extern "C" magma_int_t
magma_chetrd2_gpu(char uplo, magma_int_t n,
magmaFloatComplex *da, magma_int_t ldda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *wa, magma_int_t ldwa,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *dwork, magma_int_t ldwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CHETRD2_GPU reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version passes a workspace that is used in an optimized
GPU matrix-vector product.
Arguments
=========
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.
DA (device 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, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = 'U', the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
LDDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
D (output) COMPLEX array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
E (output) COMPLEX array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
TAU (output) COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
WA (workspace/output) COMPLEX array, dimension (LDA,N)
On exit the diagonal, the upper part (UPLO='U')
or the lower part (UPLO='L') are copies of DA
LDWA (input) INTEGER
The leading dimension of the array WA. LDWA >= max(1,N).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
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.
DWORK (workspace/output) COMPLEX array on the GPU, dim (MAX(1,LDWORK))
LDWORK (input) INTEGER
The dimension of the array DWORK.
LDWORK >= (n*n+64-1)/64 + 2*n*nb, where nb = magma_get_chetrd_nb(n)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
===================================================================== */
char uplo_[2] = {uplo, 0};
magma_int_t nb = magma_get_chetrd_nb(n);
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
float d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldw, lddw, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = lapackf77_lsame(uplo_, "U");
lquery = lwork == -1;
if (! upper && ! lapackf77_lsame(uplo_, "L")) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
} else if (ldwa < max(1,n)) {
*info = -9;
} else if (lwork < 1 && ! lquery) {
*info = -11;
}
/* Determine the block size. */
ldw = lddw = n;
lwkopt = n * nb;
if (*info == 0) {
MAGMA_C_SET2REAL( work[0], lwkopt );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
if (n < 1024)
nx = n;
else
nx = 300;
if (ldwork<(ldw*n+64-1)/64 + 2*ldw*nb) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb)
{
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), ldwa );
magma_clatrd2(uplo, i+nb, nb, A(0, 0), ldwa, e, tau,
work, ldw, dA(0, 0), ldda, dwork, lddw, dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( i + nb, nb, work, ldw, dwork, lddw );
magma_cher2k(uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork,
lddw, d_one, dA(0, 0), ldda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
MAGMA_C_SET2REAL( *A(j-1, j), e[j - 1] );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
magma_cgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), ldwa );
/* Use CPU code to reduce the last or only block */
lapackf77_chetrd(uplo_, &kk, A(0, 0), &ldwa, d, e, tau, work, &lwork, &iinfo);
magma_csetmatrix( kk, kk, A(0, 0), ldwa, dA(0, 0), ldda );
}
else
{
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb)
{
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), ldwa );
magma_clatrd2(uplo, n-i, nb, A(i, i), ldwa, &e[i],
&tau[i], work, ldw,
dA(i, i), ldda,
dwork, lddw,
dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( n-i, nb, work, ldw, dwork, lddw );
magma_cher2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda,
&dwork[nb], lddw, d_one,
dA(i+nb, i+nb), ldda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
MAGMA_C_SET2REAL( *A(j+1, j), e[j] );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
/* Use unblocked code to reduce the last or only block */
magma_cgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), ldwa );
i_n = n-i;
lapackf77_chetrd(uplo_, &i_n, A(i, i), &ldwa, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo);
magma_csetmatrix( n-i, n-i, A(i, i), ldwa, dA(i, i), ldda );
}
MAGMA_C_SET2REAL( work[0], lwkopt );
return *info;
} /* chetrd2_gpu */
/**
Purpose
-------
CHETRD2_GPU reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version passes a workspace that is used in an optimized
GPU matrix-vector product.
Arguments
---------
@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, 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, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
d COMPLEX array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
@param[out]
e COMPLEX array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower.
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
wA (workspace) COMPLEX array, dimension (LDA,N)
On exit the diagonal, the upper part (UPLO=MagmaUpper)
or the lower part (UPLO=MagmaLower) are copies of DA
@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 dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
\n
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.
@param[out]
dwork (workspace) COMPLEX array on the GPU, dim (MAX(1,LDWORK))
@param[in]
ldwork INTEGER
The dimension of the array DWORK.
LDWORK >= (n*n+64-1)/64 + 2*n*nb, where nb = magma_get_chetrd_nb(n)
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
@ingroup magma_cheev_comp
********************************************************************/
extern "C" magma_int_t
magma_chetrd2_gpu(magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *wA, magma_int_t ldwa,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *dwork, magma_int_t ldwork,
magma_int_t *info)
{
#define A(i, j) (wA + (j)*ldwa + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t nb = magma_get_chetrd_nb(n);
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
float d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldw, lddw, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
} else if (ldwa < max(1,n)) {
*info = -9;
} else if (lwork < 1 && ! lquery) {
*info = -11;
}
/* Determine the block size. */
ldw = lddw = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
if (n < 1024)
nx = n;
else
nx = 300;
if (ldwork < (ldw*n+64-1)/64 + 2*ldw*nb) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), ldwa );
magma_clatrd2(uplo, i+nb, nb, A(0, 0), ldwa, e, tau,
work, ldw, dA(0, 0), ldda, dwork, lddw, dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( i + nb, nb, work, ldw, dwork, lddw );
magma_cher2k(uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork,
lddw, d_one, dA(0, 0), ldda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j-1,j) = MAGMA_C_MAKE( e[j - 1], 0 );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
magma_cgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), ldwa );
/* Use CPU code to reduce the last or only block */
lapackf77_chetrd(uplo_, &kk, A(0, 0), &ldwa, d, e, tau, work, &lwork, &iinfo);
magma_csetmatrix( kk, kk, A(0, 0), ldwa, dA(0, 0), ldda );
}
else {
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), ldwa );
magma_clatrd2(uplo, n-i, nb, A(i, i), ldwa, &e[i],
&tau[i], work, ldw,
dA(i, i), ldda,
dwork, lddw,
dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( n-i, nb, work, ldw, dwork, lddw );
magma_cher2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda,
&dwork[nb], lddw, d_one,
dA(i+nb, i+nb), ldda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j+1,j) = MAGMA_C_MAKE( e[j], 0 );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
/* Use unblocked code to reduce the last or only block */
magma_cgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), ldwa );
i_n = n-i;
lapackf77_chetrd(uplo_, &i_n, A(i, i), &ldwa, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo);
magma_csetmatrix( n-i, n-i, A(i, i), ldwa, dA(i, i), ldda );
}
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
return *info;
} /* magma_chetrd2_gpu */
