/**
Purpose
-------
DGETF2_NOPIV computes an LU factorization of a general m-by-n
matrix A without pivoting.
The factorization has the form
A = L * U
where 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 2 BLAS version of the algorithm.
This is a CPU-only (not accelerated) version.
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 DOUBLE PRECISION 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.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -k, the k-th argument had an illegal value
- > 0: if INFO = k, U(k,k) 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_dgesv_aux
********************************************************************/
extern "C" magma_int_t
magma_dgetf2_nopiv(
magma_int_t m, magma_int_t n,
double *A, magma_int_t lda,
magma_int_t *info)
{
#define A(i_,j_) (A + (i_) + (j_)*lda)
double c_one = MAGMA_D_ONE;
double c_zero = MAGMA_D_ZERO;
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
magma_int_t min_mn, m_j, n_j;
double inv_Ajj;
magma_int_t i, j;
double sfmin;
A -= 1 + lda;
/* Function Body */
*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;
/* Compute machine safe minimum */
sfmin = lapackf77_dlamch("S");
min_mn = min(m,n);
for (j = 1; j <= min_mn; ++j) {
/* Test for singularity. */
if ( ! MAGMA_D_EQUAL( *A(j,j), c_zero)) {
/* Compute elements J+1:M of J-th column. */
if (j < m) {
if (MAGMA_D_ABS( *A(j,j) ) >= sfmin) {
m_j = m - j;
inv_Ajj = MAGMA_D_DIV(c_one, *A(j,j));
blasf77_dscal( &m_j, &inv_Ajj, A(j+1,j), &ione );
}
else {
m_j = m - j;
for (i = 1; i <= m_j; ++i) {
*A(j+i,j) = MAGMA_D_DIV( *A(j+i,j), *A(j,j) );
}
}
}
}
else if (*info == 0) {
*info = j;
}
if (j < min_mn) {
/* Update trailing submatrix. */
m_j = m - j;
n_j = n - j;
blasf77_dger( &m_j, &n_j, &c_neg_one,
A(j+1,j), &ione,
A(j,j+1), &lda,
A(j+1,j+1), &lda );
}
}
return *info;
} /* magma_dgetf2_nopiv */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dtrsm
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, cublas_perf, cublas_time, cpu_perf=0, cpu_time=0;
double magma_error, cublas_error, work[1];
magma_int_t M, N, info;
magma_int_t Ak;
magma_int_t sizeA, sizeB;
magma_int_t lda, ldb, ldda, lddb;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t *piv;
magma_err_t err;
double *h_A, *h_B, *h_Bcublas, *h_Bmagma, *h_B1, *h_X1, *h_X2, *LU, *LUT;
double *d_A, *d_B;
double c_neg_one = MAGMA_D_NEG_ONE;
double c_one = MAGMA_D_ONE;
double alpha = MAGMA_D_MAKE( 0.29, -0.86 );
magma_opts opts;
parse_opts( argc, argv, &opts );
printf("If running lapack (option --lapack), MAGMA and CUBLAS error are both computed\n"
"relative to CPU BLAS result. Else, MAGMA error is computed relative to CUBLAS result.\n\n"
"side = %c, uplo = %c, transA = %c, diag = %c \n", opts.side, opts.uplo, opts.transA, opts.diag );
printf(" M N MAGMA Gflop/s (ms) CUBLAS Gflop/s (ms) CPU Gflop/s (ms) MAGMA error CUBLAS error\n");
printf("==================================================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[i];
N = opts.nsize[i];
gflops = FLOPS_DTRSM(opts.side, M, N) / 1e9;
if ( opts.side == MagmaLeft ) {
lda = M;
Ak = M;
} else {
lda = N;
Ak = N;
}
ldb = M;
ldda = ((lda+31)/32)*32;
lddb = ((ldb+31)/32)*32;
sizeA = lda*Ak;
sizeB = ldb*N;
TESTING_MALLOC( h_A, double, lda*Ak );
TESTING_MALLOC( LU, double, lda*Ak );
TESTING_MALLOC( LUT, double, lda*Ak );
TESTING_MALLOC( h_B, double, ldb*N );
TESTING_MALLOC( h_B1, double, ldb*N );
TESTING_MALLOC( h_X1, double, ldb*N );
TESTING_MALLOC( h_X2, double, ldb*N );
TESTING_MALLOC( h_Bcublas, double, ldb*N );
TESTING_MALLOC( h_Bmagma, double, ldb*N );
TESTING_DEVALLOC( d_A, double, ldda*Ak );
TESTING_DEVALLOC( d_B, double, lddb*N );
/* Initialize the matrices */
lapackf77_dlarnv( &ione, ISEED, &sizeA, LU );
err = magma_malloc_cpu( (void**) &piv, Ak*sizeof(magma_int_t) ); assert( err == 0 );
lapackf77_dgetrf( &Ak, &Ak, LU, &lda, piv, &info );
int i, j;
for(i=0;i<Ak;i++){
for(j=0;j<Ak;j++){
LUT[j+i*lda] = LU[i+j*lda];
}
}
lapackf77_dlacpy(MagmaUpperStr, &Ak, &Ak, LUT, &lda, LU, &lda);
if(opts.uplo == MagmaLower){
lapackf77_dlacpy(MagmaLowerStr, &Ak, &Ak, LU, &lda, h_A, &lda);
}else{
lapackf77_dlacpy(MagmaUpperStr, &Ak, &Ak, LU, &lda, h_A, &lda);
}
lapackf77_dlarnv( &ione, ISEED, &sizeB, h_B );
memcpy(h_B1, h_B, sizeB*sizeof(double));
/* =====================================================================
Performs operation using MAGMA-BLAS
=================================================================== */
magma_dsetmatrix( Ak, Ak, h_A, lda, d_A, ldda );
magma_dsetmatrix( M, N, h_B, ldb, d_B, lddb );
magma_time = magma_sync_wtime( NULL );
magmablas_dtrsm( opts.side, opts.uplo, opts.transA, opts.diag,
M, N,
alpha, d_A, ldda,
d_B, lddb );
magma_time = magma_sync_wtime( NULL ) - magma_time;
magma_perf = gflops / magma_time;
magma_dgetmatrix( M, N, d_B, lddb, h_Bmagma, ldb );
/* =====================================================================
Performs operation using CUDA-BLAS
=================================================================== */
magma_dsetmatrix( M, N, h_B, ldb, d_B, lddb );
cublas_time = magma_sync_wtime( NULL );
cublasDtrsm( opts.side, opts.uplo, opts.transA, opts.diag,
M, N,
alpha, d_A, ldda,
d_B, lddb );
cublas_time = magma_sync_wtime( NULL ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_dgetmatrix( M, N, d_B, lddb, h_Bcublas, ldb );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
blasf77_dtrsm( &opts.side, &opts.uplo, &opts.transA, &opts.diag,
&M, &N,
&alpha, h_A, &lda,
h_B, &ldb );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
// ||b - Ax|| / (||A||*||x||)
memcpy(h_X1, h_Bmagma, sizeB*sizeof(double));
double alpha2 = MAGMA_D_DIV( c_one, alpha );
blasf77_dtrmm( &opts.side, &opts.uplo, &opts.transA, &opts.diag,
&M, &N,
&alpha2, h_A, &lda,
h_X1, &ldb );
blasf77_daxpy( &sizeB, &c_neg_one, h_B1, &ione, h_X1, &ione );
double norm1 = lapackf77_dlange( "M", &M, &N, h_X1, &ldb, work );
double normx = lapackf77_dlange( "M", &M, &N, h_Bmagma, &ldb, work );
double normA = lapackf77_dlange( "M", &Ak, &Ak, h_A, &lda, work );
magma_error = norm1/(normx*normA);
memcpy(h_X2, h_Bcublas, sizeB*sizeof(double));
blasf77_dtrmm( &opts.side, &opts.uplo, &opts.transA, &opts.diag,
&M, &N,
&alpha2, h_A, &lda,
h_X2, &ldb );
blasf77_daxpy( &sizeB, &c_neg_one, h_B1, &ione, h_X2, &ione );
norm1 = lapackf77_dlange( "M", &M, &N, h_X2, &ldb, work );
normx = lapackf77_dlange( "M", &M, &N, h_Bcublas, &ldb, work );
normA = lapackf77_dlange( "M", &Ak, &Ak, h_A, &lda, work );
cublas_error = norm1/(normx*normA);
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e\n",
(int) M, (int) N,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
magma_error, cublas_error );
}
else {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) --- ( --- ) %8.2e %8.2e\n",
(int) M, (int) N,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
magma_error, cublas_error );
}
TESTING_FREE( h_A );
TESTING_FREE( LU );
TESTING_FREE( LUT );
TESTING_FREE( h_B );
TESTING_FREE( h_Bcublas );
TESTING_FREE( h_Bmagma );
TESTING_FREE( h_B1 );
TESTING_FREE( h_X1 );
TESTING_FREE( h_X2 );
TESTING_DEVFREE( d_A );
TESTING_DEVFREE( d_B );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}