/**
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 */
extern "C" magma_int_t
magma_cgetrf(magma_int_t m, magma_int_t n, cuFloatComplex *a, magma_int_t lda,
magma_int_t *ipiv, magma_int_t *info)
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
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.
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 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.
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).
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 inAT(i,j) (dAT + (i)*nb*ldda + (j)*nb)
cuFloatComplex *dAT, *dA, *da, *work;
cuFloatComplex c_one = MAGMA_C_ONE;
cuFloatComplex 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;
magma_int_t num_gpus = magma_num_gpus();
if ( num_gpus > 1 ) {
/* call multi-GPU non-GPU-resident interface */
magma_int_t rval = magma_cgetrf_m(num_gpus, m, n, a, lda, ipiv, info);
if( *info >= 0 ) magma_cgetrf_piv(num_gpus, m, n, a, lda, ipiv, info);
return *info;
}
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
maxdim = max(maxm, maxn);
ldda = maxn;
work = a;
if (maxdim*maxdim < 2*maxm*maxn)
{
if (MAGMA_SUCCESS != magma_cmalloc( &dA, nb*maxm + maxdim*maxdim )) {
/* alloc failed so call non-GPU-resident version */
magma_int_t rval = magma_cgetrf_m(num_gpus, m, n, a, lda, ipiv, info);
if( *info >= 0 ) magma_cgetrf_piv(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_cinplace_transpose( dAT, ldda, ldda );
}
else
{
if (MAGMA_SUCCESS != magma_cmalloc( &dA, (nb + maxn)*maxm )) {
/* alloc failed so call non-GPU-resident version */
magma_int_t rval = magma_cgetrf_m(num_gpus, m, n, a, lda, ipiv, info);
if( *info >= 0 ) magma_cgetrf_piv(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_int_t rval = magma_cgetrf_m(num_gpus, m, n, a, lda, ipiv, info);
if( *info >= 0 ) magma_cgetrf_piv(num_gpus, m, n, a, lda, ipiv, info);
return *info;
}
magmablas_ctranspose2( dAT, ldda, da, maxm, m, n );
}
lapackf77_cgetrf( &m, &nb, work, &lda, ipiv, &iinfo);
for( i = 0; i < s; i++ )
{
// download i-th panel
cols = maxm - i*nb;
if (i>0){
magmablas_ctranspose( dA, cols, inAT(i,i), ldda, nb, cols );
magma_cgetmatrix( m-i*nb, nb, dA, cols, work, lda );
// make sure that gpu queue is empty
magma_device_sync();
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (i+1)*nb, nb,
c_one, inAT(i-1,i-1), ldda,
inAT(i-1,i+1), ldda );
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-i*nb, nb,
c_neg_one, inAT(i-1,i+1), ldda,
inAT(i, i-1), ldda,
c_one, inAT(i, i+1), ldda );
// do the cpu part
rows = m - i*nb;
lapackf77_cgetrf( &rows, &nb, work, &lda, ipiv+i*nb, &iinfo);
}
if (*info == 0 && iinfo > 0)
*info = iinfo + i*nb;
magmablas_cpermute_long2( ldda, dAT, ldda, ipiv, nb, i*nb );
// upload i-th panel
magma_csetmatrix( m-i*nb, nb, work, lda, dA, cols );
magmablas_ctranspose( inAT(i,i), ldda, dA, cols, cols, nb);
// do the small non-parallel computations
if (s > (i+1)){
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, inAT(i, i ), ldda,
inAT(i, i+1), ldda);
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
nb, m-(i+1)*nb, nb,
c_neg_one, inAT(i, i+1), ldda,
inAT(i+1, i ), ldda,
c_one, inAT(i+1, i+1), ldda );
}
else{
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, inAT(i, i ), ldda,
inAT(i, i+1), ldda);
magma_cgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-(i+1)*nb, nb,
c_neg_one, inAT(i, i+1), ldda,
inAT(i+1, i ), ldda,
c_one, inAT(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_ctranspose2( dA, cols, inAT(s,s), ldda, nb0, rows);
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_ctranspose2( inAT(s,s), ldda, dA, cols, rows, nb0);
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, inAT(s, s), ldda,
inAT(s, s)+nb0, ldda);
}
if (maxdim*maxdim< 2*maxm*maxn){
magmablas_cinplace_transpose( dAT, ldda, ldda );
magma_cgetmatrix( m, n, da, ldda, a, lda );
} else {
magmablas_ctranspose2( da, maxm, dAT, ldda, n, m );
magma_cgetmatrix( m, n, da, maxm, a, lda );
magma_free( dAT );
}
magma_free( dA );
}
return *info;
} /* magma_cgetrf */