MAGMA  1.2.0
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zhegvx.cpp File Reference
#include "common_magma.h"
Include dependency graph for zhegvx.cpp:

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Functions

void Mymagma_ztrmm (char side, char uplo, char trans, char unit, magma_int_t n, magma_int_t m, cuDoubleComplex alpha, cuDoubleComplex *db, magma_int_t lddb, cuDoubleComplex *dz, magma_int_t lddz)
void Mymagma_ztrsm (char side, char uplo, char trans, char unit, magma_int_t n, magma_int_t m, cuDoubleComplex alpha, cuDoubleComplex *db, magma_int_t lddb, cuDoubleComplex *dz, magma_int_t lddz)
magma_int_t magma_zhegvx (magma_int_t itype, char jobz, char range, char uplo, magma_int_t n, cuDoubleComplex *a, magma_int_t lda, cuDoubleComplex *b, magma_int_t ldb, double vl, double vu, magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m, double *w, cuDoubleComplex *z, magma_int_t ldz, cuDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)

Function Documentation

magma_int_t magma_zhegvx ( magma_int_t  itype,
char  jobz,
char  range,
char  uplo,
magma_int_t  n,
cuDoubleComplex *  a,
magma_int_t  lda,
cuDoubleComplex *  b,
magma_int_t  ldb,
double  vl,
double  vu,
magma_int_t  il,
magma_int_t  iu,
double  abstol,
magma_int_t *  m,
double *  w,
cuDoubleComplex *  z,
magma_int_t  ldz,
cuDoubleComplex *  work,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  iwork,
magma_int_t *  ifail,
magma_int_t *  info 
)

Definition at line 32 of file zhegvx.cpp.

References __func__, lapackf77_lsame, MAGMA_ERR_DEVICE_ALLOC, magma_free(), magma_get_zhetrd_nb(), magma_queue_create(), magma_queue_destroy(), magma_queue_sync(), MAGMA_SUCCESS, magma_xerbla(), MAGMA_Z_ONE, MAGMA_Z_SET2REAL, magma_zgetmatrix(), magma_zgetmatrix_async(), magma_zheevx_gpu(), magma_zhegst_gpu(), magma_zmalloc(), magma_zpotrf_gpu(), magma_zsetmatrix(), magma_zsetmatrix_async(), MagmaConjTrans, MagmaLeft, MagmaLowerStr, MagmaNonUnit, MagmaNoTrans, MagmaNoVectorsStr, MagmaUpperStr, MagmaVectorsStr, max, min, Mymagma_ztrmm(), Mymagma_ztrsm(), trans, and uplo.

{
/*
-- MAGMA (version 1.2.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
May 2012
ITYPE (input) INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
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 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, 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).
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'.
ABSTOL (input) DOUBLE PRECISION
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABSTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH('S').
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)
The first M elements contain the selected
eigenvalues in ascending order.
Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
If JOBZ = 'N', then Z is not referenced.
If JOBZ = 'V', then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
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. LWORK >= max(1,2*N).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for ZHETRD returned by ILAENV.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
IWORK (workspace) INTEGER array, dimension (5*N)
IFAIL (output) INTEGER array, dimension (N)
If JOBZ = 'V', then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = 'N', then IFAIL is not referenced.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPOTRF or ZHEEVX returned an error code:
<= N: if INFO = i, ZHEEVX failed to converge;
i eigenvectors failed to converge. Their indices
are stored in array IFAIL.
> 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
===================================================================== */
char uplo_[2] = {uplo, 0};
char jobz_[2] = {jobz, 0};
char range_[2] = {range, 0};
cuDoubleComplex c_one = MAGMA_Z_ONE;
cuDoubleComplex *da;
cuDoubleComplex *db;
cuDoubleComplex *dz;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lddz = n;
static magma_int_t lower;
static char trans[1];
static magma_int_t wantz;
static magma_int_t lquery;
static magma_int_t alleig, valeig, indeig;
static magma_int_t lwmin;
static cudaStream_t stream;
magma_queue_create( &stream );
wantz = lapackf77_lsame(jobz_, MagmaVectorsStr);
lower = lapackf77_lsame(uplo_, MagmaLowerStr);
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
lquery = lwork == -1;
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVectorsStr))) {
*info = -3;
} else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else if (ldz < 1 || wantz && ldz < n) {
*info = -18;
} 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_zhetrd_nb(n);
lwmin = n * (nb + 1);
MAGMA_Z_SET2REAL(work[0],(double)lwmin);
if (lwork < lwmin && ! lquery) {
*info = -20;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda ) ||
MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb ) ||
MAGMA_SUCCESS != magma_zmalloc( &dz, n*lddz )) {
*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_zpotrf_gpu(uplo_[0], n, db, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
magma_queue_sync( stream );
magma_zgetmatrix_async( n, n,
db, lddb,
b, ldb, stream );
/* Transform problem to standard eigenvalue problem and solve. */
magma_zhegst_gpu(itype, uplo, n, da, ldda, db, lddb, info);
magma_zheevx_gpu(jobz, range, uplo, n, da, ldda, vl, vu, il, iu, abstol, m, w, dz, lddz, a, lda, z, ldz, work, lwork, rwork, iwork, ifail, info);
if (wantz && *info == 0) {
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
*(unsigned char *)trans = MagmaConjTrans;
} else {
*(unsigned char *)trans = MagmaNoTrans;
}
Mymagma_ztrsm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, dz, lddz);
} 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;
}
Mymagma_ztrmm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, dz, lddz);
}
magma_zgetmatrix( n, *m, dz, lddz, z, ldz );
}
magma_queue_sync( stream );
magma_queue_destroy( stream );
magma_free( da );
magma_free( db );
magma_free( dz );
return *info;
} /* zhegvx */

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void Mymagma_ztrmm ( char  side,
char  uplo,
char  trans,
char  unit,
magma_int_t  n,
magma_int_t  m,
cuDoubleComplex  alpha,
cuDoubleComplex *  db,
magma_int_t  lddb,
cuDoubleComplex *  dz,
magma_int_t  lddz 
)

Definition at line 15 of file zhegvx.cpp.

References magma_device_sync(), and magma_ztrmm().

{
magma_ztrmm(side, uplo, trans, unit, n, m, alpha, db, lddb, dz, lddz);
magma_device_sync();
}

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void Mymagma_ztrsm ( char  side,
char  uplo,
char  trans,
char  unit,
magma_int_t  n,
magma_int_t  m,
cuDoubleComplex  alpha,
cuDoubleComplex *  db,
magma_int_t  lddb,
cuDoubleComplex *  dz,
magma_int_t  lddz 
)

Definition at line 23 of file zhegvx.cpp.

References magma_device_sync(), and magma_ztrsm().

{
magma_ztrsm(side, uplo, trans, unit, n, m, alpha, db, lddb, dz, lddz);
magma_device_sync();
}

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