/* ////////////////////////////////////////////////////////////////////////////
-- Testing zhegvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time;
magmaDoubleComplex *h_A, *h_R, *h_B, *h_S, *h_work;
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork;
magma_int_t lrwork;
#endif
/* Matrix size */
double *w1, *w2, result[2]={0,0};
magma_int_t *iwork;
magma_int_t N, n2, info, lwork, liwork;
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
double tolulp = opts.tolerance * lapackf77_dlamch("P");
magma_range_t range = MagmaRangeAll;
if (opts.fraction != 1)
range = MagmaRangeI;
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf("using: itype = %d, jobz = %s, range = %s, uplo = %s, opts.check = %d, fraction = %6.4f\n",
(int) opts.itype, lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
(int) opts.check, opts.fraction);
printf(" N M GPU Time (sec)\n");
printf("============================\n");
magma_int_t threads = magma_get_parallel_numthreads();
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
n2 = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
lwork = magma_zbulge_get_lq2(N, threads) + 2*N + N*N;
lrwork = 1 + 5*N +2*N*N;
#else
lwork = magma_zbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
liwork = 3 + 5*N;
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( w1, double, N );
TESTING_MALLOC_CPU( w2, double, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_PIN( h_S, magmaDoubleComplex, n2 );
TESTING_MALLOC_PIN( h_work, magmaDoubleComplex, lwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_MALLOC_PIN( rwork, double, lrwork);
#endif
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
magma_zmake_hpd( N, h_B, N );
magma_zmake_hermitian( N, h_A, N );
magma_int_t m1 = 0;
double vl = 0;
double vu = 0;
magma_int_t il = 0;
magma_int_t iu = 0;
if (range == MagmaRangeI) {
il = 1;
iu = (int) (opts.fraction*N);
}
// ==================================================================
// Warmup using MAGMA
// ==================================================================
if (opts.warmup) {
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_zhegvdx_2stage(opts.itype, opts.jobz, range, 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);
}
// ===================================================================
// Performs operation using MAGMA
// ===================================================================
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
gpu_time = magma_wtime();
magma_zhegvdx_2stage(opts.itype, opts.jobz, range, 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 ( opts.check && opts.jobz != MagmaNoVec ) {
/* =====================================================================
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)
double *rwork = h_work + N*N;
#endif
result[0] = 1.;
result[0] /= lapackf77_zlanhe("1", lapack_uplo_const(opts.uplo), &N, h_A, &N, rwork);
result[0] /= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork);
if (opts.itype == 1) {
blasf77_zhemm("L", lapack_uplo_const(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_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_work, &N, rwork)/N;
}
else if (opts.itype == 2) {
blasf77_zhemm("L", lapack_uplo_const(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_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
}
else if (opts.itype == 3) {
blasf77_zhemm("L", lapack_uplo_const(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_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", lapack_uplo_const(opts.uplo), &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
}
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_int_t m2 = m1;
lapackf77_zhegvd(&opts.itype, "N", lapack_uplo_const(opts.uplo), &N,
h_R, &N, h_S, &N, w2,
h_work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
&info);
double maxw=0, diff=0;
for(int j=0; j<m2; j++) {
maxw = max(maxw, fabs(w1[j]));
maxw = max(maxw, fabs(w2[j]));
diff = max(diff, fabs(w1[j] - w2[j]));
}
result[1] = diff / (m2*maxw);
}
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %5d %7.2f\n",
(int) N, (int) m1, gpu_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"));
}
printf( " | D(w/ Z) - D(w/o Z) | / |D| = %8.2e %s\n\n", result[1], (result[1] < tolulp ? "ok" : "failed"));
status += ! (result[0] < tol && result[1] < tolulp);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_S );
TESTING_FREE_PIN( h_work );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_FREE_PIN( rwork );
#endif
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
/* Shutdown */
TESTING_FINALIZE();
return status;
}
extern "C" magma_int_t
magma_zheevdx_2stage(char jobz, char range, char uplo,
magma_int_t n,
magmaDoubleComplex *a, magma_int_t lda,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input) CHARACTER*1
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU]
will be found.
= 'I': the IL-th through IU-th eigenvalues will be found.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX_16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, the first m columns
of A contains the required
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).
VL (input) DOUBLE PRECISION
VU (input) DOUBLE PRECISION
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
IL (input) INTEGER
IU (input) INTEGER
If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
M (output) INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the required m eigenvalues in ascending order.
WORK (workspace/output) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= LQ2 + N * (NB + 1).
If JOBZ = 'V' and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store
the Q2 matrix and is returned by
MAGMA_BULGE_GET_LQ2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (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: 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};
char range_[2] = {range, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t ione = 1;
magma_int_t izero = 0;
double d_one = 1.;
double d__1;
double eps;
double anrm;
magma_int_t imax;
double rmin, rmax;
double sigma;
//magma_int_t iinfo;
magma_int_t lwmin, lrwmin, liwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t iscale;
double safmin;
double bignum;
double smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
double* dwork;
/* determine the number of threads */
magma_int_t threads = magma_get_numthreads();
magma_setlapack_numthreads(threads);
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
alleig = lapackf77_lsame( range_, "A" );
valeig = lapackf77_lsame( range_, "V" );
indeig = lapackf77_lsame( range_, "I" );
lquery = lwork == -1 || lrwork == -1 || liwork == -1;
*info = 0;
if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (lda < max(1,n)) {
*info = -6;
} 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_zbulge_nb(n,threads);
magma_int_t Vblksiz = magma_zbulge_get_Vblksiz(n, nb, threads);
magma_int_t ldt = Vblksiz;
magma_int_t ldv = nb + Vblksiz;
magma_int_t blkcnt = magma_bulge_get_blkcnt(n, nb, Vblksiz);
magma_int_t lq2 = magma_zbulge_get_lq2(n, threads);
if (wantz) {
lwmin = lq2 + 2 * n + n * n;
lrwmin = 1 + 5 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
lrwmin = n;
liwmin = 1;
}
work[0] = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -14;
} else if ((lrwork < lrwmin) && ! lquery) {
*info = -16;
} else if ((liwork < liwmin) && ! lquery) {
*info = -18;
}
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] = MAGMA_Z_REAL(a[0]);
if (wantz) {
a[0] = MAGMA_Z_ONE;
}
return *info;
}
#ifdef ENABLE_TIMER
printf("using %d threads\n", threads);
#endif
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
magma_int_t ntiles = n/nb;
if( ( ntiles < 2 ) || ( 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_zheevd(jobz_, &uplo, &n,
a, &lda, w,
work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
info);
*m = n;
return *info;
}
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_zlanhe("M", uplo_, &n, a, &lda, rwork);
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_zlascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, a,
&lda, info);
}
magma_int_t indT2 = 0;
magma_int_t indTAU2 = indT2 + blkcnt*ldt*Vblksiz;
magma_int_t indV2 = indTAU2+ blkcnt*Vblksiz;
magma_int_t indtau1 = indV2 + blkcnt*ldv*Vblksiz;
magma_int_t indwrk = indtau1+ n;
//magma_int_t indwk2 = indwrk + n * n;
magma_int_t llwork = lwork - indwrk;
//magma_int_t llwrk2 = lwork - indwk2;
magma_int_t inde = 0;
magma_int_t indrwk = inde + n;
magma_int_t llrwk = lrwork - indrwk;
#ifdef ENABLE_TIMER
magma_timestr_t start, st1, st2, end;
start = get_current_time();
#endif
magmaDoubleComplex *dT1;
if (MAGMA_SUCCESS != magma_zmalloc( &dT1, n*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zhetrd_he2hb(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, dT1, threads, info);
#ifdef ENABLE_TIMER
st1 = get_current_time();
printf(" time zhetrd_he2hb = %6.2f\n" , GetTimerValue(start,st1)/1000.);
#endif
/* copy the input matrix into WORK(INDWRK) with band storage */
/* PAY ATTENTION THAT work[indwrk] should be able to be of size lda2*n which it should be checked in any future modification of lwork.*/
magma_int_t lda2 = 2*nb; //nb+1+(nb-1);
magmaDoubleComplex* A2 = &work[indwrk];
memset(A2 , 0, n*lda2*sizeof(magmaDoubleComplex));
for (magma_int_t j = 0; j < n-nb; j++)
{
cblas_zcopy(nb+1, &a[j*(lda+1)], 1, &A2[j*lda2], 1);
memset(&a[j*(lda+1)], 0, (nb+1)*sizeof(magmaDoubleComplex));
a[nb + j*(lda+1)] = c_one;
}
for (magma_int_t j = 0; j < nb; j++)
{
cblas_zcopy(nb-j, &a[(j+n-nb)*(lda+1)], 1, &A2[(j+n-nb)*lda2], 1);
memset(&a[(j+n-nb)*(lda+1)], 0, (nb-j)*sizeof(magmaDoubleComplex));
}
#ifdef ENABLE_TIMER
st2 = get_current_time();
printf(" time zhetrd_convert = %6.2f\n" , GetTimerValue(st1,st2)/1000.);
#endif
magma_zhetrd_hb2st(threads, uplo, n, nb, Vblksiz, A2, lda2, w, &rwork[inde], &work[indV2], ldv, &work[indTAU2], wantz, &work[indT2], ldt);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time zhetrd_hb2st = %6.2f\n" , GetTimerValue(st2,end)/1000.);
printf(" time zhetrd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
lapackf77_dsterf(&n, w, &rwork[inde], info);
magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time dstedc = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
} else {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, 3*n*(n/2 + 1) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zstedx(range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, dwork, info);
magma_free( dwork );
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time zstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
magmaDoubleComplex *dZ;
magma_int_t lddz = n;
magmaDoubleComplex *da;
magma_int_t ldda = n;
magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
if (MAGMA_SUCCESS != magma_zmalloc( &dZ, *m*lddz)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zbulge_back(threads, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
#ifdef ENABLE_TIMER
st1 = get_current_time();
printf(" time zbulge_back = %6.2f\n" , GetTimerValue(start,st1)/1000.);
#endif
magma_zsetmatrix( n, n, a, lda, da, ldda );
magma_zunmqr_gpu_2stages(MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, da+nb, ldda,
dZ+nb, n, dT1, nb, info);
magma_zgetmatrix( n, *m, dZ, lddz, a, lda );
magma_free(dT1);
magma_free(dZ);
magma_free(da);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time zunmqr + copy = %6.2f\n", GetTimerValue(st1,end)/1000.);
printf(" time eigenvectors backtransf. = %6.2f\n" , GetTimerValue(start,end)/1000.);
#endif
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_dscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
iwork[0] = liwmin;
return *info;
} /* magma_zheevdx_2stage */
extern "C" magma_int_t
magma_zhegvdx_2stage_m(magma_int_t nrgpu, magma_int_t itype, char jobz, char range, char uplo, magma_int_t n,
cuDoubleComplex *a, magma_int_t lda, cuDoubleComplex *b, magma_int_t ldb,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w, cuDoubleComplex *work, magma_int_t lwork, double *rwork,
magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info)
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
Purpose
=======
ZHEGVDX_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
ITYPE (input) INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
RANGE (input) CHARACTER*1
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU]
will be found.
= 'I': the IL-th through IU-th eigenvalues will be found.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
or the lower triangle (if UPLO='L') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) COMPLEX*16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = 'U', the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = 'L',
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
VL (input) DOUBLE PRECISION
VU (input) DOUBLE PRECISION
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
IL (input) INTEGER
IU (input) INTEGER
If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
M (output) INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= LQ2 + N * (NB + 1).
If JOBZ = 'V' and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store
the Q2 matrix and is returned by
MAGMA_BULGE_GET_LQ2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = 'N' and N > 1, LRWORK >= N.
If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = 'N' and N > 1, LIWORK >= 1.
If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPOTRF or ZHEEVD returned an error code:
<= N: if INFO = i and JOBZ = 'N', then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = 'V', then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Further Details
===============
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if ZHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
char range_[2] = {range, 0};
cuDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t lower;
char trans[1];
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
// magma_int_t lopt;
magma_int_t lwmin;
// magma_int_t liopt;
magma_int_t liwmin;
// magma_int_t lropt;
magma_int_t lrwmin;
cudaStream_t stream;
magma_queue_create( &stream );
wantz = lapackf77_lsame(jobz_, MagmaVectorsStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
lquery = lwork == -1 || lrwork == -1 || liwork == -1;
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVectorsStr))) {
*info = -3;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_bulge_get_nb(n);
magma_int_t lq2 = magma_zbulge_get_lq2(n);
if (wantz) {
lwmin = lq2 + 2 * n + n * n;
lrwmin = 1 + 5 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
lrwmin = n;
liwmin = 1;
}
MAGMA_Z_SET2REAL(work[0],(double)lwmin);
rwork[0] = lrwmin;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (lrwork < lrwmin && ! lquery) {
*info = -19;
} else if (liwork < liwmin && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
/* Form a Cholesky factorization of B. */
#define ENABLE_TIMER
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
magma_zpotrf_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 zpotrf_m = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
/* Transform problem to standard eigenvalue problem and solve. */
magma_zhegst_m(nrgpu, itype, uplo, n, a, lda, b, ldb, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zhegst_m = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
magma_zheevdx_2stage_m(nrgpu, jobz, range, uplo, n, a, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zheevdx_2stage_m = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
if (wantz && *info == 0) {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
*(unsigned char *)trans = MagmaConjTrans;
} else {
*(unsigned char *)trans = MagmaNoTrans;
}
magma_ztrsm_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) {
*(unsigned char *)trans = MagmaNoTrans;
} else {
*(unsigned char *)trans = MagmaConjTrans;
}
//magma_ztrmm_m(nrgpu, MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, b, ldb, a, lda);
}
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time trsm/mm_m = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
}
/*work[0].r = (doublereal) lopt, work[0].i = 0.;
rwork[0] = (doublereal) lropt;
iwork[0] = liopt;*/
printf("\n\n\n");
return *info;
} /* zhegvdx_2stage_m */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zhegvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT_MGPU();
real_Double_t mgpu_time;
magmaDoubleComplex *h_A, *h_Ainit, *h_B, *h_Binit, *h_work;
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork;
magma_int_t lrwork;
#endif
double *w1, result;
magma_int_t *iwork;
magma_int_t N, n2, info, lwork, liwork;
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_timestr_t start, end;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
char jobz = opts.jobz;
int checkres = opts.check;
char range = 'A';
char uplo = opts.uplo;
magma_int_t itype = opts.itype;
double f = opts.fraction;
if (f != 1)
range='I';
if ( checkres && jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
jobz = MagmaVec;
}
printf("using: nrgpu = %d, itype = %d, jobz = %c, range = %c, uplo = %c, checkres = %d, fraction = %6.4f\n",
(int) opts.ngpu, (int) itype, jobz, range, uplo, (int) checkres, f);
printf(" N M nr GPU MGPU Time(s) \n");
printf("====================================\n");
magma_int_t threads = magma_get_numthreads();
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
n2 = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
lwork = magma_zbulge_get_lq2(N, threads) + 2*N + N*N;
lrwork = 1 + 5*N +2*N*N;
#else
lwork = magma_zbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
liwork = 3 + 5*N;
//magma_int_t NB = 96;//magma_bulge_get_nb(N);
//magma_int_t sizvblg = magma_zbulge_get_lq2(N, threads);
//magma_int_t siz = max(sizvblg,n2)+2*(N*NB+N)+24*N;
/* Allocate host memory for the matrix */
TESTING_HOSTALLOC( h_A, magmaDoubleComplex, n2);
TESTING_HOSTALLOC( h_B, magmaDoubleComplex, n2);
TESTING_MALLOC( w1, double , N);
TESTING_HOSTALLOC(h_work, magmaDoubleComplex, lwork);
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_HOSTALLOC( rwork, double, lrwork);
#endif
TESTING_MALLOC( iwork, magma_int_t, liwork);
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
/* increase the diagonal */
{
for(int i=0; i<N; i++) {
MAGMA_Z_SET2REAL( h_B[i*N+i], ( MAGMA_Z_REAL(h_B[i*N+i]) + 1.*N ) );
MAGMA_Z_SET2REAL( h_A[i*N+i], MAGMA_Z_REAL(h_A[i*N+i]) );
}
}
if((opts.warmup)||( checkres )){
TESTING_MALLOC(h_Ainit, magmaDoubleComplex, n2);
TESTING_MALLOC(h_Binit, magmaDoubleComplex, n2);
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_Ainit, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_Binit, &N );
}
magma_int_t m1 = 0;
double vl = 0;
double vu = 0;
magma_int_t il = 0;
magma_int_t iu = 0;
if (range == 'I'){
il = 1;
iu = (int) (f*N);
}
if(opts.warmup){
// ==================================================================
// Warmup using MAGMA. I prefer to use smalltest to warmup A-
// ==================================================================
magma_zhegvdx_2stage_m(opts.ngpu, itype, jobz, range, uplo,
N, h_A, N, h_B, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_Ainit, &N, h_A, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_Binit, &N, h_B, &N );
}
// ===================================================================
// Performs operation using MAGMA
// ===================================================================
start = get_current_time();
magma_zhegvdx_2stage_m(opts.ngpu, itype, jobz, range, uplo,
N, h_A, N, h_B, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
end = get_current_time();
mgpu_time = GetTimerValue(start,end)/1000.;
if ( checkres ) {
// ===================================================================
// 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)
// ===================================================================
#if defined(PRECISION_d) || defined(PRECISION_s)
double *rwork = h_work + N*N;
#endif
result = 1.;
result /= lapackf77_zlanhe("1",&uplo, &N, h_Ainit, &N, rwork);
result /= lapackf77_zlange("1",&N , &m1, h_A, &N, rwork);
if (itype == 1){
blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Ainit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_zhemm("L", &uplo, &N, &m1, &c_neg_one, h_Binit, &N, h_A, &N, &c_one, h_work, &N);
result *= lapackf77_zlange("1", &N, &m1, h_work, &N, rwork)/N;
}
else if (itype == 2){
blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Binit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Ainit, &N, h_work, &N, &c_neg_one, h_A, &N);
result *= lapackf77_zlange("1", &N, &m1, h_A, &N, rwork)/N;
}
else if (itype == 3){
blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Ainit, &N, h_A, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_A[i*N], &ione);
blasf77_zhemm("L", &uplo, &N, &m1, &c_one, h_Binit, &N, h_work, &N, &c_neg_one, h_A, &N);
result *= lapackf77_zlange("1", &N, &m1, h_A, &N, rwork)/N;
}
}
// ===================================================================
// Print execution time
// ===================================================================
printf("%5d %5d %2d %6.2f\n",
(int) N, (int) m1, (int) opts.ngpu, mgpu_time);
if ( checkres ){
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if(itype==1)
printf("(1) | A Z - B Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : " failed") );
else if(itype==2)
printf("(1) | A B Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : " failed") );
else if(itype==3)
printf("(1) | B A Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result, (result < tol ? "" : " failed") );
}
TESTING_HOSTFREE( h_A);
TESTING_HOSTFREE( h_B);
TESTING_FREE( w1);
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_HOSTFREE( rwork);
#endif
TESTING_FREE( iwork);
TESTING_HOSTFREE(h_work);
if((opts.warmup)||( checkres )){
TESTING_FREE( h_Ainit);
TESTING_FREE( h_Binit);
}
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
/* Shutdown */
TESTING_FINALIZE_MGPU();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zhegvdx
*/
int main( int argc, char** argv)
{
//#define USE_MGPU
#ifdef USE_MGPU
TESTING_CUDA_INIT_MGPU();
#else
TESTING_CUDA_INIT();
#endif
magma_int_t nrgpu =1;
cuDoubleComplex *h_A, *h_R, *h_B, *h_S, *h_work;
double *rwork, *w1, *w2;
magma_int_t *iwork;
double gpu_time, cpu_time;
magma_timestr_t start, end;
/* Matrix size */
magma_int_t N=0, n2;
magma_int_t size[4] = {1024,2048,4100,6001};
magma_int_t i, itype, info;
magma_int_t ione = 1, izero = 0;
magma_int_t five = 5;
cuDoubleComplex c_zero = MAGMA_Z_ZERO;
cuDoubleComplex c_one = MAGMA_Z_ONE;
cuDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double d_one = 1.;
double d_neg_one = -1.;
double d_ten = 10.;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t il,iu,m1,m2;
double vl,vu;
double fraction_ev = 0;
//const char *uplo = MagmaLowerStr;
char *uplo = (char*)MagmaLowerStr;
//char *uplo = (char*)MagmaUpperStr;
char *jobz = (char*)MagmaVectorsStr;
char range = 'A';
itype = 1;
magma_int_t checkres;
double result[2];
int flagN = 0;
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i])==0){
N = atoi(argv[++i]);
if (N>0){
printf(" testing_zhegvdx -N %d\n\n", (int) N);
flagN=1;
}
else {
printf("\nUsage: \n");
printf(" testing_zhegvdx -N %d\n\n", (int) N);
exit(1);
}
}
if (strcmp("-ngpu", argv[i])==0){
nrgpu = atoi(argv[++i]);
if (nrgpu>0){
printf(" testing_zhegvdx -ngpu %d\n\n", (int) nrgpu);
}
else {
printf("\nUsage: \n");
printf(" testing_zhegvdx -ngpu %d\n\n", (int) nrgpu);
exit(1);
}
}
if (strcmp("-itype", argv[i])==0){
itype = atoi(argv[++i]);
if (itype>0 && itype <= 3){
printf(" testing_zhegvdx -itype %d\n\n", (int) itype);
}
else {
printf("\nUsage: \n");
printf(" testing_zhegvdx -itype %d\n\n", (int) itype);
exit(1);
}
}
if (strcmp("-FE", argv[i])==0){
fraction_ev = atof(argv[++i]);
if (fraction_ev > 0 && fraction_ev <= 1){
printf(" testing_zhegvdx -FE %f\n\n", fraction_ev);
}
else {
fraction_ev = 0;
}
}
if (strcmp("-L", argv[i])==0){
uplo = (char*)MagmaLowerStr;
printf(" testing_zhegvdx -L");
}
if (strcmp("-U", argv[i])==0){
uplo = (char*)MagmaUpperStr;
printf(" testing_zhegvdx -U");
}
}
} else {
printf("\nUsage: \n");
printf(" testing_zhegvdx -L/U -N %d -itype %d\n\n", 1024, 1);
}
if(!flagN)
N = size[3];
checkres = getenv("MAGMA_TESTINGS_CHECK") != NULL;
n2 = N * N;
/* Allocate host memory for the matrix */
TESTING_MALLOC( h_A, cuDoubleComplex, n2);
TESTING_MALLOC( h_B, cuDoubleComplex, n2);
TESTING_MALLOC( w1, double , N);
TESTING_MALLOC( w2, double , N);
TESTING_HOSTALLOC(h_R, cuDoubleComplex, n2);
TESTING_HOSTALLOC(h_S, cuDoubleComplex, n2);
magma_int_t nb = magma_get_zhetrd_nb(N);
magma_int_t lwork = magma_zbulge_get_lq2(N) + 2*N + N*N;
magma_int_t lrwork = 1 + 5*N +2*N*N;
magma_int_t liwork = 3 + 5*N;
TESTING_HOSTALLOC(h_work, cuDoubleComplex, lwork);
TESTING_HOSTALLOC( rwork, double, lrwork);
TESTING_MALLOC( iwork, magma_int_t, liwork);
printf(" N M GPU Time(s) \n");
printf("==========================\n");
for(i=0; i<4; i++){
if (!flagN){
N = size[i];
n2 = N*N;
}
if (fraction_ev == 0){
il = N / 10;
iu = N / 5+il;
}
else {
il = 1;
iu = (int)(fraction_ev*N);
if (iu < 1) iu = 1;
}
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
//lapackf77_zlatms( &N, &N, "U", ISEED, "P", w1, &five, &d_ten,
// &d_one, &N, &N, uplo, h_B, &N, h_work, &info);
//lapackf77_zlaset( "A", &N, &N, &c_zero, &c_one, h_B, &N);
lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
/* increase the diagonal */
{
magma_int_t i, j;
for(i=0; i<N; i++) {
MAGMA_Z_SET2REAL( h_B[i*N+i], ( MAGMA_Z_REAL(h_B[i*N+i]) + 1.*N ) );
}
}
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
#ifdef USE_MGPU
magma_zhegvdx_2stage_m(nrgpu, itype, jobz[0], range, uplo[0],
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
#else
magma_zhegvdx_2stage(itype, jobz[0], range, uplo[0],
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
#endif
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
start = get_current_time();
#ifdef USE_MGPU
magma_zhegvdx_2stage_m(nrgpu, itype, jobz[0], range, uplo[0],
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
#else
magma_zhegvdx_2stage(itype, jobz[0], range, uplo[0],
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
#endif
end = get_current_time();
gpu_time = GetTimerValue(start,end)/1000.;
if ( checkres ) {
/* =====================================================================
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 |
=================================================================== */
double temp1, temp2;
cuDoubleComplex *tau;
result[0] = 1.;
result[0] /= lapackf77_zlanhe("1",uplo, &N, h_A, &N, rwork);
result[0] /= lapackf77_zlange("1",&N , &m1, h_R, &N, rwork);
if (itype == 1){
blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", uplo, &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_work, &N, rwork)/N;
}
else if (itype == 2){
blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_B, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
}
else if (itype == 3){
blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i<m1; ++i)
blasf77_zdscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_zhemm("L", uplo, &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_zlange("1", &N, &m1, h_R, &N, rwork)/N;
}
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_zhegvdx(itype, 'N', range, uplo[0],
N, h_R, N, h_S, N, vl, vu, il, iu, &m2, w2,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&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 / temp1;
}
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %5d %6.2f\n",
(int) N, (int) m1, gpu_time);
if ( checkres ){
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if(itype==1)
printf("(1) | A Z - B Z D | / (|A| |Z| N) = %e\n", result[0]);
else if(itype==2)
printf("(1) | A B Z - Z D | / (|A| |Z| N) = %e\n", result[0]);
else if(itype==3)
printf("(1) | B A Z - Z D | / (|A| |Z| N) = %e\n", result[0]);
printf("(2) | D(w/ Z)-D(w/o Z)|/ |D| = %e\n\n", result[1]);
}
if (flagN)
break;
}
cudaSetDevice(0);
/* Memory clean up */
TESTING_FREE( h_A);
TESTING_FREE( h_B);
TESTING_FREE( w1);
TESTING_FREE( w2);
TESTING_HOSTFREE( rwork);
TESTING_FREE( iwork);
TESTING_HOSTFREE(h_work);
TESTING_HOSTFREE( h_R);
TESTING_HOSTFREE( h_S);
/* Shutdown */
#ifdef USE_MGPU
TESTING_CUDA_FINALIZE_MGPU();
#else
TESTING_CUDA_FINALIZE();
#endif
}
/**
Purpose
-------
ZHEGVDX_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
itype INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangles of A and B are stored;
- = MagmaLower: Lower triangles of A and B are stored.
@param[in]
n INTEGER
The order of the matrices A and B. N >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
\n
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper)
or the lower triangle (if UPLO=MagmaLower) of A, including the
diagonal, is destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B COMPLEX_16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
\n
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[in]
vl DOUBLE PRECISION
@param[in]
vu DOUBLE PRECISION
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + N * (NB + 1).
If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store the Q2 matrix
and is returned by magma_bulge_get_lq2.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\n
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\n
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: ZPOTRF or ZHEEVD returned an error code:
<= N: if INFO = i and JOBZ = MagmaNoVec, then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = MagmaVec, then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Further Details
---------------
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if ZHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.
@ingroup magma_zhegv_driver
********************************************************************/
extern "C" magma_int_t
magma_zhegvdx_2stage(magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *B, magma_int_t ldb,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex *dA;
magmaDoubleComplex *dB;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t lwmin;
magma_int_t liwmin;
magma_int_t lrwmin;
magma_queue_t stream;
magma_queue_create( &stream );
/* determine the number of threads */
magma_int_t parallel_threads = magma_get_parallel_numthreads();
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || (jobz == MagmaNoVec))) {
*info = -3;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_get_zbulge_nb(n, parallel_threads);
magma_int_t lq2 = magma_zbulge_get_lq2(n, parallel_threads);
if (wantz) {
lwmin = lq2 + 2 * n + n * n;
lrwmin = 1 + 5 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_dlamch("Epsilon");
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (lrwork < lrwmin && ! lquery) {
*info = -19;
} else if (liwork < liwmin && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb);
printf("--------------------------------------------------------------\n");
#endif
lapackf77_zhegvd(&itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork, info);
*m = n;
return *info;
}
// TODO: fix memory leak
if (MAGMA_SUCCESS != magma_zmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &dB, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_zsetmatrix( n, n, B, ldb, dB, lddb );
magma_zsetmatrix_async( n, n,
A, lda,
dA, ldda, stream );
magma_timer_t time=0;
timer_start( time );
magma_zpotrf_gpu(uplo, n, dB, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time zpotrf_gpu = %6.2f\n", time );
magma_queue_sync( stream );
magma_zgetmatrix_async( n, n,
dB, lddb,
B, ldb, stream );
/* Transform problem to standard eigenvalue problem and solve. */
timer_start( time );
magma_zhegst_gpu(itype, uplo, n, dA, ldda, dB, lddb, info);
timer_stop( time );
timer_printf( "time zhegst_gpu = %6.2f\n", time );
magma_zgetmatrix( n, n, dA, ldda, A, lda );
magma_queue_sync( stream );
magma_free( dA );
magma_free( dB );
timer_start( time );
magma_zheevdx_2stage(jobz, range, uplo, n, A, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info);
timer_stop( time );
timer_printf( "time zheevdx_2stage = %6.2f\n", time );
if (wantz && *info == 0) {
// TODO fix memory leak
if (MAGMA_SUCCESS != magma_zmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &dB, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
timer_start( time );
magma_zsetmatrix( n, *m, A, lda, dA, ldda );
magma_zsetmatrix( n, n, B, ldb, dB, lddb );
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
trans = MagmaConjTrans;
} else {
trans = MagmaNoTrans;
}
magma_ztrsm(MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dA, ldda);
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
trans = MagmaNoTrans;
} else {
trans = MagmaConjTrans;
}
magma_ztrmm(MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dA, ldda);
}
magma_zgetmatrix( n, *m, dA, ldda, A, lda );
timer_stop( time );
timer_printf( "time trsm/mm + getmatrix = %6.2f\n", time );
magma_free( dA );
magma_free( dB );
}
magma_queue_destroy( stream );
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
return *info;
} /* magma_zhegvdx_2stage */
/**
Purpose
-------
ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
nrgpu INTEGER
Number of GPUs to use.
@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]
A COMPLEX_16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
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]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in]
vl DOUBLE PRECISION
@param[in]
vu DOUBLE PRECISION
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w DOUBLE PRECISION array, dimension (N)
If INFO = 0, the required m eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store the Q2 matrix
and is returned by magma_bulge_get_lq2.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\n
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\n
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: 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_zheev_driver
********************************************************************/
extern "C" magma_int_t
magma_zheevdx_2stage_m(magma_int_t nrgpu, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
#define A( i_,j_) (A + (i_) + (j_)*lda)
#define A2(i_,j_) (A2 + (i_) + (j_)*lda2)
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magmaDoubleComplex c_one = MAGMA_Z_ONE;
double d_one = 1.;
magma_int_t ione = 1;
magma_int_t izero = 0;
double d__1;
double eps;
double anrm;
magma_int_t imax;
double rmin, rmax;
double sigma;
//magma_int_t iinfo;
magma_int_t lwmin, lrwmin, liwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t iscale;
double safmin;
double bignum;
double smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t len;
/* determine the number of threads */
magma_int_t parallel_threads = magma_get_parallel_numthreads();
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (! (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 (lda < max(1,n)) {
*info = -6;
} 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_zbulge_nb(n, parallel_threads);
magma_int_t Vblksiz = magma_zbulge_get_Vblksiz(n, nb, parallel_threads);
magma_int_t ldt = Vblksiz;
magma_int_t ldv = nb + Vblksiz;
magma_int_t blkcnt = magma_bulge_get_blkcnt(n, nb, Vblksiz);
magma_int_t lq2 = magma_zbulge_get_lq2(n, parallel_threads);
if (wantz) {
lwmin = lq2 + 2*n + n*n;
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 5*n + 3;
} else {
lwmin = lq2 + n + n*nb;
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_dlamch("Epsilon");
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -14;
} else if ((lrwork < lrwmin) && ! lquery) {
*info = -16;
} else if ((liwork < liwmin) && ! lquery) {
*info = -18;
}
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] = MAGMA_Z_REAL(A[0]);
if (wantz) {
A[0] = MAGMA_Z_ONE;
}
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
timer_printf("using %d parallel_threads\n", (int) parallel_threads);
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
magma_int_t ntiles = n/nb;
if ( ( ntiles < 2 ) || ( 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_zheevd(jobz_, uplo_, &n,
A, &lda, w,
work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
info);
*m = n;
return *info;
}
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_zlanhe("M", uplo_, &n, A, &lda, rwork);
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_zlascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A,
&lda, info);
}
magma_int_t indT2 = 0;
magma_int_t indTAU2 = indT2 + blkcnt*ldt*Vblksiz;
magma_int_t indV2 = indTAU2+ blkcnt*Vblksiz;
magma_int_t indtau1 = indV2 + blkcnt*ldv*Vblksiz;
magma_int_t indwrk = indtau1+ n;
magma_int_t indwk2 = indwrk + n*n;
magma_int_t llwork = lwork - indwrk;
magma_int_t llwrk2 = lwork - indwk2;
magma_int_t inde = 0;
magma_int_t indrwk = inde + n;
magma_int_t llrwk = lrwork - indrwk;
magma_timer_t time=0, time_total=0, time_alloc=0, time_dist=0, time_band=0;
timer_start( time_total );
#ifdef HE2HB_SINGLEGPU
magmaDoubleComplex *dT1;
if (MAGMA_SUCCESS != magma_zmalloc( &dT1, n*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
timer_start( time_band );
magma_zhetrd_he2hb(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, dT1, info);
timer_stop( time_band );
timer_printf( " 1 GPU seq code time zhetrd_he2hb only = %7.4f\n", time_band );
magma_free(dT1);
#else
magma_int_t nstream = max(3,nrgpu+2);
magma_queue_t streams[MagmaMaxGPUs][20];
magmaDoubleComplex *da[MagmaMaxGPUs], *dT1[MagmaMaxGPUs];
magma_int_t ldda = ((n+31)/32)*32;
magma_int_t ver = 0;
magma_int_t distblk = max(256, 4*nb);
#ifdef ENABLE_DEBUG
printf("voici ngpu %d distblk %d NB %d nstream %d version %d \n ", nrgpu, distblk, nb, nstream, ver);
#endif
timer_start( time_alloc );
for( magma_int_t dev = 0; dev < nrgpu; ++dev ) {
magma_int_t mlocal = ((n / distblk) / nrgpu + 1) * distblk;
magma_setdevice( dev );
// TODO check malloc
magma_zmalloc(&da[dev], ldda*mlocal );
magma_zmalloc(&dT1[dev], (n*nb) );
for( int i = 0; i < nstream; ++i ) {
magma_queue_create( &streams[dev][i] );
}
}
timer_stop( time_alloc );
timer_start( time_dist );
magma_zsetmatrix_1D_col_bcyclic( n, n, A, lda, da, ldda, nrgpu, distblk );
magma_setdevice(0);
timer_stop( time_dist );
timer_start( time_band );
if (ver == 30) {
magma_zhetrd_he2hb_mgpu_spec(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, info);
} else {
magma_zhetrd_he2hb_mgpu(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, info);
}
timer_stop( time_band );
timer_printf(" time alloc %7.4f, ditribution %7.4f, zhetrd_he2hb only = %7.4f\n", time_alloc, time_dist, time_band );
for( magma_int_t dev = 0; dev < nrgpu; ++dev ) {
magma_setdevice( dev );
magma_free( da[dev] );
magma_free( dT1[dev] );
for( int i = 0; i < nstream; ++i ) {
magma_queue_destroy( streams[dev][i] );
}
}
#endif // not HE2HB_SINGLEGPU
timer_stop( time_total );
timer_printf( " time zhetrd_he2hb_mgpu = %6.2f\n", time_total );
timer_start( time_total );
timer_start( time );
/* copy the input matrix into WORK(INDWRK) with band storage */
/* PAY ATTENTION THAT work[indwrk] should be able to be of size lda2*n which it should be checked in any future modification of lwork.*/
magma_int_t lda2 = 2*nb; //nb+1+(nb-1);
magmaDoubleComplex* A2 = &work[indwrk];
memset(A2, 0, n*lda2*sizeof(magmaDoubleComplex));
for (magma_int_t j = 0; j < n-nb; j++) {
len = nb+1;
blasf77_zcopy( &len, A(j,j), &ione, A2(0,j), &ione );
memset(A(j,j), 0, (nb+1)*sizeof(magmaDoubleComplex));
*A(nb+j,j) = c_one;
}
for (magma_int_t j = 0; j < nb; j++) {
len = nb-j;
blasf77_zcopy( &len, A(j+n-nb,j+n-nb), &ione, A2(0,j+n-nb), &ione );
memset(A(j+n-nb,j+n-nb), 0, (nb-j)*sizeof(magmaDoubleComplex));
}
timer_stop( time );
timer_printf( " time zhetrd_convert = %6.2f\n", time );
timer_start( time );
magma_zhetrd_hb2st(uplo, n, nb, Vblksiz, A2, lda2, w, &rwork[inde], &work[indV2], ldv, &work[indTAU2], wantz, &work[indT2], ldt);
timer_stop( time );
timer_stop( time_total );
timer_printf( " time zhetrd_hb2st = %6.2f\n", time );
timer_printf( " time zhetrd = %6.2f\n", time_total );
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
timer_start( time );
lapackf77_dsterf(&n, w, &rwork[inde], info);
magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
timer_stop( time );
timer_printf( " time dstedc = %6.2f\n", time );
}
else {
timer_start( time_total );
timer_start( time );
magma_zstedx_m(nrgpu, range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, info);
timer_stop( time );
timer_printf( " time zstedx_m = %6.2f\n", time );
timer_start( time );
magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
/*
magmaDoubleComplex *dZ;
magma_int_t lddz = n;
if (MAGMA_SUCCESS != magma_zmalloc( &dZ, *m*lddz)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zbulge_back(uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
magma_zgetmatrix( n, *m, dZ, lddz, &work[indwrk], n);
magma_free(dZ);
*/
magma_zbulge_back_m(nrgpu, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
timer_stop( time );
timer_printf( " time zbulge_back_m = %6.2f\n", time );
timer_start( time );
magma_zunmqr_m(nrgpu, MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, A+nb, lda, &work[indtau1],
&work[indwrk + n * (il-1) + nb], n, &work[indwk2], llwrk2, info);
lapackf77_zlacpy("A", &n, m, &work[indwrk + n * (il-1)], &n, A, &lda);
timer_stop( time );
timer_stop( time_total );
timer_printf( " time zunmqr_m + copy = %6.2f\n", time );
timer_printf( " time eigenvectors backtransf. = %6.2f\n", time_total );
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_dscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
magma_setdevice( orig_dev );
return *info;
} /* magma_zheevdx_2stage_m */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zhetrd_he2hb
*/
int main( int argc, char** argv)
{
TESTING_INIT_MGPU();
real_Double_t gpu_time, gpu_perf, gflops;
magmaDoubleComplex *h_A, *h_R, *h_work, *dT1;
magmaDoubleComplex *tau;
double *D, *E;
/* Matrix size */
magma_int_t N, n2, lda, lwork, ldt, lwork0;
magma_int_t info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
#if defined(CHECKEIG)
#if defined(PRECISION_z) || defined(PRECISION_d)
magma_int_t WANTZ=0;
magma_int_t THREADS=1;
#endif
#endif
magma_int_t NE = 0;
magma_int_t NB = 0;
magma_int_t ngpu = 1;
magma_opts opts;
parse_opts( argc, argv, &opts );
NB = opts.nb;
if (NB < 1)
NB = 64; //64; //magma_get_zhetrd_he2hb_nb(N);
// what is NE ?
if (NE < 1)
NE = 64; //N; //magma_get_zhetrd_he2hb_nb(N); // N not yet initialized
printf(" N GPU GFlop/s \n");
printf("=====================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
ldt = N;
n2 = N*lda;
gflops = FLOPS_ZHETRD( N ) / 1e9;
/* We suppose the magma NB is bigger than lapack NB */
lwork0 = N*NB;
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( tau, magmaDoubleComplex, N-1 );
TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, lda*N );
TESTING_MALLOC_PIN( h_work, magmaDoubleComplex, lwork0 );
TESTING_MALLOC_PIN( D, double, N );
TESTING_MALLOC_PIN( E, double, N );
//TESTING_MALLOC_DEV( dT1, magmaDoubleComplex, (2*min(N,N)+(N+31)/32*32)*NB );
TESTING_MALLOC_DEV( dT1, magmaDoubleComplex, (N*NB) );
// if (WANTZ) gflops = 2.0*gflops;
/* ====================================================================
Initialize the matrix
=================================================================== */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
magma_zmake_hermitian( N, h_A, lda );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_device_t cdev;
magma_getdevice( &cdev );
gpu_time = magma_wtime();
/*
magma_zhetrd_he2hb( opts.uplo, N, NB, h_R, lda, tau, h_work, lwork0, dT1, THREADS, &info);
tband = magma_wtime - gpu_time();
printf(" Finish BAND N %d NB %d ngpu %d timing= %f\n", N, NB, ngpu, tband);
magma_zhetrd_bhe2trc_v5(THREADS, WANTZ, opts.uplo, NE, N, NB, h_R, lda, D, E, dT1, ldt);
*/
/*
magma_zhetrd_he2hb( opts.uplo, N, NB, h_R, lda, tau, h_work, lwork, dT1, THREADS, &info);
tband = magma_wtime - gpu_time();
printf(" Finish BAND N %d NB %d ngpu %d timing= %f\n", N, NB, ngpu, tband);
magma_zhetrd_bhe2trc(THREADS, WANTZ, opts.uplo, NE, N, NB, h_R, lda, D, E, dT1, ldt);
*/
magma_range_t range = MagmaRangeAll;
magma_int_t fraction_ev = 100;
magma_int_t il, iu, m1;
double vl=0., vu=0.;
if (fraction_ev == 0) {
il = N / 10;
iu = N / 5+il;
}
else {
il = 1;
iu = (int)(fraction_ev*N);
if (iu < 1) iu = 1;
}
magmaDoubleComplex *hh_work;
magma_int_t *iwork;
magma_int_t nb, /*lwork,*/ liwork;
magma_int_t threads = magma_get_parallel_numthreads();
#if defined(PRECISION_z) || defined(PRECISION_c)
double *rwork;
magma_int_t lrwork;
lwork = magma_zbulge_get_lq2(N, threads) + 2*N + N*N;
lrwork = 1 + 5*N +2*N*N;
TESTING_MALLOC_PIN( rwork, double, lrwork );
#else
lwork = magma_zbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
liwork = 3 + 5*N;
nb = magma_get_zhetrd_nb(N);
TESTING_MALLOC_PIN( hh_work, magmaDoubleComplex, lwork );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
if (ngpu == 1) {
printf("calling zheevdx_2stage 1 GPU\n");
magma_zheevdx_2stage( opts.jobz, range, opts.uplo, N,
h_R, lda,
vl, vu, il, iu,
&m1, D,
hh_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
} else {
printf("calling zheevdx_2stage_m %d GPU\n", (int) ngpu);
magma_zheevdx_2stage_m(ngpu, opts.jobz, range, opts.uplo, N,
h_R, lda,
vl, vu, il, iu,
&m1, D,
hh_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
}
magma_setdevice( cdev );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
/* =====================================================================
Check the factorization
=================================================================== */
/*
if ( opts.check ) {
FILE *fp ;
printf("Writing input matrix in matlab_i_mat.txt ...\n");
fp = fopen ("matlab_i_mat.txt", "w") ;
if ( fp == NULL ) { printf("Couldn't open output file\n"); exit(1); }
for (j=0; j < N; j++) {
for (k=0; k < N; k++) {
#if defined(PRECISION_z) || defined(PRECISION_c)
fprintf(fp, "%5d %5d %11.8f %11.8f\n", k+1, j+1,
h_A[k+j*lda].x, h_A[k+j*lda].y);
#else
fprintf(fp, "%5d %5d %11.8f\n", k+1, j+1, h_A[k+j*lda]);
#endif
}
}
fclose( fp ) ;
printf("Writing output matrix in matlab_o_mat.txt ...\n");
fp = fopen ("matlab_o_mat.txt", "w") ;
if ( fp == NULL ) { printf("Couldn't open output file\n"); exit(1); }
for (j=0; j < N; j++) {
for (k=0; k < N; k++) {
#if defined(PRECISION_z) || defined(PRECISION_c)
fprintf(fp, "%5d %5d %11.8f %11.8f\n", k+1, j+1,
h_R[k+j*lda].x, h_R[k+j*lda].y);
#else
fprintf(fp, "%5d %5d %11.8f\n", k+1, j+1, h_R[k+j*lda]);
#endif
}
}
fclose( fp ) ;
}
*/
/* =====================================================================
Print performance and error.
=================================================================== */
#if defined(CHECKEIG)
#if defined(PRECISION_z) || defined(PRECISION_d)
if ( opts.check ) {
printf(" Total N %5d gflops %6.2f timing %6.2f seconds\n", (int) N, gpu_perf, gpu_time );
char JOBZ;
if (WANTZ == 0)
JOBZ = 'N';
else
JOBZ = 'V';
double nrmI=0.0, nrm1=0.0, nrm2=0.0;
int lwork2 = 256*N;
magmaDoubleComplex *work2, *AINIT;
double *rwork2, *D2;
// TODO free this memory !
magma_zmalloc_cpu( &work2, lwork2 );
magma_dmalloc_cpu( &rwork2, N );
magma_dmalloc_cpu( &D2, N );
magma_zmalloc_cpu( &AINIT, N*lda );
memcpy(AINIT, h_A, N*lda*sizeof(magmaDoubleComplex));
/* compute the eigenvalues using lapack routine to be able to compare to it and used as ref */
cpu_time = magma_wtime();
i= min(12, THREADS);
#if defined(USEMKL)
mkl_set_num_threads( i );
#endif
#if defined(USEACML)
omp_set_num_threads(i);
#endif
lapackf77_zheev( "N", "L", &N, h_A, &lda, D2, work2, &lwork2,
#if defined(PRECISION_z) || defined (PRECISION_c)
rwork2,
#endif
&info );
///* call eigensolver for our resulting tridiag [D E] and for Q */
//dstedc_withZ('V', N, D, E, h_R, lda);
////dsterf_( &N, D, E, &info);
////
cpu_time = magma_wtime() - cpu_time;
printf(" Finish CHECK - EIGEN timing= %f threads %d\n", cpu_time, i);
/*
for (i=0; i < 10; i++)
printf(" voici lpk D[%d] %8.2e\n", i, D2[i]);
*/
//magmaDoubleComplex mydz=0.0, mydo=1.0;
//magmaDoubleComplex *Z;
// magma_zmalloc_cpu( &Z, N*lda );
// dgemm_("N", "N", &N, &N, &N, &mydo, h_R, &lda, h_A, &lda, &mydz, Z, &lda);
/* compare result */
cmp_vals(N, D2, D, &nrmI, &nrm1, &nrm2);
magmaDoubleComplex *WORKAJETER;
double *RWORKAJETER, *RESU;
// TODO free this memory !
magma_zmalloc_cpu( &WORKAJETER, (2* N * N + N) );
magma_dmalloc_cpu( &RWORKAJETER, N );
magma_dmalloc_cpu( &RESU, 10 );
int MATYPE;
memset(RESU, 0, 10*sizeof(double));
MATYPE=3;
double NOTHING=0.0;
cpu_time = magma_wtime();
// check results
zcheck_eig_(&JOBZ, &MATYPE, &N, &NB, AINIT, &lda, &NOTHING, &NOTHING, D2, D, h_R, &lda, WORKAJETER, RWORKAJETER, RESU );
cpu_time = magma_wtime() - cpu_time;
printf(" Finish CHECK - results timing= %f\n", cpu_time);
#if defined(USEMKL)
mkl_set_num_threads( 1 );
#endif
#if defined(USEACML)
omp_set_num_threads(1);
#endif
printf("\n");
printf(" ================================================================================================================\n");
printf(" ==> INFO voici threads=%d N=%d NB=%d WANTZ=%d\n", (int) THREADS, (int) N, (int) NB, (int) WANTZ);
printf(" ================================================================================================================\n");
printf(" DSBTRD : %15s \n", "STATblgv9withQ ");
printf(" ================================================================================================================\n");
if (WANTZ > 0)
printf(" | A - U S U' | / ( |A| n ulp ) : %15.3E \n", RESU[0]);
if (WANTZ > 0)
printf(" | I - U U' | / ( n ulp ) : %15.3E \n", RESU[1]);
printf(" | D1 - EVEIGS | / (|D| ulp) : %15.3E \n", RESU[2]);
printf(" max | D1 - EVEIGS | : %15.3E \n", RESU[6]);
printf(" ================================================================================================================\n\n\n");
printf(" ****************************************************************************************************************\n");
printf(" * Hello here are the norm Infinite (max)=%8.2e norm one (sum)=%8.2e norm2(sqrt)=%8.2e *\n", nrmI, nrm1, nrm2);
printf(" ****************************************************************************************************************\n\n");
}
#endif
#endif
printf(" Total N %5d gflops %6.2f timing %6.2f seconds\n", (int) N, gpu_perf, gpu_time );
printf("============================================================================\n\n\n");
/* Memory clean up */
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( tau );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
TESTING_FREE_PIN( D );
TESTING_FREE_PIN( E );
TESTING_FREE_DEV( dT1 );
/* TODO - not all memory has been freed inside loop */
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE_MGPU();
return EXIT_SUCCESS;
}
