/* ////////////////////////////////////////////////////////////////////////////
-- Testing cheevd
*/
int main( int argc, char** argv)
{
TESTING_CUDA_INIT();
cuFloatComplex *h_A, *h_R, *h_work;
float *rwork, *w1, *w2;
magma_int_t *iwork;
float gpu_time, cpu_time;
magma_timestr_t start, end;
/* Matrix size */
magma_int_t N=0, n2;
magma_int_t size[8] = {1024,2048,3072,4032,5184,6016,7040,8064};
magma_int_t i, info;
magma_int_t ione = 1, izero = 0;
magma_int_t ISEED[4] = {0,0,0,1};
const char *uplo = MagmaLowerStr;
const char *jobz = MagmaVectorsStr;
magma_int_t checkres;
float result[3], eps = lapackf77_slamch( "E" );
if (argc != 1){
for(i = 1; i<argc; i++){
if (strcmp("-N", argv[i])==0) {
N = atoi(argv[++i]);
}
else if ( strcmp("-JV", argv[i]) == 0 ) {
jobz = MagmaVectorsStr;
}
else if ( strcmp("-JN", argv[i]) == 0 ) {
jobz = MagmaNoVectorsStr;
}
}
if (N>0)
printf(" testing_cheevd -N %d [-JV] [-JN]\n\n", (int) N);
else {
printf("\nUsage: \n");
printf(" testing_cheevd -N %d [-JV] [-JN]\n\n", (int) N);
exit(1);
}
}
else {
printf("\nUsage: \n");
printf(" testing_cheevd -N %d [-JV] [-JN]\n\n", 1024);
N = size[7];
}
checkres = getenv("MAGMA_TESTINGS_CHECK") != NULL;
if ( checkres && jobz[0] == MagmaNoVectors ) {
printf( "Cannot check results when vectors are not computed (jobz='N')\n" );
checkres = false;
}
/* Query for workspace sizes */
cuFloatComplex aux_work[1];
float aux_rwork[1];
magma_int_t aux_iwork[1];
magma_cheevd( jobz[0], uplo[0],
N, h_R, N, w1,
aux_work, -1,
aux_rwork, -1,
aux_iwork, -1,
&info );
magma_int_t lwork, lrwork, liwork;
lwork = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
lrwork = (magma_int_t) aux_rwork[0];
liwork = aux_iwork[0];
/* Allocate host memory for the matrix */
TESTING_MALLOC( h_A, cuFloatComplex, N*N );
TESTING_MALLOC( w1, float , N );
TESTING_MALLOC( w2, float , N );
TESTING_HOSTALLOC( h_R, cuFloatComplex, N*N );
TESTING_HOSTALLOC( h_work, cuFloatComplex, lwork );
TESTING_MALLOC( rwork, float, lrwork );
TESTING_MALLOC( iwork, magma_int_t, liwork );
printf(" N CPU Time(s) GPU Time(s) \n");
printf("===================================\n");
for(i=0; i<8; i++){
if (argc==1){
N = size[i];
}
n2 = N*N;
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
for( int i=0; i<N; i++) {
MAGMA_C_SET2REAL( h_A[i*N+i], MAGMA_C_REAL(h_A[i*N+i]) );
}
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
/* warm up run */
magma_cheevd(jobz[0], uplo[0],
N, h_R, N, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
/* query for optimal workspace sizes */
magma_cheevd(jobz[0], uplo[0],
N, h_R, N, w1,
h_work, -1,
rwork, -1,
iwork, -1,
&info);
int lwork_save = lwork;
int lrwork_save = lrwork;
int liwork_save = liwork;
lwork = min( lwork, (magma_int_t) MAGMA_C_REAL( h_work[0] ));
lrwork = min( lrwork, (magma_int_t) rwork[0] );
liwork = min( liwork, iwork[0] );
//printf( "lwork %d, query %d, used %d; liwork %d, query %d, used %d\n",
// lwork_save, (magma_int_t) h_work[0], lwork,
// liwork_save, iwork[0], liwork );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
start = get_current_time();
magma_cheevd(jobz[0], uplo[0],
N, h_R, N, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
end = get_current_time();
gpu_time = GetTimerValue(start,end)/1000.;
lwork = lwork_save;
lrwork = lrwork_save;
liwork = liwork_save;
if ( checkres ) {
/* =====================================================================
Check the results following the LAPACK's [zcds]drvst routine.
A is factored as A = U S U' and the following 3 tests computed:
(1) | A - U S U' | / ( |A| N )
(2) | I - U'U | / ( N )
(3) | S(with U) - S(w/o U) | / | S |
=================================================================== */
float temp1, temp2;
cuFloatComplex *tau;
lapackf77_chet21(&ione, uplo, &N, &izero,
h_A, &N,
w1, w1,
h_R, &N,
h_R, &N,
tau, h_work, rwork, &result[0]);
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
magma_cheevd('N', uplo[0],
N, h_R, N, w2,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info);
temp1 = temp2 = 0;
for(int j=0; j<N; j++){
temp1 = max(temp1, absv(w1[j]));
temp1 = max(temp1, absv(w2[j]));
temp2 = max(temp2, absv(w1[j]-w2[j]));
}
result[2] = temp2 / temp1;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
start = get_current_time();
lapackf77_cheevd(jobz, uplo,
&N, h_A, &N, w2,
h_work, &lwork,
rwork, &lrwork,
iwork, &liwork,
&info);
end = get_current_time();
if (info < 0)
printf("Argument %d of cheevd had an illegal value.\n", (int) -info);
cpu_time = GetTimerValue(start,end)/1000.;
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %6.2f %6.2f\n",
(int) N, cpu_time, gpu_time);
if ( checkres ){
printf("Testing the factorization A = U S U' for correctness:\n");
printf("(1) | A - U S U' | / (|A| N) = %e\n", result[0]*eps);
printf("(2) | I - U'U | / N = %e\n", result[1]*eps);
printf("(3) | S(w/ U)-S(w/o U)|/ |S| = %e\n\n", result[2]);
}
if (argc != 1)
break;
}
/* Memory clean up */
TESTING_FREE( h_A);
TESTING_FREE( w1);
TESTING_FREE( w2);
TESTING_FREE( rwork);
TESTING_FREE( iwork);
TESTING_HOSTFREE(h_work);
TESTING_HOSTFREE( h_R);
/* Shutdown */
TESTING_CUDA_FINALIZE();
}
extern "C" magma_int_t
magma_cheevdx_2stage_m(magma_int_t nrgpu, char jobz, char range, char uplo,
magma_int_t n,
magmaFloatComplex *a, magma_int_t lda,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
magmaFloatComplex *work, magma_int_t lwork,
float *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CHEEVD_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 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 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};
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t ione = 1;
magma_int_t izero = 0;
float d_one = 1.;
float d__1;
float eps;
float anrm;
magma_int_t imax;
float rmin, rmax;
float sigma;
//magma_int_t iinfo;
magma_int_t lwmin, lrwmin, liwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t iscale;
float safmin;
float bignum;
float smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
/* 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_cbulge_nb(n, threads);
magma_int_t Vblksiz = magma_cbulge_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_cbulge_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_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_slamch("Epsilon"));
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -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_C_REAL(a[0]);
if (wantz) {
a[0] = MAGMA_C_ONE;
}
return *info;
}
#ifdef ENABLE_DEBUG
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_cheevd(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_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_clanhe("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_clascl(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
#ifdef HE2HB_SINGLEGPU
magmaFloatComplex *dT1;
if (MAGMA_SUCCESS != magma_cmalloc( &dT1, n*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#ifdef ENABLE_TIMER
tband1 = get_current_time();
#endif
magma_chetrd_he2hb(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, dT1, threads, info);
#ifdef ENABLE_TIMER
tband2 = get_current_time();
printf(" 1 GPU seq code time chetrd_he2hb only = %7.4f\n" , GetTimerValue(tband1,tband2)/1000.);
#endif
magma_free(dT1);
#else
magma_int_t nstream = max(3,nrgpu+2);
magma_queue_t streams[MagmaMaxGPUs][20];
magmaFloatComplex *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
#ifdef ENABLE_TIMER
magma_timestr_t tband1, tband2, t1, t2, ta1, ta2;
t1 = get_current_time();
#endif
for( magma_int_t dev = 0; dev < nrgpu; ++dev ) {
magma_int_t mlocal = ((n / distblk) / nrgpu + 1) * distblk;
magma_setdevice( dev );
magma_cmalloc(&da[dev], ldda*mlocal );
magma_cmalloc(&dT1[dev], (n*nb) );
for( int i = 0; i < nstream; ++i ) {
magma_queue_create( &streams[dev][i] );
}
}
#ifdef ENABLE_TIMER
t2 = get_current_time();
#endif
magma_csetmatrix_1D_col_bcyclic( n, n, a, lda, da, ldda, nrgpu, distblk);
magma_setdevice(0);
#ifdef ENABLE_TIMER
tband1 = get_current_time();
#endif
if(ver==30){
magma_chetrd_he2hb_mgpu_spec(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, threads, info);
}else{
magma_chetrd_he2hb_mgpu(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, threads, info);
}
#ifdef ENABLE_TIMER
tband2 = get_current_time();
printf(" time alloc %7.4f, ditribution %7.4f, chetrd_he2hb only = %7.4f\n" , GetTimerValue(t1,t2)/1000., GetTimerValue(t2,tband1)/1000., GetTimerValue(tband1,tband2)/1000.);
#endif
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
#ifdef ENABLE_TIMER
st1 = get_current_time();
printf(" time chetrd_he2hb_mgpu = %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);
magmaFloatComplex* A2 = &work[indwrk];
memset(A2 , 0, n*lda2*sizeof(magmaFloatComplex));
for (magma_int_t j = 0; j < n-nb; j++)
{
cblas_ccopy(nb+1, &a[j*(lda+1)], 1, &A2[j*lda2], 1);
memset(&a[j*(lda+1)], 0, (nb+1)*sizeof(magmaFloatComplex));
a[nb + j*(lda+1)] = c_one;
}
for (magma_int_t j = 0; j < nb; j++)
{
cblas_ccopy(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(magmaFloatComplex));
}
#ifdef ENABLE_TIMER
st2 = get_current_time();
printf(" time chetrd_convert = %6.2f\n" , GetTimerValue(st1,st2)/1000.);
#endif
magma_chetrd_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 chetrd_hb2st = %6.2f\n" , GetTimerValue(st2,end)/1000.);
printf(" time chetrd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call CUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
lapackf77_ssterf(&n, w, &rwork[inde], info);
magma_smove_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
magma_cstedx_m(nrgpu, range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time cstedx_m = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
/*
magmaFloatComplex *dZ;
magma_int_t lddz = n;
if (MAGMA_SUCCESS != magma_cmalloc( &dZ, *m*lddz)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_cbulge_back(threads, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
magma_cgetmatrix( n, *m, dZ, lddz, &work[indwrk], n);
magma_free(dZ);
*/
magma_cbulge_back_m(nrgpu, threads, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
#ifdef ENABLE_TIMER
st1 = get_current_time();
printf(" time cbulge_back_m = %6.2f\n" , GetTimerValue(start,st1)/1000.);
#endif
magma_cunmqr_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_clacpy("A", &n, m, &work[indwrk + n * (il-1)], &n, a, &lda);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time cunmqr_m + 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_sscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_C_MAKE((float) lwmin, 0.);
rwork[0] = (float) lrwmin;
iwork[0] = liwmin;
return *info;
} /* magma_cheevdx_2stage_m */
/**
Purpose
-------
CHEEVDX_GPU computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian 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 COMPLEX array on the GPU,
dimension (LDDA, 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]
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) COMPLEX array, dimension (LDWA, N)
@param[in]
ldwa INTEGER
The leading dimension of the array wA. LDWA >= max(1,N).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
NB can be obtained through magma_get_chetrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) REAL array, dimension (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_cheev_driver
********************************************************************/
extern "C" magma_int_t
magma_cheevdx_gpu(magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
magmaFloatComplex *wA, magma_int_t ldwa,
magmaFloatComplex *work, magma_int_t lwork,
float *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magma_int_t ione = 1;
float d__1;
float eps;
magma_int_t inde;
float anrm;
magma_int_t imax;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t llrwk;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indrwk, indwrk, liwmin;
magma_int_t lrwmin, llwork;
float smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
float *dwork;
magmaFloatComplex *dC;
magma_int_t lddc = ldda;
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 (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_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( n + n*nb, 2*n + n*n );
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_slamch("Epsilon");
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0.);
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -16;
} else if ((lrwork < lrwmin) && ! lquery) {
*info = -18;
} else if ((liwork < liwmin) && ! lquery) {
*info = -20;
}
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
magmaFloatComplex *A;
magma_cmalloc_cpu( &A, n*n );
magma_cgetmatrix(n, n, dA, ldda, A, n);
lapackf77_cheevd(jobz_, uplo_,
&n, A, &n,
w, work, &lwork,
rwork, &lrwork,
iwork, &liwork, info);
magma_csetmatrix( n, n, A, n, dA, ldda);
magma_free_cpu(A);
*m=n;
return *info;
}
magma_queue_t stream;
magma_queue_create( &stream );
// dC and dwork are never used together, so use one buffer for both;
// unfortunately they're different types (complex and float).
// (this works better in dsyevd_gpu where they're both float).
// n*lddc for chetrd2_gpu, *2 for complex
// n for clanhe
magma_int_t ldwork = n*lddc*2;
if ( wantz ) {
// need 3n^2/2 for cstedx
ldwork = max( ldwork, 3*n*(n/2 + 1) );
}
if (MAGMA_SUCCESS != magma_smalloc( &dwork, ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dC = (magmaFloatComplex*) dwork;
/* 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_clanhe(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_clascl(uplo, 0, 0, 1., sigma, n, n, dA, ldda, info);
}
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
// chetrd rwork: e (n)
// cstedx rwork: e (n) + llrwk (1 + 4*N + 2*N**2) ==> 1 + 5n + 2n^2
inde = 0;
indrwk = inde + n;
llrwk = lrwork - indrwk;
// chetrd work: tau (n) + llwork (n*nb) ==> n + n*nb
// cstedx work: tau (n) + z (n^2)
// cunmtr work: tau (n) + z (n^2) + llwrk2 (n or n*nb) ==> 2n + n^2, or n + n*nb + n^2
indtau = 0;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
magma_timer_t time=0;
timer_start( time );
#ifdef FAST_HEMV
magma_chetrd2_gpu(uplo, n, dA, ldda, w, &rwork[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork,
dC, n*lddc, &iinfo);
#else
magma_chetrd_gpu (uplo, n, dA, ldda, w, &rwork[inde],
&work[indtau], wA, ldwa, &work[indwrk], llwork, &iinfo);
#endif
timer_stop( time );
timer_printf( "time chetrd_gpu = %6.2f\n", time );
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call CUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &rwork[inde], info);
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
}
else {
timer_start( time );
magma_cstedx(range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, dwork, info);
timer_stop( time );
timer_printf( "time cstedx = %6.2f\n", time );
timer_start( time );
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
magma_csetmatrix( n, *m, &work[indwrk + n * (il-1) ], n, dC, lddc );
magma_cunmtr_gpu(MagmaLeft, uplo, MagmaNoTrans, n, *m, dA, ldda, &work[indtau],
dC, lddc, wA, ldwa, &iinfo);
magma_ccopymatrix( n, *m, dC, lddc, dA, ldda );
timer_stop( time );
timer_printf( "time cunmtr_gpu + copy = %6.2f\n", time );
}
/* 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_sscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
magma_queue_destroy( stream );
magma_free( dwork );
return *info;
} /* magma_cheevdx_gpu */
extern "C" magma_int_t
magma_cheevdx(char jobz, char range, char uplo,
magma_int_t n,
magmaFloatComplex *a, magma_int_t lda,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
magmaFloatComplex *work, magma_int_t lwork,
float *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CHEEVDX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian 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
=========
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 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 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 >= N + N*NB.
If JOBZ = 'V' and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
NB can be obtained through magma_get_chetrd_nb(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.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK[0] 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[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, 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};
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;
magma_int_t imax;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t llrwk;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indrwk, indwrk, liwmin;
magma_int_t lrwmin, llwork;
float smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
float* dwork;
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_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( n + n*nb, 2*n + n*n );
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
work[0] = MAGMA_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.);
rwork[0] = lrwmin * (1. + lapackf77_slamch("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_C_REAL(a[0]);
if (wantz) {
a[0] = MAGMA_C_ONE;
}
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_cheevd(jobz_, uplo_,
&n, a, &lda,
w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
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_clanhe("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_clascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, a,
&lda, info);
}
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
// chetrd rwork: e (n)
// cstedx rwork: e (n) + llrwk (1 + 4*N + 2*N**2) ==> 1 + 5n + 2n^2
inde = 0;
indrwk = inde + n;
llrwk = lrwork - indrwk;
// chetrd work: tau (n) + llwork (n*nb) ==> n + n*nb
// cstedx work: tau (n) + z (n^2)
// cunmtr work: tau (n) + z (n^2) + llwrk2 (n or n*nb) ==> 2n + n^2, or n + n*nb + n^2
indtau = 0;
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
magma_chetrd(uplo_[0], n, a, lda, w, &rwork[inde],
&work[indtau], &work[indwrk], llwork, &iinfo);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time chetrd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call CUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &rwork[inde], info);
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
} else {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
if (MAGMA_SUCCESS != magma_smalloc( &dwork, 3*n*(n/2 + 1) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_cstedx(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 cstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
magma_cunmtr(MagmaLeft, uplo, MagmaNoTrans, n, *m, a, lda, &work[indtau],
&work[indwrk + n * (il-1) ], n, &work[indwk2], llwrk2, &iinfo);
lapackf77_clacpy("A", &n, m, &work[indwrk + n * (il-1)] , &n, a, &lda);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time cunmtr + copy = %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_sscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_C_MAKE( lwmin * (1. + lapackf77_slamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_slamch("Epsilon"));
iwork[0] = liwmin;
return *info;
} /* magma_cheevdx */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cheevd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time, cpu_time;
magmaFloatComplex *h_A, *h_R, *h_work, aux_work[1];
float *rwork, *w1, *w2, result[3], eps, aux_rwork[1];
magma_int_t *iwork, aux_iwork[1];
magma_int_t N, n2, info, lwork, lrwork, liwork, lda;
magma_int_t izero = 0;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
eps = lapackf77_slamch( "E" );
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");
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf("using: jobz = %s, uplo = %s\n",
lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo));
printf(" N CPU Time (sec) GPU Time (sec)\n");
printf("=======================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
n2 = N*N;
lda = N;
// query for workspace sizes
magma_cheevd( opts.jobz, opts.uplo,
N, NULL, lda, NULL,
aux_work, -1,
aux_rwork, -1,
aux_iwork, -1,
&info );
lwork = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
lrwork = (magma_int_t) aux_rwork[0];
liwork = aux_iwork[0];
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, N*lda );
TESTING_MALLOC_CPU( w1, float, N );
TESTING_MALLOC_CPU( w2, float, N );
TESTING_MALLOC_CPU( rwork, float, lrwork );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, N*lda );
TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork );
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
magma_cmake_hermitian( N, h_A, N );
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* warm up run */
if ( opts.warmup ) {
magma_cheevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info );
if (info != 0)
printf("magma_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_cheevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info );
gpu_time = magma_wtime() - gpu_time;
if (info != 0)
printf("magma_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.check ) {
/* =====================================================================
Check the results following the LAPACK's [zcds]drvst routine.
A is factored as A = U S U' and the following 3 tests computed:
(1) | A - U S U' | / ( |A| N )
(2) | I - U'U | / ( N )
(3) | S(with U) - S(w/o U) | / | S |
=================================================================== */
float temp1, temp2;
// tau=NULL is unused since itype=1
lapackf77_chet21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
h_A, &lda,
w1, w1,
h_R, &lda,
h_R, &lda,
NULL, h_work, rwork, &result[0] );
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
magma_cheevd( MagmaNoVec, opts.uplo,
N, h_R, lda, w2,
h_work, lwork,
rwork, lrwork,
iwork, liwork,
&info );
if (info != 0)
printf("magma_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
temp1 = temp2 = 0;
for( int j=0; j<N; j++ ) {
temp1 = max(temp1, fabs(w1[j]));
temp1 = max(temp1, fabs(w2[j]));
temp2 = max(temp2, fabs(w1[j]-w2[j]));
}
result[2] = temp2 / (((float)N)*temp1);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_cheevd( lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_A, &lda, w2,
h_work, &lwork,
rwork, &lrwork,
iwork, &liwork,
&info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0)
printf("lapackf77_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
printf("%5d %7.2f %7.2f\n",
(int) N, cpu_time, gpu_time);
}
else {
printf("%5d --- %7.2f\n",
(int) N, gpu_time);
}
/* =====================================================================
Print execution time
=================================================================== */
if ( opts.check ) {
printf("Testing the factorization A = U S U' for correctness:\n");
printf("(1) | A - U S U' | / (|A| N) = %8.2e %s\n", result[0]*eps, (result[0]*eps < tol ? "ok" : "failed") );
printf("(2) | I - U'U | / N = %8.2e %s\n", result[1]*eps, (result[1]*eps < tol ? "ok" : "failed") );
printf("(3) | S(w/ U) - S(w/o U) | / |S| = %8.2e %s\n\n", result[2] , (result[2] < tolulp ? "ok" : "failed") );
status += ! (result[0]*eps < tol && result[1]*eps < tol && result[2] < tolulp);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( rwork );
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/***************************************************************************//**
Purpose
-------
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian 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]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@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 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, 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[in]
vl REAL
@param[in]
vu REAL
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
- If N <= 1, LWORK >= 1.
- If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB.
- If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
NB can be obtained through magma_get_chetrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) REAL array,
dimension (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_heevdx
*******************************************************************************/
extern "C" magma_int_t
magma_cheevdx_m(
magma_int_t ngpu,
magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
magmaFloatComplex *work, magma_int_t lwork,
#ifdef COMPLEX
float *rwork, magma_int_t lrwork,
#endif
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
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;
magma_int_t imax;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t llrwk;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indrwk, indwrk, liwmin;
magma_int_t lrwmin, llwork;
float smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
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_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( n + n*nb, 2*n + n*n );
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
work[0] = magma_cmake_lwork( lwmin );
rwork[0] = magma_smake_lwork( lrwmin );
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -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_C_REAL(A[0]);
if (wantz) {
A[0] = MAGMA_C_ONE;
}
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=%lld NB=%lld, calling lapack on CPU\n", (long long) n, (long long) nb );
printf("--------------------------------------------------------------\n");
#endif
lapackf77_cheevd(jobz_, uplo_,
&n, A, &lda,
w, work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
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_clanhe("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_clascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A,
&lda, info);
}
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 0;
indtau = 0;
indwrk = indtau + n;
indrwk = inde + n;
indwk2 = indwrk + n * n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
llrwk = lrwork - indrwk;
magma_timer_t time=0;
timer_start( time );
magma_chetrd_mgpu(ngpu, 1, uplo, n, A, lda, w, &rwork[inde],
&work[indtau], &work[indwrk], llwork, &iinfo);
timer_stop( time );
timer_printf( "time chetrd = %6.2f\n", time );
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call CUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &rwork[inde], info);
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
}
else {
timer_start( time );
magma_cstedx_m(ngpu, range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, info);
timer_stop( time );
timer_printf( "time cstedc = %6.2f\n", time );
timer_start( time );
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
magma_cunmtr_m(ngpu, MagmaLeft, uplo, MagmaNoTrans, n, *m, A, lda, &work[indtau],
&work[indwrk + n * (il-1)], n, &work[indwk2], llwrk2, &iinfo);
lapackf77_clacpy("A", &n, m, &work[indwrk + n * (il-1)], &n, A, &lda);
timer_stop( time );
timer_printf( "time cunmtr + copy = %6.2f\n", time );
}
/* 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_sscal(&imax, &d__1, w, &ione);
}
work[0] = magma_cmake_lwork( lwmin );
rwork[0] = magma_smake_lwork( lrwmin );
iwork[0] = liwmin;
return *info;
} /* magma_cheevd_m */
/**
Purpose
-------
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian 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 COMPLEX array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
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) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
NB can be obtained through magma_get_chetrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) REAL array, dimension (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_cheev_driver
********************************************************************/
extern "C" magma_int_t
magma_cheevd(
magma_vec_t jobz, magma_uplo_t uplo,
magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
float *w,
magmaFloatComplex *work, magma_int_t lwork,
#ifdef COMPLEX
float *rwork, magma_int_t lrwork,
#endif
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
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;
magma_int_t imax;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t llrwk;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indrwk, indwrk, liwmin;
magma_int_t lrwmin, llwork;
float smlnum;
magma_int_t lquery;
float* dwork;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -1 || lrwork == -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_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( n + n*nb, 2*n + n*n );
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_slamch("Epsilon");
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0 );
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -8;
} else if ((lrwork < lrwmin) && ! lquery) {
*info = -10;
} else if ((liwork < liwmin) && ! lquery) {
*info = -12;
}
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_C_REAL( A[0] );
if (wantz) {
A[0] = MAGMA_C_ONE;
}
return *info;
}
/* If matrix is very small, then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
lapackf77_cheevd( jobz_, uplo_,
&n, A, &lda,
w, work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
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_clanhe( "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_clascl( uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A, &lda, info );
}
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
// chetrd rwork: e (n)
// cstedx rwork: e (n) + llrwk (1 + 4*N + 2*N**2) ==> 1 + 5n + 2n^2
inde = 0;
indrwk = inde + n;
llrwk = lrwork - indrwk;
// chetrd work: tau (n) + llwork (n*nb) ==> n + n*nb
// cstedx work: tau (n) + z (n^2)
// cunmtr work: tau (n) + z (n^2) + llwrk2 (n or n*nb) ==> 2n + n^2, or n + n*nb + n^2
indtau = 0;
indwrk = indtau + n;
indwk2 = indwrk + n*n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
magma_timer_t time=0;
timer_start( time );
magma_chetrd( uplo, n, A, lda, w, &rwork[inde],
&work[indtau], &work[indwrk], llwork, &iinfo );
timer_stop( time );
timer_printf( "time chetrd = %6.2f\n", time );
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
* CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
* tridiagonal matrix, then call CUNMTR to multiply it to the Householder
* transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf( &n, w, &rwork[inde], info );
}
else {
timer_start( time );
if (MAGMA_SUCCESS != magma_smalloc( &dwork, 3*n*(n/2 + 1) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_cstedx( MagmaRangeAll, n, 0., 0., 0, 0, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk], llrwk,
iwork, liwork, dwork, info );
magma_free( dwork );
timer_stop( time );
timer_printf( "time cstedx = %6.2f\n", time );
timer_start( time );
magma_cunmtr( MagmaLeft, uplo, MagmaNoTrans, n, n, A, lda, &work[indtau],
&work[indwrk], n, &work[indwk2], llwrk2, &iinfo );
lapackf77_clacpy( "A", &n, &n, &work[indwrk], &n, A, &lda );
timer_stop( time );
timer_printf( "time cunmtr + copy = %6.2f\n", time );
}
/* 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_sscal( &imax, &d__1, w, &ione );
}
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0 ); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
return *info;
} /* magma_cheevd */
/**
Purpose
-------
CHEEVD_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]
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 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 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[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= 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) REAL 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_cheev_driver
********************************************************************/
extern "C" magma_int_t
magma_cheevdx_2stage(
magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
magmaFloatComplex *work, magma_int_t lwork,
#ifdef COMPLEX
float *rwork, magma_int_t lrwork,
#endif
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
#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 );
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t ione = 1;
magma_int_t izero = 0;
float d_one = 1.;
float d__1;
float eps;
float anrm;
magma_int_t imax;
float rmin, rmax;
float sigma;
//magma_int_t iinfo;
magma_int_t lwmin, lrwmin, liwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t iscale;
float safmin;
float bignum;
float smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t len;
float* dwork;
/* 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_cbulge_nb(n,parallel_threads);
magma_int_t Vblksiz = magma_cbulge_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_cbulge_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_slamch("Epsilon");
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -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_C_REAL(A[0]);
if (wantz) {
A[0] = MAGMA_C_ONE;
}
return *info;
}
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_cheevd(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_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_clanhe("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_clascl(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;
timer_start( time_total );
timer_start( time );
magmaFloatComplex *dT1;
if (MAGMA_SUCCESS != magma_cmalloc( &dT1, n*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_chetrd_he2hb(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, dT1, info);
timer_stop( time );
timer_printf( " time chetrd_he2hb = %6.2f\n", time );
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);
magmaFloatComplex* A2 = &work[indwrk];
memset(A2, 0, n*lda2*sizeof(magmaFloatComplex));
for (magma_int_t j = 0; j < n-nb; j++) {
len = nb+1;
blasf77_ccopy( &len, A(j,j), &ione, A2(0,j), &ione );
memset(A(j,j), 0, (nb+1)*sizeof(magmaFloatComplex));
*A(nb+j,j) = c_one;
}
for (magma_int_t j = 0; j < nb; j++) {
len = nb-j;
blasf77_ccopy( &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(magmaFloatComplex));
}
timer_stop( time );
timer_printf( " time chetrd_convert = %6.2f\n", time );
timer_start( time );
magma_chetrd_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 chetrd_hb2st = %6.2f\n", time );
timer_printf( " time chetrd = %6.2f\n", time_total );
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call CUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
timer_start( time );
lapackf77_ssterf(&n, w, &rwork[inde], info);
magma_smove_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 );
if (MAGMA_SUCCESS != magma_smalloc( &dwork, 3*n*(n/2 + 1) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_cstedx(range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, dwork, info);
magma_free( dwork );
timer_stop( time );
timer_printf( " time cstedx = %6.2f\n", time );
timer_start( time );
magmaFloatComplex *dZ;
magma_int_t lddz = n;
magmaFloatComplex *da;
magma_int_t ldda = n;
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
if (MAGMA_SUCCESS != magma_cmalloc( &dZ, *m*lddz)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_cmalloc( &da, n*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_cbulge_back(uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
timer_stop( time );
timer_printf( " time cbulge_back = %6.2f\n", time );
timer_start( time );
magma_csetmatrix( n, n, A, lda, da, ldda );
magma_cunmqr_gpu_2stages(MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, da+nb, ldda,
dZ+nb, n, dT1, nb, info);
magma_cgetmatrix( n, *m, dZ, lddz, A, lda );
magma_free(dT1);
magma_free(dZ);
magma_free(da);
timer_stop( time );
timer_stop( time_total );
timer_printf( " time cunmqr + 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_sscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_C_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
return *info;
} /* magma_cheevdx_2stage */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cheevd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
/* Constants */
const float d_zero = 0;
const magma_int_t izero = 0;
const magma_int_t ione = 1;
/* Local variables */
real_Double_t gpu_time, cpu_time;
magmaFloatComplex *h_A, *h_R, *h_Z, *h_work, aux_work[1];
#ifdef COMPLEX
float *rwork, aux_rwork[1];
magma_int_t lrwork;
#endif
float *w1, *w2, result[4]={0, 0, 0, 0}, eps, abstol;
magma_int_t *iwork, *isuppz, *ifail, aux_iwork[1];
magma_int_t N, n2, info, lwork, liwork, lda;
magma_int_t ISEED[4] = {0,0,0,1};
eps = lapackf77_slamch( "E" );
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// checking NoVec requires LAPACK
opts.lapack |= (opts.check && opts.jobz == MagmaNoVec);
magma_range_t range = MagmaRangeAll;
if (opts.fraction != 1)
range = MagmaRangeI;
#ifdef REAL
if (opts.version == 3 || opts.version == 4) {
printf("%% magma_cheevr and magma_cheevx are not available for real precisions (single, float).\n");
return status;
}
#endif
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("P");
// pass ngpu = -1 to test multi-GPU code using 1 gpu
magma_int_t abs_ngpu = abs( opts.ngpu );
printf("%% jobz = %s, range = %s, uplo = %s, fraction = %6.4f, ngpu = %d\n",
lapack_vec_const(opts.jobz), lapack_range_const(range), lapack_uplo_const(opts.uplo),
opts.fraction, int(abs_ngpu) );
printf("%% N CPU Time (sec) GPU Time (sec) |S-S_magma| |A-USU^H| |I-U^H U|\n");
printf("%%============================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
n2 = N*N;
lda = N;
abstol = 0; // auto, in cheevr
// TODO: test vl-vu range
magma_int_t m1 = 0;
float vl = 0;
float vu = 0;
magma_int_t il = 0;
magma_int_t iu = 0;
if (opts.fraction == 0) {
il = max( 1, magma_int_t(0.1*N) );
iu = max( 1, magma_int_t(0.3*N) );
}
else {
il = 1;
iu = max( 1, magma_int_t(opts.fraction*N) );
}
// query for workspace sizes
if ( opts.version == 1 || opts.version == 2 ) {
magma_cheevd( opts.jobz, opts.uplo,
N, NULL, lda, NULL, // A, w
aux_work, -1,
#ifdef COMPLEX
aux_rwork, -1,
#endif
aux_iwork, -1,
&info );
}
else if ( opts.version == 3 ) {
#ifdef COMPLEX
magma_cheevr( opts.jobz, range, opts.uplo,
N, NULL, lda, // A
vl, vu, il, iu, abstol,
&m1, NULL, // w
NULL, lda, NULL, // Z, isuppz
aux_work, -1,
#ifdef COMPLEX
aux_rwork, -1,
#endif
aux_iwork, -1,
&info );
#endif
}
else if ( opts.version == 4 ) {
#ifdef COMPLEX
magma_cheevx( opts.jobz, range, opts.uplo,
N, NULL, lda, // A
vl, vu, il, iu, abstol,
&m1, NULL, // w
NULL, lda, // Z
aux_work, -1,
#ifdef COMPLEX
aux_rwork,
#endif
aux_iwork,
NULL, // ifail
&info );
// cheevx doesn't query rwork, iwork; set them for consistency
aux_rwork[0] = float(7*N);
aux_iwork[0] = float(5*N);
#endif
}
lwork = (magma_int_t) MAGMA_C_REAL( aux_work[0] );
#ifdef COMPLEX
lrwork = (magma_int_t) aux_rwork[0];
#endif
liwork = aux_iwork[0];
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, N*lda );
TESTING_MALLOC_CPU( w1, float, N );
TESTING_MALLOC_CPU( w2, float, N );
#ifdef COMPLEX
TESTING_MALLOC_CPU( rwork, float, lrwork );
#endif
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, N*lda );
TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork );
if (opts.version == 3) {
TESTING_MALLOC_CPU( h_Z, magmaFloatComplex, N*lda );
TESTING_MALLOC_CPU( isuppz, magma_int_t, 2*max(1,N) );
}
if (opts.version == 4) {
TESTING_MALLOC_CPU( h_Z, magmaFloatComplex, N*lda );
TESTING_MALLOC_CPU( ifail, magma_int_t, N );
}
/* Clear eigenvalues, for |S-S_magma| check when fraction < 1. */
lapackf77_slaset( "Full", &N, &ione, &d_zero, &d_zero, w1, &N );
lapackf77_slaset( "Full", &N, &ione, &d_zero, &d_zero, w2, &N );
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
magma_cmake_hermitian( N, h_A, lda );
lapackf77_clacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
if (opts.version == 1) {
if (opts.ngpu == 1) {
magma_cheevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
else {
//printf( "magma_cheevd_m, ngpu %d (%d)\n", opts.ngpu, abs_ngpu );
magma_cheevd_m( abs_ngpu, opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
}
else if ( opts.version == 2 ) { // version 2: cheevdx computes selected eigenvalues/vectors
if (opts.ngpu == 1) {
magma_cheevdx( opts.jobz, range, opts.uplo,
N, h_R, lda,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
else {
//printf( "magma_cheevdx_m, ngpu %d (%d)\n", opts.ngpu, abs_ngpu );
magma_cheevdx_m( abs_ngpu, opts.jobz, range, opts.uplo,
N, h_R, lda,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
}
//printf( "il %d, iu %d, m1 %d\n", il, iu, m1 );
}
else if ( opts.version == 3 ) { // version 3: MRRR, computes selected eigenvalues/vectors
// only complex version available
#ifdef COMPLEX
magma_cheevr( opts.jobz, range, opts.uplo,
N, h_R, lda,
vl, vu, il, iu, abstol,
&m1, w1,
h_Z, lda, isuppz,
h_work, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork,
&info );
lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_R, &lda );
#endif
}
else if ( opts.version == 4 ) { // version 3: cheevx (QR iteration), computes selected eigenvalues/vectors
// only complex version available
#ifdef COMPLEX
magma_cheevx( opts.jobz, range, opts.uplo,
N, h_R, lda,
vl, vu, il, iu, abstol,
&m1, w1,
h_Z, lda,
h_work, lwork,
#ifdef COMPLEX
rwork, /*lrwork,*/
#endif
iwork, /*liwork,*/
ifail,
&info );
lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_R, &lda );
#endif
}
gpu_time = magma_wtime() - gpu_time;
if (info != 0) {
printf("magma_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
bool okay = true;
if ( opts.check && opts.jobz != MagmaNoVec ) {
/* =====================================================================
Check the results following the LAPACK's [zcds]drvst routine.
A is factored as A = U S U^H and the following 3 tests computed:
(1) | A - U S U^H | / ( |A| N )
(2) | I - U^H U | / ( N )
(3) | S(with U) - S(w/o U) | / | S | // currently disabled, but compares to LAPACK
=================================================================== */
magmaFloatComplex *work;
TESTING_MALLOC_CPU( work, magmaFloatComplex, 2*N*N );
// e=NULL is unused since kband=0; tau=NULL is unused since itype=1
lapackf77_chet21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
h_A, &lda,
w1, NULL,
h_R, &lda,
h_R, &lda,
NULL, work,
#ifdef COMPLEX
rwork,
#endif
&result[0] );
result[0] *= eps;
result[1] *= eps;
TESTING_FREE_CPU( work ); work=NULL;
// Disable third eigenvalue check that calls routine again --
// it obscures whether error occurs in first call above or in this call.
// But see comparison to LAPACK below.
//
//lapackf77_clacpy( MagmaFullStr, &N, &N, h_A, &lda, h_R, &lda );
//magma_cheevd( MagmaNoVec, opts.uplo,
// N, h_R, lda, w2,
// h_work, lwork,
// #ifdef COMPLEX
// rwork, lrwork,
// #endif
// iwork, liwork,
// &info );
//if (info != 0) {
// printf("magma_cheevd 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[2] = diff / (N*maxw);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
if ( opts.version == 1 || opts.version == 2 ) {
lapackf77_cheevd( lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_A, &lda, w2,
h_work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork,
&info );
}
else if ( opts.version == 3 ) {
lapackf77_cheevr( lapack_vec_const(opts.jobz),
lapack_range_const(range),
lapack_uplo_const(opts.uplo),
&N, h_A, &lda,
&vl, &vu, &il, &iu, &abstol,
&m1, w2,
h_Z, &lda, isuppz,
h_work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork,
&info );
lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_A, &lda );
}
else if ( opts.version == 4 ) {
lapackf77_cheevx( lapack_vec_const(opts.jobz),
lapack_range_const(range),
lapack_uplo_const(opts.uplo),
&N, h_A, &lda,
&vl, &vu, &il, &iu, &abstol,
&m1, w2,
h_Z, &lda,
h_work, &lwork,
#ifdef COMPLEX
rwork,
#endif
iwork,
ifail,
&info );
lapackf77_clacpy( "Full", &N, &N, h_Z, &lda, h_A, &lda );
}
cpu_time = magma_wtime() - cpu_time;
if (info != 0) {
printf("lapackf77_cheevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
// compare eigenvalues
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[3] = diff / (N*maxw);
okay = okay && (result[3] < tolulp);
printf("%5d %9.4f %9.4f %8.2e ",
(int) N, cpu_time, gpu_time, result[3] );
}
else {
printf("%5d --- %9.4f --- ",
(int) N, gpu_time);
}
// print error checks
if ( opts.check && opts.jobz != MagmaNoVec ) {
okay = okay && (result[0] < tol) && (result[1] < tol);
printf(" %8.2e %8.2e", result[0], result[1] );
}
else {
printf(" --- --- ");
}
printf(" %s\n", (okay ? "ok" : "failed"));
status += ! okay;
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
#ifdef COMPLEX
TESTING_FREE_CPU( rwork );
#endif
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
if ( opts.version == 3 ) {
TESTING_FREE_CPU( h_Z );
TESTING_FREE_CPU( isuppz );
}
if ( opts.version == 4 ) {
TESTING_FREE_CPU( h_Z );
TESTING_FREE_CPU( ifail );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing chegvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time;
magmaFloatComplex *h_A, *h_R, *h_work;
#if defined(PRECISION_z) || defined(PRECISION_c)
float *rwork;
magma_int_t lrwork;
#endif
/* Matrix size */
float *w1, *w2;
magma_int_t *iwork;
magma_int_t N, n2, info, lwork, liwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};;
magma_int_t info_ortho = 0;
magma_int_t info_solution = 0;
magma_int_t info_reduction = 0;
magma_timestr_t start, end;
magma_opts opts;
parse_opts( argc, argv, &opts );
magma_int_t ngpu = opts.ngpu;
char jobz = opts.jobz;
magma_int_t checkres = opts.check;
char range = 'A';
char uplo = opts.uplo;
magma_int_t itype = opts.itype;
float 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: itype = %d, jobz = %c, range = %c, uplo = %c, checkres = %d, fraction = %6.4f\n",
(int) itype, jobz, range, uplo, (int) checkres, f);
printf(" N M GPU Time(s) \n");
printf("==========================\n");
magma_int_t threads = magma_get_numthreads();
for( magma_int_t i = 0; i < opts.ntest; ++i ) {
for( magma_int_t iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
n2 = N*N;
#if defined(PRECISION_z) || defined(PRECISION_c)
lwork = magma_cbulge_get_lq2(N, threads) + 2*N + N*N;
lrwork = 1 + 5*N +2*N*N;
#else
lwork = magma_cbulge_get_lq2(N, threads) + 1 + 6*N + 2*N*N;
#endif
liwork = 3 + 5*N;
/* Allocate host memory for the matrix */
TESTING_MALLOC( h_A, magmaFloatComplex, n2);
TESTING_MALLOC( w1, float , N);
TESTING_MALLOC( w2, float , N);
TESTING_HOSTALLOC(h_R, magmaFloatComplex, n2);
TESTING_HOSTALLOC(h_work, magmaFloatComplex, lwork);
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_HOSTALLOC( rwork, float, lrwork);
#endif
TESTING_MALLOC( iwork, magma_int_t, liwork);
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
/* Make diagonal real */
for(int i=0; i<N; i++) {
MAGMA_C_SET2REAL( h_A[i*N+i], MAGMA_C_REAL(h_A[i*N+i]) );
}
magma_int_t m1 = 0;
float vl = 0;
float 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
// ==================================================================
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
if(ngpu==1){
printf("calling cheevdx_2stage 1 GPU\n");
magma_cheevdx_2stage(jobz, range, uplo, N,
h_R, N,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
}else{
printf("calling cheevdx_2stage_m %d GPU\n", (int) ngpu);
magma_cheevdx_2stage_m(ngpu, jobz, range, uplo, N,
h_R, 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_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
start = get_current_time();
if(ngpu==1){
printf("calling cheevdx_2stage 1 GPU\n");
magma_cheevdx_2stage(jobz, range, uplo, N,
h_R, N,
vl, vu, il, iu,
&m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info);
}else{
printf("calling cheevdx_2stage_m %d GPU\n", (int) ngpu);
magma_cheevdx_2stage_m(ngpu, jobz, range, uplo, N,
h_R, 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();
gpu_time = GetTimerValue(start,end)/1000.;
if ( checkres ) {
float eps = lapackf77_slamch("E");
printf("\n");
printf("------ TESTS FOR MAGMA CHEEVD ROUTINE ------- \n");
printf(" Size of the Matrix %d by %d\n", (int) N, (int) N);
printf("\n");
printf(" The matrix A is randomly generated for each test.\n");
printf("============\n");
printf(" The relative machine precision (eps) is %8.2e\n",eps);
printf(" Computational tests pass if scaled residuals are less than 60.\n");
/* Check the orthogonality, reduction and the eigen solutions */
if (jobz == MagmaVec) {
info_ortho = check_orthogonality(N, N, h_R, N, eps);
info_reduction = check_reduction(uplo, N, 1, h_A, w1, N, h_R, eps);
}
printf("------ CALLING LAPACK CHEEVD TO COMPUTE only eigenvalue and verify elementswise ------- \n");
lapackf77_cheevd("N", "L", &N,
h_A, &N, w2,
h_work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
&info);
info_solution = check_solution(N, w2, w1, eps);
if ( (info_solution == 0) & (info_ortho == 0) & (info_reduction == 0) ) {
printf("***************************************************\n");
printf(" ---- TESTING CHEEVD ...................... PASSED !\n");
printf("***************************************************\n");
}
else {
printf("************************************************\n");
printf(" - TESTING CHEEVD ... FAILED !\n");
printf("************************************************\n");
}
}
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %5d %6.2f\n",
(int) N, (int) m1, gpu_time);
TESTING_FREE( h_A);
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);
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
/* Shutdown */
TESTING_FINALIZE();
return 0;
}
