magma_int_t magma_sbulge_get_lq2(magma_int_t n, magma_int_t threads)
{
magma_int_t nb = magma_get_sbulge_nb(n, threads);
magma_int_t Vblksiz = magma_sbulge_get_Vblksiz(n, nb, threads);
magma_int_t ldv = nb + Vblksiz;
magma_int_t ldt = Vblksiz;
return magma_bulge_get_blkcnt(n, nb, Vblksiz) * Vblksiz * (ldt + ldv + 1);
}
extern "C" magma_int_t
magma_ssyevdx_2stage(char jobz, char range, char uplo,
magma_int_t n,
float *a, magma_int_t lda,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
float *work, magma_int_t lwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input) CHARACTER*1
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU]
will be found.
= 'I': the IL-th through IU-th eigenvalues will be found.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX_16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, the first m columns
of A contains the required
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
VL (input) REAL
VU (input) REAL
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) REAL array, dimension (N)
If INFO = 0, the required m eigenvalues in ascending order.
WORK (workspace/output) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= LQ2 + N * (NB + 2).
If JOBZ = 'V' and N > 1, LWORK >= LQ2 + 1 + 6*N + 2*N**2.
where LQ2 is the size needed to store
the Q2 matrix and is returned by
MAGMA_BULGE_GET_LQ2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = 'N' and N > 1, LIWORK >= 1.
If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: 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};
float d_one = 1.;
magma_int_t ione = 1;
magma_int_t izero = 0;
float d__1;
float eps;
float anrm;
magma_int_t imax;
float rmin, rmax;
float sigma;
magma_int_t lwmin, 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;
float* dwork;
/* determine the number of threads */
magma_int_t threads = magma_get_numthreads();
magma_setlapack_numthreads(threads);
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
alleig = lapackf77_lsame( range_, "A" );
valeig = lapackf77_lsame( range_, "V" );
indeig = lapackf77_lsame( range_, "I" );
lquery = lwork == -1 || 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_sbulge_nb(n, threads);
magma_int_t Vblksiz = magma_sbulge_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_sbulge_get_lq2(n, threads);
if (wantz) {
lwmin = lq2 + 1 + 6 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
liwmin = 1;
}
work[0] = lwmin * (1. + lapackf77_slamch("Epsilon"));
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -14;
} else if ((liwork < liwmin) && ! lquery) {
*info = -16;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (n == 1) {
w[0] = a[0];
if (wantz) {
a[0] = MAGMA_S_ONE;
}
return *info;
}
#ifdef ENABLE_TIMER
printf("using %d threads\n", threads);
#endif
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
magma_int_t ntiles = n/nb;
if( ( ntiles < 2 ) || ( n <= 128 ) ){
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int ) nb);
printf("--------------------------------------------------------------\n");
#endif
lapackf77_ssyevd(jobz_, uplo_, &n,
a, &lda, w,
work, &lwork,
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_slansy("M", uplo_, &n, a, &lda, work);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
lapackf77_slascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, a,
&lda, info);
}
magma_int_t inde = 0;
magma_int_t indT2 = inde + n;
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;
#ifdef ENABLE_TIMER
magma_timestr_t start, st1, st2, end;
start = get_current_time();
#endif
float *dT1;
if (MAGMA_SUCCESS != magma_smalloc( &dT1, n*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_ssytrd_sy2sb(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, dT1, threads, info);
#ifdef ENABLE_TIMER
st1 = get_current_time();
printf(" time ssytrd_sy2sb = %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);
float* A2 = &work[indwrk];
memset(A2 , 0, n*lda2*sizeof(float));
for (magma_int_t j = 0; j < n-nb; j++)
{
cblas_scopy(nb+1, &a[j*(lda+1)], 1, &A2[j*lda2], 1);
memset(&a[j*(lda+1)], 0, (nb+1)*sizeof(float));
a[nb + j*(lda+1)] = d_one;
}
for (magma_int_t j = 0; j < nb; j++)
{
cblas_scopy(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(float));
}
#ifdef ENABLE_TIMER
st2 = get_current_time();
printf(" time ssytrd_convert = %6.2f\n" , GetTimerValue(st1,st2)/1000.);
#endif
magma_ssytrd_sb2st(threads, uplo, n, nb, Vblksiz, A2, lda2, w, &work[inde], &work[indV2], ldv, &work[indTAU2], wantz, &work[indT2], ldt);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time ssytrd_sy2st = %6.2f\n" , GetTimerValue(st2,end)/1000.);
printf(" time ssytrd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
lapackf77_ssterf(&n, w, &work[inde], info);
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time sstedc = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
} 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_sstedx(range, n, vl, vu, il, iu, w, &work[inde],
&work[indwrk], n, &work[indwk2],
llwrk2, iwork, liwork, dwork, info);
magma_free( dwork );
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time sstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
float *dZ;
magma_int_t lddz = n;
float *da;
magma_int_t ldda = n;
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
if (MAGMA_SUCCESS != magma_smalloc( &dZ, *m*lddz)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_smalloc( &da, n*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_sbulge_back(threads, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
#ifdef ENABLE_TIMER
st1 = get_current_time();
printf(" time sbulge_back = %6.2f\n" , GetTimerValue(start,st1)/1000.);
#endif
magma_ssetmatrix( n, n, a, lda, da, ldda );
magma_sormqr_gpu_2stages(MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, da+nb, ldda,
dZ+nb, n, dT1, nb, info);
magma_sgetmatrix( n, *m, dZ, lddz, a, lda );
magma_free(dT1);
magma_free(dZ);
magma_free(da);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time sormqr + 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] = lwmin * (1. + lapackf77_slamch("Epsilon"));
iwork[0] = liwmin;
return *info;
} /* magma_zheevdx_2stage */
