extern "C" magma_int_t
magma_cdtohpo(magma_int_t num_gpus, char *uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb, magma_int_t NB,
magmaFloatComplex *a, magma_int_t lda,
magmaFloatComplex *dwork[], magma_int_t ldda,
magma_queue_t stream[][3], magma_int_t *info)
{
magma_int_t k;
if( lapackf77_lsame(uplo, "U") ) {
magma_int_t j, jj, jb, mj;
/* go through each column */
for (j=off_j+NB; j<n; j+=nb) {
jj = (j-off_j)/(nb*num_gpus);
k = ((j-off_j)/nb)%num_gpus;
jb = min(nb, (n-j));
if(j+jb < off_j+m)
mj = (j-off_i)+jb;
else
mj = m;
magma_setdevice(k);
magma_cgetmatrix_async( mj, jb,
dA(k, 0, jj*nb), ldda,
A(off_i, j), lda,
stream[k][0] );
magma_queue_sync( stream[k][0] );
}
} else {
magma_int_t i, ii, ib, ni;
/* go through each row */
for(i=off_i+NB; i<m; i+=nb){
ii = (i-off_i)/(nb*num_gpus);
k = ((i-off_i)/nb)%num_gpus;
ib = min(nb, (m-i));
if(i+ib < off_i+n)
ni = (i-off_i)+ib;
else
ni = n;
magma_setdevice(k);
magma_cgetmatrix_async( ib, ni,
dA(k, ii*nb, 0), ldda,
A(i, off_j), lda,
stream[k][0] );
magma_queue_sync( stream[k][0] );
}
}
/*for( k=0; k<num_gpus; k++ ) {
magma_setdevice(k);
magma_queue_sync( stream[k][0] );
}*/
magma_setdevice(0);
return *info;
}
// --------------------
extern "C" void
magma_cgetvector_async(
magma_int_t n,
magmaFloatComplex_const_ptr dx_src, size_t dx_offset, magma_int_t incx,
magmaFloatComplex* hy_dst, magma_int_t incy,
magma_queue_t queue, magma_event_t *event )
{
if (n <= 0)
return;
if (incx == 1 && incy == 1) {
cl_int err = clEnqueueReadBuffer(
queue, dx_src, CL_FALSE,
dx_offset*sizeof(magmaFloatComplex), n*sizeof(magmaFloatComplex),
hy_dst, 0, NULL, event);
check_error( err );
}
else {
magma_int_t ldda = incx;
magma_int_t ldhb = incy;
magma_cgetmatrix_async( 1, n,
dx_src, dx_offset, ldda,
hy_dst, ldhb,
queue, event);
}
}
/**
Purpose
-------
CLATRD reduces NB rows and columns of a complex Hermitian matrix A to
Hermitian tridiagonal form by an orthogonal similarity
transformation Q' * A * Q, and returns the matrices V and W which are
needed to apply the transformation to the unreduced part of A.
If UPLO = MagmaUpper, CLATRD reduces the last NB rows and columns of a
matrix, of which the upper triangle is supplied;
if UPLO = MagmaLower, CLATRD reduces the first NB rows and columns of a
matrix, of which the lower triangle is supplied.
This is an auxiliary routine called by CHETRD.
Arguments
---------
@param[in]
uplo magma_uplo_t
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
- = MagmaUpper: Upper triangular
- = MagmaLower: Lower triangular
@param[in]
n INTEGER
The order of the matrix A.
@param[in]
nb INTEGER
The number of rows and columns to be reduced.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, 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 last NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements above the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors;
- if UPLO = MagmaLower, the first NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements below the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors.
See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= (1,N).
@param[out]
e COMPLEX array, dimension (N-1)
If UPLO = MagmaUpper, E(n-nb:n-1) contains the superdiagonal
elements of the last NB columns of the reduced matrix;
if UPLO = MagmaLower, E(1:nb) contains the subdiagonal elements of
the first NB columns of the reduced matrix.
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors, stored in
TAU(n-nb:n-1) if UPLO = MagmaUpper, and in TAU(1:nb) if UPLO = MagmaLower.
See Further Details.
@param[out]
W COMPLEX array, dimension (LDW,NB)
The n-by-nb matrix W required to update the unreduced part
of A.
@param[in]
ldw INTEGER
The leading dimension of the array W. LDW >= max(1,N).
@param
dA TODO: dimension (ldda, n)?
@param
ldda TODO: ldda >= n?
@param
dW TODO: dimension (lddw, ??)
@param
lddw TODO: lddw >= n ??
@param[in]
queue magma_queue_t
Queue to execute in.
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n) H(n-1) . . . H(n-nb+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:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
and tau in TAU(i-1).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(nb).
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+1:n) is stored on exit in A(i+1:n,i),
and tau in TAU(i).
The elements of the vectors v together form the n-by-nb matrix V
which is needed, with W, to apply the transformation to the unreduced
part of the matrix, using a Hermitian rank-2k update of the form:
A := A - V*W' - W*V'.
The contents of A on exit are illustrated by the following examples
with n = 5 and nb = 2:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( a a a v4 v5 ) ( d )
( a a v4 v5 ) ( 1 d )
( a 1 v5 ) ( v1 1 a )
( d 1 ) ( v1 v2 a a )
( d ) ( v1 v2 a a a )
where d denotes a diagonal element of the reduced matrix, a denotes
an element of the original matrix that is unchanged, and vi denotes
an element of the vector defining H(i).
@ingroup magma_cheev_aux
********************************************************************/
extern "C" magma_int_t
magma_clatrd(
magma_uplo_t uplo, magma_int_t n, magma_int_t nb,
magmaFloatComplex *A, magma_int_t lda,
float *e, magmaFloatComplex *tau,
magmaFloatComplex *W, magma_int_t ldw,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magmaFloatComplex_ptr dW, magma_int_t lddw,
magma_queue_t queue )
{
#define A(i_, j_) (A + (i_) + (j_)*lda)
#define W(i_, j_) (W + (i_) + (j_)*ldw)
#define dA(i_, j_) (dA + (i_) + (j_)*ldda)
#define dW(i_, j_) (dW + (i_) + (j_)*lddw)
/* Constants */
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magma_int_t ione = 1;
/* Local variables */
magmaFloatComplex alpha, value;
magma_int_t i, i_n, i_1, iw;
/* Check arguments */
magma_int_t info = 0;
if ( uplo != MagmaLower && uplo != MagmaUpper ) {
info = -1;
} else if ( n < 0 ) {
info = -2;
} else if ( nb < 1 ) {
info = -3;
} else if ( lda < max(1,n) ) {
info = -5;
} else if ( ldw < max(1,n) ) {
info = -9;
} else if ( ldda < max(1,n) ) {
info = -11;
} else if ( lddw < max(1,n) ) {
info = -13;
}
if (info != 0) {
magma_xerbla( __func__, -(info) );
return info;
}
/* Quick return if possible */
if (n == 0) {
return info;
}
if (uplo == MagmaUpper) {
/* Reduce last NB columns of upper triangle */
for (i = n-1; i >= n - nb; --i) {
i_1 = i + 1;
i_n = n - i - 1;
iw = i - n + nb;
if (i < n-1) {
/* Update A(1:i,i) */
#ifdef COMPLEX
lapackf77_clacgv( &i_n, W(i, iw+1), &ldw );
#endif
blasf77_cgemv( "No transpose", &i_1, &i_n, &c_neg_one, A(0, i+1), &lda,
W(i, iw+1), &ldw, &c_one, A(0, i), &ione );
#ifdef COMPLEX
lapackf77_clacgv( &i_n, W(i, iw+1), &ldw );
lapackf77_clacgv( &i_n, A(i, i+1), &lda );
#endif
blasf77_cgemv( "No transpose", &i_1, &i_n, &c_neg_one, W(0, iw+1), &ldw,
A(i, i+1), &lda, &c_one, A(0, i), &ione );
#ifdef COMPLEX
lapackf77_clacgv( &i_n, A(i, i+1), &lda );
#endif
}
if (i > 0) {
/* Generate elementary reflector H(i) to annihilate A(1:i-2,i) */
alpha = *A(i-1, i);
lapackf77_clarfg( &i, &alpha, A(0, i), &ione, &tau[i - 1] );
e[i-1] = MAGMA_C_REAL( alpha );
*A(i-1,i) = MAGMA_C_ONE;
/* Compute W(1:i-1,i) */
// 1. Send the block reflector A(0:n-i-1,i) to the GPU
magma_csetvector( i, A(0, i), 1, dA(0, i), 1, queue );
magma_chemv( MagmaUpper, i, c_one, dA(0, 0), ldda,
dA(0, i), ione, c_zero, dW(0, iw), ione, queue );
// 2. Start putting the result back (asynchronously)
magma_cgetmatrix_async( i, 1,
dW(0, iw), lddw,
W(0, iw), ldw, queue );
if (i < n-1) {
blasf77_cgemv( MagmaConjTransStr, &i, &i_n, &c_one, W(0, iw+1), &ldw,
A(0, i), &ione, &c_zero, W(i+1, iw), &ione );
}
// 3. Here is where we need it // TODO find the right place
magma_queue_sync( queue );
if (i < n-1) {
blasf77_cgemv( "No transpose", &i, &i_n, &c_neg_one, A(0, i+1), &lda,
W(i+1, iw), &ione, &c_one, W(0, iw), &ione );
blasf77_cgemv( MagmaConjTransStr, &i, &i_n, &c_one, A(0, i+1), &lda,
A(0, i), &ione, &c_zero, W(i+1, iw), &ione );
blasf77_cgemv( "No transpose", &i, &i_n, &c_neg_one, W(0, iw+1), &ldw,
W(i+1, iw), &ione, &c_one, W(0, iw), &ione );
}
blasf77_cscal( &i, &tau[i - 1], W(0, iw), &ione );
value = magma_cblas_cdotc( i, W(0,iw), ione, A(0,i), ione );
alpha = tau[i - 1] * -0.5f * value;
blasf77_caxpy( &i, &alpha, A(0, i), &ione,
W(0, iw), &ione );
}
}
}
else {
/* Reduce first NB columns of lower triangle */
for (i = 0; i < nb; ++i) {
/* Update A(i:n,i) */
i_n = n - i;
#ifdef COMPLEX
lapackf77_clacgv( &i, W(i, 0), &ldw );
#endif
blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, A(i, 0), &lda,
W(i, 0), &ldw, &c_one, A(i, i), &ione );
#ifdef COMPLEX
lapackf77_clacgv( &i, W(i, 0), &ldw );
lapackf77_clacgv( &i, A(i, 0), &lda );
#endif
blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, W(i, 0), &ldw,
A(i, 0), &lda, &c_one, A(i, i), &ione );
#ifdef COMPLEX
lapackf77_clacgv( &i, A(i, 0), &lda );
#endif
if (i < n-1) {
/* Generate elementary reflector H(i) to annihilate A(i+2:n,i) */
i_n = n - i - 1;
alpha = *A(i+1, i);
lapackf77_clarfg( &i_n, &alpha, A(min(i+2,n-1), i), &ione, &tau[i] );
e[i] = MAGMA_C_REAL( alpha );
*A(i+1,i) = MAGMA_C_ONE;
/* Compute W(i+1:n,i) */
// 1. Send the block reflector A(i+1:n,i) to the GPU
magma_csetvector( i_n, A(i+1, i), 1, dA(i+1, i), 1, queue );
magma_chemv( MagmaLower, i_n, c_one, dA(i+1, i+1), ldda,
dA(i+1, i), ione, c_zero, dW(i+1, i), ione, queue );
// 2. Start putting the result back (asynchronously)
magma_cgetmatrix_async( i_n, 1,
dW(i+1, i), lddw,
W(i+1, i), ldw, queue );
blasf77_cgemv( MagmaConjTransStr, &i_n, &i, &c_one, W(i+1, 0), &ldw,
A(i+1, i), &ione, &c_zero, W(0, i), &ione );
blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, A(i+1, 0), &lda,
W(0, i), &ione, &c_zero, work, &ione );
blasf77_cgemv( MagmaConjTransStr, &i_n, &i, &c_one, A(i+1, 0), &lda,
A(i+1, i), &ione, &c_zero, W(0, i), &ione );
// 3. Here is where we need it
magma_queue_sync( queue );
if (i != 0)
blasf77_caxpy( &i_n, &c_one, work, &ione, W(i+1, i), &ione );
blasf77_cgemv( "No transpose", &i_n, &i, &c_neg_one, W(i+1, 0), &ldw,
W(0, i), &ione, &c_one, W(i+1, i), &ione );
blasf77_cscal( &i_n, &tau[i], W(i+1,i), &ione );
value = magma_cblas_cdotc( i_n, W(i+1,i), ione, A(i+1,i), ione );
alpha = tau[i] * -0.5f * value;
blasf77_caxpy( &i_n, &alpha, A(i+1, i), &ione, W(i+1,i), &ione );
}
}
}
return info;
} /* magma_clatrd */
/**
Purpose
-------
CLATRD2 reduces NB rows and columns of a complex Hermitian matrix A to
Hermitian tridiagonal form by an orthogonal similarity
transformation Q' * A * Q, and returns the matrices V and W which are
needed to apply the transformation to the unreduced part of A.
If UPLO = MagmaUpper, CLATRD reduces the last NB rows and columns of a
matrix, of which the upper triangle is supplied;
if UPLO = MagmaLower, CLATRD reduces the first NB rows and columns of a
matrix, of which the lower triangle is supplied.
This is an auxiliary routine called by CHETRD2_GPU. It uses an
accelerated HEMV that needs extra memory.
Arguments
---------
@param[in]
uplo magma_uplo_t
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
- = MagmaUpper: Upper triangular
- = MagmaLower: Lower triangular
@param[in]
n INTEGER
The order of the matrix A.
@param[in]
nb INTEGER
The number of rows and columns to be reduced.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, 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 last NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements above the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors;
- if UPLO = MagmaLower, the first NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements below the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors.
See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= (1,N).
@param[out]
e COMPLEX array, dimension (N-1)
If UPLO = MagmaUpper, E(n-nb:n-1) contains the superdiagonal
elements of the last NB columns of the reduced matrix;
if UPLO = MagmaLower, E(1:nb) contains the subdiagonal elements of
the first NB columns of the reduced matrix.
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors, stored in
TAU(n-nb:n-1) if UPLO = MagmaUpper, and in TAU(1:nb) if UPLO = MagmaLower.
See Further Details.
@param[out]
W COMPLEX array, dimension (LDW,NB)
The n-by-nb matrix W required to update the unreduced part
of A.
@param[in]
ldw INTEGER
The leading dimension of the array W. LDW >= max(1,N).
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n) H(n-1) . . . H(n-nb+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:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
and tau in TAU(i-1).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(nb).
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+1:n) is stored on exit in A(i+1:n,i),
and tau in TAU(i).
The elements of the vectors v together form the n-by-nb matrix V
which is needed, with W, to apply the transformation to the unreduced
part of the matrix, using a Hermitian rank-2k update of the form:
A := A - V*W' - W*V'.
The contents of A on exit are illustrated by the following examples
with n = 5 and nb = 2:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( a a a v4 v5 ) ( d )
( a a v4 v5 ) ( 1 d )
( a 1 v5 ) ( v1 1 a )
( d 1 ) ( v1 v2 a a )
( d ) ( v1 v2 a a a )
where d denotes a diagonal element of the reduced matrix, a denotes
an element of the original matrix that is unchanged, and vi denotes
an element of the vector defining H(i).
@ingroup magma_cheev_aux
********************************************************************/
extern "C" magma_int_t
magma_clatrd2(magma_uplo_t uplo, magma_int_t n, magma_int_t nb,
magmaFloatComplex *A, magma_int_t lda,
float *e, magmaFloatComplex *tau,
magmaFloatComplex *W, magma_int_t ldw,
magmaFloatComplex *dA, magma_int_t ldda,
magmaFloatComplex *dW, magma_int_t lddw,
magmaFloatComplex *dwork, magma_int_t ldwork)
{
#define A(i, j) (A + (j)*lda + (i))
#define W(i, j) (W + (j)*ldw + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
#define dW(i, j) (dW + (j)*lddw + (i))
magma_int_t i;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex value = MAGMA_C_ZERO;
magma_int_t ione = 1;
magma_int_t i_n, i_1, iw;
magmaFloatComplex alpha;
magmaFloatComplex *f;
if (n <= 0) {
return 0;
}
magma_queue_t stream;
magma_queue_create( &stream );
magma_cmalloc_cpu( &f, n );
assert( f != NULL ); // TODO return error, or allocate outside clatrd
if (uplo == MagmaUpper) {
/* Reduce last NB columns of upper triangle */
for (i = n-1; i >= n - nb; --i) {
i_1 = i + 1;
i_n = n - i - 1;
iw = i - n + nb;
if (i < n-1) {
/* Update A(1:i,i) */
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i_n, W(i, iw+1), &ldw);
#endif
blasf77_cgemv("No transpose", &i_1, &i_n, &c_neg_one, A(0, i+1), &lda,
W(i, iw+1), &ldw, &c_one, A(0, i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i_n, W(i, iw+1), &ldw);
lapackf77_clacgv(&i_n, A(i, i+1), &ldw);
#endif
blasf77_cgemv("No transpose", &i_1, &i_n, &c_neg_one, W(0, iw+1), &ldw,
A(i, i+1), &lda, &c_one, A(0, i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i_n, A(i, i+1), &ldw);
#endif
}
if (i > 0) {
/* Generate elementary reflector H(i) to annihilate A(1:i-2,i) */
alpha = *A(i-1, i);
lapackf77_clarfg(&i, &alpha, A(0, i), &ione, &tau[i - 1]);
e[i-1] = MAGMA_C_REAL( alpha );
*A(i-1,i) = MAGMA_C_MAKE( 1, 0 );
/* Compute W(1:i-1,i) */
// 1. Send the block reflector A(0:n-i-1,i) to the GPU
magma_csetvector( i, A(0, i), 1, dA(0, i), 1 );
//#if (GPUSHMEM < 200)
//magma_chemv(MagmaUpper, i, c_one, dA(0, 0), ldda,
// dA(0, i), ione, c_zero, dW(0, iw), ione);
//#else
magmablas_chemv_work(MagmaUpper, i, c_one, dA(0, 0), ldda,
dA(0, i), ione, c_zero, dW(0, iw), ione,
dwork, ldwork);
//#endif
// 2. Start putting the result back (asynchronously)
magma_cgetmatrix_async( i, 1,
dW(0, iw), lddw,
W(0, iw) /*test*/, ldw, stream );
if (i < n-1) {
blasf77_cgemv(MagmaConjTransStr, &i, &i_n, &c_one, W(0, iw+1), &ldw,
A(0, i), &ione, &c_zero, W(i+1, iw), &ione);
}
// 3. Here is where we need it // TODO find the right place
magma_queue_sync( stream );
if (i < n-1) {
blasf77_cgemv("No transpose", &i, &i_n, &c_neg_one, A(0, i+1), &lda,
W(i+1, iw), &ione, &c_one, W(0, iw), &ione);
blasf77_cgemv(MagmaConjTransStr, &i, &i_n, &c_one, A(0, i+1), &lda,
A(0, i), &ione, &c_zero, W(i+1, iw), &ione);
blasf77_cgemv("No transpose", &i, &i_n, &c_neg_one, W(0, iw+1), &ldw,
W(i+1, iw), &ione, &c_one, W(0, iw), &ione);
}
blasf77_cscal(&i, &tau[i - 1], W(0, iw), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
cblas_cdotc_sub( i, W(0,iw), ione, A(0,i), ione, &value );
#else
value = cblas_cdotc( i, W(0,iw), ione, A(0,i), ione );
#endif
alpha = tau[i - 1] * -0.5f * value;
blasf77_caxpy(&i, &alpha, A(0, i), &ione,
W(0, iw), &ione);
}
}
}
else {
/* Reduce first NB columns of lower triangle */
for (i = 0; i < nb; ++i) {
/* Update A(i:n,i) */
i_n = n - i;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i, W(i, 0), &ldw);
#endif
blasf77_cgemv("No transpose", &i_n, &i, &c_neg_one, A(i, 0), &lda,
W(i, 0), &ldw, &c_one, A(i, i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i, W(i, 0), &ldw);
lapackf77_clacgv(&i, A(i, 0), &lda);
#endif
blasf77_cgemv("No transpose", &i_n, &i, &c_neg_one, W(i, 0), &ldw,
A(i, 0), &lda, &c_one, A(i, i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv(&i, A(i, 0), &lda);
#endif
if (i < n-1) {
/* Generate elementary reflector H(i) to annihilate A(i+2:n,i) */
i_n = n - i - 1;
alpha = *A(i+1, i);
lapackf77_clarfg(&i_n, &alpha, A(min(i+2,n-1), i), &ione, &tau[i]);
e[i] = MAGMA_C_REAL( alpha );
*A(i+1,i) = MAGMA_C_MAKE( 1, 0 );
/* Compute W(i+1:n,i) */
// 1. Send the block reflector A(i+1:n,i) to the GPU
magma_csetvector( i_n, A(i+1, i), 1, dA(i+1, i), 1 );
//#if (GPUSHMEM < 200)
//magma_chemv(MagmaLower, i_n, c_one, dA(i+1, i+1), ldda, dA(i+1, i), ione, c_zero,
// dW(i+1, i), ione);
//#else
magmablas_chemv_work(MagmaLower, i_n, c_one, dA(i+1, i+1), ldda, dA(i+1, i), ione, c_zero,
dW(i+1, i), ione,
dwork, ldwork);
//#endif
// 2. Start putting the result back (asynchronously)
magma_cgetmatrix_async( i_n, 1,
dW(i+1, i), lddw,
W(i+1, i), ldw, stream );
blasf77_cgemv(MagmaConjTransStr, &i_n, &i, &c_one, W(i+1, 0), &ldw,
A(i+1, i), &ione, &c_zero, W(0, i), &ione);
blasf77_cgemv("No transpose", &i_n, &i, &c_neg_one, A(i+1, 0), &lda,
W(0, i), &ione, &c_zero, f, &ione);
blasf77_cgemv(MagmaConjTransStr, &i_n, &i, &c_one, A(i+1, 0), &lda,
A(i+1, i), &ione, &c_zero, W(0, i), &ione);
// 3. Here is where we need it
magma_queue_sync( stream );
if (i != 0)
blasf77_caxpy(&i_n, &c_one, f, &ione, W(i+1, i), &ione);
blasf77_cgemv("No transpose", &i_n, &i, &c_neg_one, W(i+1, 0), &ldw,
W(0, i), &ione, &c_one, W(i+1, i), &ione);
blasf77_cscal(&i_n, &tau[i], W(i+1,i), &ione);
#if defined(PRECISION_z) || defined(PRECISION_c)
cblas_cdotc_sub( i_n, W(i+1,i), ione, A(i+1,i), ione, &value );
#else
value = cblas_cdotc( i_n, W(i+1,i), ione, A(i+1,i), ione );
#endif
alpha = tau[i] * -0.5f * value;
blasf77_caxpy(&i_n, &alpha, A(i+1, i), &ione, W(i+1,i), &ione);
}
}
}
magma_free_cpu(f);
magma_queue_destroy( stream );
return 0;
} /* magma_clatrd */
extern "C" magma_int_t
magma_ctrtri_gpu(
magma_uplo_t uplo, magma_diag_t diag, magma_int_t n,
magmaFloatComplex_ptr dA, size_t dA_offset, magma_int_t ldda,
magma_queue_t queues[2],
magma_int_t *info)
{
/* -- clMAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date November 2014
Purpose
=======
CTRTRI computes the inverse of a real upper or lower triangular
matrix dA.
This is the Level 3 BLAS version of the algorithm.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
dA (input/output) COMPLEX array ON THE GPU, dimension (LDDA,N)
On entry, the triangular matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of the array dA contains
the upper triangular matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of the array dA contains
the lower triangular matrix, and the strictly upper
triangular part of A is not referenced. If DIAG = 'U', the
diagonal elements of A are also not referenced and are
assumed to be 1.
On exit, the (triangular) inverse of the original matrix, in
the same storage format.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, dA(i,i) is exactly zero. The triangular
matrix is singular and its inverse cannot be computed.
(Singularity check is currently disabled.)
===================================================================== */
/* Local variables */
magma_int_t nb, nn, j, jb;
//magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *work;
int upper = (uplo == MagmaUpper);
int nounit = (diag == MagmaNonUnit);
*info = 0;
if (! upper && uplo != MagmaLower)
*info = -1;
else if (! nounit && diag != MagmaUnit)
*info = -2;
else if (n < 0)
*info = -3;
else if (ldda < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Check for singularity if non-unit */
/* cannot do here with matrix dA on GPU -- need kernel */
/*
if (nounit) {
for (j=0; j < n; ++j) {
if ( MAGMA_C_EQUAL( *dA(j,j), c_zero )) {
*info = j+1; // Fortran index
return *info;
}
}
}
*/
/* Determine the block size for this environment */
nb = magma_get_cpotrf_nb(n);
/* Create Queues */
//magma_queue_t queues[2];
//magma_device_t device[MagmaMaxGPUs];
//magma_int_t num = 0;
//magma_int_t err;
//
//err = magma_getdevices( device, MagmaMaxGPUs, &num );
//if ( err != 0 || num < 1 ) {
// fprintf( stderr, "magma_getdevices failed: %d\n", err );
// exit(-1);
//}
//err = magma_queue_create( device[0], &queues[0] );
//if ( err != 0 ) {
// fprintf( stderr, "magma_queue_create 0 failed: %d\n", err );
// exit(-1);
//}
//err = magma_queue_create( device[0], &queues[1] );
//if ( err != 0 ) {
// fprintf( stderr, "magma_queue_create 1 failed: %d\n", err );
// exit(-1);
//}
if (MAGMA_SUCCESS != magma_cmalloc_cpu( &work, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if (nb <= 1 || nb >= n) {
magma_cgetmatrix( n, n, dA, dA_offset, ldda, work, n, queues[0] );
lapackf77_ctrtri( lapack_const(uplo), lapack_const(diag), &n, work, &n, info );
magma_csetmatrix( n, n, work, n, dA, dA_offset, ldda, queues[0] );
}
else {
if (upper) {
/* Compute inverse of upper triangular matrix */
for (j=0; j < n; j += nb) {
jb = min(nb, (n-j));
/* Compute rows 1:j-1 of current block column */
magma_ctrmm( MagmaLeft, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_one, dA(0,0), ldda, dA(0, j), ldda,
queues[0] );
magma_ctrsm( MagmaRight, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_neg_one, dA(j,j), ldda, dA(0, j), ldda,
queues[0] );
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, queues[1], NULL );
magma_queue_sync( queues[1] );
/* Compute inverse of current diagonal block */
lapackf77_ctrtri( MagmaUpperStr, lapack_const(diag), &jb, work, &jb, info );
/*
magma_csetmatrix_async( jb, jb,
work, 0, jb,
dA(j, j), ldda, queues[0], NULL );
*/
magma_csetmatrix( jb, jb,
work, jb,
dA(j, j), ldda, queues[0] );
}
}
else {
/* Compute inverse of lower triangular matrix */
nn = ((n-1)/nb)*nb+1;
for(j=nn-1; j >= 0; j -= nb) {
jb = min(nb,(n-j));
if((j+jb) < n) {
/* Compute rows j+jb:n of current block column */
magma_ctrmm( MagmaLeft, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_one, dA(j+jb,j+jb), ldda, dA(j+jb, j), ldda,
queues[0] );
magma_ctrsm( MagmaRight, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_neg_one, dA(j,j), ldda, dA(j+jb, j), ldda,
queues[0] );
}
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, queues[1], NULL );
magma_queue_sync( queues[1] );
/* Compute inverse of current diagonal block */
lapackf77_ctrtri( MagmaLowerStr, lapack_const(diag), &jb, work, &jb, info );
/*
magma_csetmatrix_async( jb, jb,
work, 0, jb,
dA(j, j), ldda, queues[0], NULL );
*/
magma_csetmatrix( jb, jb,
work, jb,
dA(j, j), ldda, queues[0] );
}
}
}
//magma_queue_destroy( queues[0] );
//magma_queue_destroy( queues[1] );
magma_free_cpu( work );
return *info;
}
/**
Purpose
-------
CSYTRF_nopiv_gpu computes the LDLt factorization of a complex symmetric
matrix A.
The factorization has the form
A = U^T * D * U, if UPLO = MagmaUpper, or
A = L * D * L^T, if UPLO = MagmaLower,
where U is an upper triangular matrix, L is lower triangular, and
D is a diagonal matrix.
This is the block version of the algorithm, calling Level 3 BLAS.
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 on the GPU, dimension (LDDA,N)
On entry, the symmetric 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.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U^H D U or A = L D L^H.
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using cudaMallocHost.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
if INFO = -6, the GPU memory allocation failed
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_csysv_comp
******************************************************************* */
extern "C" magma_int_t
magma_csytrf_nopiv_gpu(
magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magma_int_t *info)
{
#define A(i, j) (A)
#define dA(i, j) (dA +(j)*ldda + (i))
#define dW(i, j) (dW +(j)*ldda + (i))
#define dWt(i, j) (dW +(j)*nb + (i))
/* Constants */
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
/* Local variables */
bool upper = (uplo == MagmaUpper);
magma_int_t j, k, jb, nb, ib, iinfo;
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return */
if ( n == 0 )
return *info;
nb = magma_get_chetrf_nopiv_nb(n);
ib = min(32, nb); // inner-block for diagonal factorization
magma_queue_t queues[2];
magma_event_t event;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
magma_event_create( &event );
trace_init( 1, 1, 2, queues );
// CPU workspace
magmaFloatComplex *A;
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &A, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
// GPU workspace
magmaFloatComplex_ptr dW;
if (MAGMA_SUCCESS != magma_cmalloc( &dW, (1+nb)*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Use hybrid blocked code. */
if (upper) {
//=========================================================
// Compute the LDLt factorization A = U'*D*U without pivoting.
// main loop
for (j=0; j < n; j += nb) {
jb = min(nb, (n-j));
// copy A(j,j) back to CPU
trace_gpu_start( 0, 0, "get", "get" );
magma_event_sync( event );
magma_cgetmatrix_async( jb, jb, dA(j, j), ldda, A(j,j), nb, queues[1] );
trace_gpu_end( 0, 0 );
// factorize the diagonal block
magma_queue_sync( queues[1] );
trace_cpu_start( 0, "potrf", "potrf" );
magma_csytrf_nopiv_cpu( MagmaUpper, jb, ib, A(j, j), nb, info );
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
// copy A(j,j) back to GPU
trace_gpu_start( 0, 0, "set", "set" );
magma_csetmatrix_async( jb, jb, A(j, j), nb, dA(j, j), ldda, queues[0] );
trace_gpu_end( 0, 0 );
if ( (j+jb) < n) {
// compute the off-diagonal blocks of current block column
trace_gpu_start( 0, 0, "trsm", "trsm" );
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaUnit,
jb, (n-j-jb),
c_one, dA(j, j), ldda,
dA(j, j+jb), ldda, queues[0] );
magma_ccopymatrix( jb, n-j-jb, dA( j, j+jb ), ldda, dWt( 0, j+jb ), nb, queues[0] );
// update the trailing submatrix with D
magmablas_clascl_diag( MagmaUpper, jb, n-j-jb,
dA(j, j), ldda,
dA(j, j+jb), ldda,
queues[0], &iinfo );
trace_gpu_end( 0, 0 );
// update the trailing submatrix with U and W
trace_gpu_start( 0, 0, "gemm", "gemm" );
for (k=j+jb; k < n; k += nb) {
magma_int_t kb = min(nb,n-k);
magma_cgemm( MagmaTrans, MagmaNoTrans, kb, n-k, jb,
c_neg_one, dWt(0, k), nb,
dA(j, k), ldda,
c_one, dA(k, k), ldda, queues[0] );
if (k == j+jb)
magma_event_record( event, queues[0] );
}
trace_gpu_end( 0, 0 );
}
}
} else {
//=========================================================
// Compute the LDLt factorization A = L*D*L' without pivoting.
// main loop
for (j=0; j < n; j += nb) {
jb = min(nb, (n-j));
// copy A(j,j) back to CPU
trace_gpu_start( 0, 0, "get", "get" );
magma_event_sync( event );
magma_cgetmatrix_async( jb, jb, dA(j, j), ldda, A(j,j), nb, queues[1] );
trace_gpu_end( 0, 0 );
// factorize the diagonal block
magma_queue_sync( queues[1] );
trace_cpu_start( 0, "potrf", "potrf" );
magma_csytrf_nopiv_cpu( MagmaLower, jb, ib, A(j, j), nb, info );
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
// copy A(j,j) back to GPU
trace_gpu_start( 0, 0, "set", "set" );
magma_csetmatrix_async( jb, jb, A(j, j), nb, dA(j, j), ldda, queues[0] );
trace_gpu_end( 0, 0 );
if ( (j+jb) < n) {
// compute the off-diagonal blocks of current block column
trace_gpu_start( 0, 0, "trsm", "trsm" );
magma_ctrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
(n-j-jb), jb,
c_one, dA(j, j), ldda,
dA(j+jb, j), ldda, queues[0] );
magma_ccopymatrix( n-j-jb,jb, dA( j+jb, j ), ldda, dW( j+jb, 0 ), ldda, queues[0] );
// update the trailing submatrix with D
magmablas_clascl_diag(MagmaLower, n-j-jb, jb,
dA(j, j), ldda,
dA(j+jb, j), ldda,
queues[0], &iinfo);
trace_gpu_end( 0, 0 );
// update the trailing submatrix with L and W
trace_gpu_start( 0, 0, "gemm", "gemm" );
for (k=j+jb; k < n; k += nb) {
magma_int_t kb = min(nb,n-k);
magma_cgemm( MagmaNoTrans, MagmaTrans, n-k, kb, jb,
c_neg_one, dA(k, j), ldda,
dW(k, 0), ldda,
c_one, dA(k, k), ldda, queues[0] );
if (k == j+jb)
magma_event_record( event, queues[0] );
}
trace_gpu_end( 0, 0 );
}
}
}
trace_finalize( "chetrf.svg","trace.css" );
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_event_destroy( event );
magma_free( dW );
magma_free_pinned( A );
return *info;
} /* magma_csytrf_nopiv */
/**
Purpose
-------
CGETRF_NOPIV_GPU computes an LU factorization of a general M-by-N
matrix A without any pivoting.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the right-looking Level 3 BLAS version of the algorithm.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dA COMPLEX array on the GPU, dimension (LDDA,N).
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,M).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
- > 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
@ingroup magma_cgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_cgetrf_nopiv_gpu(
magma_int_t m, magma_int_t n,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magma_int_t *info)
{
#define dA(i,j) (dA + (i)*nb + (j)*nb*ldda)
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t iinfo, nb;
magma_int_t maxm, mindim;
magma_int_t i, rows, s, lddwork;
magmaFloatComplex *work;
/* Check arguments */
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0)
*info = -2;
else if (ldda < max(1,m))
*info = -4;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
mindim = min(m, n);
nb = magma_get_cgetrf_nb(m);
s = mindim / nb;
if (nb <= 1 || nb >= min(m,n)) {
/* Use CPU code. */
magma_cmalloc_cpu( &work, m * n );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_cgetmatrix( m, n, dA, ldda, work, m );
magma_cgetrf_nopiv( m, n, work, m, info);
magma_csetmatrix( m, n, work, m, dA, ldda );
magma_free_cpu(work);
}
else {
/* Use hybrid blocked code. */
maxm = ((m + 31)/32)*32;
lddwork = maxm;
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &work, maxm*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
/* Define user stream if current stream is NULL */
magma_queue_t stream[2];
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
magma_queue_create( &stream[0] );
if (orig_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else {
stream[1] = orig_stream;
}
for( i=0; i < s; i++ ) {
// download i-th panel
magma_queue_sync( stream[1] );
magma_cgetmatrix_async( m-i*nb, nb, dA(i,i), ldda, work, lddwork, stream[0] );
if ( i > 0 ) {
magma_ctrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,
nb, n - (i+1)*nb,
c_one, dA(i-1,i-1), ldda,
dA(i-1,i+1), ldda );
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
m-i*nb, n-(i+1)*nb, nb,
c_neg_one, dA(i, i-1), ldda, dA(i-1,i+1), ldda,
c_one, dA(i, i+1), ldda );
}
// do the cpu part
rows = m - i*nb;
magma_queue_sync( stream[0] );
magma_cgetrf_nopiv( rows, nb, work, lddwork, &iinfo );
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + i*nb;
// upload i-th panel
magma_csetmatrix_async( m-i*nb, nb, work, lddwork, dA(i, i), ldda, stream[0] );
magma_queue_sync( stream[0] );
// do the small non-parallel computations
if ( s > (i+1) ) {
magma_ctrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dA(i, i ), ldda,
dA(i, i+1), ldda);
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
m-(i+1)*nb, nb, nb,
c_neg_one, dA(i+1, i ), ldda, dA(i, i+1), ldda,
c_one, dA(i+1, i+1), ldda );
}
else {
magma_ctrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,
nb, n-s*nb,
c_one, dA(i, i ), ldda,
dA(i, i+1), ldda);
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
m-(i+1)*nb, n-(i+1)*nb, nb,
c_neg_one, dA(i+1, i ), ldda, dA(i, i+1), ldda,
c_one, dA(i+1, i+1), ldda );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
rows = m - s*nb;
magma_cgetmatrix( rows, nb0, dA(s,s), ldda, work, lddwork );
// make sure that gpu queue is empty
magma_device_sync();
// do the cpu part
magma_cgetrf_nopiv( rows, nb0, work, lddwork, &iinfo );
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + s*nb;
// upload i-th panel
magma_csetmatrix( rows, nb0, work, lddwork, dA(s,s), ldda );
magma_ctrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,
nb0, n-s*nb-nb0,
c_one, dA(s,s), ldda,
dA(s,s)+nb0, ldda);
magma_free_pinned( work );
magma_queue_destroy( stream[0] );
if (orig_stream == NULL) {
magma_queue_destroy( stream[1] );
}
magmablasSetKernelStream( orig_stream );
}
return *info;
} /* magma_cgetrf_nopiv_gpu */
extern "C" magma_int_t
magma_cgeqrf2_mgpu( magma_int_t num_gpus, magma_int_t m, magma_int_t n,
magmaFloatComplex **dlA, magma_int_t ldda,
magmaFloatComplex *tau,
magma_int_t *info )
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
CGEQRF2_MGPU computes a QR factorization of a complex M-by-N matrix A:
A = Q * R. This is a GPU interface of the routine.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
dA (input/output) COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix dA.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
===================================================================== */
#define dlA(dev, i, j) (dlA[dev] + (i) + (j)*(ldda))
#define hpanel(i) (hpanel + (i))
// set to NULL to make cleanup easy: free(NULL) does nothing.
magmaFloatComplex *dwork[MagmaMaxGPUs]={NULL}, *dpanel[MagmaMaxGPUs]={NULL};
magmaFloatComplex *hwork=NULL, *hpanel=NULL;
magma_queue_t stream[MagmaMaxGPUs][2]={{NULL}};
magma_event_t panel_event[MagmaMaxGPUs]={NULL};
magma_int_t i, j, min_mn, dev, ldhpanel, lddwork, rows;
magma_int_t ib, nb;
magma_int_t lhwork, lwork;
magma_int_t panel_dev, i_local, i_nb_local, n_local[MagmaMaxGPUs], la_dev, dpanel_offset;
magma_queue_t cqueue;
magmablasGetKernelStream( &cqueue );
magma_device_t cdevice;
magma_getdevice( &cdevice );
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
min_mn = min(m,n);
if (min_mn == 0)
return *info;
nb = magma_get_cgeqrf_nb( m );
/* dwork is (n*nb) --- for T (nb*nb) and clarfb work ((n-nb)*nb) ---
* + dpanel (ldda*nb), on each GPU.
* I think clarfb work could be smaller, max(n_local[:]).
* Oddly, T and clarfb work get stacked on top of each other, both with lddwork=n.
* on GPU that owns panel, set dpanel = dlA(dev,i,i_local).
* on other GPUs, set dpanel = dwork[dev] + dpanel_offset. */
lddwork = n;
dpanel_offset = lddwork*nb;
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
if ( MAGMA_SUCCESS != magma_cmalloc( &(dwork[dev]), (lddwork + ldda)*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
}
/* hwork is MAX( workspace for cgeqrf (n*nb), two copies of T (2*nb*nb) )
* + hpanel (m*nb).
* for last block, need 2*n*nb total. */
ldhpanel = m;
lhwork = max( n*nb, 2*nb*nb );
lwork = max( lhwork + ldhpanel*nb, 2*n*nb );
if ( MAGMA_SUCCESS != magma_cmalloc_pinned( &hwork, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
goto CLEANUP;
}
hpanel = hwork + lhwork;
/* Set the number of local n for each GPU */
for( dev=0; dev < num_gpus; dev++ ) {
n_local[dev] = ((n/nb)/num_gpus)*nb;
if (dev < (n/nb) % num_gpus)
n_local[dev] += nb;
else if (dev == (n/nb) % num_gpus)
n_local[dev] += n % nb;
}
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_queue_create( &stream[dev][0] );
magma_queue_create( &stream[dev][1] );
magma_event_create( &panel_event[dev] );
}
if ( nb < min_mn ) {
/* Use blocked code initially */
// Note: as written, ib cannot be < nb.
for( i = 0; i < min_mn-nb; i += nb ) {
/* Set the GPU number that holds the current panel */
panel_dev = (i/nb) % num_gpus;
/* Set the local index where the current panel is (j==i) */
i_local = i/(nb*num_gpus)*nb;
ib = min(min_mn-i, nb);
rows = m-i;
/* Send current panel to the CPU, after panel_event indicates it has been updated */
magma_setdevice( panel_dev );
magma_queue_wait_event( stream[panel_dev][1], panel_event[panel_dev] );
magma_cgetmatrix_async( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hpanel(i), ldhpanel, stream[panel_dev][1] );
magma_queue_sync( stream[panel_dev][1] );
// Factor panel
lapackf77_cgeqrf( &rows, &ib, hpanel(i), &ldhpanel, tau+i,
hwork, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %d\n", (int) *info );
}
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
hpanel(i), &ldhpanel, tau+i, hwork, &ib );
cpanel_to_q( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
// Send the current panel back to the GPUs
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
if (dev == panel_dev)
dpanel[dev] = dlA(dev, i, i_local);
else
dpanel[dev] = dwork[dev] + dpanel_offset;
magma_csetmatrix_async( rows, ib,
hpanel(i), ldhpanel,
dpanel[dev], ldda, stream[dev][0] );
}
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( stream[dev][0] );
}
// TODO: if cpanel_to_q copied whole block, wouldn't need to restore
// -- just send the copy to the GPUs.
// TODO: also, could zero out the lower triangle and use Azzam's larfb w/ gemm.
/* Restore the panel */
cq_to_panel( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
if (i + ib < n) {
/* Send the T matrix to the GPU. */
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_csetmatrix_async( ib, ib,
hwork, ib,
dwork[dev], lddwork, stream[dev][0] );
}
la_dev = (panel_dev+1) % num_gpus;
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magmablasSetKernelStream( stream[dev][0] );
if (dev == la_dev && i+nb < min_mn-nb) {
// If not last panel,
// for look-ahead panel, apply H' to A(i:m,i+ib:i+2*ib)
i_nb_local = (i+nb)/(nb*num_gpus)*nb;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local), ldda, // C
dwork[dev]+ib, lddwork ); // work
magma_event_record( panel_event[dev], stream[dev][0] );
// for trailing matrix, apply H' to A(i:m,i+2*ib:n)
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[dev]-(i_nb_local+ib), ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local+ib), ldda, // C
dwork[dev]+ib, lddwork ); // work
}
else {
// for trailing matrix, apply H' to A(i:m,i+ib:n)
i_nb_local = i_local;
if (dev <= panel_dev) {
i_nb_local += ib;
}
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[dev]-i_nb_local, ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local), ldda, // C
dwork[dev]+ib, lddwork ); // work
}
}
// Restore top of panel (after larfb is done)
magma_setdevice( panel_dev );
magma_csetmatrix_async( ib, ib,
hpanel(i), ldhpanel,
dlA(panel_dev, i, i_local), ldda, stream[panel_dev][0] );
}
}
}
else {
i = 0;
}
/* Use unblocked code to factor the last or only block row. */
if (i < min_mn) {
rows = m-i;
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % num_gpus;
i_local = j/(nb*num_gpus)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_cgetmatrix( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hwork + (j-i)*rows, rows );
}
// needs lwork >= 2*n*nb:
// needs (m-i)*(n-i) for last block row, bounded by nb*n.
// needs (n-i)*nb for cgeqrf work, bounded by n*nb.
ib = n-i; // total columns in block row
lhwork = lwork - ib*rows;
lapackf77_cgeqrf( &rows, &ib, hwork, &rows, tau+i, hwork + ib*rows, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %d\n", (int) *info );
}
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % num_gpus;
i_local = j/(nb*num_gpus)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_csetmatrix( rows, ib,
hwork + (j-i)*rows, rows,
dlA(panel_dev, i, i_local), ldda );
}
}
CLEANUP:
// free(NULL) does nothing.
// check that queues and events are non-zero before destroying them, though.
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
if ( stream[dev][0] ) { magma_queue_destroy( stream[dev][0] ); }
if ( stream[dev][1] ) { magma_queue_destroy( stream[dev][1] ); }
if ( panel_event[dev] ) { magma_event_destroy( panel_event[dev] ); }
magma_free( dwork[dev] );
}
magma_free_pinned( hwork );
magma_setdevice( cdevice );
magmablasSetKernelStream( cqueue );
return *info;
} /* magma_cgeqrf2_mgpu */
extern "C" magma_err_t
magma_cgeqrf(magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info,
magma_queue_t* queue )
{
/* -- clMAGMA (version 1.1.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2014
Purpose
=======
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A:
A = Q * R. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
If the current stream is NULL, this version replaces it with user defined
stream to overlap computation with communication.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max( N*NB, 2*NB*NB ),
where NB can be obtained through magma_get_cgeqrf_nb(M).
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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
===================================================================== */
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(i,j) dA, dA_offset + (i) + (j)*ldda
magmaFloatComplex_ptr dA, dwork, dT;
size_t dA_offset, dwork_offset, dT_offset;
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t i, k, lddwork, old_i, old_ib;
magma_int_t ib, ldda;
*info = 0;
magma_int_t nb = magma_get_cgeqrf_nb(min(m, n));
// need 2*nb*nb to store T and upper triangle of V simultaneously
magma_int_t lwkopt = max(n*nb, 2*nb*nb);
work[0] = MAGMA_C_MAKE( (float)lwkopt, 0 );
int lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1, lwkopt) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
k = min(m,n);
if (k == 0) {
work[0] = c_one;
return *info;
}
// largest N for larfb is n-nb (trailing matrix lacks 1st panel)
lddwork = ((n+31)/32)*32 - nb;
ldda = ((m+31)/32)*32;
magma_int_t num_gpus = magma_num_gpus();
if( num_gpus > 1 ) {
/* call multiple-GPU interface */
printf("multiple-GPU verison not implemented\n");
return MAGMA_ERR_NOT_IMPLEMENTED;
//return magma_cgeqrf4(num_gpus, m, n, A, lda, tau, work, lwork, info);
}
// allocate space for dA, dwork, and dT
if (MAGMA_SUCCESS != magma_cmalloc( &dA, (n*ldda + nb*lddwork + nb*nb) )) {
/* Switch to the "out-of-core" (out of GPU-memory) version */
printf("non-GPU-resident version not implemented\n");
return MAGMA_ERR_NOT_IMPLEMENTED;
//return magma_cgeqrf_ooc(m, n, A, lda, tau, work, lwork, info);
}
dA_offset = 0;
dwork = dA;
dwork_offset = n*ldda;
dT = dA;
dT_offset = n*ldda + nb*lddwork;
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially.
Asynchronously send the matrix to the GPU except the first panel. */
magma_csetmatrix_async( m, n-nb,
A(0,nb), 0, lda,
dA(0,nb), ldda, queue[0], NULL );
old_i = 0;
old_ib = nb;
for (i = 0; i < k-nb; i += nb) {
ib = min(k-i, nb);
if (i>0) {
/* download i-th panel */
magma_queue_sync( queue[1] );
magma_cgetmatrix_async( m-i, ib,
dA(i,i), ldda,
A(i,i), 0, lda, queue[0], NULL );
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i), ldda, dT, dT_offset, nb,
dA(old_i, old_i+2*old_ib), ldda, dwork, dwork_offset, lddwork, queue[1]);
magma_cgetmatrix_async( i, ib,
dA(0,i), ldda,
A(0,i), 0, lda, queue[1], NULL );
magma_queue_sync( queue[0] );
}
magma_int_t rows = m-i;
lapackf77_cgeqrf(&rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(i,i), &lda, tau+i, work, &ib);
cpanel_to_q(MagmaUpper, ib, A(i,i), lda, work+ib*ib);
/* download the i-th V matrix */
magma_csetmatrix_async( rows, ib, A(i,i), 0, lda, dA(i,i), ldda, queue[0], NULL );
/* download the T matrix */
magma_queue_sync( queue[1] );
magma_csetmatrix_async( ib, ib, work, 0, ib, dT, dT_offset, nb, queue[0], NULL );
magma_queue_sync( queue[0] );
if (i + ib < n) {
if (i+ib < k-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left (look-ahead) */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT, dT_offset, nb,
dA(i, i+ib), ldda, dwork, dwork_offset, lddwork, queue[1]);
cq_to_panel(MagmaUpper, ib, A(i,i), lda, work+ib*ib);
}
else {
/* After last panel, update whole trailing matrix. */
/* Apply H' to A(i:m,i+ib:n) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dT, dT_offset, nb,
dA(i, i+ib), ldda, dwork, dwork_offset, lddwork, queue[1]);
cq_to_panel(MagmaUpper, ib, A(i,i), lda, work+ib*ib);
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
if (i != 0) {
magma_cgetmatrix( m, ib, dA(0,i), ldda, A(0,i), 0, lda, queue[1] );
}
magma_int_t rows = m-i;
lapackf77_cgeqrf(&rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info);
}
magma_queue_sync(queue[0]);
magma_queue_sync(queue[1]);
magma_free( dA );
return *info;
} /* magma_cgeqrf */
/**
Purpose
-------
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A:
A = Q * R. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
This uses 2 queues to overlap communication and computation.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max( N*NB, 2*NB*NB ),
where NB can be obtained through magma_get_cgeqrf_nb( M, N ).
\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.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_cgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqrf(
magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info )
{
#define A(i_,j_) (A + (i_) + (j_)*lda)
#ifdef HAVE_clBLAS
#define dA(i_,j_) dA, ((i_) + (j_)*ldda + dA_offset)
#define dT(i_,j_) dT, ((i_) + (j_)*nb + dT_offset)
#define dwork(i_) dwork, ((i_) + dwork_offset)
#else
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dT(i_,j_) (dT + (i_) + (j_)*nb)
#define dwork(i_) (dwork + (i_))
#endif
/* Constants */
const magmaFloatComplex c_one = MAGMA_C_ONE;
/* Local variables */
magmaFloatComplex_ptr dA, dT, dwork;
magma_int_t i, ib, min_mn, ldda, lddwork, old_i, old_ib;
/* Function Body */
*info = 0;
magma_int_t nb = magma_get_cgeqrf_nb( m, n );
// need 2*nb*nb to store T and upper triangle of V simultaneously
magma_int_t lwkopt = max( n*nb, 2*nb*nb );
work[0] = magma_cmake_lwork( lwkopt );
bool lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1, lwkopt) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
min_mn = min( m, n );
if (min_mn == 0) {
work[0] = c_one;
return *info;
}
// largest N for larfb is n-nb (trailing matrix lacks 1st panel)
lddwork = magma_roundup( n, 32 ) - nb;
ldda = magma_roundup( m, 32 );
magma_int_t ngpu = magma_num_gpus();
if ( ngpu > 1 ) {
/* call multiple-GPU interface */
return magma_cgeqrf_m( ngpu, m, n, A, lda, tau, work, lwork, info );
}
// allocate space for dA, dwork, and dT
if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda + nb*lddwork + nb*nb )) {
/* alloc failed so call non-GPU-resident version */
return magma_cgeqrf_ooc( m, n, A, lda, tau, work, lwork, info );
}
dwork = dA + n*ldda;
dT = dA + n*ldda + nb*lddwork;
magma_queue_t queues[2];
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
if ( (nb > 1) && (nb < min_mn) ) {
/* Use blocked code initially.
Asynchronously send the matrix to the GPU except the first panel. */
magma_csetmatrix_async( m, n-nb,
A(0,nb), lda,
dA(0,nb), ldda, queues[0] );
old_i = 0;
old_ib = nb;
for (i = 0; i < min_mn-nb; i += nb) {
ib = min( min_mn-i, nb );
if (i > 0) {
/* get i-th panel from device */
magma_queue_sync( queues[1] );
magma_cgetmatrix_async( m-i, ib,
dA(i,i), ldda,
A(i,i), lda, queues[0] );
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i), ldda, dT(0,0), nb,
dA(old_i, old_i+2*old_ib), ldda, dwork(0), lddwork, queues[1] );
magma_cgetmatrix_async( i, ib,
dA(0,i), ldda,
A(0,i), lda, queues[1] );
magma_queue_sync( queues[0] );
}
magma_int_t rows = m-i;
lapackf77_cgeqrf( &rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info );
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(i,i), &lda, tau+i, work, &ib );
magma_cpanel_to_q( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
/* put i-th V matrix onto device */
magma_csetmatrix_async( rows, ib, A(i,i), lda, dA(i,i), ldda, queues[0] );
/* put T matrix onto device */
magma_queue_sync( queues[1] );
magma_csetmatrix_async( ib, ib, work, ib, dT(0,0), nb, queues[0] );
magma_queue_sync( queues[0] );
if (i + ib < n) {
if (i+ib < min_mn-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left (look-ahead) */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT(0,0), nb,
dA(i, i+ib), ldda, dwork(0), lddwork, queues[1] );
magma_cq_to_panel( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
}
else {
/* After last panel, update whole trailing matrix. */
/* Apply H' to A(i:m,i+ib:n) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dT(0,0), nb,
dA(i, i+ib), ldda, dwork(0), lddwork, queues[1] );
magma_cq_to_panel( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < min_mn) {
ib = n-i;
if (i != 0) {
magma_cgetmatrix( m, ib, dA(0,i), ldda, A(0,i), lda, queues[1] );
}
magma_int_t rows = m-i;
lapackf77_cgeqrf( &rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info );
}
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
return *info;
} /* magma_cgeqrf */
/**
Purpose
-------
CTRTRI computes the inverse of a real upper or lower triangular
matrix dA.
This is the Level 3 BLAS version of the algorithm.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: A is upper triangular;
- = MagmaLower: A is lower triangular.
@param[in]
diag magma_diag_t
- = MagmaNonUnit: A is non-unit triangular;
- = MagmaUnit: A is unit triangular.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA COMPLEX array ON THE GPU, dimension (LDDA,N)
On entry, the triangular matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of the array dA contains
the upper triangular matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of the array dA contains
the lower triangular matrix, and the strictly upper
triangular part of A is not referenced. If DIAG = MagmaUnit, the
diagonal elements of A are also not referenced and are
assumed to be 1.
On exit, the (triangular) inverse of the original matrix, in
the same storage format.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, dA(i,i) is exactly zero. The triangular
matrix is singular and its inverse cannot be computed.
(Singularity check is currently disabled.)
@ingroup magma_cgesv_aux
********************************************************************/
extern "C" magma_int_t
magma_ctrtri_gpu(
magma_uplo_t uplo, magma_diag_t diag, magma_int_t n,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magma_int_t *info)
{
#define dA(i, j) (dA+(j)*ldda + (i))
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
const char* diag_ = lapack_diag_const( diag );
magma_int_t nb, nn, j, jb;
//magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *work;
int upper = (uplo == MagmaUpper);
int nounit = (diag == MagmaNonUnit);
*info = 0;
if (! upper && uplo != MagmaLower)
*info = -1;
else if (! nounit && diag != MagmaUnit)
*info = -2;
else if (n < 0)
*info = -3;
else if (ldda < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Check for singularity if non-unit */
/* cannot do here with matrix dA on GPU -- need kernel */
/*
if (nounit) {
for (j=0; j < n; ++j) {
if ( MAGMA_C_EQUAL( *dA(j,j), c_zero )) {
*info = j+1; // Fortran index
return *info;
}
}
}
*/
/* Determine the block size for this environment */
nb = magma_get_cpotrf_nb(n);
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &work, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
if (nb <= 1 || nb >= n) {
magma_cgetmatrix( n, n, dA, ldda, work, n );
lapackf77_ctrtri( uplo_, diag_, &n, work, &n, info );
magma_csetmatrix( n, n, work, n, dA, ldda );
}
else {
if (upper) {
/* Compute inverse of upper triangular matrix */
for (j=0; j < n; j += nb) {
jb = min(nb, (n-j));
/* Compute rows 1:j-1 of current block column */
magma_ctrmm( MagmaLeft, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_one, dA(0,0), ldda, dA(0, j), ldda );
magma_ctrsm( MagmaRight, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_neg_one, dA(j,j), ldda, dA(0, j), ldda );
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, stream[1] );
magma_queue_sync( stream[1] );
/* Compute inverse of current diagonal block */
lapackf77_ctrtri( MagmaUpperStr, diag_, &jb, work, &jb, info );
magma_csetmatrix_async( jb, jb,
work, jb,
dA(j, j), ldda, stream[0] );
}
}
else {
/* Compute inverse of lower triangular matrix */
nn = ((n-1)/nb)*nb+1;
for (j=nn-1; j >= 0; j -= nb) {
jb = min(nb,(n-j));
if ((j+jb) < n) {
/* Compute rows j+jb:n of current block column */
magma_ctrmm( MagmaLeft, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_one, dA(j+jb,j+jb), ldda, dA(j+jb, j), ldda );
magma_ctrsm( MagmaRight, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_neg_one, dA(j,j), ldda, dA(j+jb, j), ldda );
}
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, stream[1] );
magma_queue_sync( stream[1] );
/* Compute inverse of current diagonal block */
lapackf77_ctrtri( MagmaLowerStr, diag_, &jb, work, &jb, info );
magma_csetmatrix_async( jb, jb,
work, jb,
dA(j, j), ldda, stream[0] );
}
}
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free_pinned( work );
return *info;
}
/**
Purpose
-------
CHEGVX computes selected eigenvalues, and optionally, 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.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
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 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, 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,out]
B COMPLEX 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 REAL
@param[in]
vu REAL
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[in]
abstol REAL
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
\n
ABSTOL + EPS * max( |a|,|b| ),
\n
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.
\n
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*SLAMCH('S'), not zero.
If this routine returns with INFO > 0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*SLAMCH('S').
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w REAL array, dimension (N)
The first M elements contain the selected
eigenvalues in ascending order.
@param[out]
Z COMPLEX array, dimension (LDZ, max(1,M))
If JOBZ = MagmaNoVec, then Z is not referenced.
If JOBZ = MagmaVec, 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.
\n
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 = MagmaRangeV, the exact value of M
is not known in advance and an upper bound must be used.
@param[in]
ldz INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = MagmaVec, LDZ >= max(1,N).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. LWORK >= max(1,2*N).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for CHETRD returned by ILAENV.
\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
rwork (workspace) REAL array, dimension (7*N)
@param
iwork (workspace) INTEGER array, dimension (5*N)
@param[out]
ifail INTEGER array, dimension (N)
If JOBZ = MagmaVec, 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 = MagmaNoVec, then IFAIL is not referenced.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: CPOTRF or CHEEVX returned an error code:
<= N: if INFO = i, CHEEVX 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
@ingroup magma_chegv_driver
********************************************************************/
extern "C" magma_int_t
magma_chegvx(
magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu, float abstol,
magma_int_t *m, float *w, magmaFloatComplex *Z, magma_int_t ldz,
magmaFloatComplex *work, magma_int_t lwork, float *rwork,
magma_int_t *iwork, magma_int_t *ifail,
magma_int_t *info)
{
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex *dA;
magmaFloatComplex *dB;
magmaFloatComplex *dZ;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lddz = 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_queue_t stream;
magma_queue_create( &stream );
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -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 (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_chetrd_nb(n);
lwmin = n * (nb + 1);
work[0] = MAGMA_C_MAKE( lwmin, 0 );
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_cmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_cmalloc( &dB, n*lddb ) ||
MAGMA_SUCCESS != magma_cmalloc( &dZ, n*lddz )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Form a Cholesky factorization of B. */
magma_csetmatrix( n, n, B, ldb, dB, lddb );
magma_csetmatrix_async( n, n,
A, lda,
dA, ldda, stream );
magma_cpotrf_gpu(uplo, n, dB, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
magma_queue_sync( stream );
magma_cgetmatrix_async( n, n,
dB, lddb,
B, ldb, stream );
/* Transform problem to standard eigenvalue problem and solve. */
magma_chegst_gpu(itype, uplo, n, dA, ldda, dB, lddb, info);
magma_cheevx_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) {
trans = MagmaConjTrans;
} else {
trans = MagmaNoTrans;
}
magma_ctrsm(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) {
trans = MagmaNoTrans;
} else {
trans = MagmaConjTrans;
}
magma_ctrmm(MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dZ, lddz);
}
magma_cgetmatrix( 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;
} /* magma_chegvx */
/**
Purpose
-------
CLABRD reduces the first NB rows and columns of a complex general
m by n matrix A to upper or lower bidiagonal form by an orthogonal
transformation Q' * A * P, and returns the matrices X and Y which
are needed to apply the transformation to the unreduced part of A.
If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
bidiagonal form.
This is an auxiliary routine called by CGEBRD.
Arguments
---------
@param[in]
m INTEGER
The number of rows in the matrix A.
@param[in]
n INTEGER
The number of columns in the matrix A.
@param[in]
nb INTEGER
The number of leading rows and columns of A to be reduced.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the m by n general matrix to be reduced.
On exit, the first NB rows and columns of the matrix are
overwritten; the rest of the array is unchanged.
If m >= n, elements on and below the diagonal in the first NB
columns, with the array TAUQ, represent the orthogonal
matrix Q as a product of elementary reflectors; and
elements above the diagonal in the first NB rows, with the
array TAUP, represent the orthogonal matrix P as a product
of elementary reflectors.
\n
If m < n, elements below the diagonal in the first NB
columns, with the array TAUQ, represent the orthogonal
matrix Q as a product of elementary reflectors, and
elements on and above the diagonal in the first NB rows,
with the array TAUP, represent the orthogonal matrix P as
a product of elementary reflectors.
See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[in,out]
dA COMPLEX array, dimension (LDDA,N)
Copy of A on GPU.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
@param[out]
d COMPLEX array, dimension (NB)
The diagonal elements of the first NB rows and columns of
the reduced matrix. D(i) = A(i,i).
@param[out]
e COMPLEX array, dimension (NB)
The off-diagonal elements of the first NB rows and columns of
the reduced matrix.
@param[out]
tauq COMPLEX array dimension (NB)
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Q. See Further Details.
@param[out]
taup COMPLEX array, dimension (NB)
The scalar factors of the elementary reflectors which
represent the orthogonal matrix P. See Further Details.
@param[out]
X COMPLEX array, dimension (LDX,NB)
The m-by-nb matrix X required to update the unreduced part
of A.
@param[in]
ldx INTEGER
The leading dimension of the array X. LDX >= M.
@param[out]
dX COMPLEX array, dimension (LDDX,NB)
Copy of X on GPU.
@param[in]
lddx INTEGER
The leading dimension of the array dX. LDDX >= M.
@param[out]
Y COMPLEX array, dimension (LDY,NB)
The n-by-nb matrix Y required to update the unreduced part
of A.
@param[in]
ldy INTEGER
The leading dimension of the array Y. LDY >= N.
@param[out]
dY COMPLEX array, dimension (LDDY,NB)
Copy of Y on GPU.
@param[in]
lddy INTEGER
The leading dimension of the array dY. LDDY >= N.
Further Details
---------------
The matrices Q and P are represented as products of elementary
reflectors:
Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb)
Each H(i) and G(i) has the form:
H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
where tauq and taup are complex scalars, and v and u are complex vectors.
If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in
A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in
A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in
A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in
A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
The elements of the vectors v and u together form the m-by-nb matrix
V and the nb-by-n matrix U' which are needed, with X and Y, to apply
the transformation to the unreduced part of the matrix, using a block
update of the form: A := A - V*Y' - X*U'.
The contents of A on exit are illustrated by the following examples
with nb = 2:
@verbatim
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 )
( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 )
( v1 v2 a a a ) ( v1 1 a a a a )
( v1 v2 a a a ) ( v1 v2 a a a a )
( v1 v2 a a a ) ( v1 v2 a a a a )
( v1 v2 a a a )
@endverbatim
where a denotes an element of the original matrix which is unchanged,
vi denotes an element of the vector defining H(i), and ui an element
of the vector defining G(i).
@ingroup magma_cgesvd_aux
********************************************************************/
extern "C" magma_int_t
magma_clabrd_gpu(
magma_int_t m, magma_int_t n, magma_int_t nb,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex_ptr dA, magma_int_t ldda,
float *d, float *e, magmaFloatComplex *tauq, magmaFloatComplex *taup,
magmaFloatComplex *X, magma_int_t ldx,
magmaFloatComplex_ptr dX, magma_int_t lddx,
magmaFloatComplex *Y, magma_int_t ldy,
magmaFloatComplex_ptr dY, magma_int_t lddy)
{
#define A(i_,j_) (A + (i_) + (j_)*lda)
#define X(i_,j_) (X + (i_) + (j_)*ldx)
#define Y(i_,j_) (Y + (i_) + (j_)*ldy)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dY(i_,j_) (dY + (i_) + (j_)*lddy)
#define dX(i_,j_) (dX + (i_) + (j_)*lddx)
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magma_int_t ione = 1;
magma_int_t i__2, i__3;
magma_int_t i;
magmaFloatComplex alpha;
A -= 1 + lda;
X -= 1 + ldx;
dX -= 1 + lddx;
Y -= 1 + ldy;
dY -= 1 + lddy;
--d;
--e;
--tauq;
--taup;
/* Quick return if possible */
magma_int_t info = 0;
if (m <= 0 || n <= 0) {
return info;
}
magmaFloatComplex *f;
magma_queue_t stream;
magma_queue_create( &stream );
magma_cmalloc_cpu( &f, max(n,m) );
if ( f == NULL ) {
info = MAGMA_ERR_HOST_ALLOC;
return info;
}
if (m >= n) {
/* Reduce to upper bidiagonal form */
for (i = 1; i <= nb; ++i) {
/* Update A(i:m,i) */
i__2 = m - i + 1;
i__3 = i - 1;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__3, Y(i,1), &ldy );
#endif
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_neg_one,
A(i,1), &lda,
Y(i,1), &ldy, &c_one,
A(i,i), &ione );
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__3, Y(i,1), &ldy );
#endif
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_neg_one,
X(i,1), &ldx,
A(1,i), &ione, &c_one,
A(i,i), &ione );
/* Generate reflection Q(i) to annihilate A(i+1:m,i) */
alpha = *A(i,i);
i__2 = m - i + 1;
i__3 = i + 1;
lapackf77_clarfg( &i__2, &alpha, A(min(i__3,m),i), &ione, &tauq[i] );
d[i] = MAGMA_C_REAL( alpha );
if (i < n) {
*A(i,i) = c_one;
/* Compute Y(i+1:n,i) */
i__2 = m - i + 1;
i__3 = n - i;
// 1. Send the block reflector A(i+1:m,i) to the GPU ------
magma_csetvector( i__2,
A(i,i), 1,
dA(i-1,i-1), 1 );
// 2. Multiply ---------------------------------------------
magma_cgemv( MagmaConjTrans, i__2, i__3, c_one,
dA(i-1,i), ldda,
dA(i-1,i-1), ione, c_zero,
dY(i+1,i), ione );
// 3. Put the result back ----------------------------------
magma_cgetmatrix_async( i__3, 1,
dY(i+1,i), lddy,
Y(i+1,i), ldy, stream );
i__2 = m - i + 1;
i__3 = i - 1;
blasf77_cgemv( MagmaConjTransStr, &i__2, &i__3, &c_one,
A(i,1), &lda,
A(i,i), &ione, &c_zero,
Y(1,i), &ione );
i__2 = n - i;
i__3 = i - 1;
blasf77_cgemv( "N", &i__2, &i__3, &c_neg_one,
Y(i+1,1), &ldy,
Y(1,i), &ione, &c_zero,
f, &ione );
i__2 = m - i + 1;
i__3 = i - 1;
blasf77_cgemv( MagmaConjTransStr, &i__2, &i__3, &c_one,
X(i,1), &ldx,
A(i,i), &ione, &c_zero,
Y(1,i), &ione );
// 4. Sync to make sure the result is back ----------------
magma_queue_sync( stream );
if (i__3 != 0) {
i__2 = n - i;
blasf77_caxpy( &i__2, &c_one, f, &ione, Y(i+1,i), &ione );
}
i__2 = i - 1;
i__3 = n - i;
blasf77_cgemv( MagmaConjTransStr, &i__2, &i__3, &c_neg_one,
A(1,i+1), &lda,
Y(1,i), &ione, &c_one,
Y(i+1,i), &ione );
i__2 = n - i;
blasf77_cscal( &i__2, &tauq[i], Y(i+1,i), &ione );
/* Update A(i,i+1:n) */
i__2 = n - i;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__2, A(i,i+1), &lda );
lapackf77_clacgv( &i, A(i,1), &lda );
#endif
blasf77_cgemv( "No transpose", &i__2, &i, &c_neg_one,
Y(i+1,1), &ldy,
A(i,1), &lda, &c_one,
A(i,i+1), &lda );
i__2 = i - 1;
i__3 = n - i;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i, A(i,1), &lda );
lapackf77_clacgv( &i__2, X(i,1), &ldx );
#endif
blasf77_cgemv( MagmaConjTransStr, &i__2, &i__3, &c_neg_one,
A(1,i+1), &lda,
X(i,1), &ldx, &c_one,
A(i,i+1), &lda );
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__2, X(i,1), &ldx );
#endif
/* Generate reflection P(i) to annihilate A(i,i+2:n) */
i__2 = n - i;
i__3 = i + 2;
alpha = *A(i,i+1);
lapackf77_clarfg( &i__2, &alpha, A(i,min(i__3,n)), &lda, &taup[i] );
e[i] = MAGMA_C_REAL( alpha );
*A(i,i+1) = c_one;
/* Compute X(i+1:m,i) */
i__2 = m - i;
i__3 = n - i;
// 1. Send the block reflector A(i+1:m,i) to the GPU ------
magma_csetvector( i__3,
A(i,i+1), lda,
dA(i-1,i), ldda );
// 2. Multiply ---------------------------------------------
//magma_ccopy( i__3, dA(i-1,i), ldda, dY(1,1), 1 );
magma_cgemv( MagmaNoTrans, i__2, i__3, c_one,
dA(i,i), ldda,
dA(i-1,i), ldda,
//dY(1,1), 1,
c_zero,
dX(i+1,i), ione );
// 3. Put the result back ----------------------------------
magma_cgetmatrix_async( i__2, 1,
dX(i+1,i), lddx,
X(i+1,i), ldx, stream );
i__2 = n - i;
blasf77_cgemv( MagmaConjTransStr, &i__2, &i, &c_one,
Y(i+1,1), &ldy,
A(i,i+1), &lda, &c_zero,
X(1,i), &ione );
i__2 = m - i;
blasf77_cgemv( "N", &i__2, &i, &c_neg_one,
A(i+1,1), &lda,
X(1,i), &ione, &c_zero,
f, &ione );
i__2 = i - 1;
i__3 = n - i;
blasf77_cgemv( "N", &i__2, &i__3, &c_one,
A(1,i+1), &lda,
A(i,i+1), &lda, &c_zero,
X(1,i), &ione );
// 4. Sync to make sure the result is back ----------------
magma_queue_sync( stream );
if (i != 0) {
i__2 = m - i;
blasf77_caxpy( &i__2, &c_one, f, &ione, X(i+1,i), &ione );
}
i__2 = m - i;
i__3 = i - 1;
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_neg_one,
X(i+1,1), &ldx,
X(1,i), &ione, &c_one,
X(i+1,i), &ione );
i__2 = m - i;
blasf77_cscal( &i__2, &taup[i], X(i+1,i), &ione );
#if defined(PRECISION_z) || defined(PRECISION_c)
i__2 = n - i;
lapackf77_clacgv( &i__2, A(i,i+1), &lda );
// 4. Send the block reflector A(i+1:m,i) to the GPU after CLACGV()
magma_csetvector( i__2,
A(i,i+1), lda,
dA(i-1,i), ldda );
#endif
}
}
}
else {
/* Reduce to lower bidiagonal form */
for (i = 1; i <= nb; ++i) {
/* Update A(i,i:n) */
i__2 = n - i + 1;
i__3 = i - 1;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__2, A(i,i), &lda );
lapackf77_clacgv( &i__3, A(i,1), &lda );
#endif
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_neg_one,
Y(i,1), &ldy,
A(i,1), &lda, &c_one,
A(i,i), &lda );
i__2 = i - 1;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__3, A(i,1), &lda );
lapackf77_clacgv( &i__3, X(i,1), &ldx );
#endif
i__3 = n - i + 1;
blasf77_cgemv( MagmaConjTransStr, &i__2, &i__3, &c_neg_one,
A(1,i), &lda,
X(i,1), &ldx, &c_one,
A(i,i), &lda );
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__2, X(i,1), &ldx );
#endif
/* Generate reflection P(i) to annihilate A(i,i+1:n) */
i__2 = n - i + 1;
i__3 = i + 1;
alpha = *A(i,i);
lapackf77_clarfg( &i__2, &alpha, A(i,min(i__3,n)), &lda, &taup[i] );
d[i] = MAGMA_C_REAL( alpha );
if (i < m) {
*A(i,i) = c_one;
/* Compute X(i+1:m,i) */
i__2 = m - i;
i__3 = n - i + 1;
// 1. Send the block reflector A(i,i+1:n) to the GPU ------
magma_csetvector( i__3,
A(i,i), lda,
dA(i-1,i-1), ldda );
// 2. Multiply ---------------------------------------------
//magma_ccopy( i__3, dA(i-1,i-1), ldda, dY(1,1), 1 );
magma_cgemv( MagmaNoTrans, i__2, i__3, c_one,
dA(i,i-1), ldda,
dA(i-1,i-1), ldda,
//dY(1,1), 1,
c_zero,
dX(i+1,i), ione );
// 3. Put the result back ----------------------------------
magma_cgetmatrix_async( i__2, 1,
dX(i+1,i), lddx,
X(i+1,i), ldx, stream );
i__2 = n - i + 1;
i__3 = i - 1;
blasf77_cgemv( MagmaConjTransStr, &i__2, &i__3, &c_one,
Y(i,1), &ldy,
A(i,i), &lda, &c_zero,
X(1,i), &ione );
i__2 = m - i;
i__3 = i - 1;
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_neg_one,
A(i+1,1), &lda,
X(1,i), &ione, &c_zero,
f, &ione );
i__2 = i - 1;
i__3 = n - i + 1;
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_one,
A(1,i), &lda,
A(i,i), &lda, &c_zero,
X(1,i), &ione );
// 4. Sync to make sure the result is back ----------------
magma_queue_sync( stream );
if (i__2 != 0) {
i__3 = m - i;
blasf77_caxpy( &i__3, &c_one, f, &ione, X(i+1,i), &ione );
}
i__2 = m - i;
i__3 = i - 1;
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_neg_one,
X(i+1,1), &ldx,
X(1,i), &ione, &c_one,
X(i+1,i), &ione );
i__2 = m - i;
blasf77_cscal( &i__2, &taup[i], X(i+1,i), &ione );
i__2 = n - i + 1;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__2, A(i,i), &lda );
magma_csetvector( i__2,
A(i,i), lda,
dA(i-1,i-1), ldda );
#endif
/* Update A(i+1:m,i) */
i__2 = m - i;
i__3 = i - 1;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__3, Y(i,1), &ldy );
#endif
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_neg_one,
A(i+1,1), &lda,
Y(i,1), &ldy, &c_one,
A(i+1,i), &ione );
i__2 = m - i;
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_clacgv( &i__3, Y(i,1), &ldy );
#endif
blasf77_cgemv( "No transpose", &i__2, &i, &c_neg_one,
X(i+1,1), &ldx,
A(1,i), &ione, &c_one,
A(i+1,i), &ione );
/* Generate reflection Q(i) to annihilate A(i+2:m,i) */
i__2 = m - i;
i__3 = i + 2;
alpha = *A(i+1,i);
lapackf77_clarfg( &i__2, &alpha, A(min(i__3,m),i), &ione, &tauq[i] );
e[i] = MAGMA_C_REAL( alpha );
*A(i+1,i) = c_one;
/* Compute Y(i+1:n,i) */
i__2 = m - i;
i__3 = n - i;
// 1. Send the block reflector A(i+1:m,i) to the GPU ------
magma_csetvector( i__2,
A(i+1,i), 1,
dA(i,i-1), 1 );
// 2. Multiply ---------------------------------------------
magma_cgemv( MagmaConjTrans, i__2, i__3, c_one,
dA(i,i), ldda,
dA(i,i-1), ione, c_zero,
dY(i+1,i), ione );
// 3. Put the result back ----------------------------------
magma_cgetmatrix_async( i__3, 1,
dY(i+1,i), lddy,
Y(i+1,i), ldy, stream );
i__2 = m - i;
i__3 = i - 1;
blasf77_cgemv( MagmaConjTransStr, &i__2, &i__3, &c_one,
A(i+1,1), &lda,
A(i+1,i), &ione, &c_zero,
Y(1,i), &ione );
i__2 = n - i;
i__3 = i - 1;
blasf77_cgemv( "No transpose", &i__2, &i__3, &c_neg_one,
Y(i+1,1), &ldy,
Y(1,i), &ione, &c_zero,
f, &ione );
i__2 = m - i;
blasf77_cgemv( MagmaConjTransStr, &i__2, &i, &c_one,
X(i+1,1), &ldx,
A(i+1,i), &ione, &c_zero,
Y(1,i), &ione );
// 4. Sync to make sure the result is back ----------------
magma_queue_sync( stream );
if (i__3 != 0) {
i__2 = n - i;
blasf77_caxpy( &i__2, &c_one, f, &ione, Y(i+1,i), &ione );
}
i__2 = n - i;
blasf77_cgemv( MagmaConjTransStr, &i, &i__2, &c_neg_one,
A(1,i+1), &lda,
Y(1,i), &ione, &c_one,
Y(i+1,i), &ione );
i__2 = n - i;
blasf77_cscal( &i__2, &tauq[i], Y(i+1,i), &ione );
}
#if defined(PRECISION_z) || defined(PRECISION_c)
else {
i__2 = n - i + 1;
lapackf77_clacgv( &i__2, A(i,i), &lda );
magma_csetvector( i__2,
A(i,i), lda,
dA(i-1,i-1), ldda );
}
#endif
}
}
magma_queue_destroy( stream );
magma_free_cpu( f );
return info;
} /* magma_clabrd_gpu */
/**
Purpose
-------
CGEQRF3 computes a QR factorization of a complex M-by-N matrix A:
A = Q * R.
This version stores the triangular dT matrices used in
the block QR factorization so that they can be applied directly (i.e.,
without being recomputed) later. As a result, the application
of Q is much faster. Also, the upper triangular matrices for V have 0s
in them and the corresponding parts of the upper triangular R are
stored separately in dT.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dA COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
tau COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
dT (workspace) COMPLEX array on the GPU,
dimension (2*MIN(M, N) + (N+31)/32*32 )*NB,
where NB can be obtained through magma_get_cgeqrf_nb(M).
It starts with MIN(M,N)*NB block that store the triangular T
matrices, followed by the MIN(M,N)*NB block of the diagonal
matrices for the R matrix. The rest of the array is used as workspace.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_cgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqrf3_gpu( magma_int_t m, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
magmaFloatComplex *tau, magmaFloatComplex *dT,
magma_int_t *info )
{
#define dA(a_1,a_2) (dA + (a_2)*(ldda) + (a_1))
#define dT(a_1) (dT + (a_1)*nb)
#define d_ref(a_1) (dT + ( minmn+(a_1))*nb)
#define dd_ref(a_1) (dT + (2*minmn+(a_1))*nb)
#define work(a_1) (work + (a_1))
#define hwork (work + (nb)*(m))
magma_int_t i, k, minmn, old_i, old_ib, rows, cols;
magma_int_t ib, nb;
magma_int_t ldwork, lddwork, lwork, lhwork;
magmaFloatComplex *work, *ut;
/* check arguments */
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
k = minmn = min(m,n);
if (k == 0)
return *info;
nb = magma_get_cgeqrf_nb(m);
lwork = (m + n + nb)*nb;
lhwork = lwork - m*nb;
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &work, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
ut = hwork+nb*(n);
memset( ut, 0, nb*nb*sizeof(magmaFloatComplex));
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
ldwork = m;
lddwork= n;
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially */
old_i = 0; old_ib = nb;
for (i = 0; i < k-nb; i += nb) {
ib = min(k-i, nb);
rows = m -i;
magma_cgetmatrix_async( rows, ib,
dA(i,i), ldda,
work(i), ldwork, stream[1] );
if (i > 0) {
/* Apply H' to A(i:m,i+2*ib:n) from the left */
cols = n-old_i-2*old_ib;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, cols, old_ib,
dA(old_i, old_i ), ldda, dT(old_i), nb,
dA(old_i, old_i+2*old_ib), ldda, dd_ref(0), lddwork);
/* store the diagonal */
magma_csetmatrix_async( old_ib, old_ib,
ut, old_ib,
d_ref(old_i), old_ib, stream[0] );
}
magma_queue_sync( stream[1] );
lapackf77_cgeqrf(&rows, &ib, work(i), &ldwork, tau+i, hwork, &lhwork, info);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
work(i), &ldwork, tau+i, hwork, &ib);
/* Put 0s in the upper triangular part of a panel (and 1s on the
diagonal); copy the upper triangular in ut. */
magma_queue_sync( stream[0] );
csplit_diag_block3(ib, work(i), ldwork, ut);
magma_csetmatrix( rows, ib, work(i), ldwork, dA(i,i), ldda );
if (i + ib < n) {
/* Send the triangular factor T to the GPU */
magma_csetmatrix( ib, ib, hwork, ib, dT(i), nb );
if (i+nb < k-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT(i), nb,
dA(i, i+ib), ldda, dd_ref(0), lddwork);
}
else {
cols = n-i-ib;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, cols, ib,
dA(i, i ), ldda, dT(i), nb,
dA(i, i+ib), ldda, dd_ref(0), lddwork);
/* Fix the diagonal block */
magma_csetmatrix( ib, ib, ut, ib, d_ref(i), ib );
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
rows = m-i;
magma_cgetmatrix( rows, ib, dA(i, i), ldda, work, rows );
lhwork = lwork - rows*ib;
lapackf77_cgeqrf(&rows, &ib, work, &rows, tau+i, work+ib*rows, &lhwork, info);
magma_csetmatrix( rows, ib, work, rows, dA(i, i), ldda );
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free_pinned( work );
return *info;
} /* magma_cgeqrf_gpu */
/**
Purpose
-------
CHETRD reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
nqueue INTEGER
The number of GPU queues used for update. 10 >= nqueue > 0.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, 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]
lda 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]
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 >= N*NB, where NB is the
optimal blocksize given by magma_get_chetrd_nb().
\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]
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_chetrd_mgpu(
magma_int_t ngpu,
magma_int_t nqueue, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define dA(id, i, j) (dA[(id)] + (j)*ldda + (i))
#define dW(id, i, j) (dW[(id)] + (j)*ldda + (i))
/* Constants */
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const float d_one = MAGMA_D_ONE;
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t nlocal, ldda;
magma_int_t nb = magma_get_chetrd_nb(n), ib, ib2;
#ifdef PROFILE_SY2RK
float mv_time = 0.0;
float up_time = 0.0;
#endif
magma_int_t kk, nx;
magma_int_t i, ii, iii, j, dev, i_n;
magma_int_t iinfo;
magma_int_t ldwork, lddw, lwkopt, ldwork2, lhwork;
// set pointers to NULL so it is safe to goto CLEANUP if any malloc fails.
magma_queue_t queues[MagmaMaxGPUs][10] = { { NULL, NULL } };
magma_queue_t queues0[MagmaMaxGPUs] = { NULL };
magmaFloatComplex *hwork = NULL;
magmaFloatComplex_ptr dwork2[MagmaMaxGPUs] = { NULL };
magmaFloatComplex_ptr dA[MagmaMaxGPUs] = { NULL };
magmaFloatComplex_ptr dW[MagmaMaxGPUs] = { NULL };
*info = 0;
bool upper = (uplo == MagmaUpper);
bool lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < nb*n && ! lquery) {
*info = -9;
} else if ( nqueue > 2 ) {
*info = 2; // TODO fix
}
/* Determine the block size. */
ldwork = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = magma_cmake_lwork( 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;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
//#define PROFILE_SY2RK
#ifdef PROFILE_SY2RK
float times[11] = { 0 };
magma_event_t start, stop;
float etime;
magma_setdevice( 0 );
magma_event_create( &start );
magma_event_create( &stop );
#endif
ldda = magma_roundup( lda, 32 );
lddw = ldda;
nlocal = nb*(1 + n/(nb*ngpu));
ldwork2 = ldda*( magma_ceildiv( n, nb ) + 1); // i.e., ldda*(blocks + 1)
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
// TODO fix memory leak
if ( MAGMA_SUCCESS != magma_cmalloc( &dA[dev], nlocal*ldda + 3*lddw*nb ) ||
MAGMA_SUCCESS != magma_cmalloc( &dwork2[dev], ldwork2 ) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
dW[dev] = dA[dev] + nlocal*ldda;
for( kk=0; kk < nqueue; kk++ ) {
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[dev][kk] );
}
queues0[dev] = queues[dev][0];
}
lhwork = nqueue*ngpu*n;
if ( MAGMA_SUCCESS != magma_cmalloc_pinned( &hwork, lhwork ) ) {
*info = MAGMA_ERR_HOST_ALLOC;
goto CLEANUP;
}
// nx <= n is required
// use LAPACK for n < 3000, otherwise switch at 512
if (n < 3000)
nx = n;
else
nx = 512;
if (upper) {
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_chtodhe( ngpu, uplo, n, nb, A, lda, dA, ldda, queues, &iinfo );
}
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
for (i = nb*((n-1)/nb); i >= nx; i -= nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*ngpu));
dev = (i/nb)%ngpu;
/* wait for the next panel */
if (i != nb*((n-1)/nb)) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
magma_clatrd_mgpu( ngpu, uplo, i+ib, ib, nb,
A(0, 0), lda, e, tau,
work, ldwork,
dA, ldda, 0,
dW, i+ib,
hwork, lhwork,
dwork2, ldwork2,
queues0 );
magma_cher2k_mgpu( ngpu, MagmaUpper, MagmaNoTrans, nb, i, ib,
c_neg_one, dW, i+ib, 0,
d_one, dA, ldda, 0,
nqueue, queues );
/* get the next panel */
if (i-nb >= nx ) {
ib2 = min(nb, n-(i-nb));
ii = nb*((i-nb)/(nb*ngpu));
dev = ((i-nb)/nb)%ngpu;
magma_setdevice( dev );
magma_cgetmatrix_async( (i-nb)+ib2, ib2,
dA(dev, 0, ii), ldda,
A(0, i-nb), lda,
queues[dev][0] );
}
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j > 0 ) {
*A(j-1,j) = MAGMA_C_MAKE( e[j - 1], 0 );
}
d[j] = MAGMA_C_REAL( *A(j, j) );
}
} /* end of for i=... */
if ( nx > 0 ) {
if (1 <= n-nx) { /* else A is already on CPU */
for (i=0; i < nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*ngpu));
dev = (i/nb)%ngpu;
magma_setdevice( dev );
magma_cgetmatrix_async( nx, ib,
dA(dev, 0, ii), ldda,
A(0, i), lda,
queues[dev][0] );
}
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
/* Use CPU code to reduce the last or only block */
lapackf77_chetrd( uplo_, &nx, A(0, 0), &lda, d, e, tau,
work, &lwork, &iinfo );
}
}
else {
trace_init( 1, ngpu, nqueue, queues );
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_chtodhe( ngpu, uplo, n, nb, A, lda, dA, ldda, queues, &iinfo );
}
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*ngpu));
dev = (i/nb)%ngpu;
/* Reduce columns i:i+ib-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != 0) {
magma_setdevice( dev );
trace_gpu_start( dev, 0, "comm", "get" );
magma_cgetmatrix_async( n-i, ib,
dA(dev, i, ii), ldda,
A(i,i), lda,
queues[dev][0] );
trace_gpu_end( dev, 0 );
magma_queue_sync( queues[dev][0] );
magma_setdevice( 0 );
}
magma_clatrd_mgpu( ngpu, uplo, n-i, ib, nb,
A(i, i), lda, &e[i], &tau[i],
work, ldwork,
dA, ldda, i,
dW, n-i,
hwork, lhwork,
dwork2, ldwork2,
queues0 );
#ifdef PROFILE_SY2RK
magma_setdevice( 0 );
if ( i > 0 ) {
cudaEventElapsedTime( &etime, start, stop );
up_time += (etime/1000.0);
}
magma_event_record( start, 0 );
#endif
magma_cher2k_mgpu( ngpu, MagmaLower, MagmaNoTrans, nb, n-i-ib, ib,
c_neg_one, dW, n-i, ib,
d_one, dA, ldda, i+ib, nqueue, queues );
#ifdef PROFILE_SY2RK
magma_setdevice( 0 );
magma_event_record( stop, 0 );
#endif
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j+1 < n ) {
*A(j+1,j) = MAGMA_C_MAKE( e[j], 0 );
}
d[j] = MAGMA_C_REAL( *A(j, j) );
}
} /* for i=... */
/* Use CPU code to reduce the last or only block */
if ( i < n ) {
iii = i;
i_n = n-i;
if ( i > 0 ) {
for (; i < n; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*ngpu));
dev = (i/nb)%ngpu;
magma_setdevice( dev );
magma_cgetmatrix_async( i_n, ib,
dA(dev, iii, ii), ldda,
A(iii, i), lda,
queues[dev][0] );
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
}
lapackf77_chetrd( uplo_, &i_n, A(iii, iii), &lda, &d[iii], &e[iii],
&tau[iii], work, &lwork, &iinfo );
}
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
for( kk=0; kk < nqueue; kk++ ) {
magma_queue_sync( queues[dev][kk] );
}
}
#ifdef PROFILE_SY2RK
magma_setdevice( 0 );
if ( n > nx ) {
cudaEventElapsedTime( &etime, start, stop );
up_time += (etime/1000.0);
}
magma_event_destroy( start );
magma_event_destroy( stop );
#endif
trace_finalize( "chetrd.svg", "trace.css" );
#ifdef PROFILE_SY2RK
printf( " n=%d nb=%d\n", n, nb );
printf( " Time in CLARFG: %.2e seconds\n", times[0] );
//printf( " Time in CHEMV : %.2e seconds\n", mv_time );
printf( " Time in CHER2K: %.2e seconds\n", up_time );
#endif
CLEANUP:
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
for( kk=0; kk < nqueue; kk++ ) {
magma_queue_destroy( queues[dev][kk] );
}
magma_free( dA[dev] );
magma_free( dwork2[dev] );
}
magma_free_pinned( hwork );
magma_setdevice( orig_dev );
work[0] = magma_cmake_lwork( lwkopt );
return *info;
} /* magma_chetrd */
extern "C" magma_int_t
magma_cpotrf_gpu(char uplo, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
If the current stream is NULL, this version replaces it with user defined
stream to overlap computation with communication.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
magma_int_t j, jb, nb;
char uplo_[2] = {uplo, 0};
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *work;
float d_one = 1.0;
float d_neg_one = -1.0;
int upper = lapackf77_lsame(uplo_, "U");
*info = 0;
if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
nb = magma_get_cpotrf_nb(n);
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &work, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
/* Define user stream if current stream is NULL */
cudaStream_t stream[2], current_stream;
magmablasGetKernelStream(¤t_stream);
magma_queue_create( &stream[0] );
if (current_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else
stream[1] = current_stream;
if ((nb <= 1) || (nb >= n)) {
/* Use unblocked code. */
magma_cgetmatrix_async( n, n, dA, ldda, work, n, stream[1] );
magma_queue_sync( stream[1] );
lapackf77_cpotrf(uplo_, &n, work, &n, info);
magma_csetmatrix_async( n, n, work, n, dA, ldda, stream[1] );
}
else {
/* Use blocked code. */
if (upper) {
/* Compute the Cholesky factorization A = U'*U. */
for (j=0; j<n; j+=nb) {
/* Update and factorize the current diagonal block and test
for non-positive-definiteness. Computing MIN */
jb = min(nb, (n-j));
magma_cherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dA(0, j), ldda,
d_one, dA(j, j), ldda);
magma_queue_sync( stream[1] );
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, stream[0] );
if ( (j+jb) < n) {
/* Compute the current block row. */
magma_cgemm(MagmaConjTrans, MagmaNoTrans,
jb, (n-j-jb), j,
c_neg_one, dA(0, j ), ldda,
dA(0, j+jb), ldda,
c_one, dA(j, j+jb), ldda);
}
magma_queue_sync( stream[0] );
lapackf77_cpotrf(MagmaUpperStr, &jb, work, &jb, info);
magma_csetmatrix_async( jb, jb,
work, jb,
dA(j, j), ldda, stream[1] );
if (*info != 0) {
*info = *info + j;
break;
}
if ( (j+jb) < n) {
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, (n-j-jb),
c_one, dA(j, j ), ldda,
dA(j, j+jb), ldda);
}
}
}
else {
//=========================================================
// Compute the Cholesky factorization A = L*L'.
for (j=0; j<n; j+=nb) {
// Update and factorize the current diagonal block and test
// for non-positive-definiteness. Computing MIN
jb = min(nb, (n-j));
magma_cherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dA(j, 0), ldda,
d_one, dA(j, j), ldda);
magma_queue_sync( stream[1] );
magma_cgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, stream[0] );
if ( (j+jb) < n) {
magma_cgemm( MagmaNoTrans, MagmaConjTrans,
(n-j-jb), jb, j,
c_neg_one, dA(j+jb, 0), ldda,
dA(j, 0), ldda,
c_one, dA(j+jb, j), ldda);
}
magma_queue_sync( stream[0] );
lapackf77_cpotrf(MagmaLowerStr, &jb, work, &jb, info);
magma_csetmatrix_async( jb, jb,
work, jb,
dA(j, j), ldda, stream[1] );
if (*info != 0) {
*info = *info + j;
break;
}
if ( (j+jb) < n) {
magma_ctrsm(MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
(n-j-jb), jb,
c_one, dA(j, j), ldda,
dA(j+jb, j), ldda);
}
}
}
}
magma_free_pinned( work );
magma_queue_destroy( stream[0] );
if (current_stream == NULL) {
magma_queue_destroy( stream[1] );
magmablasSetKernelStream(NULL);
}
return *info;
} /* magma_cpotrf_gpu */
/**
Purpose
-------
CHETRD reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q\*\*H * A * Q = T.
Arguments
---------
@param[in]
num_gpus INTEGER
The number of GPUs. num_gpus > 0.
@param[in]
num_streams INTEGER
The number of GPU streams used for update. 10 >= num_streams > 0.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, 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]
lda 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]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) 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]
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_chetrd_mgpu(
magma_int_t num_gpus, magma_int_t num_streams, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define dA(id, i, j) (dA[(id)] + (j)*ldda + (i))
#define dW(id, i, j) (dwork[(id)] + (j)*ldda + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t ln, ldda;
magma_int_t nb = magma_get_chetrd_nb(n), ib;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
float d_one = MAGMA_D_ONE;
float mv_time = 0.0;
#ifdef PROFILE_SY2RK
float up_time = 0.0;
#endif
magma_int_t kk, nx;
magma_int_t i = 0, ii, iii, j, did, i_n;
magma_int_t iinfo;
magma_int_t ldwork, lddwork, lwkopt, ldwork2;
magma_int_t lquery;
magma_queue_t stream[MagmaMaxGPUs][10];
magmaFloatComplex *dx[MagmaMaxGPUs], *dy[MagmaMaxGPUs], *hwork;
magmaFloatComplex *dwork2[MagmaMaxGPUs];
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
printf( " uplo = %c\n",uplo );
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < nb*n && ! lquery) {
*info = -9;
} else if ( num_streams > 2 ) {
*info = 2;
}
/* Determine the block size. */
ldwork = lddwork = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return MAGMA_ERR_ILLEGAL_VALUE;
}
else if (lquery)
return 0;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return 0;
}
magmaFloatComplex *dA[MagmaMaxGPUs];
magmaFloatComplex *dwork[MagmaMaxGPUs];
float times[11];
for( did=0; did < 11; did++ )
times[did] = 0;
//#define PROFILE_SY2RK
#ifdef PROFILE_SY2RK
magma_event_t start, stop;
float etime;
magma_setdevice(0);
magma_event_create( &start );
magma_event_create( &stop );
#endif
ldda = lda;
ln = ((nb*(1+n/(nb*num_gpus))+31)/32)*32;
ldwork2 = (1+ n / nb + (n % nb != 0)) * ldda;
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
// TODO fix memory leak
if ( MAGMA_SUCCESS != magma_cmalloc(&dA[did], ln*ldda+3*lddwork*nb) ||
MAGMA_SUCCESS != magma_cmalloc(&dx[did], num_streams*n) ||
MAGMA_SUCCESS != magma_cmalloc(&dy[did], num_streams*n) ||
MAGMA_SUCCESS != magma_cmalloc(&dwork2[did], ldwork2 ) ) {
for( i=0; i < did; i++ ) {
magma_setdevice(i);
magma_free(dA[i]);
magma_free(dx[i]);
magma_free(dy[i]);
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dwork[did] = dA[did] + ln*ldda;
for( kk=0; kk < num_streams; kk++ )
magma_queue_create(&stream[did][kk]);
}
magma_setdevice(0);
// TODO fix memory leak dwork2
if ( MAGMA_SUCCESS != magma_cmalloc_pinned( &hwork, num_streams*num_gpus*n ) ) {
for( i=0; i < num_gpus; i++ ) {
magma_setdevice(i);
magma_free(dA[i]);
magma_free(dx[i]);
magma_free(dy[i]);
}
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if (n < 2048)
nx = n;
else
nx = 512;
if (upper) {
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_chtodhe(num_gpus, uplo, n, nb, A, lda, dA, ldda, stream, &iinfo );
}
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
for (i = nb*((n-1)/nb); i >= nx; i -= nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
/* wait for the next panel */
if (i != nb*((n-1)/nb)) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
magma_clatrd_mgpu(num_gpus, uplo, n, i+ib, ib, nb,
A(0, 0), lda, e, tau,
work, ldwork,
dA, ldda, 0,
dwork, i+ib,
dwork2, ldwork2,
1, dx, dy, hwork,
stream, times);
magma_cher2k_mgpu(num_gpus, MagmaUpper, MagmaNoTrans, nb, i, ib,
c_neg_one, dwork, i+ib, 0,
d_one, dA, ldda, 0,
num_streams, stream);
/* get the next panel */
if (i-nb >= nx ) {
ib = min(nb, n-(i-nb));
ii = nb*((i-nb)/(nb*num_gpus));
did = ((i-nb)/nb)%num_gpus;
magma_setdevice(did);
magma_cgetmatrix_async( (i-nb)+ib, ib,
dA(did, 0, ii), ldda,
A(0, i-nb), lda,
stream[did][0] );
}
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j > 0 ) {
*A(j-1,j) = MAGMA_C_MAKE( e[j - 1], 0 );
}
d[j] = MAGMA_C_REAL( *A(j, j) );
}
} /* end of for i=... */
if ( nx > 0 ) {
if (1 <= n-nx) { /* else A is already on CPU */
for (i=0; i < nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
magma_setdevice(did);
magma_cgetmatrix_async( nx, ib,
dA(did, 0, ii), ldda,
A(0, i), lda,
stream[did][0] );
}
}
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
/* Use unblocked code to reduce the last or only block */
lapackf77_chetd2(uplo_, &nx, A(0, 0), &lda, d, e, tau, &iinfo);
}
}
else {
trace_init( 1, num_gpus, num_streams, (CUstream_st**)stream );
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_chtodhe(num_gpus, uplo, n, nb, A, lda, dA, ldda, stream, &iinfo );
}
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
/* Reduce columns i:i+ib-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != 0) {
magma_setdevice(did);
trace_gpu_start( did, 0, "comm", "get" );
magma_cgetmatrix_async( n-i, ib,
dA(did, i, ii), ldda,
A(i,i), lda,
stream[did][0] );
trace_gpu_end( did, 0 );
magma_queue_sync(stream[did][0]);
magma_setdevice(0);
}
mv_time +=
magma_clatrd_mgpu(num_gpus, uplo, n, n-i, ib, nb,
A(i, i), lda, &e[i],
&tau[i], work, ldwork,
dA, ldda, i,
dwork, (n-i),
dwork2, ldwork2,
1, dx, dy, hwork,
stream, times );
#ifdef PROFILE_SY2RK
magma_setdevice(0);
if ( i > 0 ) {
cudaEventElapsedTime(&etime, start, stop);
up_time += (etime/1000.0);
}
magma_event_record(start, 0);
#endif
magma_cher2k_mgpu(num_gpus, MagmaLower, MagmaNoTrans, nb, n-i-ib, ib,
c_neg_one, dwork, n-i, ib,
d_one, dA, ldda, i+ib, num_streams, stream);
#ifdef PROFILE_SY2RK
magma_setdevice(0);
magma_event_record(stop, 0);
#endif
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j+1 < n ) {
*A(j+1,j) = MAGMA_C_MAKE( e[j], 0 );
}
d[j] = MAGMA_C_REAL( *A(j, j) );
}
} /* for i=... */
/* Use unblocked code to reduce the last or only block */
if ( i < n ) {
iii = i;
i_n = n-i;
if ( i > 0 ) {
for (; i < n; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
magma_setdevice(did);
magma_cgetmatrix_async( i_n, ib,
dA(did, iii, ii), ldda,
A(iii, i), lda,
stream[did][0] );
}
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
}
lapackf77_chetrd(uplo_, &i_n, A(iii, iii), &lda, &d[iii], &e[iii],
&tau[iii], work, &lwork, &iinfo);
}
}
#ifdef PROFILE_SY2RK
magma_setdevice(0);
if ( n > nx ) {
cudaEventElapsedTime(&etime, start, stop);
up_time += (etime/1000.0);
}
magma_event_destroy( start );
magma_event_destroy( stop );
#endif
trace_finalize( "chetrd.svg", "trace.css" );
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
for( kk=0; kk < num_streams; kk++ )
magma_queue_sync(stream[did][kk]);
for( kk=0; kk < num_streams; kk++ )
magma_queue_destroy(stream[did][kk]);
magma_free(dA[did]);
magma_free(dx[did]);
magma_free(dy[did]);
magma_free(dwork2[did]);
}
magma_setdevice(0);
magma_free_pinned(hwork);
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
#ifdef PROFILE_SY2RK
printf( " n=%d nb=%d\n",n,nb );
printf( " Time in CLARFG: %.2e seconds\n",times[0] );
printf( " Time in CHEMV : %.2e seconds\n",mv_time );
printf( " Time in CHER2K: %.2e seconds\n",up_time );
#endif
return MAGMA_SUCCESS;
} /* magma_chetrd */
/**
Purpose
-------
CHEGST_GPU reduces a complex Hermitian-definite generalized
eigenproblem to standard form.
If ITYPE = 1, the problem is A*x = lambda*B*x,
and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
B must have been previously factorized as U**H*U or L*L**H by CPOTRF.
Arguments
---------
@param[in]
itype INTEGER
= 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
= 2 or 3: compute U*A*U**H or L**H*A*L.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored and B is factored as
U**H*U;
- = MagmaLower: Lower triangle of A is stored and B is factored as
L*L**H.
@param[in]
n INTEGER
The order of the matrices A and B. 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.
\n
On exit, if INFO = 0, the transformed matrix, stored in the
same format as A.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in]
dB COMPLEX array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by CPOTRF.
@param[in]
lddb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_cheev_comp
********************************************************************/
extern "C" magma_int_t
magma_chegst_gpu(magma_int_t itype, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
magmaFloatComplex *dB, magma_int_t lddb, magma_int_t *info)
{
#define A(i, j) (w + (j)*lda + (i))
#define B(i, j) (w + nb*lda + (j)*ldb + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
#define dB(i, j) (dB + (j)*lddb + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t nb;
magma_int_t k, kb, kb2;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_half = MAGMA_C_HALF;
magmaFloatComplex c_neg_half = MAGMA_C_NEG_HALF;
magmaFloatComplex *w;
magma_int_t lda;
magma_int_t ldb;
float d_one = 1.0;
int upper = (uplo == MagmaUpper);
/* Test the input parameters. */
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! upper && uplo != MagmaLower) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
} else if (lddb < max(1,n)) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return */
if ( n == 0 )
return *info;
nb = magma_get_chegst_nb(n);
lda = nb;
ldb = nb;
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &w, 2*nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t stream[3];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
magma_queue_create( &stream[2] );
/* Use hybrid blocked code */
if (itype == 1) {
if (upper) {
kb = min(n,nb);
/* Compute inv(U')*A*inv(U) */
magma_cgetmatrix_async( kb, kb,
dB(0, 0), lddb,
B(0, 0), nb, stream[2] );
magma_cgetmatrix_async( kb, kb,
dA(0, 0), ldda,
A(0, 0), nb, stream[1] );
for (k = 0; k < n; k += nb) {
kb = min(n-k,nb);
kb2= min(n-k-nb,nb);
/* Update the upper triangle of A(k:n,k:n) */
magma_queue_sync( stream[2] );
magma_queue_sync( stream[1] );
lapackf77_chegst( &itype, uplo_, &kb, A(0,0), &lda, B(0,0), &ldb, info);
magma_csetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[0] );
if (k+kb < n) {
// Start copying the new B block
magma_cgetmatrix_async( kb2, kb2,
dB(k+kb, k+kb), lddb,
B(0, 0), nb, stream[2] );
magma_ctrsm(MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
kb, n-k-kb,
c_one, dB(k,k), lddb,
dA(k,k+kb), ldda);
magma_queue_sync( stream[0] );
magma_chemm(MagmaLeft, MagmaUpper,
kb, n-k-kb,
c_neg_half, dA(k,k), ldda,
dB(k,k+kb), lddb,
c_one, dA(k, k+kb), ldda);
magma_cher2k(MagmaUpper, MagmaConjTrans,
n-k-kb, kb,
c_neg_one, dA(k,k+kb), ldda,
dB(k,k+kb), lddb,
d_one, dA(k+kb,k+kb), ldda);
magma_cgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(0, 0), lda, stream[1] );
magma_chemm(MagmaLeft, MagmaUpper,
kb, n-k-kb,
c_neg_half, dA(k,k), ldda,
dB(k,k+kb), lddb,
c_one, dA(k, k+kb), ldda);
magma_ctrsm(MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
kb, n-k-kb,
c_one, dB(k+kb,k+kb), lddb,
dA(k,k+kb), ldda);
}
}
magma_queue_sync( stream[0] );
}
else {
kb = min(n,nb);
/* Compute inv(L)*A*inv(L') */
magma_cgetmatrix_async( kb, kb,
dB(0, 0), lddb,
B(0, 0), nb, stream[2] );
magma_cgetmatrix_async( kb, kb,
dA(0, 0), ldda,
A(0, 0), nb, stream[1] );
for (k = 0; k < n; k += nb) {
kb= min(n-k,nb);
kb2= min(n-k-nb,nb);
/* Update the lower triangle of A(k:n,k:n) */
magma_queue_sync( stream[2] );
magma_queue_sync( stream[1] );
lapackf77_chegst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_csetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[0] );
if (k+kb < n) {
// Start copying the new B block
magma_cgetmatrix_async( kb2, kb2,
dB(k+kb, k+kb), lddb,
B(0, 0), nb, stream[2] );
magma_ctrsm(MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
n-k-kb, kb,
c_one, dB(k,k), lddb,
dA(k+kb,k), ldda);
magma_queue_sync( stream[0] );
magma_chemm(MagmaRight, MagmaLower,
n-k-kb, kb,
c_neg_half, dA(k,k), ldda,
dB(k+kb,k), lddb,
c_one, dA(k+kb, k), ldda);
magma_cher2k(MagmaLower, MagmaNoTrans,
n-k-kb, kb,
c_neg_one, dA(k+kb,k), ldda,
dB(k+kb,k), lddb,
d_one, dA(k+kb,k+kb), ldda);
magma_cgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(0, 0), lda, stream[1] );
magma_chemm(MagmaRight, MagmaLower,
n-k-kb, kb,
c_neg_half, dA(k,k), ldda,
dB(k+kb,k), lddb,
c_one, dA(k+kb, k), ldda);
magma_ctrsm(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaNonUnit,
n-k-kb, kb,
c_one, dB(k+kb,k+kb), lddb,
dA(k+kb,k), ldda);
}
}
}
magma_queue_sync( stream[0] );
}
else {
if (upper) {
/* Compute U*A*U' */
for (k = 0; k < n; k += nb) {
kb= min(n-k,nb);
magma_cgetmatrix_async( kb, kb,
dB(k, k), lddb,
B(0, 0), nb, stream[2] );
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
if (k > 0) {
magma_ctrmm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
k, kb,
c_one, dB(0,0), lddb,
dA(0,k), ldda);
magma_chemm(MagmaRight, MagmaUpper,
k, kb,
c_half, dA(k,k), ldda,
dB(0,k), lddb,
c_one, dA(0, k), ldda);
magma_queue_sync( stream[1] );
}
magma_cgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(0, 0), lda, stream[0] );
if (k > 0) {
magma_cher2k(MagmaUpper, MagmaNoTrans,
k, kb,
c_one, dA(0,k), ldda,
dB(0,k), lddb,
d_one, dA(0,0), ldda);
magma_chemm(MagmaRight, MagmaUpper,
k, kb,
c_half, dA(k,k), ldda,
dB(0,k), lddb,
c_one, dA(0, k), ldda);
magma_ctrmm(MagmaRight, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
k, kb,
c_one, dB(k,k), lddb,
dA(0,k), ldda);
}
magma_queue_sync( stream[2] );
magma_queue_sync( stream[0] );
lapackf77_chegst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_csetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[1] );
}
magma_queue_sync( stream[1] );
}
else {
/* Compute L'*A*L */
for (k = 0; k < n; k += nb) {
kb= min(n-k,nb);
magma_cgetmatrix_async( kb, kb,
dB(k, k), lddb,
B(0, 0), nb, stream[2] );
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
if (k > 0) {
magma_ctrmm(MagmaRight, MagmaLower, MagmaNoTrans, MagmaNonUnit,
kb, k,
c_one, dB(0,0), lddb,
dA(k,0), ldda);
magma_chemm(MagmaLeft, MagmaLower,
kb, k,
c_half, dA(k,k), ldda,
dB(k,0), lddb,
c_one, dA(k, 0), ldda);
magma_queue_sync( stream[1] );
}
magma_cgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(0, 0), lda, stream[0] );
if (k > 0) {
magma_cher2k(MagmaLower, MagmaConjTrans,
k, kb,
c_one, dA(k,0), ldda,
dB(k,0), lddb,
d_one, dA(0,0), ldda);
magma_chemm(MagmaLeft, MagmaLower,
kb, k,
c_half, dA(k,k), ldda,
dB(k,0), lddb,
c_one, dA(k, 0), ldda);
magma_ctrmm(MagmaLeft, MagmaLower, MagmaConjTrans, MagmaNonUnit,
kb, k,
c_one, dB(k,k), lddb,
dA(k,0), ldda);
}
magma_queue_sync( stream[2] );
magma_queue_sync( stream[0] );
lapackf77_chegst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_csetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[1] );
}
magma_queue_sync( stream[1] );
}
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_queue_destroy( stream[2] );
magma_free_pinned( w );
return *info;
} /* magma_chegst_gpu */
/**
Purpose
-------
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A:
A = Q * R. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
If the current stream is NULL, this version replaces it with user defined
stream to overlap computation with communication.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max( N*NB, 2*NB*NB ),
where NB can be obtained through magma_get_cgeqrf_nb(M).
\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.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_cgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqrf(magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info )
{
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(i,j) (dA + (i) + (j)*ldda)
magmaFloatComplex *dA, *dwork, *dT;
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t i, k, lddwork, old_i, old_ib;
magma_int_t ib, ldda;
/* Function Body */
*info = 0;
magma_int_t nb = magma_get_cgeqrf_nb(min(m, n));
// need 2*nb*nb to store T and upper triangle of V simultaneously
magma_int_t lwkopt = max(n*nb, 2*nb*nb);
work[0] = MAGMA_C_MAKE( (float)lwkopt, 0 );
int lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1, lwkopt) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
k = min(m,n);
if (k == 0) {
work[0] = c_one;
return *info;
}
// largest N for larfb is n-nb (trailing matrix lacks 1st panel)
lddwork = ((n+31)/32)*32 - nb;
ldda = ((m+31)/32)*32;
magma_int_t num_gpus = magma_num_gpus();
if ( num_gpus > 1 ) {
/* call multiple-GPU interface */
return magma_cgeqrf4(num_gpus, m, n, A, lda, tau, work, lwork, info);
}
// allocate space for dA, dwork, and dT
if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda + nb*lddwork + nb*nb )) {
/* Switch to the "out-of-core" (out of GPU-memory) version */
return magma_cgeqrf_ooc(m, n, A, lda, tau, work, lwork, info);
}
/* Define user stream if current stream is NULL */
magma_queue_t stream[2], current_stream;
magmablasGetKernelStream(¤t_stream);
magma_queue_create( &stream[0] );
if (current_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else {
stream[1] = current_stream;
}
dwork = dA + n*ldda;
dT = dA + n*ldda + nb*lddwork;
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially.
Asynchronously send the matrix to the GPU except the first panel. */
magma_csetmatrix_async( m, n-nb,
A(0,nb), lda,
dA(0,nb), ldda, stream[0] );
old_i = 0;
old_ib = nb;
for (i = 0; i < k-nb; i += nb) {
ib = min(k-i, nb);
if (i > 0) {
/* download i-th panel */
magma_queue_sync( stream[1] );
magma_cgetmatrix_async( m-i, ib,
dA(i,i), ldda,
A(i,i), lda, stream[0] );
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i), ldda, dT, nb,
dA(old_i, old_i+2*old_ib), ldda, dwork, lddwork);
magma_cgetmatrix_async( i, ib,
dA(0,i), ldda,
A(0,i), lda, stream[1] );
magma_queue_sync( stream[0] );
}
magma_int_t rows = m-i;
lapackf77_cgeqrf(&rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(i,i), &lda, tau+i, work, &ib);
cpanel_to_q(MagmaUpper, ib, A(i,i), lda, work+ib*ib);
/* download the i-th V matrix */
magma_csetmatrix_async( rows, ib, A(i,i), lda, dA(i,i), ldda, stream[0] );
/* download the T matrix */
magma_queue_sync( stream[1] );
magma_csetmatrix_async( ib, ib, work, ib, dT, nb, stream[0] );
magma_queue_sync( stream[0] );
if (i + ib < n) {
if (i+ib < k-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left (look-ahead) */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT, nb,
dA(i, i+ib), ldda, dwork, lddwork);
cq_to_panel(MagmaUpper, ib, A(i,i), lda, work+ib*ib);
}
else {
/* After last panel, update whole trailing matrix. */
/* Apply H' to A(i:m,i+ib:n) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dT, nb,
dA(i, i+ib), ldda, dwork, lddwork);
cq_to_panel(MagmaUpper, ib, A(i,i), lda, work+ib*ib);
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
if (i != 0) {
magma_cgetmatrix_async( m, ib, dA(0,i), ldda, A(0,i), lda, stream[1] );
magma_queue_sync( stream[1] );
}
magma_int_t rows = m-i;
lapackf77_cgeqrf(&rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info);
}
magma_queue_destroy( stream[0] );
if (current_stream == NULL) {
magma_queue_destroy( stream[1] );
magmablasSetKernelStream(NULL);
}
magma_free( dA );
return *info;
} /* magma_cgeqrf */
extern "C" magma_int_t
magma_chetrd_he2hb_mgpu( char uplo, magma_int_t n, magma_int_t nb,
magmaFloatComplex *a, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *dAmgpu[], magma_int_t ldda,
magmaFloatComplex *dTmgpu[], magma_int_t lddt,
magma_int_t ngpu, magma_int_t distblk,
magma_queue_t streams[][20], magma_int_t nstream,
magma_int_t threads, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CHETRD_HE2HB reduces a complex Hermitian matrix A to real symmetric
band-diagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version stores the triangular matrices T used in the accumulated
Householder transformations (I - V T V').
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.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, 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 Upper band-diagonal of A is
overwritten by the corresponding elements of the
band-diagonal matrix T, and the elements above the band
diagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the the Lower band-diagonal of A is overwritten by
the corresponding elements of the band-diagonal
matrix T, and the elements below the band-diagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
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.
dT (output) COMPLEX array on the GPU, dimension N*NB,
where NB is the optimal blocksize.
On exit dT holds the upper triangular matrices T from the
accumulated Householder transformations (I - V T V') used
in the factorization. The nb x nb matrices T are ordered
consecutively in memory one after another.
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).
===================================================================== */
#define a_ref(a_1,a_2) ( a + ((a_2)-1)*( lda) + (a_1)-1)
#define da_ref(a_1,a_2) (da + ((a_2)-1)*(ldda) + (a_1)-1)
#define tau_ref(a_1) (tau + (a_1)-1)
#define t_ref(a_1) (dT + ((a_1)-1)*(lddt))
#define Atest(a_1,a_2) ( Atest + ((a_2)-1)*( lda) + (a_1)-1)
#define dttest(a_0, a_1, a_2) (dTmgpu[a_0] + ((a_2)-1)*(lddt))
#define datest(a_0, a_1, a_2) (dAmgpu[a_0] + ((a_2)-1)*(ldda) + (a_1)-1)
char uplo_[2] = {uplo, 0};
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_neg_half = MAGMA_C_NEG_HALF;
magmaFloatComplex c_one = MAGMA_C_ONE ;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
float d_one = MAGMA_D_ONE;
magma_int_t pm, pn, indi, indj, pk;
magma_int_t pm_old=0, pn_old=0, indi_old=0, indj_old=0, flipV=-1;
magma_int_t iblock, idev, di;
int i;
int lwkopt;
int lquery;
assert (nstream>=3);
assert (nstream>=(ngpu+1));
*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 (lda < max(1,n)) {
*info = -4;
} else if (lwork < 1 && ! lquery) {
*info = -9;
}
/* Determine the block size. */
lwkopt = n * nb;
if (*info == 0) {
MAGMA_C_SET2REAL( work[0], lwkopt );
}
if (*info != 0)
return *info;
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
magma_int_t mklth = min(threads,16);
magma_setlapack_numthreads(mklth);
magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2];
magma_int_t nbcmplx=0;
magma_buildconnection_mgpu(gnode, &nbcmplx, ngpu);
#ifdef ENABLE_DEBUG
printf(" Initializing communication pattern.... GPU-ncmplx %d\n\n" , nbcmplx);
#endif
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_t cstream;
magmablasGetKernelStream(&cstream);
magmaFloatComplex *dspace[MagmaMaxGPUs];
magmaFloatComplex *dwork[MagmaMaxGPUs], *dworkbis[MagmaMaxGPUs];
magmaFloatComplex *dvall[MagmaMaxGPUs], *dv[MagmaMaxGPUs], *dw[MagmaMaxGPUs];
magmaFloatComplex *workngpu[MagmaMaxGPUs+1];
magma_event_t redevents[MagmaMaxGPUs][MagmaMaxGPUs*MagmaMaxGPUs+10];
magma_int_t nbevents = MagmaMaxGPUs*MagmaMaxGPUs;
magma_int_t lddv = ldda;
magma_int_t lddw = lddv;
magma_int_t dwrk2siz = ldda*nb*(ngpu+1);
magma_int_t worksiz = n*nb;
magma_int_t devworksiz = 2*nb*lddv + nb*lddw + nb*ldda + dwrk2siz; // 2*dv(dv0+dv1) + dw + dwork +dworkbis
// local allocation and stream creation
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
magma_cmalloc( &dspace[dev], devworksiz );
magma_cmalloc_pinned ( &workngpu[dev], worksiz);
dvall[dev] = dspace[dev];
dw[dev] = dvall[dev] + 2*nb*lddv;
dwork[dev] = dw[dev] + nb*lddw;
dworkbis[dev] = dwork[dev] + nb*ldda;
magmablasSetKernelStream( streams[ dev ][ 0 ] );
for( magma_int_t i = 0; i < nbevents; ++i ) {
cudaEventCreateWithFlags(&redevents[dev][i],cudaEventDisableTiming);
}
}
magma_cmalloc_pinned ( &workngpu[ngpu], worksiz);
magmaFloatComplex *worktest = NULL; //(magmaFloatComplex *) malloc(n*nb*sizeof(magmaFloatComplex)); // not used
// ======================
magmaFloatComplex *hT = work + lwork - nb*nb;
lwork -= nb*nb;
memset( hT, 0, nb*nb*sizeof(magmaFloatComplex));
if (upper) {
printf("CHETRD_HE2HB is not yet implemented for upper matrix storage. Exit.\n");
exit(1);
}else {
/* Reduce the lower triangle of A */
for (i = 1; i <= n-nb; i += nb)
{
indi = i+nb;
indj = i;
pm = n - i - nb + 1;
//pn = min(i+nb-1, n-nb) -i + 1;
pn = nb;
/* Get the current panel (no need for the 1st iteration) */
if (i > 1 ){
// cpanel_to_q copy the upper oof diagonal part of
// the matrix to work to be restored later. acctually
// the zero's and one's putted are not used this is only
// because we don't have a function that copy only the
// upper part of A to be restored after copying the
// lookahead panel that has been computted from GPU to CPU.
cpanel_to_q(MagmaUpper, pn-1, a_ref(i, i+1), lda, work);
// find the device who own the panel then send it to the CPU.
// below a -1 was added and then a -1 was done on di because of the fortran indexing
iblock = ((i-1) / distblk) / ngpu; // local block id
di = iblock*distblk + (i-1)%distblk; // local index in parent matrix
idev = ((i-1) / distblk) % ngpu; // device with this block
//printf("Receiving panel ofsize %d %d from idev %d A(%d,%d) \n",(pm+pn), pn,idev,i-1,di);
magma_setdevice( idev );
//magma_device_sync();
magma_cgetmatrix_async( (pm+pn), pn,
datest(idev, i, di+1), ldda,
a_ref ( i, i), lda, streams[ idev ][ nstream-1 ] );
/*
magma_device_sync();
cudaMemcpy2DAsync(a_ref(i,i), lda*sizeof(magmaFloatComplex),
datest(idev,i,di+1), ldda*sizeof(magmaFloatComplex),
(pm+pn)*sizeof(magmaFloatComplex), pn,
cudaMemcpyDeviceToHost, streams[ idev ][ nstream-1 ]);
*/
//magma_setdevice( 0 );
//printf("updating cher2k on A(%d,%d) of size %d %d \n",indi_old+pn_old-1,indi_old+pn_old-1,pm_old-pn_old,pn_old);
// compute CHER2K_MGPU
magmablas_cher2k_mgpu2(
MagmaLower, MagmaNoTrans, pm_old-pn_old, pn_old,
c_neg_one, dv, pm_old, pn_old,
dw, pm_old, pn_old,
d_one, dAmgpu, ldda, indi_old+pn_old-1,
ngpu, distblk, streams, 2 );
//magma_setdevice( 0 );
magma_setdevice( idev );
magma_queue_sync( streams[idev][ nstream-1 ] );
//magma_setdevice( 0 );
cq_to_panel(MagmaUpper, pn-1, a_ref(i, i+1), lda, work);
}
/* ==========================================================
QR factorization on a panel starting nb off of the diagonal.
Prepare the V and T matrices.
========================================================== */
lapackf77_cgeqrf(&pm, &pn, a_ref(indi, indj), &lda,
tau_ref(i), work, &lwork, info);
/* Form the matrix T */
pk=min(pm,pn);
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&pm, &pk, a_ref(indi, indj), &lda,
tau_ref(i), hT, &nb);
/* Prepare V - put 0s in the upper triangular part of the panel
(and 1s on the diagonal), temporaly storing the original in work */
cpanel_to_q(MagmaUpper, pk, a_ref(indi, indj), lda, work);
/* Send V and T from the CPU to the GPU */
// To be able to overlap the GET with the CHER2K
// it should be done on last stream.
// TO Avoid a BUG that is overwriting the old_V
// used atthis moment by cher2k with the new_V
// send it now, we decide to have a flipflop
// vector of Vs. if step%2=0 use V[0] else use V[nb*n]
flipV = ((i-1)/nb)%2;
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
dv[dev] = dvall[dev] + flipV*nb*lddv;
}
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
// send V
magma_csetmatrix_async( pm, pk,
a_ref(indi, indj), lda,
dv[dev], pm, streams[dev][nstream-1] );
// Send the triangular factor T to the GPU
magma_csetmatrix_async( pk, pk,
hT, nb,
dttest(dev, 1, i), lddt, streams[dev][nstream-1] );
}
/* ==========================================================
Compute W:
1. X = A (V T)
2. W = X - 0.5* V * (T' * (V' * X))
========================================================== */
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
// dwork = V T
magma_setdevice( dev );
magmablasSetKernelStream( streams[ dev ][ nstream-1 ] );
magma_queue_sync( streams[dev][nstream-1] );
magma_cgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk,
c_one, dv[dev], pm,
dttest(dev, 1, i), lddt,
c_zero, dwork[dev], pm);
}
// ===============================================
// SYNC TO BE SURE THAT BOTH V AND T WERE
// RECEIVED AND VT IS COMPUTED and SYR2K is done
// ===============================================
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
for( magma_int_t s = 0; s < nstream; ++s )
magma_queue_sync( streams[dev][s] );
}
// compute CHEMM_MGPU
// The broadcast of the result done inside this function
// should be done in stream [0] because i am assuming this
// for the GEMMs below otherwise I have to SYNC over the
// Broadcasting stream.
if(ngpu==1){
magmablasSetKernelStream( streams[ 0 ][ 0 ] );
magma_chemm(MagmaLeft, uplo, pm, pk,
c_one, dAmgpu[0]+(indi-1)*ldda+(indi-1), ldda,
dwork[0], pm,
c_zero, dw[0], pm);
}else{
magmablas_chemm_mgpu_com(
MagmaLeft, uplo, pm, pk,
c_one, dAmgpu, ldda, indi-1,
dwork, pm,
c_zero, dw, pm, dworkbis, dwrk2siz, worktest, pm, workngpu, worksiz,
ngpu, distblk, streams, nstream-1, redevents, nbevents, gnode, nbcmplx);
}
/* dwork = V*T already ==> dwork' = T'*V'
* compute T'*V'*X ==> dwork'*W ==>
* dwork + pm*nb = ((T' * V') * X) = dwork' * X = dwork' * W */
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
// Here we have to wait until the broadcast of CHEMM has been done.
// Note that the broadcast should be done on stream[0] so in a way
// we can continue here on the same stream and avoid a sync
magma_setdevice( dev );
magmablasSetKernelStream( streams[ dev ][ 0 ] );
// magma_queue_sync( streams[dev][0] );
magma_cgemm(MagmaConjTrans, MagmaNoTrans, pk, pk, pm,
c_one, dwork[dev], pm,
dw[dev], pm,
c_zero, dworkbis[dev], nb);
/* W = X - 0.5 * V * T'*V'*X
* = X - 0.5 * V * (dwork + pm*nb) = W - 0.5 * V * (dwork + pm*nb) */
magma_cgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk,
c_neg_half, dv[dev], pm,
dworkbis[dev], nb,
c_one, dw[dev], pm);
}
/* restore the panel it is put here to overlap with the previous GEMM*/
cq_to_panel(MagmaUpper, pk, a_ref(indi, indj), lda, work);
// ===============================================
// SYNC TO BE SURE THAT BOTH V AND W ARE DONE
// ===============================================
// Synchronise to be sure that W has been computed
// because next CHER2K use streaming and may happen
// that lunch a gemm on stream 2 while stream 0
// which compute those 2 GEMM above has not been
// computed and also used for the same reason in
// the panel update below and also for the last HER2K
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
magma_queue_sync( streams[dev][0] );
}
/* ==========================================================
Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V'
========================================================== */
if (i + nb <= n-nb){
/* There would be next iteration;
do lookahead - update the next panel */
// below a -1 was added and then a -1 was done on di because of the fortran indexing
iblock = ((indi-1) / distblk) / ngpu; // local block id
di = iblock*distblk + (indi-1)%distblk; // local index in parent matrix
idev = ((indi-1) / distblk) % ngpu; // device with this block
magma_setdevice( idev );
magmablasSetKernelStream( streams[ idev ][ nstream-1 ] );
//magma_queue_sync( streams[idev][0] ); removed because the sync has been done in the loop above
magma_cgemm(MagmaNoTrans, MagmaConjTrans, pm, pn, pn, c_neg_one,
dv[idev], pm,
dw[idev] , pm, c_one,
datest(idev, indi, di+1), ldda);
magma_cgemm(MagmaNoTrans, MagmaConjTrans, pm, pn, pn, c_neg_one,
dw[idev] , pm,
dv[idev], pm, c_one,
datest(idev, indi, di+1), ldda);
//printf("updating next panel distblk %d idev %d on A(%d,%d) of size %d %d %d \n",distblk,idev,indi-1,di,pm,pn,pn);
}
else {
/* no look-ahead as this is last iteration */
// below a -1 was added and then a -1 was done on di because of the fortran indexing
iblock = ((indi-1) / distblk) / ngpu; // local block id
di = iblock*distblk + (indi-1)%distblk; // local index in parent matrix
idev = ((indi-1) / distblk) % ngpu; // device with this block
magma_setdevice( idev );
magmablasSetKernelStream( streams[ idev ][ 0 ] );
//printf("LAST CHER2K idev %d on A(%d,%d) of size %d \n",idev, indi-1,di,pk);
magma_cher2k(MagmaLower, MagmaNoTrans, pk, pk, c_neg_one,
dv[idev], pm,
dw[idev] , pm, d_one,
datest(idev, indi, di+1), ldda);
/* Send the last block to the CPU */
cpanel_to_q(MagmaUpper, pk-1, a_ref(n-pk+1, n-pk+2), lda, work);
magma_cgetmatrix( pk, pk,
datest(idev, indi, di+1), ldda,
a_ref(n-pk+1, n-pk+1), lda );
cq_to_panel(MagmaUpper, pk-1, a_ref(n-pk+1, n-pk+2), lda, work);
}
indi_old = indi;
indj_old = indj;
pm_old = pm;
pn_old = pn;
} // end loop for(i)
}// end of LOWER
//magma_setdevice( 0 );
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
magma_free( dspace[dev]);
magma_free_pinned(workngpu[dev]);
for( magma_int_t e = 0; e < nbevents; ++e ) {
cudaEventDestroy(redevents[dev][e]);
}
}
magma_free_pinned(workngpu[ngpu]);
free(worktest);
magma_setdevice( cdev );
magmablasSetKernelStream( cstream );
MAGMA_C_SET2REAL( work[0], lwkopt );
magma_setlapack_numthreads(1);
return *info;
} /* chetrd_he2hb_ */
extern "C" magma_int_t
magma_cgeqrf_gpu( magma_int_t m, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
magmaFloatComplex *tau, magmaFloatComplex *dT,
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CGEQRF computes a QR factorization of a complex M-by-N matrix A:
A = Q * R.
This version stores the triangular dT matrices used in
the block QR factorization so that they can be applied directly (i.e.,
without being recomputed) later. As a result, the application
of Q is much faster. Also, the upper triangular matrices for V have 0s
in them. The corresponding parts of the upper triangular R are inverted
and stored separately in dT.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
dA (input/output) COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
dT (workspace/output) COMPLEX array on the GPU,
dimension (2*MIN(M, N) + (N+31)/32*32 )*NB,
where NB can be obtained through magma_get_cgeqrf_nb(M).
It starts with MIN(M,N)*NB block that store the triangular T
matrices, followed by the MIN(M,N)*NB block of the diagonal
inverses for the R matrix. The rest of the array is used as workspace.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
===================================================================== */
#define a_ref(a_1,a_2) (dA+(a_2)*(ldda) + (a_1))
#define t_ref(a_1) (dT+(a_1)*nb)
#define d_ref(a_1) (dT+(minmn+(a_1))*nb)
#define dd_ref(a_1) (dT+(2*minmn+(a_1))*nb)
#define work_ref(a_1) ( work + (a_1))
#define hwork ( work + (nb)*(m))
magma_int_t i, k, minmn, old_i, old_ib, rows, cols;
magma_int_t ib, nb;
magma_int_t ldwork, lddwork, lwork, lhwork;
magmaFloatComplex *work, *ut;
/* check arguments */
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
k = minmn = min(m,n);
if (k == 0)
return *info;
nb = magma_get_cgeqrf_nb(m);
lwork = (m + n + nb)*nb;
lhwork = lwork - m*nb;
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &work, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
ut = hwork+nb*(n);
memset( ut, 0, nb*nb*sizeof(magmaFloatComplex));
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
ldwork = m;
lddwork= n;
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially */
old_i = 0; old_ib = nb;
for (i = 0; i < k-nb; i += nb) {
ib = min(k-i, nb);
rows = m -i;
magma_cgetmatrix_async( rows, ib,
a_ref(i,i), ldda,
work_ref(i), ldwork, stream[1] );
if (i>0){
/* Apply H' to A(i:m,i+2*ib:n) from the left */
cols = n-old_i-2*old_ib;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, cols, old_ib,
a_ref(old_i, old_i ), ldda, t_ref(old_i), nb,
a_ref(old_i, old_i+2*old_ib), ldda, dd_ref(0), lddwork);
/* store the diagonal */
magma_csetmatrix_async( old_ib, old_ib,
ut, old_ib,
d_ref(old_i), old_ib, stream[0] );
}
magma_queue_sync( stream[1] );
lapackf77_cgeqrf(&rows, &ib, work_ref(i), &ldwork, tau+i, hwork, &lhwork, info);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
work_ref(i), &ldwork, tau+i, hwork, &ib);
/* Put 0s in the upper triangular part of a panel (and 1s on the
diagonal); copy the upper triangular in ut and invert it. */
magma_queue_sync( stream[0] );
csplit_diag_block(ib, work_ref(i), ldwork, ut);
magma_csetmatrix( rows, ib, work_ref(i), ldwork, a_ref(i,i), ldda );
if (i + ib < n) {
/* Send the triangular factor T to the GPU */
magma_csetmatrix( ib, ib, hwork, ib, t_ref(i), nb );
if (i+nb < k-nb){
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
a_ref(i, i ), ldda, t_ref(i), nb,
a_ref(i, i+ib), ldda, dd_ref(0), lddwork);
}
else {
cols = n-i-ib;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, cols, ib,
a_ref(i, i ), ldda, t_ref(i), nb,
a_ref(i, i+ib), ldda, dd_ref(0), lddwork);
/* Fix the diagonal block */
magma_csetmatrix( ib, ib, ut, ib, d_ref(i), ib );
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
rows = m-i;
magma_cgetmatrix( rows, ib, a_ref(i, i), ldda, work, rows );
lhwork = lwork - rows*ib;
lapackf77_cgeqrf(&rows, &ib, work, &rows, tau+i, work+ib*rows, &lhwork, info);
magma_csetmatrix( rows, ib, work, rows, a_ref(i, i), ldda );
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free_pinned( work );
return *info;
/* End of MAGMA_CGEQRF */
} /* magma_cgeqrf */
/**
Purpose
-------
CGEQRF3 computes a QR factorization of a complex M-by-N matrix A:
A = Q * R.
This version stores the triangular dT matrices used in
the block QR factorization so that they can be applied directly (i.e.,
without being recomputed) later. As a result, the application
of Q is much faster. Also, the upper triangular matrices for V have 0s
in them. The corresponding parts of the upper triangular R are
stored separately in dT.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dA COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
tau COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
dT (workspace) COMPLEX array on the GPU,
dimension (2*MIN(M, N) + ceil(N/32)*32 )*NB,
where NB can be obtained through magma_get_cgeqrf_nb( M, N ).
It starts with a MIN(M,N)*NB block that stores the triangular T
matrices, followed by a MIN(M,N)*NB block that stores
the diagonal blocks of the R matrix.
The rest of the array is used as workspace.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v^H
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_cgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqrf3_gpu(
magma_int_t m, magma_int_t n,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magmaFloatComplex *tau,
magmaFloatComplex_ptr dT,
magma_int_t *info )
{
#ifdef HAVE_clBLAS
#define dA(i_, j_) dA, (dA_offset + (i_) + (j_)*(ldda))
#define dT(i_) dT, (dT_offset + (i_)*nb)
#define dR(i_) dT, (dT_offset + ( minmn + (i_))*nb)
#define dwork(i_) dT, (dT_offset + (2*minmn + (i_))*nb)
#else
#define dA(i_, j_) (dA + (i_) + (j_)*(ldda))
#define dT(i_) (dT + (i_)*nb)
#define dR(i_) (dT + ( minmn + (i_))*nb)
#define dwork(i_) (dT + (2*minmn + (i_))*nb)
#endif
magmaFloatComplex *work, *hwork, *R;
magma_int_t cols, i, ib, ldwork, lddwork, lhwork, lwork, minmn, nb, old_i, old_ib, rows;
// check arguments
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
minmn = min( m, n );
if (minmn == 0)
return *info;
// TODO: use min(m,n), but that affects dT
nb = magma_get_cgeqrf_nb( m, n );
// dT contains 3 blocks:
// dT is minmn*nb
// dR is minmn*nb
// dwork is n*nb
lddwork = n;
// work is m*nb for panel
// hwork is n*nb, and at least nb*nb for T in larft
// R is nb*nb
ldwork = m;
lhwork = max( n*nb, nb*nb );
lwork = ldwork*nb + lhwork + nb*nb;
// last block needs rows*cols for matrix and prefers cols*nb for work
// worst case is n > m*nb, m a small multiple of nb:
// needs n*nb + n > (m+n)*nb
// prefers 2*n*nb, about twice above (m+n)*nb.
i = ((minmn-1)/nb)*nb;
lwork = max( lwork, (m-i)*(n-i) + (n-i)*nb );
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &work, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
hwork = work + ldwork*nb;
R = work + ldwork*nb + lhwork;
memset( R, 0, nb*nb*sizeof(magmaFloatComplex) );
magma_queue_t queues[2];
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
if ( nb > 1 && nb < minmn ) {
// need nb*nb for T in larft
assert( lhwork >= nb*nb );
// Use blocked code initially
old_i = 0; old_ib = nb;
for (i = 0; i < minmn-nb; i += nb) {
ib = min( minmn-i, nb );
rows = m - i;
// get i-th panel from device
magma_cgetmatrix_async( rows, ib,
dA(i,i), ldda,
work, ldwork, queues[1] );
if (i > 0) {
// Apply H^H to A(i:m,i+2*ib:n) from the left
cols = n - old_i - 2*old_ib;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, cols, old_ib,
dA(old_i, old_i ), ldda, dT(old_i), nb,
dA(old_i, old_i+2*old_ib), ldda, dwork(0), lddwork, queues[0] );
// Fix the diagonal block
magma_csetmatrix_async( old_ib, old_ib,
R, old_ib,
dR(old_i), old_ib, queues[0] );
}
magma_queue_sync( queues[1] ); // wait to get work(i)
lapackf77_cgeqrf( &rows, &ib, work, &ldwork, &tau[i], hwork, &lhwork, info );
// Form the triangular factor of the block reflector in hwork
// H = H(i) H(i+1) . . . H(i+ib-1)
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
work, &ldwork, &tau[i], hwork, &ib );
// wait for previous trailing matrix update (above) to finish with R
magma_queue_sync( queues[0] );
// copy the upper triangle of panel to R and invert it, and
// set the upper triangle of panel (V) to identity
csplit_diag_block( ib, work, ldwork, R );
// send i-th V matrix to device
magma_csetmatrix( rows, ib,
work, ldwork,
dA(i,i), ldda, queues[1] );
if (i + ib < n) {
// send T matrix to device
magma_csetmatrix( ib, ib,
hwork, ib,
dT(i), nb, queues[1] );
if (i+nb < minmn-nb) {
// Apply H^H to A(i:m,i+ib:i+2*ib) from the left
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT(i), nb,
dA(i, i+ib), ldda, dwork(0), lddwork, queues[1] );
// wait for larfb to finish with dwork before larfb in next iteration starts
magma_queue_sync( queues[1] );
}
else {
// Apply H^H to A(i:m,i+ib:n) from the left
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dT(i), nb,
dA(i, i+ib), ldda, dwork(0), lddwork, queues[1] );
// Fix the diagonal block
magma_csetmatrix( ib, ib,
R, ib,
dR(i), ib, queues[1] );
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
// Use unblocked code to factor the last or only block.
if (i < minmn) {
rows = m-i;
cols = n-i;
magma_cgetmatrix( rows, cols, dA(i, i), ldda, work, rows, queues[1] );
// see comments for lwork above
lhwork = lwork - rows*cols;
lapackf77_cgeqrf( &rows, &cols, work, &rows, &tau[i], &work[rows*cols], &lhwork, info );
magma_csetmatrix( rows, cols, work, rows, dA(i, i), ldda, queues[1] );
}
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free_pinned( work );
return *info;
} // magma_cgeqrf_gpu
extern "C" magma_int_t
magma_cgetrf_gpu(magma_int_t m, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
magma_int_t *ipiv, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CGETRF computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the right-looking Level 3 BLAS version of the algorithm.
If the current stream is NULL, this version replaces it with user defined
stream to overlap computation with communication.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX array on the GPU, dimension (LDDA,N).
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
LDDA (input) INTEGER
The leading dimension of the array A. LDDA >= max(1,M).
IPIV (output) INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
> 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
===================================================================== */
#define dAT(i,j) (dAT + (i)*nb*lddat + (j)*nb)
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t iinfo, nb;
magma_int_t maxm, maxn, mindim;
magma_int_t i, rows, cols, s, lddat, lddwork;
magmaFloatComplex *dAT, *dAP, *work;
/* Check arguments */
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0)
*info = -2;
else if (ldda < max(1,m))
*info = -4;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
mindim = min(m, n);
nb = magma_get_cgetrf_nb(m);
s = mindim / nb;
if (nb <= 1 || nb >= min(m,n)) {
/* Use CPU code. */
magma_cmalloc_cpu( &work, m * n );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_cgetmatrix( m, n, dA, ldda, work, m );
lapackf77_cgetrf(&m, &n, work, &m, ipiv, info);
magma_csetmatrix( m, n, work, m, dA, ldda );
magma_free_cpu(work);
}
else {
/* Use hybrid blocked code. */
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
lddat = maxn;
lddwork = maxm;
dAT = dA;
if (MAGMA_SUCCESS != magma_cmalloc( &dAP, nb*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if ( m == n ) {
lddat = ldda;
magmablas_ctranspose_inplace( m, dAT, ldda );
}
else {
if (MAGMA_SUCCESS != magma_cmalloc( &dAT, maxm*maxn )) {
magma_free( dAP );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmablas_ctranspose2( dAT, lddat, dA, ldda, m, n );
}
if (MAGMA_SUCCESS != magma_cmalloc_pinned( &work, maxm*nb )) {
magma_free( dAP );
if ( ! (m == n))
magma_free( dAT );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
/* Define user stream if current stream is NULL */
cudaStream_t stream[2], current_stream;
magmablasGetKernelStream(¤t_stream);
magma_queue_create( &stream[0] );
if (current_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else
stream[1] = current_stream;
for( i=0; i<s; i++ )
{
// download i-th panel
cols = maxm - i*nb;
//magmablas_ctranspose( dAP, cols, dAT(i,i), lddat, nb, cols );
magmablas_ctranspose2( dAP, cols, dAT(i,i), lddat, nb, m-i*nb );
// make sure that that the transpose has completed
magma_queue_sync( stream[1] );
magma_cgetmatrix_async( m-i*nb, nb, dAP, cols, work, lddwork,
stream[0]);
if ( i>0 ){
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (i+1)*nb, nb,
c_one, dAT(i-1,i-1), lddat,
dAT(i-1,i+1), lddat );
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-i*nb, nb,
c_neg_one, dAT(i-1,i+1), lddat,
dAT(i, i-1), lddat,
c_one, dAT(i, i+1), lddat );
}
// do the cpu part
rows = m - i*nb;
magma_queue_sync( stream[0] );
lapackf77_cgetrf( &rows, &nb, work, &lddwork, ipiv+i*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + i*nb;
// upload i-th panel
magma_csetmatrix_async( m-i*nb, nb, work, lddwork, dAP, maxm,
stream[0]);
magmablas_cpermute_long2( n, dAT, lddat, ipiv, nb, i*nb );
magma_queue_sync( stream[0] );
//magmablas_ctranspose(dAT(i,i), lddat, dAP, maxm, cols, nb);
magmablas_ctranspose2(dAT(i,i), lddat, dAP, maxm, m-i*nb, nb);
// do the small non-parallel computations (next panel update)
if ( s > (i+1) ) {
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dAT(i, i ), lddat,
dAT(i, i+1), lddat);
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
nb, m-(i+1)*nb, nb,
c_neg_one, dAT(i, i+1), lddat,
dAT(i+1, i ), lddat,
c_one, dAT(i+1, i+1), lddat );
}
else {
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, dAT(i, i ), lddat,
dAT(i, i+1), lddat);
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-(i+1)*nb, nb,
c_neg_one, dAT(i, i+1), lddat,
dAT(i+1, i ), lddat,
c_one, dAT(i+1, i+1), lddat );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
rows = m - s*nb;
cols = maxm - s*nb;
magmablas_ctranspose2( dAP, maxm, dAT(s,s), lddat, nb0, rows);
magma_cgetmatrix( rows, nb0, dAP, maxm, work, lddwork );
// do the cpu part
lapackf77_cgetrf( &rows, &nb0, work, &lddwork, ipiv+s*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + s*nb;
magmablas_cpermute_long2( n, dAT, lddat, ipiv, nb0, s*nb );
// upload i-th panel
magma_csetmatrix( rows, nb0, work, lddwork, dAP, maxm );
magmablas_ctranspose2( dAT(s,s), lddat, dAP, maxm, rows, nb0);
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, dAT(s,s), lddat,
dAT(s,s)+nb0, lddat);
if ( m == n ) {
magmablas_ctranspose_inplace( m, dAT, lddat );
}
else {
magmablas_ctranspose2( dA, ldda, dAT, lddat, n, m );
magma_free( dAT );
}
magma_free( dAP );
magma_free_pinned( work );
magma_queue_destroy( stream[0] );
if (current_stream == NULL) {
magma_queue_destroy( stream[1] );
magmablasSetKernelStream(NULL);
}
}
return *info;
} /* End of MAGMA_CGETRF_GPU */
extern "C" magma_int_t
magma_cpotrf3_mgpu(magma_int_t num_gpus, char uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaFloatComplex *d_lA[], magma_int_t ldda,
magmaFloatComplex *d_lP[], magma_int_t lddp,
magmaFloatComplex *a, magma_int_t lda, magma_int_t h,
magma_queue_t stream[][3], magma_event_t event[][5],
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
Auxiliary subroutine for cpotrf2_ooc. It is multiple gpu interface to compute
Cholesky of a "rectangular" matrix.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
magma_int_t j, jb, nb0, nb2, d, dd, id, j_local, j_local2, buf;
char uplo_[2] = {uplo, 0};
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
float d_one = 1.0;
float d_neg_one = -1.0;
int upper = lapackf77_lsame(uplo_, "U");
magmaFloatComplex *dlpanel;
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
const magma_int_t stream1 = 0, stream2 = 1, stream3 = 2;
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(CTRSM_WORK)
/* used by ctrsm_work */
int trsm_nb = 128;
int trsm_n = trsm_nb*((nb+trsm_nb-1)/trsm_nb);
magmaFloatComplex *d_dinvA[MagmaMaxGPUs];
magmaFloatComplex *d_x[MagmaMaxGPUs];
#define dinvA(d,j) &(d_dinvA[(d)][(j)*trsm_nb*trsm_n])
#define dx(d,j) &(d_x[(d)][(j)*nb*m])
/*
* Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
if ( (MAGMA_SUCCESS != magma_cmalloc( &d_dinvA[d], 2*trsm_nb*trsm_n )) ||
(MAGMA_SUCCESS != magma_cmalloc( &d_x[d], 2*nb*(upper ? n : m) )) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
magma_setdevice(0);
#endif
*info = 0;
if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper && num_gpus*ldda < max(1,n)) {
*info = -4;
} else if (upper && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* initialization */
for( d=0; d<num_gpus; d++ ) {
/* local-n and local-ld */
if (upper) {
n_local[d] = (n/(nb*num_gpus))*nb;
if (d < (n/nb)%num_gpus)
n_local[d] += nb;
else if (d == (n/nb)%num_gpus)
n_local[d] += n%nb;
} else {
n_local[d] = (m/(nb*num_gpus))*nb;
if (d < (m/nb)%num_gpus)
n_local[d] += nb;
else if (d == (m/nb)%num_gpus)
n_local[d] += m%nb;
}
}
/* == initialize the trace */
trace_init( 1, num_gpus, 3, (CUstream_st**)stream );
if (upper)
{
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus; // right now, we have num_gpu buffers, so id and buf are the same..
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_cherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda);
trace_gpu_end( id, stream1 );
}
/* send the diagonal to cpu on stream1 */
trace_gpu_start( id, stream1, "comm", "D to CPU" );
magma_cgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
/* update off-diagonal blocks in the panel */
if( j > 0 ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2; // number of local columns in the panel, while jb is panel-size (number of rows)
if( n_local[d] > nb0 ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d,0,nb*j_local);
ldpanel = ldda;
// the GPU owns the row from start, and no need of synch.
//magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
} else {
dlpanel = dlP(d,nb,0,buf);
ldpanel = lddp;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
trace_gpu_start( d, stream2, "gemm", "gemm" );
magma_cgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda);
trace_gpu_end( d, stream2 );
magma_event_record( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for panel and factorize it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_cpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
magma_setdevice(d);
trace_gpu_start( d, stream1, "comm", "comm" );
magma_csetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
trace_gpu_end( d, stream1 );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream1, "comm", "comm" );
magma_csetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
}
/* panel-factorize the off-diagonal */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d,j,nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
nb2 = n_local[d] - j_local2*nb;
magma_setdevice(d);
if( j+jb < m && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead next block on stream1 */
nb0 = min(nb, nb2);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(CTRSM_WORK)
magmablas_claset( MagmaUpperLower, trsm_nb, trsm_n, dinvA(d,0),trsm_nb );
magmablas_claset( MagmaUpperLower, nb0,jb, dx(d,0),nb0 );
magmablas_ctrsm_work( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ctrsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
trace_gpu_end( d, stream1 );
} else if( nb2 > 0 ) {
/* update all the blocks on stream2 */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
trace_gpu_start( d, stream2, "trsm", "trsm" );
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(CTRSM_WORK)
magmablas_claset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,0),trsm_nb );
magmablas_claset( MagmaUpperLower, nb2,jb, dx(d,0),nb2 );
magmablas_ctrsm_work( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ctrsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream2 );
}
d = (d+1)%num_gpus;
} /* end of for */
/* ========================================================== */
if( j+jb < m ) {
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, off-diagonals are copied to cpu (synchronize at the end). *
* so we have the Cholesky factor, but only diagonal submatrix of the big panel, *
* on cpu at the end. */
int d2, buf2;
magma_setdevice(d);
/* lookahead done */
magma_queue_wait_event( stream[d][stream3], event[d][4] );
trace_gpu_start( d, stream3, "comm", "row to CPU" );
magma_cgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
stream[d][stream3] );
trace_gpu_end( d, stream3 );
magma_event_record( event[d][3], stream[d][stream3] );
/* needed on pluto */
//magma_queue_sync( stream[d][stream3] );
/* broadcast rows to gpus on stream2 */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
trace_gpu_start( d2, stream3, "comm", "row to GPUs" );
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // rows arrived at cpu on stream3
magma_csetmatrix_async( j+jb, nb0,
Aup(0,j+jb), lda,
dlP(d2,nb,0,buf2), lddp,
stream[d2][stream3] );
trace_gpu_end( d2, stream3 );
magma_event_record( event[d2][0], stream[d2][stream3] );
}
}
/* =========================== */
/* update the remaining blocks */
nb2 = n_local[d]-(nb*j_local2 + nb0);
if( nb2 > 0 ) {
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
trace_gpu_start( d, stream2, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(CTRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( stream[d][stream2], event[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_claset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,flag),trsm_nb );
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
}
magmablas_claset( MagmaUpperLower, nb2,jb, dx(d,1),nb2 );
magmablas_ctrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
flag, dinvA(d,flag), dx(d,1) );
#else
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda);
#endif
trace_gpu_end( d, stream2 );
}
}
} /* end of ctrsm */
} /* end of for j=1, .., n */
} else {
/* ---------------------------------------------- */
/* Lower-triangular case */
/* > Compute the Cholesky factorization A = L*L'. */
/* ---------------------------------------------- */
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (n-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
magma_cherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda);
}
/* send the diagonal to cpu on stream1 */
magma_cgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
stream[id][stream1] );
/* update off-diagonal blocks of the panel */
if( j > 0 ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( nb0 < n_local[d] ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,nb,buf);
ldpanel = nb;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
magma_cgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, ldpanel,
c_one, dlA(d, nb0, j), ldda);
magma_event_record( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for the panel and factorized it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
lapackf77_cpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < m) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
magma_setdevice(d);
magma_csetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
magma_csetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
stream[id][stream1] );
}
/* panel factorize the off-diagonal */
if ( (j+jb) < m) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2);
magma_setdevice(d);
if( j+nb < n && d == (j/nb+1)%num_gpus ) { /* owns next column, look-ahead next block on stream1 */
if ( j > 0 ) magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
magmablasSetKernelStream(stream[d][stream1]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(CTRSM_WORK)
magmablas_claset( MagmaUpperLower, trsm_nb, trsm_n, dinvA(d,0),trsm_nb );
magmablas_claset( MagmaUpperLower, nb0,jb, dx(d,0),nb0 );
magmablas_ctrsm_work( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ctrsm( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
} else if( nb2 > 0 ) { /* other gpus updating all the blocks on stream2 */
/* update the entire column */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for the cholesky factor
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(CTRSM_WORK)
magmablas_claset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,0),trsm_nb );
magmablas_claset( MagmaUpperLower, nb2,jb, dx(d,0),nb2 );
magmablas_ctrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%num_gpus;
} /* end for d */
/* ========================================================== */
if( j+jb < n ) {
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, we copy off-diagonal to cpu (but don't synchronize). */
/* so we have the Cholesky factor on cpu at the end. */
int d2, buf2;
//#define CPOTRF_DEVICE_TO_DEVICE
#ifdef CPOTRF_DEVICE_TO_DEVICE
// lookahead done
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][4] );
if( d2 != d ) {
magma_ccopymatrix_async( nb0, j+jb,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
dlA(d, nb*j_local2, 0), ldda,
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[d2][stream3] );
} else {
magma_cgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
}
}
#else
// lookahead done
magma_setdevice(d);
magma_queue_wait_event( stream[d][stream3], event[d][4] );
magma_cgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
magma_event_record( event[d][3], stream[d][stream3] );
/* syn on rows on CPU, seem to be needed on Pluto */
//magma_queue_sync( stream[d][stream3] );
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // getmatrix done
magma_csetmatrix_async( nb0, j+jb,
Alo(j+jb,0), lda,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[d2][stream3] );
}
}
#endif
/* =================================== */
/* updates remaining blocks on stream2 */
nb2 = n_local[d] - (j_local2*nb + nb0);
if( nb2 > 0 ) {
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,0,buf);
ldpanel = nb;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
/* update the remaining blocks in the column */
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(CTRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( stream[d][stream2], event[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_claset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,flag),trsm_nb );
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
}
magmablas_claset( MagmaUpperLower, nb2,jb, dx(d,1),nb2 );
magmablas_ctrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
flag, dinvA(d,flag), dx(d,1) );
#else
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda);
#endif
}
}
}
}
} /* end of else not upper */
/* == finalize the trace == */
trace_finalize( "cpotrf.svg","trace.css" );
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<3; j++ ) {
magma_queue_sync( stream[d][j] );
}
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(CTRSM_WORK)
magma_free( d_dinvA[d] );
magma_free( d_x[d] );
#endif
magmablasSetKernelStream(NULL);
}
magma_setdevice(0);
return *info;
} /* magma_cpotrf_mgpu */
/**
Purpose
-------
CGETRF computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges. This version does not
require work space on the GPU passed as input. GPU memory is allocated
in the routine.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the right-looking Level 3 BLAS version of the algorithm.
If the current stream is NULL, this version replaces it with user defined
stream to overlap computation with communication.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
ipiv INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
- > 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
@ingroup magma_cgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_cgetrf(magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda,
magma_int_t *ipiv, magma_int_t *info)
{
#define dAT(i,j) (dAT + (i)*nb*ldda + (j)*nb)
magmaFloatComplex *dAT, *dA, *da, *work;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t iinfo, nb;
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0)
*info = -2;
else if (lda < max(1,m))
*info = -4;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
nb = magma_get_cgetrf_nb(m);
if ( (nb <= 1) || (nb >= min(m,n)) ) {
/* Use CPU code. */
lapackf77_cgetrf(&m, &n, A, &lda, ipiv, info);
} else {
/* Use hybrid blocked code. */
magma_int_t maxm, maxn, ldda, maxdim;
magma_int_t i, rows, cols, s = min(m, n)/nb;
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
maxdim = max(maxm, maxn);
/* set number of GPUs */
magma_int_t num_gpus = magma_num_gpus();
if ( num_gpus > 1 ) {
/* call multi-GPU non-GPU-resident interface */
magma_cgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
return *info;
}
/* explicitly checking the memory requirement */
size_t freeMem, totalMem;
cudaMemGetInfo( &freeMem, &totalMem );
freeMem /= sizeof(magmaFloatComplex);
int h = 1+(2+num_gpus), num_gpus2 = num_gpus;
int NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
const char* ngr_nb_char = getenv("MAGMA_NGR_NB");
if ( ngr_nb_char != NULL )
NB = max( nb, min( NB, atoi(ngr_nb_char) ) );
if ( num_gpus > ceil((float)NB/nb) ) {
num_gpus2 = (int)ceil((float)NB/nb);
h = 1+(2+num_gpus2);
NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
}
if ( num_gpus2*NB < n ) {
/* require too much memory, so call non-GPU-resident version */
magma_cgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
return *info;
}
ldda = maxn;
work = A;
if (maxdim*maxdim < 2*maxm*maxn) {
// if close to square, allocate square matrix and transpose in-place
if (MAGMA_SUCCESS != magma_cmalloc( &dA, nb*maxm + maxdim*maxdim )) {
/* alloc failed so call non-GPU-resident version */
magma_cgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
return *info;
}
da = dA + nb*maxm;
ldda = maxdim;
magma_csetmatrix( m, n, A, lda, da, ldda );
dAT = da;
magmablas_ctranspose_inplace( ldda, dAT, ldda );
}
else {
// if very rectangular, allocate dA and dAT and transpose out-of-place
if (MAGMA_SUCCESS != magma_cmalloc( &dA, (nb + maxn)*maxm )) {
/* alloc failed so call non-GPU-resident version */
magma_cgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
return *info;
}
da = dA + nb*maxm;
magma_csetmatrix( m, n, A, lda, da, maxm );
if (MAGMA_SUCCESS != magma_cmalloc( &dAT, maxm*maxn )) {
/* alloc failed so call non-GPU-resident version */
magma_free( dA );
magma_cgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
return *info;
}
magmablas_ctranspose( m, n, da, maxm, dAT, ldda );
}
lapackf77_cgetrf( &m, &nb, work, &lda, ipiv, &iinfo);
/* Define user stream if current stream is NULL */
cudaStream_t stream[2], current_stream;
magmablasGetKernelStream(¤t_stream);
magma_queue_create( &stream[0] );
if (current_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else
stream[1] = current_stream;
for( i = 0; i < s; i++ ) {
// download i-th panel
cols = maxm - i*nb;
if (i > 0) {
// download i-th panel
magmablas_ctranspose( nb, cols, dAT(i,i), ldda, dA, cols );
// make sure that gpu queue is empty
magma_device_sync();
magma_cgetmatrix_async( m-i*nb, nb, dA, cols, work, lda,
stream[0]);
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (i+1)*nb, nb,
c_one, dAT(i-1,i-1), ldda,
dAT(i-1,i+1), ldda );
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-i*nb, nb,
c_neg_one, dAT(i-1,i+1), ldda,
dAT(i, i-1), ldda,
c_one, dAT(i, i+1), ldda );
// do the cpu part
rows = m - i*nb;
magma_queue_sync( stream[0] );
lapackf77_cgetrf( &rows, &nb, work, &lda, ipiv+i*nb, &iinfo);
}
if (*info == 0 && iinfo > 0)
*info = iinfo + i*nb;
// upload i-th panel
magma_csetmatrix_async( m-i*nb, nb, work, lda, dA, cols,
stream[0]);
magmablas_cpermute_long2( ldda, dAT, ldda, ipiv, nb, i*nb );
magma_queue_sync( stream[0] );
magmablas_ctranspose( cols, nb, dA, cols, dAT(i,i), ldda );
// do the small non-parallel computations
if (s > (i+1)) {
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dAT(i, i ), ldda,
dAT(i, i+1), ldda);
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
nb, m-(i+1)*nb, nb,
c_neg_one, dAT(i, i+1), ldda,
dAT(i+1, i ), ldda,
c_one, dAT(i+1, i+1), ldda );
}
else {
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, dAT(i, i ), ldda,
dAT(i, i+1), ldda);
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-(i+1)*nb, nb,
c_neg_one, dAT(i, i+1), ldda,
dAT(i+1, i ), ldda,
c_one, dAT(i+1, i+1), ldda );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
if ( nb0 > 0 ) {
rows = m - s*nb;
cols = maxm - s*nb;
magmablas_ctranspose( nb0, rows, dAT(s,s), ldda, dA, cols );
magma_cgetmatrix( rows, nb0, dA, cols, work, lda );
// make sure that gpu queue is empty
magma_device_sync();
// do the cpu part
lapackf77_cgetrf( &rows, &nb0, work, &lda, ipiv+s*nb, &iinfo);
if (*info == 0 && iinfo > 0)
*info = iinfo + s*nb;
magmablas_cpermute_long2( ldda, dAT, ldda, ipiv, nb0, s*nb );
magma_csetmatrix( rows, nb0, work, lda, dA, cols );
magmablas_ctranspose( rows, nb0, dA, cols, dAT(s,s), ldda );
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, dAT(s, s), ldda,
dAT(s, s)+nb0, ldda);
}
if (maxdim*maxdim < 2*maxm*maxn) {
magmablas_ctranspose_inplace( ldda, dAT, ldda );
magma_cgetmatrix( m, n, da, ldda, A, lda );
} else {
magmablas_ctranspose( n, m, dAT, ldda, da, maxm );
magma_cgetmatrix( m, n, da, maxm, A, lda );
magma_free( dAT );
}
magma_free( dA );
magma_queue_destroy( stream[0] );
if (current_stream == NULL) {
magma_queue_destroy( stream[1] );
magmablasSetKernelStream(NULL);
}
}
return *info;
} /* magma_cgetrf */
/**
Purpose
-------
CGEQLF computes a QL factorization of a COMPLEX M-by-N matrix A:
A = Q * L.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, if m >= n, the lower triangle of the subarray
A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
if m <= n, the elements on and below the (n-m)-th
superdiagonal contain the M-by-N lower trapezoidal matrix L;
the remaining elements, with the array TAU, represent the
orthogonal matrix Q as a product of elementary reflectors
(see Further Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max(1,N,2*NB^2).
For optimum performance LWORK >= max(N*NB, 2*NB^2) where NB can be obtained
through magma_get_cgeqlf_nb(M).
\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]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(k) . . . H(2) H(1), where k = min(m,n).
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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).
@ingroup magma_cgeqlf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqlf(
magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dwork(i_) (dwork + (i_))
magmaFloatComplex_ptr dA, dwork;
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t i, k, lddwork, old_i, old_ib, nb;
magma_int_t rows, cols;
magma_int_t ib, ki, kk, mu, nu, iinfo, ldda;
int lquery;
nb = magma_get_cgeqlf_nb(m);
*info = 0;
lquery = (lwork == -1);
// silence "uninitialized" warnings
old_ib = nb;
old_i = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
}
k = min(m,n);
if (*info == 0) {
if (k == 0)
work[0] = c_one;
else {
work[0] = MAGMA_C_MAKE( max(n*nb, 2*nb*nb), 0 );
}
if (lwork < max(max(1,n), 2*nb*nb) && ! lquery)
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (k == 0)
return *info;
lddwork = ((n+31)/32)*32;
ldda = ((m+31)/32)*32;
if (MAGMA_SUCCESS != magma_cmalloc( &dA, (n)*ldda + nb*lddwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dwork = dA + ldda*n;
magma_queue_t queues[2];
magma_queue_create( &queues[0] );
magma_queue_create( &queues[1] );
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially.
The last kk columns are handled by the block method.
First, copy the matrix on the GPU except the last kk columns */
magma_csetmatrix_async( m, n-nb,
A(0, 0), lda,
dA(0, 0), ldda, queues[0] );
ki = ((k - nb - 1) / nb) * nb;
kk = min(k, ki + nb);
for (i = k - kk + ki; i >= k -kk; i -= nb) {
ib = min(k-i,nb);
if (i < k - kk + ki) {
/* 1. Copy asynchronously the current panel to the CPU.
2. Copy asynchronously the submatrix below the panel
to the CPU) */
rows = m - k + i + ib;
magma_cgetmatrix_async( rows, ib,
dA(0, n-k+i), ldda,
A(0, n-k+i), lda, queues[1] );
magma_cgetmatrix_async( m-rows, ib,
dA(rows, n-k+i), ldda,
A(rows, n-k+i), lda, queues[0] );
/* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left in
two steps - implementing the lookahead techniques.
This is the main update from the lookahead techniques. */
rows = m - k + old_i + old_ib;
cols = n - k + old_i - old_ib;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, cols, old_ib,
dA(0, cols+old_ib), ldda, dwork(0), lddwork,
dA(0, 0 ), ldda, dwork(old_ib), lddwork);
}
magma_queue_sync( queues[1] );
/* Compute the QL factorization of the current block
A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) */
rows = m - k + i + ib;
cols = n - k + i;
lapackf77_cgeqlf( &rows, &ib, A(0,cols), &lda, tau+i, work, &lwork, &iinfo );
if (cols > 0) {
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
lapackf77_clarft( MagmaBackwardStr, MagmaColumnwiseStr,
&rows, &ib,
A(0, cols), &lda, tau + i, work, &ib);
cpanel_to_q( MagmaLower, ib, A(rows-ib,cols), lda, work+ib*ib);
magma_csetmatrix( rows, ib,
A(0,cols), lda,
dA(0,cols), ldda );
cq_to_panel( MagmaLower, ib, A(rows-ib,cols), lda, work+ib*ib);
// Send the triangular part on the GPU
magma_csetmatrix( ib, ib, work, ib, dwork(0), lddwork );
/* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left in
two steps - implementing the lookahead techniques.
This is the update of first ib columns. */
if (i-ib >= k -kk)
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, ib, ib,
dA(0, cols), ldda, dwork(0), lddwork,
dA(0,cols-ib), ldda, dwork(ib), lddwork);
else {
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, cols, ib,
dA(0, cols), ldda, dwork(0), lddwork,
dA(0, 0 ), ldda, dwork(ib), lddwork);
}
old_i = i;
old_ib = ib;
}
}
mu = m - k + i + nb;
nu = n - k + i + nb;
magma_cgetmatrix( m, nu, dA(0,0), ldda, A(0,0), lda );
} else {
mu = m;
nu = n;
}
/* Use unblocked code to factor the last or only block */
if (mu > 0 && nu > 0)
lapackf77_cgeqlf(&mu, &nu, A(0,0), &lda, tau, work, &lwork, &iinfo);
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
return *info;
} /* magma_cgeqlf */
extern "C" magma_int_t
magma_cgeqrf_ooc(magma_int_t m, magma_int_t n,
magmaFloatComplex *a, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CGEQRF_OOC computes a QR factorization of a COMPLEX M-by-N matrix A:
A = Q * R. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
This is an out-of-core (ooc) version that is similar to magma_cgeqrf but
the difference is that this version can use a GPU even if the matrix
does not fit into the GPU memory at once.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= N*NB,
where NB can be obtained through magma_get_cgeqrf_nb(M).
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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
===================================================================== */
#define a_ref(a_1,a_2) ( a+(a_2)*(lda) + (a_1))
#define da_ref(a_1,a_2) (da+(a_2)*ldda + (a_1))
magmaFloatComplex *da, *dwork;
magmaFloatComplex c_one = MAGMA_C_ONE;
int k, lddwork, ldda;
*info = 0;
int nb = magma_get_cgeqrf_nb(min(m, n));
int lwkopt = n * nb;
work[0] = MAGMA_C_MAKE( (float)lwkopt, 0 );
int lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1,n) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Check how much memory do we have */
size_t freeMem, totalMem;
cudaMemGetInfo( &freeMem, &totalMem );
freeMem /= sizeof(magmaFloatComplex);
magma_int_t IB, NB = (magma_int_t)(0.8*freeMem/m);
NB = (NB / nb) * nb;
if (NB >= n)
return magma_cgeqrf(m, n, a, lda, tau, work, lwork, info);
k = min(m,n);
if (k == 0) {
work[0] = c_one;
return *info;
}
lddwork = ((NB+31)/32)*32+nb;
ldda = ((m+31)/32)*32;
if (MAGMA_SUCCESS != magma_cmalloc( &da, (NB + nb)*ldda + nb*lddwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
// magmablasSetKernelStream(stream[1]);
magmaFloatComplex *ptr = da + ldda * NB;
dwork = da + ldda*(NB + nb);
/* start the main loop over the blocks that fit in the GPU memory */
for(int i=0; i<n; i+=NB) {
IB = min(n-i, NB);
//printf("Processing %5d columns -- %5d to %5d ... \n", IB, i, i+IB);
/* 1. Copy the next part of the matrix to the GPU */
magma_csetmatrix_async( (m), IB,
a_ref(0,i), lda,
da_ref(0,0), ldda, stream[0] );
magma_queue_sync( stream[0] );
/* 2. Update it with the previous transformations */
for(int j=0; j<min(i,k); j+=nb) {
magma_int_t ib = min(k-j, nb);
/* Get a panel in ptr. */
// 1. Form the triangular factor of the block reflector
// 2. Send it to the GPU.
// 3. Put 0s in the upper triangular part of V.
// 4. Send V to the GPU in ptr.
// 5. Update the matrix.
// 6. Restore the upper part of V.
magma_int_t rows = m-j;
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, a_ref(j,j), &lda, tau+j, work, &ib);
magma_csetmatrix_async( ib, ib,
work, ib,
dwork, lddwork, stream[1] );
cpanel_to_q(MagmaUpper, ib, a_ref(j,j), lda, work+ib*ib);
magma_csetmatrix_async( rows, ib,
a_ref(j,j), lda,
ptr, rows, stream[1] );
magma_queue_sync( stream[1] );
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, IB, ib,
ptr, rows, dwork, lddwork,
da_ref(j, 0), ldda, dwork+ib, lddwork);
cq_to_panel(MagmaUpper, ib, a_ref(j,j), lda, work+ib*ib);
}
/* 3. Do a QR on the current part */
if (i<k)
magma_cgeqrf2_gpu(m-i, IB, da_ref(i,0), ldda, tau+i, info);
/* 4. Copy the current part back to the CPU */
magma_cgetmatrix_async( (m), IB,
da_ref(0,0), ldda,
a_ref(0,i), lda, stream[0] );
}
magma_queue_sync( stream[0] );
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free( da );
return *info;
} /* magma_cgeqrf_ooc */
extern "C" magma_int_t
magma_cpotrf2_msub(
magma_int_t num_subs, magma_int_t num_gpus, magma_uplo_t uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaFloatComplex_ptr *d_lA, size_t d_lA_offset, magma_int_t ldda,
magmaFloatComplex_ptr *d_lP, magma_int_t lddp,
magmaFloatComplex *a, magma_int_t lda, magma_int_t h,
magma_queue_t *queues,
magma_int_t *info )
{
/* -- clMAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date November 2014
Purpose
=======
CPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
int tot_subs = num_subs*num_gpus;
magma_int_t j, jb, nb0, nb2, dd, d, id, j_local, j_local2;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
float d_one = 1.0;
float d_neg_one = -1.0;
magmaFloatComplex_ptr dlpanel;
size_t dlpanel_offset;
magma_int_t n_local[MagmaMaxSubs * MagmaMaxGPUs], ldpanel;
// initialize trace
trace_init(1, num_gpus, 2, queues);
*info = 0;
if ( (uplo != MagmaUpper) && (uplo != MagmaLower) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if ((uplo != MagmaUpper) && tot_subs*ldda < max(1,n)) {
*info = -4;
} else if ((uplo == MagmaUpper) && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
for (d=0; d<tot_subs; d++) {
/* local-n and local-ld */
if (uplo == MagmaUpper) {
n_local[d] = ((n/nb)/tot_subs)*nb;
if (d < (n/nb)%tot_subs)
n_local[d] += nb;
else if (d == (n/nb)%tot_subs)
n_local[d] += n%nb;
} else {
n_local[d] = ((m/nb)/tot_subs)*nb;
if (d < (m/nb)%tot_subs)
n_local[d] += nb;
else if (d == (m/nb)%tot_subs)
n_local[d] += m%nb;
}
}
/* Use blocked code. */
if (uplo == MagmaUpper) {
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%tot_subs;
/* Set the local index where the current panel is */
j_local = j/(nb*tot_subs);
jb = min(nb, (m-j));
if (j > 0) {
// Wait for the column on CPU
magma_queue_sync(queues[2*(id%num_gpus)]);
/* broadcast off-diagonal column to all gpus */
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d != id%num_gpus) {
magma_csetmatrix_async( j, jb,
Aup(0,j), lda,
dlP(d,jb,0,id%num_gpus), lddp,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-col") );
}
d = (d+1)%num_gpus;
}
/* Update the current diagonal block */
trace_gpu_start(id%num_gpus, 1, "herk", "herk");
magma_cherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda,
queues[2*(id%num_gpus)+1]);
magma_queue_sync(queues[2*(id%num_gpus)+1]); // Wait for syrk
}
/* Send the diagonal to cpu */
magma_cgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "get", "get-diag") );
if (j > 0) {
/* Compute the local block column of the panel. */
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
j_local2 = j_local+1;
if (d > id) j_local2 --;
nb0 = nb*j_local2;
if (n_local[d] > nb0) {
if (d%num_gpus != id%num_gpus) {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlP_offset(jb, 0, id%num_gpus);
ldpanel = lddp;
/* Wait for the offdiagonal column */
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
} else {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(0, nb*j_local);
ldpanel = ldda;
}
/* update the panel */
trace_gpu_start(d%num_gpus, 1, "gemm", "gemm");
magma_cgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, dlpanel_offset, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
/* factor the diagonal */
magma_queue_sync( queues[2*(id%num_gpus)] ); // wait for the diagonal
trace_cpu_start(0, "potrf", "potrf");
lapackf77_cpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end(0);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ((j+jb) < n) {
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = d_lP[d];
dlpanel_offset = dlP_offset(0, 0, id%num_gpus);
ldpanel = lddp;
}
magma_csetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, dlpanel_offset, ldpanel,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-diag"));
d = (d+1)%num_gpus;
}
} else {
magma_csetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "set", "set-diag") );
}
/* panel-factorize the off-diagonal */
if ((j+jb) < n) {
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
/* next column */
j_local2 = j_local+1;
if (d > id) j_local2--;
if (d%num_gpus == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlP_offset(0, 0, id%num_gpus);
ldpanel = lddp;
}
nb2 = n_local[d]-nb*j_local2;
nb0 = min(nb, nb2);
if (dd < num_gpus) magma_queue_sync( queues[2*(d%num_gpus)] ); // wait for the diagonal
if (j+jb < m && d == (j/nb+1)%tot_subs) {
/* owns the next column, look-ahead the column */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2), ldda,
queues[2*(d%num_gpus)+1] );
/* send the column to cpu */
magma_queue_sync(queues[2*(d%num_gpus)+1]); // wait for lookahead
magma_cgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
queues[2*(d%num_gpus)],
trace_gpu_event(d%num_gpus, 0, "get", "get-col") );
/* update the remaining blocks */
nb2 = nb2 - nb0;
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
queues[2*(d%num_gpus)+1] );
} else if (nb2 > 0) {
/* update the entire trailing matrix */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2), ldda,
queues[2*(d%num_gpus)+1] );
}
d = (d+1)%tot_subs;
}
}
}
} else {
/* -------------------------------------------- */
/* Lower-triangular case */
/* Compute the Cholesky factorization A = L*L'. */
/* -------------------------------------------- */
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%tot_subs;
/* Set the local index where the current panel is */
j_local = j/(nb*tot_subs);
jb = min(nb, (n-j));
if (j > 0) {
if (num_gpus > 1) {
// Wait for the row on CPU to broadcast
magma_queue_sync(queues[2*(id%num_gpus)]);
}
/* broadcast off-diagonal row to all the GPUs */
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d != id%num_gpus) {
/* send it to GPU-d */
magma_csetmatrix_async( jb, j,
Alo(j,0), lda,
dlPT(d,0,jb,id%num_gpus), nb,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-row") );
}
d = (d+1)%num_gpus;
}
/* Update the current diagonal block */
trace_gpu_start(id%num_gpus, 1, "herk", "herk");
magma_cherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda,
queues[2*(id%num_gpus)+1]);
magma_queue_sync(queues[2*(id%num_gpus)+1]); // wait for syrk
}
/* send the diagonal to cpu */
magma_cgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "get", "get") );
/* update the offdiagonal blocks */
if (j > 0) {
/* compute the block-rows of the panel */
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
j_local2 = j_local+1;
if (d > id) j_local2 --;
nb0 = nb*j_local2;
if (nb0 < n_local[d]) {
if (d%num_gpus != id%num_gpus) {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlPT_offset(0, jb, id%num_gpus);
ldpanel = nb;
/* Wait for offdiagonal row */
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
} else {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, 0);
ldpanel = ldda;
}
/* Update the panel */
trace_gpu_start(d%num_gpus, 1, "gemm", "gemm");
magma_cgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, dlpanel_offset, ldpanel,
c_one, dlA(d, nb0, j), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
/* factor the diagonal */
magma_queue_sync( queues[2*(id%num_gpus)] );
trace_cpu_start(0, "potrf", "potrf");
lapackf77_cpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
trace_cpu_end(0);
if (*info != 0) {
printf( " cpotrf returned %d (id=%d,j=%d,j_local=%d,jb=%d)\n",*info,id,j,j_local,jb );
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ((j+jb) < m) {
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = d_lP[d];
dlpanel_offset = dlPT_offset(0, 0, id%num_gpus);
ldpanel = nb;
}
magma_csetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, dlpanel_offset, ldpanel,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-diag") );
d = (d+1)%num_gpus;
}
} else {
magma_csetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "set", "set-diag") );
}
/* factorize off-diagonal blocks */
if ((j+jb) < m) {
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
/* next column */
j_local2 = j_local+1;
if (d > id) j_local2--;
if (d%num_gpus == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlPT_offset(0, 0, id%num_gpus);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2 );
// wait for the diagonal
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
if (j+jb < n && d == (j/nb+1)%tot_subs) {
/* owns the next column, look-ahead the column */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2, j), ldda,
queues[2*(d%num_gpus)+1]);
/* send the column to cpu */
magma_queue_sync( queues[2*(d%num_gpus)+1] ); // wait for lookahead
magma_cgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
queues[2*(d%num_gpus)],
trace_gpu_event(d%num_gpus, 0, "get", "get") );
/* update the remaining blocks */
nb2 = nb2 - nb0;
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
queues[2*(d%num_gpus)+1]);
} else if (nb2 > 0) {
/* update the entire trailing matrix */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2, j), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
}
} /* end of else not upper */
/* clean up */
for( d=0; d<num_gpus; d++ ) {
magma_queue_sync( queues[2*d] );
magma_queue_sync( queues[2*d+1] );
}
trace_finalize("cpotrf_msub.svg", "trace.css");
return *info;
} /* magma_cpotrf2_msub */
/**
Purpose
-------
CGEQRF_OOC computes a QR factorization of a COMPLEX M-by-N matrix A:
A = Q * R. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
This is an out-of-core (ooc) version that is similar to magma_cgeqrf but
the difference is that this version can use a GPU even if the matrix
does not fit into the GPU memory at once.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= N*NB,
where NB can be obtained through magma_get_cgeqrf_nb( M, N ).
\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.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_cgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqrf_ooc(
magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info )
{
#define A(i_,j_) ( A + (i_) + (j_)*lda )
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
/* Constants */
const magmaFloatComplex c_one = MAGMA_C_ONE;
/* Local variables */
magmaFloatComplex_ptr dA, dwork;
magma_int_t i, ib, IB, j, min_mn, lddwork, ldda, rows;
magma_int_t nb = magma_get_cgeqrf_nb( m, n );
magma_int_t lwkopt = n * nb;
work[0] = magma_cmake_lwork( lwkopt );
bool lquery = (lwork == -1);
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1,n) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Check how much memory do we have */
size_t freeMem, totalMem;
cudaMemGetInfo( &freeMem, &totalMem );
freeMem /= sizeof(magmaFloatComplex);
magma_int_t NB = magma_int_t(0.8*freeMem/m);
NB = (NB / nb) * nb;
if (NB >= n)
return magma_cgeqrf(m, n, A, lda, tau, work, lwork, info);
min_mn = min(m,n);
if (min_mn == 0) {
work[0] = c_one;
return *info;
}
lddwork = magma_roundup( NB, 32 ) + nb;
ldda = magma_roundup( m, 32 );
if (MAGMA_SUCCESS != magma_cmalloc( &dA, (NB + nb)*ldda + nb*lddwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t queues[2];
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
magmaFloatComplex_ptr ptr = dA + ldda*NB;
dwork = dA + ldda*(NB + nb);
/* start the main loop over the blocks that fit in the GPU memory */
for (i=0; i < n; i += NB) {
IB = min( n-i, NB );
//printf("Processing %5d columns -- %5d to %5d ... \n", IB, i, i+IB);
/* 1. Copy the next part of the matrix to the GPU */
magma_csetmatrix_async( m, IB,
A(0,i), lda,
dA(0,0), ldda, queues[0] );
magma_queue_sync( queues[0] );
/* 2. Update it with the previous transformations */
for (j=0; j < min(i,min_mn); j += nb) {
ib = min( min_mn-j, nb );
/* Get a panel in ptr. */
// 1. Form the triangular factor of the block reflector
// 2. Send it to the GPU.
// 3. Put 0s in the upper triangular part of V.
// 4. Send V to the GPU in ptr.
// 5. Update the matrix.
// 6. Restore the upper part of V.
rows = m-j;
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(j,j), &lda, tau+j, work, &ib);
magma_csetmatrix_async( ib, ib,
work, ib,
dwork, lddwork, queues[1] );
magma_cpanel_to_q( MagmaUpper, ib, A(j,j), lda, work+ib*ib );
magma_csetmatrix_async( rows, ib,
A(j,j), lda,
ptr, rows, queues[1] );
magma_queue_sync( queues[1] );
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, IB, ib,
ptr, rows, dwork, lddwork,
dA(j, 0), ldda, dwork+ib, lddwork, queues[1] );
magma_cq_to_panel( MagmaUpper, ib, A(j,j), lda, work+ib*ib );
}
/* 3. Do a QR on the current part */
if (i < min_mn)
magma_cgeqrf2_gpu( m-i, IB, dA(i,0), ldda, tau+i, info );
/* 4. Copy the current part back to the CPU */
magma_cgetmatrix_async( m, IB,
dA(0,0), ldda,
A(0,i), lda, queues[0] );
}
magma_queue_sync( queues[0] );
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
return *info;
} /* magma_cgeqrf_ooc */
/***************************************************************************//**
Purpose
-------
CLAQPS computes a step of QR factorization with column pivoting
of a complex M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.
In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.
Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0
@param[in]
offset INTEGER
The number of rows of A that have been factorized in
previous steps.
@param[in]
nb INTEGER
The number of columns to factorize.
@param[out]
kb INTEGER
The number of columns actually factorized.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[in,out]
dA COMPLEX array, dimension (LDA,N)
Copy of A on the GPU.
Portions of A are updated on the CPU;
portions of dA are updated on the GPU. See code for details.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
@param[in,out]
jpvt INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.
@param[out]
tau COMPLEX array, dimension (KB)
The scalar factors of the elementary reflectors.
@param[in,out]
vn1 REAL array, dimension (N)
The vector with the partial column norms.
@param[in,out]
vn2 REAL array, dimension (N)
The vector with the exact column norms.
@param[in,out]
auxv COMPLEX array, dimension (NB)
Auxiliar vector.
@param[in,out]
F COMPLEX array, dimension (LDF,NB)
Matrix F' = L*Y'*A.
@param[in]
ldf INTEGER
The leading dimension of the array F. LDF >= max(1,N).
@param[in,out]
dF COMPLEX array, dimension (LDDF,NB)
Copy of F on the GPU. See code for details.
@param[in]
lddf INTEGER
The leading dimension of the array dF. LDDF >= max(1,N).
@ingroup magma_laqps
*******************************************************************************/
extern "C" magma_int_t
magma_claqps(
magma_int_t m, magma_int_t n, magma_int_t offset,
magma_int_t nb, magma_int_t *kb,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex_ptr dA, magma_int_t ldda,
magma_int_t *jpvt, magmaFloatComplex *tau, float *vn1, float *vn2,
magmaFloatComplex *auxv,
magmaFloatComplex *F, magma_int_t ldf,
magmaFloatComplex_ptr dF, magma_int_t lddf)
{
#define A(i, j) (A + (i) + (j)*(lda ))
#define dA(i, j) (dA + (i) + (j)*(ldda))
#define F(i, j) (F + (i) + (j)*(ldf ))
#define dF(i, j) (dF + (i) + (j)*(lddf))
magmaFloatComplex c_zero = MAGMA_C_MAKE( 0.,0.);
magmaFloatComplex c_one = MAGMA_C_MAKE( 1.,0.);
magmaFloatComplex c_neg_one = MAGMA_C_MAKE(-1.,0.);
magma_int_t ione = 1;
magma_int_t i__1, i__2;
float d__1;
magmaFloatComplex z__1;
magma_int_t j, k, rk;
magmaFloatComplex Akk;
magma_int_t pvt;
float temp, temp2, tol3z;
magma_int_t itemp;
magma_int_t lsticc;
magma_int_t lastrk;
lastrk = min( m, n + offset );
tol3z = magma_ssqrt( lapackf77_slamch("Epsilon"));
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
lsticc = 0;
k = 0;
while( k < nb && lsticc == 0 ) {
rk = offset + k;
/* Determine ith pivot column and swap if necessary */
// subtract 1 from Fortran isamax; pvt, k are 0-based.
i__1 = n-k;
pvt = k + blasf77_isamax( &i__1, &vn1[k], &ione ) - 1;
if (pvt != k) {
if (pvt >= nb) {
/* 1. Start copy from GPU */
magma_cgetmatrix_async( m - offset - nb, 1,
dA(offset + nb, pvt), ldda,
A (offset + nb, pvt), lda, queue );
}
/* F gets swapped so F must be sent at the end to GPU */
i__1 = k;
blasf77_cswap( &i__1, F(pvt,0), &ldf, F(k,0), &ldf );
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[k];
jpvt[k] = itemp;
vn1[pvt] = vn1[k];
vn2[pvt] = vn2[k];
if (pvt < nb) {
/* no need of transfer if pivot is within the panel */
blasf77_cswap( &m, A(0, pvt), &ione, A(0, k), &ione );
}
else {
/* 1. Finish copy from GPU */
magma_queue_sync( queue );
/* 2. Swap as usual on CPU */
blasf77_cswap(&m, A(0, pvt), &ione, A(0, k), &ione);
/* 3. Restore the GPU */
magma_csetmatrix_async( m - offset - nb, 1,
A (offset + nb, pvt), lda,
dA(offset + nb, pvt), ldda, queue );
}
}
/* Apply previous Householder reflectors to column K:
A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
Optimization: multiply with beta=0; wait for vector and subtract */
if (k > 0) {
#ifdef COMPLEX
for (j = 0; j < k; ++j) {
*F(k,j) = MAGMA_C_CONJ( *F(k,j) );
}
#endif
i__1 = m - rk;
i__2 = k;
blasf77_cgemv( MagmaNoTransStr, &i__1, &i__2,
&c_neg_one, A(rk, 0), &lda,
F(k, 0), &ldf,
&c_one, A(rk, k), &ione );
#ifdef COMPLEX
for (j = 0; j < k; ++j) {
*F(k,j) = MAGMA_C_CONJ( *F(k,j) );
}
#endif
}
/* Generate elementary reflector H(k). */
if (rk < m-1) {
i__1 = m - rk;
lapackf77_clarfg( &i__1, A(rk, k), A(rk + 1, k), &ione, &tau[k] );
} else {
lapackf77_clarfg( &ione, A(rk, k), A(rk, k), &ione, &tau[k] );
}
Akk = *A(rk, k);
*A(rk, k) = c_one;
/* Compute Kth column of F:
Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) on the GPU */
if (k < n-1) {
i__1 = m - rk;
i__2 = n - k - 1;
/* Send the vector to the GPU */
magma_csetmatrix( i__1, 1, A(rk, k), lda, dA(rk,k), ldda, queue );
/* Multiply on GPU */
// was CALL CGEMV( 'Conjugate transpose', M-RK+1, N-K,
// TAU( K ), A( RK, K+1 ), LDA,
// A( RK, K ), 1,
// CZERO, F( K+1, K ), 1 )
magma_int_t i__3 = nb-k-1;
magma_int_t i__4 = i__2 - i__3;
magma_int_t i__5 = nb-k;
magma_cgemv( MagmaConjTrans, i__1 - i__5, i__2 - i__3,
tau[k], dA(rk +i__5, k+1+i__3), ldda,
dA(rk +i__5, k ), ione,
c_zero, dF(k+1+i__3, k ), ione, queue );
magma_cgetmatrix_async( i__2-i__3, 1,
dF(k + 1 +i__3, k), i__2,
F (k + 1 +i__3, k), i__2, queue );
blasf77_cgemv( MagmaConjTransStr, &i__1, &i__3,
&tau[k], A(rk, k+1), &lda,
A(rk, k ), &ione,
&c_zero, F(k+1, k ), &ione );
magma_queue_sync( queue );
blasf77_cgemv( MagmaConjTransStr, &i__5, &i__4,
&tau[k], A(rk, k+1+i__3), &lda,
A(rk, k ), &ione,
&c_one, F(k+1+i__3, k ), &ione );
}
/* Padding F(1:K,K) with zeros. */
for (j = 0; j < k; ++j) {
*F(j, k) = c_zero;
}
/* Incremental updating of F:
F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K). */
if (k > 0) {
i__1 = m - rk;
i__2 = k;
z__1 = MAGMA_C_NEGATE( tau[k] );
blasf77_cgemv( MagmaConjTransStr, &i__1, &i__2,
&z__1, A(rk, 0), &lda,
A(rk, k), &ione,
&c_zero, auxv, &ione );
i__1 = k;
blasf77_cgemv( MagmaNoTransStr, &n, &i__1,
&c_one, F(0,0), &ldf,
auxv, &ione,
&c_one, F(0,k), &ione );
}
/* Optimization: On the last iteration start sending F back to the GPU */
/* Update the current row of A:
A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. */
if (k < n-1) {
i__1 = n - k - 1;
i__2 = k + 1;
blasf77_cgemm( MagmaNoTransStr, MagmaConjTransStr, &ione, &i__1, &i__2,
&c_neg_one, A(rk, 0 ), &lda,
F(k+1,0 ), &ldf,
&c_one, A(rk, k+1), &lda );
}
/* Update partial column norms. */
if (rk < lastrk) {
for (j = k + 1; j < n; ++j) {
if (vn1[j] != 0.) {
/* NOTE: The following 4 lines follow from the analysis in
Lapack Working Note 176. */
temp = MAGMA_C_ABS( *A(rk,j) ) / vn1[j];
temp = max( 0., ((1. + temp) * (1. - temp)) );
d__1 = vn1[j] / vn2[j];
temp2 = temp * (d__1 * d__1);
if (temp2 <= tol3z) {
vn2[j] = (float) lsticc;
lsticc = j;
} else {
vn1[j] *= magma_ssqrt(temp);
}
}
}
}
*A(rk, k) = Akk;
++k;
}
// leave k as the last column done
--k;
*kb = k + 1;
rk = offset + *kb - 1;
/* Apply the block reflector to the rest of the matrix:
A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)' */
if (*kb < min(n, m - offset)) {
i__1 = m - rk - 1;
i__2 = n - *kb;
/* Send F to the GPU */
magma_csetmatrix( i__2, *kb,
F (*kb, 0), ldf,
dF(*kb, 0), i__2, queue );
magma_cgemm( MagmaNoTrans, MagmaConjTrans, i__1, i__2, *kb,
c_neg_one, dA(rk+1, 0 ), ldda,
dF(*kb, 0 ), i__2,
c_one, dA(rk+1, *kb), ldda, queue );
}
/* Recomputation of difficult columns. */
while( lsticc > 0 ) {
itemp = (magma_int_t)(vn2[lsticc] >= 0. ? floor(vn2[lsticc] + .5) : -floor(.5 - vn2[lsticc]));
i__1 = m - rk - 1;
if (lsticc <= nb) {
vn1[lsticc] = magma_cblas_scnrm2( i__1, A(rk+1,lsticc), ione );
}
else {
/* Where is the data, CPU or GPU ? */
float r1, r2;
r1 = magma_cblas_scnrm2( nb-k, A(rk+1,lsticc), ione );
r2 = magma_scnrm2( m-offset-nb, dA(offset + nb + 1, lsticc), ione, queue );
//vn1[lsticc] = magma_scnrm2( i__1, dA(rk + 1, lsticc), ione, queue );
vn1[lsticc] = magma_ssqrt(r1*r1 + r2*r2);
}
/* NOTE: The computation of VN1( LSTICC ) relies on the fact that
SNRM2 does not fail on vectors with norm below the value of SQRT(SLAMCH('S')) */
vn2[lsticc] = vn1[lsticc];
lsticc = itemp;
}
magma_queue_destroy( queue );
return MAGMA_SUCCESS;
} /* magma_claqps */
