer_stop( time );
timer_printf( "time sormtr + copy = %6.2f\n", time );
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
d__1 = 1. / sigma;
blasf77_sscal(&n, &d__1, w, &ione);
}
work[0] = lwmin * one_eps; // round up
iwork[0] = liwmin;
magma_queue_destroy( stream );
magma_free( dwork );
return *info;
} /* magma_ssyevd_gpu */
/**
Purpose
-------
SSYEVD_GPU computes all eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA REAL array on the GPU,
dimension (LDDA, 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.
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower)
or the upper triangle (if UPLO=MagmaUpper) of A, including the
diagonal, is destroyed.
@param[in]
ldda INTEGER
The leading dimension of the array DA. LDDA >= max(1,N).
@param[out]
w REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param
wA (workspace) REAL array, dimension (LDWA, N)
@param[in]
ldwa INTEGER
The leading dimension of the array wA. LDWA >= max(1,N).
@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: 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).
Further Details
---------------
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
@ingroup magma_ssyev_driver
********************************************************************/
extern "C" magma_int_t
magma_ssyevd_gpu(
magma_vec_t jobz, magma_uplo_t uplo,
magma_int_t n,
magmaFloat_ptr dA, magma_int_t ldda,
float *w,
float *wA, magma_int_t ldwa,
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)
{
magma_int_t ione = 1;
float d__1;
float eps;
magma_int_t inde;
float anrm;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indwrk, liwmin;
magma_int_t llwork;
float smlnum;
magma_int_t lquery;
magmaFloat_ptr dwork;
magma_int_t lddc = ldda;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -1 || liwork == -1);
*info = 0;
if (! (wantz || (jobz == MagmaNoVec))) {
*info = -1;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
}
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 = -10;
} else if ((liwork < liwmin) && ! lquery) {
*info = -12;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
/* If matrix is very small, then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
magma_int_t lda = n;
float *A;
magma_smalloc_cpu( &A, lda*n );
magma_sgetmatrix( n, n, dA, ldda, A, lda, queue );
lapackf77_ssyevd( lapack_vec_const(jobz), lapack_uplo_const(uplo),
&n, A, &lda,
w, work, &lwork,
iwork, &liwork, info );
magma_ssetmatrix( n, n, A, lda, dA, ldda, queue );
magma_free_cpu( A );
magma_queue_destroy( queue );
return *info;
}
// ssytrd2_gpu requires ldda*ceildiv(n,64) + 2*ldda*nb
// sormtr_gpu requires lddc*n
// slansy requires n
magma_int_t ldwork = max( ldda*magma_ceildiv(n,64) + 2*ldda*nb, lddc*n );
ldwork = max( ldwork, n );
if ( wantz ) {
// sstedx requires 3n^2/2
ldwork = max( ldwork, 3*n*(n/2 + 1) );
}
if (MAGMA_SUCCESS != magma_smalloc( &dwork, ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Get machine constants. */
safmin = lapackf77_slamch("Safe minimum");
eps = lapackf77_slamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_ssqrt( smlnum );
rmax = magma_ssqrt( bignum );
/* Scale matrix to allowable range, if necessary. */
anrm = magmablas_slansy( MagmaMaxNorm, uplo, n, dA, ldda, dwork, ldwork, queue );
iscale = 0;
sigma = 1;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
magmablas_slascl( uplo, 0, 0, 1., sigma, n, n, dA, ldda, queue, info );
}
/* Call SSYTRD to reduce symmetric matrix to tridiagonal form. */
// ssytrd work: e (n) + tau (n) + llwork (n*nb) ==> 2n + n*nb
// sstedx work: e (n) + tau (n) + z (n*n) + llwrk2 (1 + 4*n + n^2) ==> 1 + 6n + 2n^2
inde = 0;
indtau = inde + n;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
magma_timer_t time=0;
timer_start( time );
#ifdef FAST_SYMV
magma_ssytrd2_gpu( uplo, n, dA, ldda, w, &work[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork,
dwork, ldwork, &iinfo );
#else
magma_ssytrd_gpu( uplo, n, dA, ldda, w, &work[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork,
&iinfo );
#endif
timer_stop( time );
#ifdef FAST_SYMV
timer_printf( "time ssytrd2 = %6.2f\n", time );
#else
timer_printf( "time ssytrd = %6.2f\n", time );
#endif
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call SORMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf( &n, w, &work[inde], info );
}
else {
timer_start( time );
magma_sstedx( MagmaRangeAll, n, 0., 0., 0, 0, w, &work[inde],
&work[indwrk], n, &work[indwk2],
llwrk2, iwork, liwork, dwork, info );
timer_stop( time );
timer_printf( "time sstedx = %6.2f\n", time );
timer_start( time );
magma_ssetmatrix( n, n, &work[indwrk], n, dwork, lddc, queue );
magma_sormtr_gpu( MagmaLeft, uplo, MagmaNoTrans, n, n, dA, ldda, &work[indtau],
dwork, lddc, wA, ldwa, &iinfo );
magma_scopymatrix( n, n, dwork, lddc, dA, ldda, queue );
timer_stop( time );
timer_printf( "time sormtr + copy = %6.2f\n", time );
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
d__1 = 1. / sigma;
blasf77_sscal( &n, &d__1, w, &ione );
}
work[0] = magma_smake_lwork( lwmin );
iwork[0] = liwmin;
magma_queue_destroy( queue );
magma_free( dwork );
return *info;
} /* magma_ssyevd_gpu */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ssygvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time /*cpu_time*/;
float *h_A, *h_R, *h_B, *h_S, *h_work;
float *w1, *w2, vl=0, vu=0;
float result[2] = {0};
magma_int_t *iwork;
magma_int_t N, n2, info, il, iu, m1, m2, nb, lwork, liwork;
float c_zero = MAGMA_S_ZERO;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
#if defined(PRECISION_z) || defined(PRECISION_c)
float *rwork;
magma_int_t lrwork;
#endif
//float d_one = 1.;
//float d_ten = 10.;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("P");
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf(" N M GPU Time (sec)\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;
nb = magma_get_ssytrd_nb(N);
#if defined(PRECISION_z) || defined(PRECISION_c)
lwork = 2*N*nb + N*N;
lrwork = 1 + 5*N +2*N*N;
#else
lwork = 1 + 6*N*nb + 2* N*N;
#endif
liwork = 3 + 5*N;
if ( opts.fraction == 0 ) {
il = N / 10;
iu = N / 5+il;
}
else {
il = 1;
iu = (int) (opts.fraction*N);
if (iu < 1) iu = 1;
}
TESTING_MALLOC( h_A, float, n2 );
TESTING_MALLOC( h_B, float, n2 );
TESTING_MALLOC( w1, float, N );
TESTING_MALLOC( w2, float, N );
TESTING_MALLOC( iwork, magma_int_t, liwork );
TESTING_HOSTALLOC( h_R, float, n2 );
TESTING_HOSTALLOC( h_S, float, n2 );
TESTING_HOSTALLOC( h_work, float, lwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_HOSTALLOC( rwork, float, lrwork);
#endif
/* Initialize the matrix */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
lapackf77_slarnv( &ione, ISEED, &n2, h_B );
/* increase the diagonal */
for(int i=0; i<N; i++) {
MAGMA_S_SET2REAL( h_B[i*N+i], ( MAGMA_S_REAL(h_B[i*N+i]) + 1.*N ) );
MAGMA_S_SET2REAL( h_A[i*N+i], MAGMA_S_REAL(h_A[i*N+i]) );
}
// ==================================================================
// Warmup using MAGMA
// ==================================================================
if(opts.warmup){
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_ssygvdx( opts.itype, opts.jobz, 'I', opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info );
if (info != 0)
printf("magma_ssygvdx returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
gpu_time = magma_wtime();
magma_ssygvdx( opts.itype, opts.jobz, 'I', opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info );
gpu_time = magma_wtime() - gpu_time;
if (info != 0)
printf("magma_ssygvdx 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) | S(with V) - S(w/o V) | / | S |
=================================================================== */
#if defined(PRECISION_d) || defined(PRECISION_s)
float *rwork = h_work + N*N;
#endif
float temp1, temp2;
result[0] = 1.;
result[0] /= lapackf77_slansy("1", &opts.uplo, &N, h_A, &N, rwork);
result[0] /= lapackf77_slange("1", &N, &m1, h_R, &N, rwork);
if (opts.itype == 1) {
blasf77_ssymm("L", &opts.uplo, &N, &m1, &c_one, h_A, &N, h_R, &N, &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", &opts.uplo, &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &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", &opts.uplo, &N, &m1, &c_one, h_B, &N, h_R, &N, &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", &opts.uplo, &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_slange("1", &N, &m1, h_R, &N, rwork)/N;
}
else if (opts.itype == 3) {
blasf77_ssymm("L", &opts.uplo, &N, &m1, &c_one, h_A, &N, h_R, &N, &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", &opts.uplo, &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_slange("1", &N, &m1, h_R, &N, rwork)/N;
}
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_ssygvdx( opts.itype, 'N', 'I', opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m2, w2,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info );
if (info != 0)
printf("magma_ssygvdx returned error %d: %s.\n",
(int) info, magma_strerror( info ));
temp1 = temp2 = 0;
for(int j=0; j < m2; j++) {
temp1 = max(temp1, absv(w1[j]));
temp1 = max(temp1, absv(w2[j]));
temp2 = max(temp2, absv(w1[j]-w2[j]));
}
result[1] = temp2 / (((float)m2)*temp1);
}
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %5d %7.2f\n",
(int) N, (int) m1, gpu_time);
if ( opts.check ) {
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if (opts.itype==1)
printf("(1) | A Z - B Z D | / (|A| |Z| N) = %8.2e%s\n", result[0], (result[0] < tol ? "" : " failed"));
else if (opts.itype==2)
printf("(1) | A B Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result[0], (result[0] < tol ? "" : " failed"));
else if (opts.itype==3)
printf("(1) | B A Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result[0], (result[0] < tol ? "" : " failed"));
printf( "(2) | D(w/ Z) - D(w/o Z) | / |D| = %8.2e%s\n\n", result[1], (result[1] < tolulp ? "" : " failed"));
}
TESTING_FREE( h_A );
TESTING_FREE( h_B );
TESTING_FREE( w1 );
TESTING_FREE( w2 );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_HOSTFREE( rwork);
#endif
TESTING_FREE( iwork );
TESTING_HOSTFREE( h_work );
TESTING_HOSTFREE( h_R );
TESTING_HOSTFREE( h_S );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}
/**
Purpose
-------
SSYTRD2_GPU reduces a real symmetric matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version passes a workspace that is used in an optimized
GPU matrix-vector product.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA REAL array on the GPU, dimension (LDDA,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, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,N).
@param[out]
d REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
@param[out]
e REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower.
@param[out]
tau REAL array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
A (workspace) REAL array, dimension (LDA,N)
On exit the diagonal, the upper part (if uplo=MagmaUpper)
or the lower part (if uplo=MagmaLower) are copies of DA
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@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 dimension of the array WORK. LWORK >= N*NB, where NB is the
optimal blocksize given by magma_get_ssytrd_nb().
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
dwork (workspace) REAL array on the GPU, dim (MAX(1,LDWORK))
@param[in]
ldwork INTEGER
The dimension of the array DWORK.
LDWORK >= ldda*ceil(n/64) + 2*ldda*nb, where nb = magma_get_ssytrd_nb(n),
and 64 is for the blocksize of magmablas_ssymv.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
@ingroup magma_ssyev_comp
********************************************************************/
extern "C" magma_int_t
magma_ssytrd2_gpu(
magma_uplo_t uplo, magma_int_t n,
magmaFloat_ptr dA, magma_int_t ldda,
float *d, float *e, float *tau,
float *A, magma_int_t lda,
float *work, magma_int_t lwork,
magmaFloat_ptr dwork, magma_int_t ldwork,
magma_int_t *info)
{
#define A(i_, j_) ( A + (i_) + (j_)*lda )
#define dA(i_, j_) (dA + (i_) + (j_)*ldda)
/* Constants */
const float c_zero = MAGMA_S_ZERO;
const float c_neg_one = MAGMA_S_NEG_ONE;
const float c_one = MAGMA_S_ONE;
const float d_one = MAGMA_D_ONE;
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t nb = magma_get_ssytrd_nb( n );
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldw, lddw, lwkopt;
magma_int_t lquery;
*info = 0;
bool upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
} else if (lda < max(1,n)) {
*info = -9;
} else if (lwork < nb*n && ! lquery) {
*info = -11;
} else if (ldwork < ldda*magma_ceildiv(n,64) + 2*ldda*nb) {
*info = -13;
}
/* Determine the block size. */
ldw = n;
lddw = ldda; // hopefully ldda is rounded up to multiple of 32; ldwork is in terms of ldda, so lddw can't be > ldda.
lwkopt = n * nb;
if (*info == 0) {
work[0] = magma_smake_lwork( lwkopt );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
// nx <= n is required
// use LAPACK for n < 3000, otherwise switch at 512
if (n < 3000)
nx = n;
else
nx = 512;
float *work2;
if (MAGMA_SUCCESS != magma_smalloc_cpu( &work2, n )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_queue_t queue = NULL;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
// clear out dwork in case it has NANs (used as y in ssymv)
// rest of dwork (used as work in magmablas_ssymv) doesn't need to be cleared
magmablas_slaset( MagmaFull, n, nb, c_zero, c_zero, dwork, lddw, queue );
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - magma_roundup( n - nx, nb );
for (i = n - nb; i >= kk; i -= nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_sgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), lda, queue );
magma_slatrd2( uplo, i+nb, nb, A(0, 0), lda, e, tau,
work, ldw, work2, n, dA(0, 0), ldda, dwork, lddw,
dwork + 2*lddw*nb, ldwork - 2*lddw*nb, queue );
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_ssetmatrix( i + nb, nb, work, ldw, dwork, lddw, queue );
magma_ssyr2k( uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork, lddw,
d_one, dA(0, 0), ldda, queue );
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j-1,j) = MAGMA_S_MAKE( e[j - 1], 0 );
d[j] = MAGMA_S_REAL( *A(j, j) );
}
}
magma_sgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), lda, queue );
/* Use CPU code to reduce the last or only block */
lapackf77_ssytrd( uplo_, &kk, A(0, 0), &lda, d, e, tau, work, &lwork, &iinfo );
magma_ssetmatrix( kk, kk, A(0, 0), lda, dA(0, 0), ldda, queue );
}
else {
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_sgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), lda, queue );
magma_slatrd2( uplo, n-i, nb, A(i, i), lda, &e[i], &tau[i],
work, ldw, work2, n, dA(i, i), ldda, dwork, lddw,
dwork + 2*lddw*nb, ldwork - 2*lddw*nb, queue );
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_ssetmatrix( n-i, nb, work, ldw, dwork, lddw, queue );
// cublas 6.5 crashes here if lddw % 32 != 0, e.g., N=250.
magma_ssyr2k( MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda, &dwork[nb], lddw,
d_one, dA(i+nb, i+nb), ldda, queue );
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j+1,j) = MAGMA_S_MAKE( e[j], 0 );
d[j] = MAGMA_S_REAL( *A(j, j) );
}
}
/* Use CPU code to reduce the last or only block */
magma_sgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), lda, queue );
i_n = n-i;
lapackf77_ssytrd( uplo_, &i_n, A(i, i), &lda, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo );
magma_ssetmatrix( n-i, n-i, A(i, i), lda, dA(i, i), ldda, queue );
}
magma_free_cpu( work2 );
magma_queue_destroy( queue );
work[0] = magma_smake_lwork( lwkopt );
return *info;
} /* magma_ssytrd2_gpu */