magma_int_t magma_zbulge_get_lq2(magma_int_t n, magma_int_t threads)
{
magma_int_t nb = magma_get_zbulge_nb(n, threads);
magma_int_t Vblksiz = magma_zbulge_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_zbulge_getlwstg2(magma_int_t n, magma_int_t threads, magma_int_t wantz,
magma_int_t *Vblksiz, magma_int_t *ldv, magma_int_t *ldt,
magma_int_t *blkcnt, magma_int_t *sizTAU2,
magma_int_t *sizT2, magma_int_t *sizV2)
{
magma_int_t nb = magma_get_zbulge_nb(n, threads);
magma_get_zbulge_VTsiz(n, nb, threads, Vblksiz, ldv, ldt);
return magma_zbulge_getstg2size(n, nb, wantz, Vblksiz[0], ldv[0], ldt[0], blkcnt, sizTAU2, sizT2, sizV2);
}
extern "C" magma_int_t
magma_get_zbulge_lq2(magma_int_t n, magma_int_t threads, magma_int_t wantz)
{
if (wantz == 0)
return 2*n*2;
magma_int_t nb = magma_get_zbulge_nb(n, threads);
magma_int_t Vblksiz = magma_get_zbulge_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" void
magma_zheevdx_getworksize(magma_int_t n, magma_int_t threads,
magma_int_t wantz,
magma_int_t *lwmin,
#ifdef COMPLEX
magma_int_t *lrwmin,
#endif
magma_int_t *liwmin)
{
magma_int_t lda2=0;
magma_int_t Vblksiz;
magma_int_t ldv;
magma_int_t ldt;
magma_int_t blkcnt;
magma_int_t sizTAU2;
magma_int_t sizT2;
magma_int_t sizV2;
magma_int_t nb = magma_get_zbulge_nb( n, threads );
magma_int_t lwstg1 = magma_bulge_getlwstg1( n, nb, &lda2 );
magma_int_t lwstg2 = magma_zbulge_getlwstg2( n, threads, wantz, &Vblksiz, &ldv, &ldt, &blkcnt, &sizTAU2, &sizT2, &sizV2 );
#ifdef COMPLEX
if (wantz) {
*lwmin = lwstg2 + 2*n + max(lwstg1, n*n);
*lrwmin = 1 + 5*n + 2*n*n;
*liwmin = 5*n + 3;
} else {
*lwmin = lwstg2 + n + lwstg1;
*lrwmin = n;
*liwmin = 1;
}
#else
if (wantz) {
*lwmin = lwstg2 + 1 + 6*n + max(lwstg1, 2*n*n);
*liwmin = 5*n + 3;
} else {
*lwmin = lwstg2 + 2*n + lwstg1;
*liwmin = 1;
}
#endif
}
extern "C" magma_int_t
magma_zheevdx_2stage(char jobz, char range, char uplo,
magma_int_t n,
magmaDoubleComplex *a, magma_int_t lda,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input) CHARACTER*1
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU]
will be found.
= 'I': the IL-th through IU-th eigenvalues will be found.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX_16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, the first m columns
of A contains the required
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
VL (input) DOUBLE PRECISION
VU (input) DOUBLE PRECISION
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
IL (input) INTEGER
IU (input) INTEGER
If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
M (output) INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the required m eigenvalues in ascending order.
WORK (workspace/output) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= LQ2 + N * (NB + 1).
If JOBZ = 'V' and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store
the Q2 matrix and is returned by
MAGMA_BULGE_GET_LQ2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = 'N' and N > 1, LRWORK >= N.
If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = 'N' and N > 1, LIWORK >= 1.
If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i and JOBZ = 'N', then the algorithm failed
to converge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
if INFO = i and JOBZ = 'V', then the algorithm failed
to compute an eigenvalue while working on the submatrix
lying in rows and columns INFO/(N+1) through
mod(INFO,N+1).
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
char range_[2] = {range, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t ione = 1;
magma_int_t izero = 0;
double d_one = 1.;
double d__1;
double eps;
double anrm;
magma_int_t imax;
double rmin, rmax;
double sigma;
//magma_int_t iinfo;
magma_int_t lwmin, lrwmin, liwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t iscale;
double safmin;
double bignum;
double smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
double* dwork;
/* determine the number of threads */
magma_int_t threads = magma_get_numthreads();
magma_setlapack_numthreads(threads);
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
alleig = lapackf77_lsame( range_, "A" );
valeig = lapackf77_lsame( range_, "V" );
indeig = lapackf77_lsame( range_, "I" );
lquery = lwork == -1 || lrwork == -1 || liwork == -1;
*info = 0;
if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (lda < max(1,n)) {
*info = -6;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -8;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -9;
} else if (iu < min(n,il) || iu > n) {
*info = -10;
}
}
}
magma_int_t nb = magma_get_zbulge_nb(n,threads);
magma_int_t Vblksiz = magma_zbulge_get_Vblksiz(n, nb, threads);
magma_int_t ldt = Vblksiz;
magma_int_t ldv = nb + Vblksiz;
magma_int_t blkcnt = magma_bulge_get_blkcnt(n, nb, Vblksiz);
magma_int_t lq2 = magma_zbulge_get_lq2(n, threads);
if (wantz) {
lwmin = lq2 + 2 * n + n * n;
lrwmin = 1 + 5 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
lrwmin = n;
liwmin = 1;
}
work[0] = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -14;
} else if ((lrwork < lrwmin) && ! lquery) {
*info = -16;
} else if ((liwork < liwmin) && ! lquery) {
*info = -18;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (n == 1) {
w[0] = MAGMA_Z_REAL(a[0]);
if (wantz) {
a[0] = MAGMA_Z_ONE;
}
return *info;
}
#ifdef ENABLE_TIMER
printf("using %d threads\n", threads);
#endif
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
magma_int_t ntiles = n/nb;
if( ( ntiles < 2 ) || ( n <= 128 ) ){
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb);
printf("--------------------------------------------------------------\n");
#endif
lapackf77_zheevd(jobz_, &uplo, &n,
a, &lda, w,
work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
info);
*m = n;
return *info;
}
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_zlanhe("M", uplo_, &n, a, &lda, rwork);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
lapackf77_zlascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, a,
&lda, info);
}
magma_int_t indT2 = 0;
magma_int_t indTAU2 = indT2 + blkcnt*ldt*Vblksiz;
magma_int_t indV2 = indTAU2+ blkcnt*Vblksiz;
magma_int_t indtau1 = indV2 + blkcnt*ldv*Vblksiz;
magma_int_t indwrk = indtau1+ n;
//magma_int_t indwk2 = indwrk + n * n;
magma_int_t llwork = lwork - indwrk;
//magma_int_t llwrk2 = lwork - indwk2;
magma_int_t inde = 0;
magma_int_t indrwk = inde + n;
magma_int_t llrwk = lrwork - indrwk;
#ifdef ENABLE_TIMER
magma_timestr_t start, st1, st2, end;
start = get_current_time();
#endif
magmaDoubleComplex *dT1;
if (MAGMA_SUCCESS != magma_zmalloc( &dT1, n*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zhetrd_he2hb(uplo, n, nb, a, lda, &work[indtau1], &work[indwrk], llwork, dT1, threads, info);
#ifdef ENABLE_TIMER
st1 = get_current_time();
printf(" time zhetrd_he2hb = %6.2f\n" , GetTimerValue(start,st1)/1000.);
#endif
/* copy the input matrix into WORK(INDWRK) with band storage */
/* PAY ATTENTION THAT work[indwrk] should be able to be of size lda2*n which it should be checked in any future modification of lwork.*/
magma_int_t lda2 = 2*nb; //nb+1+(nb-1);
magmaDoubleComplex* A2 = &work[indwrk];
memset(A2 , 0, n*lda2*sizeof(magmaDoubleComplex));
for (magma_int_t j = 0; j < n-nb; j++)
{
cblas_zcopy(nb+1, &a[j*(lda+1)], 1, &A2[j*lda2], 1);
memset(&a[j*(lda+1)], 0, (nb+1)*sizeof(magmaDoubleComplex));
a[nb + j*(lda+1)] = c_one;
}
for (magma_int_t j = 0; j < nb; j++)
{
cblas_zcopy(nb-j, &a[(j+n-nb)*(lda+1)], 1, &A2[(j+n-nb)*lda2], 1);
memset(&a[(j+n-nb)*(lda+1)], 0, (nb-j)*sizeof(magmaDoubleComplex));
}
#ifdef ENABLE_TIMER
st2 = get_current_time();
printf(" time zhetrd_convert = %6.2f\n" , GetTimerValue(st1,st2)/1000.);
#endif
magma_zhetrd_hb2st(threads, uplo, n, nb, Vblksiz, A2, lda2, w, &rwork[inde], &work[indV2], ldv, &work[indTAU2], wantz, &work[indT2], ldt);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time zhetrd_hb2st = %6.2f\n" , GetTimerValue(st2,end)/1000.);
printf(" time zhetrd = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
lapackf77_dsterf(&n, w, &rwork[inde], info);
magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time dstedc = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
} else {
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, 3*n*(n/2 + 1) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zstedx(range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, dwork, info);
magma_free( dwork );
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time zstedx = %6.2f\n", GetTimerValue(start,end)/1000.);
start = get_current_time();
#endif
magmaDoubleComplex *dZ;
magma_int_t lddz = n;
magmaDoubleComplex *da;
magma_int_t ldda = n;
magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
if (MAGMA_SUCCESS != magma_zmalloc( &dZ, *m*lddz)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zbulge_back(threads, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
#ifdef ENABLE_TIMER
st1 = get_current_time();
printf(" time zbulge_back = %6.2f\n" , GetTimerValue(start,st1)/1000.);
#endif
magma_zsetmatrix( n, n, a, lda, da, ldda );
magma_zunmqr_gpu_2stages(MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, da+nb, ldda,
dZ+nb, n, dT1, nb, info);
magma_zgetmatrix( n, *m, dZ, lddz, a, lda );
magma_free(dT1);
magma_free(dZ);
magma_free(da);
#ifdef ENABLE_TIMER
end = get_current_time();
printf(" time zunmqr + copy = %6.2f\n", GetTimerValue(st1,end)/1000.);
printf(" time eigenvectors backtransf. = %6.2f\n" , GetTimerValue(start,end)/1000.);
#endif
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_dscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
iwork[0] = liwmin;
return *info;
} /* magma_zheevdx_2stage */
/**
Purpose
-------
ZHEGVDX_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
itype INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangles of A and B are stored;
- = MagmaLower: Lower triangles of A and B are stored.
@param[in]
n INTEGER
The order of the matrices A and B. N >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
\n
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper)
or the lower triangle (if UPLO=MagmaLower) of A, including the
diagonal, is destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B COMPLEX_16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
\n
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[in]
vl DOUBLE PRECISION
@param[in]
vu DOUBLE PRECISION
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + N * (NB + 1).
If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store the Q2 matrix
and is returned by magma_bulge_get_lq2.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\n
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\n
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: ZPOTRF or ZHEEVD returned an error code:
<= N: if INFO = i and JOBZ = MagmaNoVec, then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = MagmaVec, then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Further Details
---------------
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if ZHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.
@ingroup magma_zhegv_driver
********************************************************************/
extern "C" magma_int_t
magma_zhegvdx_2stage(magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
magmaDoubleComplex *B, magma_int_t ldb,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex *dA;
magmaDoubleComplex *dB;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t lwmin;
magma_int_t liwmin;
magma_int_t lrwmin;
magma_queue_t stream;
magma_queue_create( &stream );
/* determine the number of threads */
magma_int_t parallel_threads = magma_get_parallel_numthreads();
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || (jobz == MagmaNoVec))) {
*info = -3;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_get_zbulge_nb(n, parallel_threads);
magma_int_t lq2 = magma_zbulge_get_lq2(n, parallel_threads);
if (wantz) {
lwmin = lq2 + 2 * n + n * n;
lrwmin = 1 + 5 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_dlamch("Epsilon");
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (lrwork < lrwmin && ! lquery) {
*info = -19;
} else if (liwork < liwmin && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb);
printf("--------------------------------------------------------------\n");
#endif
lapackf77_zhegvd(&itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork, info);
*m = n;
return *info;
}
// TODO: fix memory leak
if (MAGMA_SUCCESS != magma_zmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &dB, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_zsetmatrix( n, n, B, ldb, dB, lddb );
magma_zsetmatrix_async( n, n,
A, lda,
dA, ldda, stream );
magma_timer_t time=0;
timer_start( time );
magma_zpotrf_gpu(uplo, n, dB, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time zpotrf_gpu = %6.2f\n", time );
magma_queue_sync( stream );
magma_zgetmatrix_async( n, n,
dB, lddb,
B, ldb, stream );
/* Transform problem to standard eigenvalue problem and solve. */
timer_start( time );
magma_zhegst_gpu(itype, uplo, n, dA, ldda, dB, lddb, info);
timer_stop( time );
timer_printf( "time zhegst_gpu = %6.2f\n", time );
magma_zgetmatrix( n, n, dA, ldda, A, lda );
magma_queue_sync( stream );
magma_free( dA );
magma_free( dB );
timer_start( time );
magma_zheevdx_2stage(jobz, range, uplo, n, A, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info);
timer_stop( time );
timer_printf( "time zheevdx_2stage = %6.2f\n", time );
if (wantz && *info == 0) {
// TODO fix memory leak
if (MAGMA_SUCCESS != magma_zmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &dB, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
timer_start( time );
magma_zsetmatrix( n, *m, A, lda, dA, ldda );
magma_zsetmatrix( n, n, B, ldb, dB, lddb );
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
trans = MagmaConjTrans;
} else {
trans = MagmaNoTrans;
}
magma_ztrsm(MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dA, ldda);
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
trans = MagmaNoTrans;
} else {
trans = MagmaConjTrans;
}
magma_ztrmm(MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dA, ldda);
}
magma_zgetmatrix( n, *m, dA, ldda, A, lda );
timer_stop( time );
timer_printf( "time trsm/mm + getmatrix = %6.2f\n", time );
magma_free( dA );
magma_free( dB );
}
magma_queue_destroy( stream );
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
return *info;
} /* magma_zhegvdx_2stage */
extern "C" magma_int_t
magma_zhegvdx_2stage(magma_int_t itype, char jobz, char range, char uplo, magma_int_t n,
magmaDoubleComplex *a, magma_int_t lda,
magmaDoubleComplex *b, magma_int_t ldb,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
ZHEGVDX_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
ITYPE (input) INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
RANGE (input) CHARACTER*1
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU]
will be found.
= 'I': the IL-th through IU-th eigenvalues will be found.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input/output) COMPLEX_16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
or the lower triangle (if UPLO='L') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) COMPLEX_16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = 'U', the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = 'L',
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
VL (input) DOUBLE PRECISION
VU (input) DOUBLE PRECISION
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
IL (input) INTEGER
IU (input) INTEGER
If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
M (output) INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= LQ2 + N * (NB + 1).
If JOBZ = 'V' and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store
the Q2 matrix and is returned by
MAGMA_BULGE_GET_LQ2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = 'N' and N > 1, LRWORK >= N.
If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = 'N' and N > 1, LIWORK >= 1.
If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPOTRF or ZHEEVD returned an error code:
<= N: if INFO = i and JOBZ = 'N', then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = 'V', then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Further Details
===============
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if ZHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
char range_[2] = {range, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex *da;
magmaDoubleComplex *db;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lower;
char trans[1];
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
// magma_int_t lopt;
magma_int_t lwmin;
// magma_int_t liopt;
magma_int_t liwmin;
// magma_int_t lropt;
magma_int_t lrwmin;
magma_queue_t stream;
magma_queue_create( &stream );
/* determine the number of threads */
magma_int_t threads = magma_get_numthreads();
magma_setlapack_numthreads(threads);
wantz = lapackf77_lsame(jobz_, MagmaVecStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
lquery = lwork == -1 || lrwork == -1 || liwork == -1;
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) {
*info = -3;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_get_zbulge_nb(n, threads);
magma_int_t lq2 = magma_zbulge_get_lq2(n, threads);
if (wantz) {
lwmin = lq2 + 2 * n + n * n;
lrwmin = 1 + 5 * n + 2 * n * n;
liwmin = 5 * n + 3;
} else {
lwmin = lq2 + n * (nb + 1);
lrwmin = n;
liwmin = 1;
}
work[0] = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -17;
} else if (lrwork < lrwmin && ! lquery) {
*info = -19;
} else if (liwork < liwmin && ! lquery) {
*info = -21;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
if (n <= 128){
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb);
printf("--------------------------------------------------------------\n");
#endif
lapackf77_zhegvd(&itype, jobz_, uplo_,
&n, a, &lda, b, &ldb,
w, work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork, info);
*m = n;
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_zsetmatrix( n, n, b, ldb, db, lddb );
magma_zsetmatrix_async( n, n,
a, lda,
da, ldda, stream );
#ifdef ENABLE_TIMER
magma_timestr_t start, end;
start = get_current_time();
#endif
magma_zpotrf_gpu(uplo_[0], n, db, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zpotrf_gpu = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_queue_sync( stream );
magma_zgetmatrix_async( n, n,
db, lddb,
b, ldb, stream );
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
/* Transform problem to standard eigenvalue problem and solve. */
magma_zhegst_gpu(itype, uplo, n, da, ldda, db, lddb, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zhegst_gpu = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_zgetmatrix( n, n, da, ldda, a, lda );
magma_queue_sync( stream );
magma_free( da );
magma_free( db );
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
magma_zheevdx_2stage(jobz, range, uplo, n, a, lda, vl, vu, il, iu, m, w, work, lwork, rwork, lrwork, iwork, liwork, info);
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time zheevdx_2stage = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
if (wantz && *info == 0) {
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#ifdef ENABLE_TIMER
start = get_current_time();
#endif
magma_zsetmatrix( n, *m, a, lda, da, ldda );
magma_zsetmatrix( n, n, b, ldb, db, lddb );
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
*(unsigned char *)trans = MagmaConjTrans;
} else {
*(unsigned char *)trans = MagmaNoTrans;
}
magma_ztrsm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, da, ldda);
} else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
*(unsigned char *)trans = MagmaNoTrans;
} else {
*(unsigned char *)trans = MagmaConjTrans;
}
magma_ztrmm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, da, ldda);
}
magma_zgetmatrix( n, *m, da, ldda, a, lda );
#ifdef ENABLE_TIMER
end = get_current_time();
printf("time trsm/mm + getmatrix = %6.2f\n", GetTimerValue(start,end)/1000.);
#endif
magma_free( da );
magma_free( db );
}
magma_queue_destroy( stream );
work[0] = MAGMA_Z_MAKE( lwmin * (1. + lapackf77_dlamch("Epsilon")), 0.); // round up
rwork[0] = lrwmin * (1. + lapackf77_dlamch("Epsilon"));
iwork[0] = liwmin;
return *info;
} /* zhegvdx_2stage */
/**
Purpose
-------
ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. It uses a two-stage algorithm for the tridiagonalization.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
nrgpu INTEGER
Number of GPUs to use.
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = MagmaVec, then if INFO = 0, the first m columns
of A contains the required
orthonormal eigenvectors of the matrix A.
If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower)
or the upper triangle (if UPLO=MagmaUpper) of A, including the
diagonal, is destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in]
vl DOUBLE PRECISION
@param[in]
vu DOUBLE PRECISION
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w DOUBLE PRECISION array, dimension (N)
If INFO = 0, the required m eigenvalues in ascending order.
@param[out]
work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= LQ2 + N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= LQ2 + 2*N + N**2.
where LQ2 is the size needed to store the Q2 matrix
and is returned by magma_bulge_get_lq2.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) DOUBLE PRECISION array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\n
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\n
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i and JOBZ = MagmaNoVec, then the algorithm failed
to converge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
if INFO = i and JOBZ = MagmaVec, then the algorithm failed
to compute an eigenvalue while working on the submatrix
lying in rows and columns INFO/(N+1) through
mod(INFO,N+1).
Further Details
---------------
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
@ingroup magma_zheev_driver
********************************************************************/
extern "C" magma_int_t
magma_zheevdx_2stage_m(magma_int_t nrgpu, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
double vl, double vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, double *w,
magmaDoubleComplex *work, magma_int_t lwork,
double *rwork, magma_int_t lrwork,
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
#define A( i_,j_) (A + (i_) + (j_)*lda)
#define A2(i_,j_) (A2 + (i_) + (j_)*lda2)
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magmaDoubleComplex c_one = MAGMA_Z_ONE;
double d_one = 1.;
magma_int_t ione = 1;
magma_int_t izero = 0;
double d__1;
double eps;
double anrm;
magma_int_t imax;
double rmin, rmax;
double sigma;
//magma_int_t iinfo;
magma_int_t lwmin, lrwmin, liwmin;
magma_int_t lower;
magma_int_t wantz;
magma_int_t iscale;
double safmin;
double bignum;
double smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t len;
/* determine the number of threads */
magma_int_t parallel_threads = magma_get_parallel_numthreads();
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (! (wantz || (jobz == MagmaNoVec))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (lda < max(1,n)) {
*info = -6;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -8;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -9;
} else if (iu < min(n,il) || iu > n) {
*info = -10;
}
}
}
magma_int_t nb = magma_get_zbulge_nb(n, parallel_threads);
magma_int_t Vblksiz = magma_zbulge_get_Vblksiz(n, nb, parallel_threads);
magma_int_t ldt = Vblksiz;
magma_int_t ldv = nb + Vblksiz;
magma_int_t blkcnt = magma_bulge_get_blkcnt(n, nb, Vblksiz);
magma_int_t lq2 = magma_zbulge_get_lq2(n, parallel_threads);
if (wantz) {
lwmin = lq2 + 2*n + n*n;
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 5*n + 3;
} else {
lwmin = lq2 + n + n*nb;
lrwmin = n;
liwmin = 1;
}
// multiply by 1+eps (in Double!) to ensure length gets rounded up,
// if it cannot be exactly represented in floating point.
real_Double_t one_eps = 1. + lapackf77_dlamch("Epsilon");
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -14;
} else if ((lrwork < lrwmin) && ! lquery) {
*info = -16;
} else if ((liwork < liwmin) && ! lquery) {
*info = -18;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (n == 1) {
w[0] = MAGMA_Z_REAL(A[0]);
if (wantz) {
A[0] = MAGMA_Z_ONE;
}
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
timer_printf("using %d parallel_threads\n", (int) parallel_threads);
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
magma_int_t ntiles = n/nb;
if ( ( ntiles < 2 ) || ( n <= 128 ) ) {
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb);
printf("--------------------------------------------------------------\n");
#endif
lapackf77_zheevd(jobz_, uplo_, &n,
A, &lda, w,
work, &lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, &lrwork,
#endif
iwork, &liwork,
info);
*m = n;
return *info;
}
/* Get machine constants. */
safmin = lapackf77_dlamch("Safe minimum");
eps = lapackf77_dlamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_dsqrt(smlnum);
rmax = magma_dsqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_zlanhe("M", uplo_, &n, A, &lda, rwork);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
lapackf77_zlascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A,
&lda, info);
}
magma_int_t indT2 = 0;
magma_int_t indTAU2 = indT2 + blkcnt*ldt*Vblksiz;
magma_int_t indV2 = indTAU2+ blkcnt*Vblksiz;
magma_int_t indtau1 = indV2 + blkcnt*ldv*Vblksiz;
magma_int_t indwrk = indtau1+ n;
magma_int_t indwk2 = indwrk + n*n;
magma_int_t llwork = lwork - indwrk;
magma_int_t llwrk2 = lwork - indwk2;
magma_int_t inde = 0;
magma_int_t indrwk = inde + n;
magma_int_t llrwk = lrwork - indrwk;
magma_timer_t time=0, time_total=0, time_alloc=0, time_dist=0, time_band=0;
timer_start( time_total );
#ifdef HE2HB_SINGLEGPU
magmaDoubleComplex *dT1;
if (MAGMA_SUCCESS != magma_zmalloc( &dT1, n*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
timer_start( time_band );
magma_zhetrd_he2hb(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, dT1, info);
timer_stop( time_band );
timer_printf( " 1 GPU seq code time zhetrd_he2hb only = %7.4f\n", time_band );
magma_free(dT1);
#else
magma_int_t nstream = max(3,nrgpu+2);
magma_queue_t streams[MagmaMaxGPUs][20];
magmaDoubleComplex *da[MagmaMaxGPUs], *dT1[MagmaMaxGPUs];
magma_int_t ldda = ((n+31)/32)*32;
magma_int_t ver = 0;
magma_int_t distblk = max(256, 4*nb);
#ifdef ENABLE_DEBUG
printf("voici ngpu %d distblk %d NB %d nstream %d version %d \n ", nrgpu, distblk, nb, nstream, ver);
#endif
timer_start( time_alloc );
for( magma_int_t dev = 0; dev < nrgpu; ++dev ) {
magma_int_t mlocal = ((n / distblk) / nrgpu + 1) * distblk;
magma_setdevice( dev );
// TODO check malloc
magma_zmalloc(&da[dev], ldda*mlocal );
magma_zmalloc(&dT1[dev], (n*nb) );
for( int i = 0; i < nstream; ++i ) {
magma_queue_create( &streams[dev][i] );
}
}
timer_stop( time_alloc );
timer_start( time_dist );
magma_zsetmatrix_1D_col_bcyclic( n, n, A, lda, da, ldda, nrgpu, distblk );
magma_setdevice(0);
timer_stop( time_dist );
timer_start( time_band );
if (ver == 30) {
magma_zhetrd_he2hb_mgpu_spec(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, info);
} else {
magma_zhetrd_he2hb_mgpu(uplo, n, nb, A, lda, &work[indtau1], &work[indwrk], llwork, da, ldda, dT1, nb, nrgpu, distblk, streams, nstream, info);
}
timer_stop( time_band );
timer_printf(" time alloc %7.4f, ditribution %7.4f, zhetrd_he2hb only = %7.4f\n", time_alloc, time_dist, time_band );
for( magma_int_t dev = 0; dev < nrgpu; ++dev ) {
magma_setdevice( dev );
magma_free( da[dev] );
magma_free( dT1[dev] );
for( int i = 0; i < nstream; ++i ) {
magma_queue_destroy( streams[dev][i] );
}
}
#endif // not HE2HB_SINGLEGPU
timer_stop( time_total );
timer_printf( " time zhetrd_he2hb_mgpu = %6.2f\n", time_total );
timer_start( time_total );
timer_start( time );
/* copy the input matrix into WORK(INDWRK) with band storage */
/* PAY ATTENTION THAT work[indwrk] should be able to be of size lda2*n which it should be checked in any future modification of lwork.*/
magma_int_t lda2 = 2*nb; //nb+1+(nb-1);
magmaDoubleComplex* A2 = &work[indwrk];
memset(A2, 0, n*lda2*sizeof(magmaDoubleComplex));
for (magma_int_t j = 0; j < n-nb; j++) {
len = nb+1;
blasf77_zcopy( &len, A(j,j), &ione, A2(0,j), &ione );
memset(A(j,j), 0, (nb+1)*sizeof(magmaDoubleComplex));
*A(nb+j,j) = c_one;
}
for (magma_int_t j = 0; j < nb; j++) {
len = nb-j;
blasf77_zcopy( &len, A(j+n-nb,j+n-nb), &ione, A2(0,j+n-nb), &ione );
memset(A(j+n-nb,j+n-nb), 0, (nb-j)*sizeof(magmaDoubleComplex));
}
timer_stop( time );
timer_printf( " time zhetrd_convert = %6.2f\n", time );
timer_start( time );
magma_zhetrd_hb2st(uplo, n, nb, Vblksiz, A2, lda2, w, &rwork[inde], &work[indV2], ldv, &work[indTAU2], wantz, &work[indT2], ldt);
timer_stop( time );
timer_stop( time_total );
timer_printf( " time zhetrd_hb2st = %6.2f\n", time );
timer_printf( " time zhetrd = %6.2f\n", time_total );
/* For eigenvalues only, call DSTERF. For eigenvectors, first call
ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call ZUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
timer_start( time );
lapackf77_dsterf(&n, w, &rwork[inde], info);
magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
timer_stop( time );
timer_printf( " time dstedc = %6.2f\n", time );
}
else {
timer_start( time_total );
timer_start( time );
magma_zstedx_m(nrgpu, range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, info);
timer_stop( time );
timer_printf( " time zstedx_m = %6.2f\n", time );
timer_start( time );
magma_dmove_eig(range, n, w, &il, &iu, vl, vu, m);
/*
magmaDoubleComplex *dZ;
magma_int_t lddz = n;
if (MAGMA_SUCCESS != magma_zmalloc( &dZ, *m*lddz)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_zbulge_back(uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n, dZ, lddz,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
magma_zgetmatrix( n, *m, dZ, lddz, &work[indwrk], n);
magma_free(dZ);
*/
magma_zbulge_back_m(nrgpu, uplo, n, nb, *m, Vblksiz, &work[indwrk + n * (il-1)], n,
&work[indV2], ldv, &work[indTAU2], &work[indT2], ldt, info);
timer_stop( time );
timer_printf( " time zbulge_back_m = %6.2f\n", time );
timer_start( time );
magma_zunmqr_m(nrgpu, MagmaLeft, MagmaNoTrans, n-nb, *m, n-nb, A+nb, lda, &work[indtau1],
&work[indwrk + n * (il-1) + nb], n, &work[indwk2], llwrk2, info);
lapackf77_zlacpy("A", &n, m, &work[indwrk + n * (il-1)], &n, A, &lda);
timer_stop( time );
timer_stop( time_total );
timer_printf( " time zunmqr_m + copy = %6.2f\n", time );
timer_printf( " time eigenvectors backtransf. = %6.2f\n", time_total );
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_dscal(&imax, &d__1, w, &ione);
}
work[0] = MAGMA_Z_MAKE( lwmin * one_eps, 0.); // round up
rwork[0] = lrwmin * one_eps;
iwork[0] = liwmin;
magma_setdevice( orig_dev );
return *info;
} /* magma_zheevdx_2stage_m */