extern "C" void
magmablas_clacpy_cnjg(
magma_int_t n,
magmaFloatComplex_ptr dA1T, size_t dA1T_offset, magma_int_t lda1,
magmaFloatComplex_ptr dA2T, size_t dA2T_offset, magma_int_t lda2,
magma_queue_t queue)
{
int blocksize = 64;
size_t LocalWorkSize[1] = {blocksize};
size_t GlobalWorkSize[1] = { ( (n+blocksize-1) / blocksize) * LocalWorkSize[0] };
if ( n <=0 ) {
return;
}
cl_int ciErrNum;
cl_kernel ckKernel = NULL;
ckKernel = g_runtime.get_kernel( "clacpy_cnjg_kernel" );
if(!ckKernel){
printf ("Error: cannot locate kernel in line %d, file %s\n", __LINE__, __FILE__);
return;
}
int offset_A = (int)dA1T_offset;
int offset_B = (int)dA2T_offset;
int nn = 0;
ciErrNum = clSetKernelArg( ckKernel, nn++, sizeof(cl_int), (void*)&n );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(cl_mem), (void*)&dA1T );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(cl_int), (void*)&offset_A );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(cl_int), (void*)&lda1 );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(cl_mem), (void*)&dA2T );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(cl_int), (void*)&offset_B );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(cl_int), (void*)&lda2 );
if (ciErrNum != CL_SUCCESS){
printf("Error: clSetKernelArg at %d in file %s, %s\n", __LINE__, __FILE__,
magma_strerror(ciErrNum));
return;
}
// launch kernel
ciErrNum = clEnqueueNDRangeKernel(
queue, ckKernel, 1, NULL, GlobalWorkSize, LocalWorkSize, 0, NULL, NULL);
if (ciErrNum != CL_SUCCESS)
{
printf("Error: clEnqueueNDRangeKernel at %d in file %s \"%s\"\n",
__LINE__, __FILE__, magma_strerror(ciErrNum));
return;
}
}
// --------------------
void magma_xerror( magma_int_t err, const char* func, const char* file, int line )
{
if ( err != MAGMA_SUCCESS ) {
fprintf( stderr, "MAGMA error: %s (%d) in %s at %s:%d\n",
magma_strerror( err ), (int) err, func, file, line );
}
}
int main()
{
//Magma initialization
magma_init();
//Declaration of local variables
double *a, *b, *dev_a, results=0;
const int N=4098;
int i,j;
magma_int_t info=0, lda=N, ngpu=2;
//Memory Allocation Segment
magma_malloc_pinned((void**) &a,(N*N)*sizeof(double));
magma_malloc_pinned((void**) &b,(N*N)*sizeof(double));
//Generate two copies of Symmetric Positive Definite Matrix
for(i=0;i<N;i++)
{
for(j=0;j<i;j++)
{
a[i*N+j] = 1e-9* (double)rand();
a[j*N+i] = a[i*N+j];
b[i*N+j] = a[i*N+j];
b[j*N+i] = b[i*N+j];
}
a[i*N+i] = 1e-9*(double)rand() + 1000.0;
b[i*N+i] = a[i*N+i];
}
//Call custom Magma Cholesky for obtaining results
rr_dpotrf_m(ngpu,MagmaUpper,N,a,N,&info);
//Call Standard Magma Cholesky for result validation
magma_dpotrf(MagmaUpper,N,b,N,&info);
if(info != 0)
{
printf("magma_dpotrf original returned error %d: %s. \n",(int) info, magma_strerror(info));
}
//Validate the results; Compute the RMS error value.
for(i=0;i<N;i++)
for(j=0;j<N;j++)
results = results + (a[i*N+j] - b[i*N+j]) * (a[i*N+j] - b[i*N+j]);
//Display the results of the test
if(results < 1e-5)
printf("The two functions have identical results\n");
else
printf("The custom function had significant errors. The RMS value was %g\n",results);
magma_free_pinned(a);
magma_free_pinned(b);
magma_finalize();
return 0;
}
// On input, A and ipiv is LU factorization of A. On output, A is overwritten.
// Requires m == n.
// Uses init_matrix() to re-generate original A as needed.
// Generates random RHS b and solves Ax=b.
// Returns residual, |Ax - b| / (n |A| |x|).
float get_residual(
magma_opts &opts,
magma_int_t m, magma_int_t n,
float *A, magma_int_t lda,
magma_int_t *ipiv )
{
if ( m != n ) {
printf( "\nERROR: residual check defined only for square matrices\n" );
return -1;
}
const float c_one = MAGMA_S_ONE;
const float c_neg_one = MAGMA_S_NEG_ONE;
const magma_int_t ione = 1;
// this seed should be DIFFERENT than used in init_matrix
// (else x is column of A, so residual can be exactly zero)
magma_int_t ISEED[4] = {0,0,0,2};
magma_int_t info = 0;
float *x, *b;
// initialize RHS
TESTING_MALLOC_CPU( x, float, n );
TESTING_MALLOC_CPU( b, float, n );
lapackf77_slarnv( &ione, ISEED, &n, b );
blasf77_scopy( &n, b, &ione, x, &ione );
// solve Ax = b
lapackf77_sgetrs( "Notrans", &n, &ione, A, &lda, ipiv, x, &n, &info );
if (info != 0) {
printf("lapackf77_sgetrs returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
// reset to original A
init_matrix( opts, m, n, A, lda );
// compute r = Ax - b, saved in b
blasf77_sgemv( "Notrans", &m, &n, &c_one, A, &lda, x, &ione, &c_neg_one, b, &ione );
// compute residual |Ax - b| / (n*|A|*|x|)
float norm_x, norm_A, norm_r, work[1];
norm_A = lapackf77_slange( "F", &m, &n, A, &lda, work );
norm_r = lapackf77_slange( "F", &n, &ione, b, &n, work );
norm_x = lapackf77_slange( "F", &n, &ione, x, &n, work );
//printf( "r=\n" ); magma_sprint( 1, n, b, 1 );
TESTING_FREE_CPU( x );
TESTING_FREE_CPU( b );
//printf( "r=%.2e, A=%.2e, x=%.2e, n=%d\n", norm_r, norm_A, norm_x, n );
return norm_r / (n * norm_A * norm_x);
}
/*
Compute the snrm2 of da, da+ldda, ..., da +(num-1)*ldda where the vectors are
of size m. The resulting norms are written in the dxnorm array.
The computation can be done using num blocks (default) or on one SM (commented).
*/
extern "C" magma_int_t
magmablas_snrm2(int m, int num, magmaFloat_ptr da, size_t da_offset, magma_int_t ldda,
magmaFloat_ptr dxnorm, size_t dxnorm_offset, magma_queue_t queue)
{
size_t GlobalWorkSize[1]={0}, LocalWorkSize[1]={0};
LocalWorkSize[0] = BLOCK_SIZE;
GlobalWorkSize[0] = num * LocalWorkSize[0];
cl_int ciErrNum; // Error code var
cl_kernel ckKernel=NULL;
ckKernel = g_runtime.get_kernel( "magmablas_snrm2_kernel" );
if (!ckKernel)
{
printf ("Error: cannot locate kernel in line %d, file %s\n", __LINE__, __FILE__);
return MAGMA_ERR_UNKNOWN;
}
int nn = 0;
ciErrNum = clSetKernelArg( ckKernel, nn++, sizeof(int), (void*)&m );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(magmaFloat_ptr), (void*)&da );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(int), (void*)&da_offset );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(int), (void*)&ldda );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(magmaFloat_ptr), (void*)&dxnorm );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(int), (void*)&dxnorm_offset );
if (ciErrNum != CL_SUCCESS)
{
printf("Error: clSetKernelArg at %d in file %s!\n", __LINE__, __FILE__);
return MAGMA_ERR_UNKNOWN;
}
// launch kernel
ciErrNum = clEnqueueNDRangeKernel(
queue, ckKernel, 1, NULL, GlobalWorkSize, LocalWorkSize, 0, NULL, NULL);
if (ciErrNum != CL_SUCCESS)
{
printf("Error: clEnqueueNDRangeKernel at %d in file %s \"%s\"\n",
__LINE__, __FILE__, magma_strerror(ciErrNum));
return MAGMA_ERR_UNKNOWN;
}
clFlush(queue);
return MAGMA_SUCCESS;
}
/*
Adjust the norm of c to give the norm of c[k+1:], assumin that
c was changed with orthogonal transformations.
*/
extern "C" magma_int_t
magmablas_snrm2_adjust(int k, magmaFloat_ptr xnorm, size_t xnorm_offset, magmaFloat_ptr c, size_t c_offset, magma_queue_t queue)
{
size_t GlobalWorkSize[1]={0}, LocalWorkSize[1]={0};
LocalWorkSize[0] = k;
GlobalWorkSize[0] = 1*LocalWorkSize[0];
cl_int ciErrNum; // Error code var
cl_kernel ckKernel=NULL;
ckKernel = g_runtime.get_kernel( "magmablas_snrm2_adjust_kernel" );
if (!ckKernel)
{
printf ("Error: cannot locate kernel in line %d, file %s\n", __LINE__, __FILE__);
return MAGMA_ERR_UNKNOWN;
}
int nn = 0;
ciErrNum = clSetKernelArg( ckKernel, nn++, sizeof(magmaFloat_ptr), (void*)&xnorm );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(int), (void*)&xnorm_offset );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(magmaFloat_ptr), (void*)&c );
ciErrNum |= clSetKernelArg( ckKernel, nn++, sizeof(int), (void*)&c_offset );
//magma_snrm2_adjust_kernel<<< 1, k, 0, magma_stream >>> (xnorm, c);
// launch kernel
ciErrNum = clEnqueueNDRangeKernel(
queue, ckKernel, 1, NULL, GlobalWorkSize, LocalWorkSize, 0, NULL, NULL);
if (ciErrNum != CL_SUCCESS)
{
printf("Error: clEnqueueNDRangeKernel at %d in file %s \"%s\"\n",
__LINE__, __FILE__, magma_strerror(ciErrNum));
printf("block: %d, group: %d\n", (int) LocalWorkSize[0], (int) GlobalWorkSize[0]);
return MAGMA_ERR_UNKNOWN;
}
clFlush(queue);
return MAGMA_SUCCESS;
}
void magma_xerbla(const char *srname, magma_int_t minfo)
{
// the first 3 cases are unusual for calling xerbla;
// normally runtime errors are passed back in info.
if ( minfo < 0 ) {
fprintf( stderr, "Error in %s, function-specific error (info = %d)\n",
srname, (int) -minfo );
}
else if ( minfo == 0 ) {
fprintf( stderr, "No error, why is %s calling xerbla? (info = %d)\n",
srname, (int) -minfo );
}
else if ( minfo >= -MAGMA_ERR ) {
fprintf( stderr, "Error in %s, %s (info = %d)\n",
srname, magma_strerror(-minfo), (int) -minfo );
}
else {
// this is the normal case for calling xerbla;
// invalid parameter values are usually logic errors, not runtime errors.
fprintf( stderr, "On entry to %s, parameter %d had an illegal value (info = %d)\n",
srname, (int) minfo, (int) -minfo );
}
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cunmlq
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float Cnorm, error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t mm, m, n, k, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max;
magmaFloatComplex *C, *R, *A, *W, *tau;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
float tol = opts.tolerance * lapackf77_slamch("E");
// test all combinations of input parameters
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { Magma_ConjTrans, MagmaNoTrans };
printf("%% M N K side trans CPU Gflop/s (sec) GPU Gflop/s (sec) ||R||_F / ||QC||_F\n");
printf("%%==============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
nb = magma_get_cgelqf_nb( m, n );
ldc = m;
// A is k x m (left) or k x n (right)
mm = (side[iside] == MagmaLeft ? m : n);
lda = k;
gflops = FLOPS_CUNMLQ( m, n, k, side[iside] ) / 1e9;
if ( side[iside] == MagmaLeft && m < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=left and m < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaRight && n < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=right and n < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
// need at least 2*nb*nb for gelqf
lwork_max = max( max( m*nb, n*nb ), 2*nb*nb );
// this rounds it up slightly if needed to agree with lwork query
lwork_max = int( real( magma_cmake_lwork( lwork_max )));
TESTING_MALLOC_CPU( C, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( R, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( A, magmaFloatComplex, lda*mm );
TESTING_MALLOC_CPU( W, magmaFloatComplex, lwork_max );
TESTING_MALLOC_CPU( tau, magmaFloatComplex, k );
// C is full, m x n
size = ldc*n;
lapackf77_clarnv( &ione, ISEED, &size, C );
lapackf77_clacpy( "Full", &m, &n, C, &ldc, R, &ldc );
size = lda*mm;
lapackf77_clarnv( &ione, ISEED, &size, A );
// compute LQ factorization to get Householder vectors in A, tau
magma_cgelqf( k, mm, A, lda, tau, W, lwork_max, &info );
if (info != 0) {
printf("magma_cgelqf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_cunmlq( lapack_side_const( side[iside] ), lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, W, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_cunmlq returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_cunmlq( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
if (info != 0) {
printf("magma_cunmlq (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = (magma_int_t) MAGMA_C_REAL( W[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("Warning: optimal lwork %d > allocated lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
gpu_time = magma_wtime();
magma_cunmlq( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_cunmlq returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
size = ldc*n;
blasf77_caxpy( &size, &c_neg_one, C, &ione, R, &ione );
Cnorm = lapackf77_clange( "Fro", &m, &n, C, &ldc, work );
error = lapackf77_clange( "Fro", &m, &n, R, &ldc, work ) / (magma_ssqrt(m*n) * Cnorm);
printf( "%5d %5d %5d %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( W );
TESTING_FREE_CPU( tau );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}} // end iside, itran
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cposv_gpu
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, cpu_perf, cpu_time, gpu_perf, gpu_time;
float error, Rnorm, Anorm, Xnorm, *work;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *h_A, *h_B, *h_X;
magmaFloatComplex_ptr d_A, d_B;
magma_int_t N, lda, ldb, ldda, lddb, info, sizeA, sizeB;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
printf("uplo = %s\n", lapack_uplo_const(opts.uplo) );
printf(" N NRHS CPU Gflop/s (sec) GPU GFlop/s (sec) ||B - AX|| / N*||A||*||X||\n");
printf("================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = ldb = N;
ldda = ((N+31)/32)*32;
lddb = ldda;
gflops = ( FLOPS_CPOTRF( N ) + FLOPS_CPOTRS( N, opts.nrhs ) ) / 1e9;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, lda*N );
TESTING_MALLOC_CPU( h_B, magmaFloatComplex, ldb*opts.nrhs );
TESTING_MALLOC_CPU( h_X, magmaFloatComplex, ldb*opts.nrhs );
TESTING_MALLOC_CPU( work, float, N );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*N );
TESTING_MALLOC_DEV( d_B, magmaFloatComplex, lddb*opts.nrhs );
/* ====================================================================
Initialize the matrix
=================================================================== */
sizeA = lda*N;
sizeB = ldb*opts.nrhs;
lapackf77_clarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_clarnv( &ione, ISEED, &sizeB, h_B );
magma_cmake_hpd( N, h_A, lda );
magma_csetmatrix( N, N, h_A, N, d_A, ldda );
magma_csetmatrix( N, opts.nrhs, h_B, N, d_B, lddb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_cposv_gpu( opts.uplo, N, opts.nrhs, d_A, ldda, d_B, lddb, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_cpotrf_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Residual
=================================================================== */
magma_cgetmatrix( N, opts.nrhs, d_B, lddb, h_X, ldb );
Anorm = lapackf77_clange("I", &N, &N, h_A, &lda, work);
Xnorm = lapackf77_clange("I", &N, &opts.nrhs, h_X, &ldb, work);
blasf77_cgemm( MagmaNoTransStr, MagmaNoTransStr, &N, &opts.nrhs, &N,
&c_one, h_A, &lda,
h_X, &ldb,
&c_neg_one, h_B, &ldb );
Rnorm = lapackf77_clange("I", &N, &opts.nrhs, h_B, &ldb, work);
error = Rnorm/(N*Anorm*Xnorm);
status += ! (error < tol);
/* ====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_cposv( lapack_uplo_const(opts.uplo), &N, &opts.nrhs, h_A, &lda, h_B, &ldb, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_cposv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
printf( "%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) N, (int) opts.nrhs, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
}
else {
printf( "%5d %5d --- ( --- ) %7.2f (%7.2f) %8.2e %s\n",
(int) N, (int) opts.nrhs, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( work );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgeqrf_mgpu
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
double error, work[1];
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_R, *tau, *h_work, tmp[1];
double *d_lA[ MagmaMaxGPUs ];
magma_int_t M, N, n2, lda, ldda, n_local, ngpu;
magma_int_t info, min_mn, nb, lhwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1}, ISEED2[4];
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= (opts.check == 2); // check (-c2) implies lapack (-l)
magma_int_t status = 0;
double tol, eps = lapackf77_dlamch("E");
tol = opts.tolerance * eps;
printf("ngpu %d\n", (int) opts.ngpu );
if ( opts.check == 1 ) {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R-Q'A||_1 / (M*||A||_1) ||I-Q'Q||_1 / M\n");
printf("================================================================================================\n");
} else {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F /(M*||A||_F)\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];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
nb = magma_get_dgeqrf_nb( M );
gflops = FLOPS_DGEQRF( M, N ) / 1e9;
// ngpu must be at least the number of blocks
ngpu = min( opts.ngpu, int((N+nb-1)/nb) );
if ( ngpu < opts.ngpu ) {
printf( " * too many GPUs for the matrix size, using %d GPUs\n", (int) ngpu );
}
// query for workspace size
lhwork = -1;
lapackf77_dgeqrf( &M, &N, h_A, &M, tau, tmp, &lhwork, &info );
lhwork = (magma_int_t) MAGMA_D_REAL( tmp[0] );
// Allocate host memory for the matrix
TESTING_MALLOC( tau, double, min_mn );
TESTING_MALLOC( h_A, double, n2 );
TESTING_HOSTALLOC( h_R, double, n2 );
TESTING_MALLOC( h_work, double, lhwork );
// Allocate device memory
for( int dev = 0; dev < ngpu; dev++ ) {
n_local = ((N/nb)/ngpu)*nb;
if (dev < (N/nb) % ngpu)
n_local += nb;
else if (dev == (N/nb) % ngpu)
n_local += N % nb;
magma_setdevice( dev );
TESTING_DEVALLOC( d_lA[dev], double, ldda*n_local );
}
/* Initialize the matrix */
for ( int j=0; j<4; j++ ) ISEED2[j] = ISEED[j]; // saving seeds
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
double *tau;
TESTING_MALLOC( tau, double, min_mn );
cpu_time = magma_wtime();
lapackf77_dgeqrf( &M, &N, h_A, &M, tau, h_work, &lhwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapack_dgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
TESTING_FREE( tau );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_dsetmatrix_1D_col_bcyclic( M, N, h_R, lda, d_lA, ldda, ngpu, nb );
gpu_time = magma_wtime();
magma_dgeqrf2_mgpu( ngpu, M, N, d_lA, ldda, tau, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_dgeqrf2 returned error %d: %s.\n",
(int) info, magma_strerror( info ));
magma_dgetmatrix_1D_col_bcyclic( M, N, d_lA, ldda, h_R, lda, ngpu, nb );
magma_queue_sync( NULL );
if ( opts.check == 1 ) {
/* =====================================================================
Check the result
=================================================================== */
magma_int_t lwork = n2+N;
double *h_W1, *h_W2, *h_W3;
double *h_RW, results[2];
TESTING_MALLOC( h_W1, double, n2 ); // Q
TESTING_MALLOC( h_W2, double, n2 ); // R
TESTING_MALLOC( h_W3, double, lwork ); // WORK
TESTING_MALLOC( h_RW, double, M ); // RWORK
lapackf77_dlarnv( &ione, ISEED2, &n2, h_A );
lapackf77_dqrt02( &M, &N, &min_mn, h_A, h_R, h_W1, h_W2, &lda, tau, h_W3, &lwork,
h_RW, results );
results[0] *= eps;
results[1] *= eps;
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, results[0],results[1] );
printf("%s\n", (results[0] < tol ? "" : " failed"));
} else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) %8.2e %8.2e",
(int) M, (int) N, gpu_perf, gpu_time, results[0],results[1] );
printf("%s\n", (results[0] < tol ? "" : " failed"));
}
status |= ! (results[0] < tol);
TESTING_FREE( h_W1 );
TESTING_FREE( h_W2 );
TESTING_FREE( h_W3 );
TESTING_FREE( h_RW );
} else if ( opts.check == 2 ) {
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
error = lapackf77_dlange("f", &M, &N, h_A, &lda, work );
blasf77_daxpy( &n2, &c_neg_one, h_A, &ione, h_R, &ione );
error = lapackf77_dlange("f", &M, &N, h_R, &lda, work ) / (min_mn*error);
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time, error );
printf("%s\n", (error < tol ? "" : " failed"));
status |= ! (error < tol);
}
else {
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) ---\n",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
} else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, gpu_time);
}
}
TESTING_FREE( tau );
TESTING_FREE( h_A );
TESTING_FREE( h_work );
TESTING_HOSTFREE( h_R );
for( int dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
TESTING_DEVFREE( d_lA[dev] );
}
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgeqrs
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double gpu_error, cpu_error, matnorm, work[1];
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_A2, *h_B, *h_X, *h_R, *tau, *h_work, tmp[1];
magmaDoubleComplex *d_A, *d_B;
magma_int_t M, N, n2, nrhs, lda, ldb, ldda, lddb, min_mn, max_mn, nb, info;
magma_int_t lworkgpu, lhwork, lhwork2;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
parse_opts( argc, argv, &opts );
magma_int_t status = 0;
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
printf(" ||b-Ax|| / (N||A||)\n");
printf(" M N NRHS CPU GFlop/s (sec) GPU GFlop/s (sec) CPU GPU \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];
if ( M < N ) {
printf( "skipping M=%d, N=%d because M < N is not yet supported.\n", (int) M, (int) N );
continue;
}
min_mn = min(M, N);
max_mn = max(M, N);
lda = M;
ldb = max_mn;
n2 = lda*N;
ldda = ((M+31)/32)*32;
lddb = ((max_mn+31)/32)*32;
nb = magma_get_zgeqrf_nb(M);
gflops = (FLOPS_ZGEQRF( M, N ) + FLOPS_ZGEQRS( M, N, nrhs )) / 1e9;
// query for workspace size
lworkgpu = (M - N + nb)*(nrhs + nb) + nrhs*nb;
lhwork = -1;
lapackf77_zgeqrf(&M, &N, h_A, &M, tau, tmp, &lhwork, &info);
lhwork2 = (magma_int_t) MAGMA_Z_REAL( tmp[0] );
lhwork = -1;
lapackf77_zunmqr( MagmaLeftStr, MagmaConjTransStr,
&M, &nrhs, &min_mn, h_A, &lda, tau,
h_X, &ldb, tmp, &lhwork, &info);
lhwork = (magma_int_t) MAGMA_Z_REAL( tmp[0] );
lhwork = max( max( lhwork, lhwork2 ), lworkgpu );
TESTING_MALLOC( tau, magmaDoubleComplex, min_mn );
TESTING_MALLOC( h_A, magmaDoubleComplex, lda*N );
TESTING_MALLOC( h_A2, magmaDoubleComplex, lda*N );
TESTING_MALLOC( h_B, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC( h_X, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC( h_R, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC( h_work, magmaDoubleComplex, lhwork );
TESTING_DEVALLOC( d_A, magmaDoubleComplex, ldda*N );
TESTING_DEVALLOC( d_B, magmaDoubleComplex, lddb*nrhs );
/* Initialize the matrices */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_A2, &lda );
// make random RHS
n2 = M*nrhs;
lapackf77_zlarnv( &ione, ISEED, &n2, h_B );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
// make consistent RHS
//n2 = N*nrhs;
//lapackf77_zlarnv( &ione, ISEED, &n2, h_X );
//blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
// &c_one, h_A, &lda,
// h_X, &ldb,
// &c_zero, h_B, &ldb );
//lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
gpu_time = magma_wtime();
magma_zgels3_gpu( MagmaNoTrans, M, N, nrhs, d_A, ldda,
d_B, lddb, h_work, lworkgpu, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgels returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// Get the solution in h_X
magma_zgetmatrix( N, nrhs, d_B, lddb, h_X, ldb );
// compute the residual
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A, &lda,
h_X, &ldb,
&c_one, h_R, &ldb);
matnorm = lapackf77_zlange("f", &M, &N, h_A, &lda, work);
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_zgels( MagmaNoTransStr, &M, &N, &nrhs,
h_A, &lda, h_X, &ldb, h_work, &lhwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgels returned error %d: %s.\n",
(int) info, magma_strerror( info ));
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A2, &lda,
h_X, &ldb,
&c_one, h_B, &ldb);
cpu_error = lapackf77_zlange("f", &M, &nrhs, h_B, &ldb, work) / (min_mn*matnorm);
gpu_error = lapackf77_zlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*matnorm);
printf("%5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e",
(int) M, (int) N, (int) nrhs,
cpu_perf, cpu_time, gpu_perf, gpu_time, cpu_error, gpu_error );
printf("%s\n", (gpu_error < tol ? "" : " failed"));
status |= ! (gpu_error < tol);
TESTING_FREE( tau );
TESTING_FREE( h_A );
TESTING_FREE( h_A2 );
TESTING_FREE( h_B );
TESTING_FREE( h_X );
TESTING_FREE( h_R );
TESTING_FREE( h_work );
TESTING_DEVFREE( d_A );
TESTING_DEVFREE( d_B );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing sormbr
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float Cnorm, error, dwork[1];
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t ione = 1;
magma_int_t m, n, k, mi, ni, mm, nn, nq, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max;
float *C, *R, *A, *work, *tau, *tauq, *taup;
float *d, *e;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
float tol = opts.tolerance * lapackf77_slamch("E");
// test all combinations of input parameters
magma_vect_t vect [] = { MagmaQ, MagmaP };
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { MagmaTrans, MagmaNoTrans };
printf("%% M N K vect side trans CPU Gflop/s (sec) GPU Gflop/s (sec) ||R||_F / ||QC||_F\n");
printf("%%==============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int ivect = 0; ivect < 2; ++ivect ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
nb = magma_get_sgebrd_nb( m, n );
ldc = m;
// A is nq x k (vect=Q) or k x nq (vect=P)
// where nq=m (left) or nq=n (right)
nq = (side[iside] == MagmaLeft ? m : n );
mm = (vect[ivect] == MagmaQ ? nq : k );
nn = (vect[ivect] == MagmaQ ? k : nq);
lda = mm;
// MBR calls either MQR or MLQ in various ways
if ( vect[ivect] == MagmaQ ) {
if ( nq >= k ) {
gflops = FLOPS_SORMQR( m, n, k, side[iside] ) / 1e9;
}
else {
if ( side[iside] == MagmaLeft ) {
mi = m - 1;
ni = n;
}
else {
mi = m;
ni = n - 1;
}
gflops = FLOPS_SORMQR( mi, ni, nq-1, side[iside] ) / 1e9;
}
}
else {
if ( nq > k ) {
gflops = FLOPS_SORMLQ( m, n, k, side[iside] ) / 1e9;
}
else {
if ( side[iside] == MagmaLeft ) {
mi = m - 1;
ni = n;
}
else {
mi = m;
ni = n - 1;
}
gflops = FLOPS_SORMLQ( mi, ni, nq-1, side[iside] ) / 1e9;
}
}
// workspace for gebrd is (mm + nn)*nb
// workspace for unmbr is m*nb or n*nb, depending on side
lwork_max = max( (mm + nn)*nb, max( m*nb, n*nb ));
// this rounds it up slightly if needed to agree with lwork query below
lwork_max = int( real( magma_smake_lwork( lwork_max )));
TESTING_MALLOC_CPU( C, float, ldc*n );
TESTING_MALLOC_CPU( R, float, ldc*n );
TESTING_MALLOC_CPU( A, float, lda*nn );
TESTING_MALLOC_CPU( work, float, lwork_max );
TESTING_MALLOC_CPU( d, float, min(mm,nn) );
TESTING_MALLOC_CPU( e, float, min(mm,nn) );
TESTING_MALLOC_CPU( tauq, float, min(mm,nn) );
TESTING_MALLOC_CPU( taup, float, min(mm,nn) );
// C is full, m x n
size = ldc*n;
lapackf77_slarnv( &ione, ISEED, &size, C );
lapackf77_slacpy( "Full", &m, &n, C, &ldc, R, &ldc );
size = lda*nn;
lapackf77_slarnv( &ione, ISEED, &size, A );
// compute BRD factorization to get Householder vectors in A, tauq, taup
//lapackf77_sgebrd( &mm, &nn, A, &lda, d, e, tauq, taup, work, &lwork_max, &info );
magma_sgebrd( mm, nn, A, lda, d, e, tauq, taup, work, lwork_max, &info );
if (info != 0) {
printf("magma_sgebrd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
if ( vect[ivect] == MagmaQ ) {
tau = tauq;
} else {
tau = taup;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_sormbr( lapack_vect_const( vect[ivect] ),
lapack_side_const( side[iside] ),
lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, work, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_sormbr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_sormbr( vect[ivect], side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, work, lwork, &info );
if (info != 0) {
printf("magma_sormbr (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = (magma_int_t) MAGMA_S_REAL( work[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("Warning: optimal lwork %d > allocated lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
gpu_time = magma_wtime();
magma_sormbr( vect[ivect], side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, work, lwork, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_sormbr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
size = ldc*n;
blasf77_saxpy( &size, &c_neg_one, C, &ione, R, &ione );
Cnorm = lapackf77_slange( "Fro", &m, &n, C, &ldc, dwork );
error = lapackf77_slange( "Fro", &m, &n, R, &ldc, dwork ) / (magma_ssqrt(m*n) * Cnorm);
printf( "%5d %5d %5d %c %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_vect_const( vect[ivect] ),
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( d );
TESTING_FREE_CPU( e );
TESTING_FREE_CPU( taup );
TESTING_FREE_CPU( tauq );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}}} // end ivect, iside, itran
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetri_batched
*/
int main( int argc, char** argv)
{
TESTING_INIT();
// constants
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A, *h_Ainv, *h_R, *work;
magmaDoubleComplex_ptr d_A, d_invA;
magmaDoubleComplex_ptr *dA_array;
magmaDoubleComplex_ptr *dinvA_array;
magma_int_t **dipiv_array;
magma_int_t *dinfo_array;
magma_int_t *ipiv, *cpu_info;
magma_int_t *d_ipiv, *d_info;
magma_int_t N, n2, lda, ldda, info, info1, info2, lwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex tmp;
double error, rwork[1];
magma_int_t columns;
magma_int_t status = 0;
magma_opts opts( MagmaOptsBatched );
opts.parse_opts( argc, argv );
magma_int_t batchCount = opts.batchcount;
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% batchCount N CPU Gflop/s (ms) GPU Gflop/s (ms) ||I - A*A^{-1}||_1 / (N*cond(A))\n");
printf("%%===============================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N * batchCount;
ldda = magma_roundup( N, opts.align ); // multiple of 32 by default
// This is the correct flops but since this getri_batched is based on
// 2 trsm = getrs and to know the real flops I am using the getrs one
//gflops = (FLOPS_ZGETRF( N, N ) + FLOPS_ZGETRI( N ))/ 1e9 * batchCount;
gflops = (FLOPS_ZGETRF( N, N ) + FLOPS_ZGETRS( N, N ))/ 1e9 * batchCount;
// query for workspace size
lwork = -1;
lapackf77_zgetri( &N, NULL, &lda, NULL, &tmp, &lwork, &info );
if (info != 0) {
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = magma_int_t( MAGMA_Z_REAL( tmp ));
TESTING_MALLOC_CPU( cpu_info, magma_int_t, batchCount );
TESTING_MALLOC_CPU( ipiv, magma_int_t, N * batchCount );
TESTING_MALLOC_CPU( work, magmaDoubleComplex, lwork*batchCount );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_Ainv, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N * batchCount );
TESTING_MALLOC_DEV( d_invA, magmaDoubleComplex, ldda*N * batchCount );
TESTING_MALLOC_DEV( d_ipiv, magma_int_t, N * batchCount );
TESTING_MALLOC_DEV( d_info, magma_int_t, batchCount );
TESTING_MALLOC_DEV( dA_array, magmaDoubleComplex*, batchCount );
TESTING_MALLOC_DEV( dinvA_array, magmaDoubleComplex*, batchCount );
TESTING_MALLOC_DEV( dinfo_array, magma_int_t, batchCount );
TESTING_MALLOC_DEV( dipiv_array, magma_int_t*, batchCount );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
columns = N * batchCount;
lapackf77_zlacpy( MagmaFullStr, &N, &columns, h_A, &lda, h_R, &lda );
lapackf77_zlacpy( MagmaFullStr, &N, &columns, h_A, &lda, h_Ainv, &lda );
magma_zsetmatrix( N, columns, h_R, lda, d_A, ldda, opts.queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_zset_pointer( dA_array, d_A, ldda, 0, 0, ldda * N, batchCount, opts.queue );
magma_zset_pointer( dinvA_array, d_invA, ldda, 0, 0, ldda * N, batchCount, opts.queue );
magma_iset_pointer( dipiv_array, d_ipiv, 1, 0, 0, N, batchCount, opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
info1 = magma_zgetrf_batched( N, N, dA_array, ldda, dipiv_array, dinfo_array, batchCount, opts.queue);
info2 = magma_zgetri_outofplace_batched( N, dA_array, ldda, dipiv_array, dinvA_array, ldda, dinfo_array, batchCount, opts.queue);
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gflops / gpu_time;
// check correctness of results throught "dinfo_magma" and correctness of argument throught "info"
magma_getvector( batchCount, sizeof(magma_int_t), dinfo_array, 1, cpu_info, 1, opts.queue );
for (magma_int_t i=0; i < batchCount; i++)
{
if (cpu_info[i] != 0 ) {
printf("magma_zgetrf_batched matrix %d returned error %d\n", (int) i, (int)cpu_info[i] );
}
}
if (info1 != 0) printf("magma_zgetrf_batched returned argument error %d: %s.\n", (int) info1, magma_strerror( info1 ));
if (info2 != 0) printf("magma_zgetri_batched returned argument error %d: %s.\n", (int) info2, magma_strerror( info2 ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
#if !defined (BATCHED_DISABLE_PARCPU) && defined(_OPENMP)
magma_int_t nthreads = magma_get_lapack_numthreads();
magma_set_lapack_numthreads(1);
magma_set_omp_numthreads(nthreads);
#pragma omp parallel for schedule(dynamic)
#endif
for (int i=0; i < batchCount; i++)
{
magma_int_t locinfo;
lapackf77_zgetrf(&N, &N, h_Ainv + i*lda*N, &lda, ipiv + i*N, &locinfo);
if (locinfo != 0) {
printf("lapackf77_zgetrf returned error %d: %s.\n",
(int) locinfo, magma_strerror( locinfo ));
}
lapackf77_zgetri(&N, h_Ainv + i*lda*N, &lda, ipiv + i*N, work + i*lwork, &lwork, &locinfo );
if (locinfo != 0) {
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) locinfo, magma_strerror( locinfo ));
}
}
#if !defined (BATCHED_DISABLE_PARCPU) && defined(_OPENMP)
magma_set_lapack_numthreads(nthreads);
#endif
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
printf("%10d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) batchCount, (int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000. );
}
else {
printf("%10d %5d --- ( --- ) %7.2f (%7.2f)",
(int) batchCount, (int) N, gpu_perf, gpu_time*1000. );
}
/* =====================================================================
Check the result
=================================================================== */
if ( opts.check ) {
magma_igetvector( N*batchCount, d_ipiv, 1, ipiv, 1, opts.queue );
magma_zgetmatrix( N, N*batchCount, d_invA, ldda, h_Ainv, lda, opts.queue );
error = 0;
for (magma_int_t i=0; i < batchCount; i++)
{
for (magma_int_t k=0; k < N; k++) {
if (ipiv[i*N+k] < 1 || ipiv[i*N+k] > N )
{
printf("error for matrix %d ipiv @ %d = %d\n", (int) i, (int) k, (int) ipiv[i*N+k]);
error = -1;
}
}
if (error == -1) {
break;
}
// compute 1-norm condition number estimate, following LAPACK's zget03
double normA, normAinv, rcond, err;
normA = lapackf77_zlange( "1", &N, &N, h_A + i*lda*N, &lda, rwork );
normAinv = lapackf77_zlange( "1", &N, &N, h_Ainv + i*lda*N, &lda, rwork );
if ( normA <= 0 || normAinv <= 0 ) {
rcond = 0;
err = 1 / (tol/opts.tolerance); // == 1/eps
}
else {
rcond = (1 / normA) / normAinv;
// R = I
// R -= A*A^{-1}
// err = ||I - A*A^{-1}|| / ( N ||A||*||A^{-1}|| ) = ||R|| * rcond / N, using 1-norm
lapackf77_zlaset( "full", &N, &N, &c_zero, &c_one, h_R + i*lda*N, &lda );
blasf77_zgemm( "no", "no", &N, &N, &N, &c_neg_one,
h_A + i*lda*N, &lda,
h_Ainv + i*lda*N, &lda, &c_one,
h_R + i*lda*N, &lda );
err = lapackf77_zlange( "1", &N, &N, h_R + i*lda*N, &lda, rwork );
err = err * rcond / N;
}
if ( isnan(err) || isinf(err) ) {
error = err;
break;
}
error = max( err, error );
}
bool okay = (error < tol);
status += ! okay;
printf(" %8.2e %s\n", error, (okay ? "ok" : "failed") );
}
else {
printf("\n");
}
TESTING_FREE_CPU( cpu_info );
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_Ainv );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_invA );
TESTING_FREE_DEV( d_ipiv );
TESTING_FREE_DEV( d_info );
TESTING_FREE_DEV( dA_array );
TESTING_FREE_DEV( dinvA_array );
TESTING_FREE_DEV( dinfo_array );
TESTING_FREE_DEV( dipiv_array );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing sgeqrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float error, work[1];
float c_neg_one = MAGMA_S_NEG_ONE;
float *h_A, *h_R, *tau, *dtau, *h_work, tmp[1];
float *d_A;
float *dwork;
magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
printf(" M N CPU GFlop/s (ms) GPU GFlop/s (ms) ||R||_F / ||A||_F\n");
printf("=======================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = FLOPS_SGEQRF( M, N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_sgeqrf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_S_REAL( tmp[0] );
TESTING_MALLOC_CPU( tau, float, min_mn );
TESTING_MALLOC_CPU( h_A, float, n2 );
TESTING_MALLOC_CPU( h_work, float, lwork );
TESTING_MALLOC_PIN( h_R, float, n2 );
TESTING_MALLOC_DEV( d_A, float, ldda*N );
TESTING_MALLOC_DEV( dtau, float, min_mn );
TESTING_MALLOC_DEV( dwork, float, min_mn );
/* Initialize the matrix */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
lapackf77_slacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_ssetmatrix( M, N, h_R, lda, d_A, ldda );
// warmup
if ( opts.warmup ) {
magma_sgeqr2_gpu( M, N, d_A, ldda, dtau, dwork, &info );
magma_ssetmatrix( M, N, h_R, lda, d_A, ldda );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_sync_wtime( 0 );
magma_sgeqr2_gpu( M, N, d_A, ldda, dtau, dwork, &info );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_sgeqr2_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.lapack ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_sgeqrf(&M, &N, h_A, &lda, tau, h_work, &lwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_sgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
magma_sgetmatrix( M, N, d_A, ldda, h_R, M );
error = lapackf77_slange("f", &M, &N, h_A, &lda, work);
blasf77_saxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_slange("f", &M, &N, h_R, &lda, work) / error;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) M, (int) N, cpu_perf, 1000.*cpu_time, gpu_perf, 1000.*gpu_time,
error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, 1000.*gpu_time );
}
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_work );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( dtau );
TESTING_FREE_DEV( dwork );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dlansy
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gbytes, gpu_perf, gpu_time, cpu_perf, cpu_time;
double *h_A;
double *h_work;
double *d_A;
double *d_work;
magma_int_t N, n2, lda, ldda;
magma_int_t idist = 3; // normal distribution (otherwise max norm is always ~ 1)
magma_int_t ISEED[4] = {0,0,0,1};
double error, norm_magma, norm_lapack;
magma_int_t status = 0;
bool mkl_warning = false;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
magma_uplo_t uplo[] = { MagmaLower, MagmaUpper };
magma_norm_t norm[] = { MagmaInfNorm, MagmaOneNorm, MagmaMaxNorm };
// Double-Complex inf-norm not supported on Tesla (CUDA arch 1.x)
#if defined(PRECISION_z)
magma_int_t arch = magma_getdevice_arch();
if ( arch < 200 ) {
printf("!!!! NOTE: Double-Complex %s and %s norm are not supported\n"
"!!!! on CUDA architecture %d; requires arch >= 200.\n"
"!!!! It should report \"parameter number 1 had an illegal value\" below.\n\n",
MagmaInfNormStr, MagmaOneNormStr, (int) arch );
for( int inorm = 0; inorm < 2; ++inorm ) {
for( int iuplo = 0; iuplo < 2; ++iuplo ) {
printf( "Testing that magmablas_dlansy( %s, %s, ... ) returns -1 error...\n",
lapack_norm_const( norm[inorm] ),
lapack_uplo_const( uplo[iuplo] ));
norm_magma = magmablas_dlansy( norm[inorm], uplo[iuplo], 1, NULL, 1, NULL );
if ( norm_magma != -1 ) {
printf( "expected magmablas_dlansy to return -1 error, but got %f\n", norm_magma );
status = 1;
}
}
}
printf( "...return values %s\n\n", (status == 0 ? "ok" : "failed") );
}
#endif
printf(" N norm uplo CPU GByte/s (ms) GPU GByte/s (ms) error \n");
printf("=======================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int inorm = 0; inorm < 3; ++inorm ) {
for( int iuplo = 0; iuplo < 2; ++iuplo ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N;
ldda = roundup( N, opts.pad );
// read upper or lower triangle
gbytes = 0.5*(N+1)*N*sizeof(double) / 1e9;
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_CPU( h_work, double, N );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
TESTING_MALLOC_DEV( d_work, double, N );
/* Initialize the matrix */
lapackf77_dlarnv( &idist, ISEED, &n2, h_A );
//magma_dmake_symmetric( N, h_A, lda );
// make diagonal real -- according to docs, should NOT be necesary
//for( int i=0; i < N; ++i ) {
// h_A[i + i*lda] = MAGMA_D_MAKE( MAGMA_D_REAL( h_A[i + i*lda] ), 0 );
//}
magma_dsetmatrix( N, N, h_A, lda, d_A, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
norm_magma = magmablas_dlansy( norm[inorm], uplo[iuplo], N, d_A, ldda, d_work );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gbytes / gpu_time;
if (norm_magma == -1) {
printf( "%5d %4c skipped because it isn't supported on this GPU\n",
(int) N, lapacke_norm_const( norm[inorm] ));
continue;
}
if (norm_magma < 0)
printf("magmablas_dlansy returned error %f: %s.\n",
norm_magma, magma_strerror( (int) norm_magma ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
norm_lapack = lapackf77_dlansy(
lapack_norm_const( norm[inorm] ),
lapack_uplo_const( uplo[iuplo] ),
&N, h_A, &lda, h_work );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
if (norm_lapack < 0)
printf("lapackf77_dlansy returned error %f: %s.\n",
norm_lapack, magma_strerror( (int) norm_lapack ));
/* =====================================================================
Check the result compared to LAPACK
Note: MKL (11.1.0) has bug for uplo=Lower with multiple threads.
Try with $MKL_NUM_THREADS = 1.
=================================================================== */
error = fabs( norm_magma - norm_lapack ) / norm_lapack;
double tol2 = tol;
if ( norm[inorm] == MagmaMaxNorm ) {
// max-norm depends on only one element, so for Real precisions,
// MAGMA and LAPACK should exactly agree (tol2 = 0),
// while Complex precisions incur roundoff in fabs.
#if defined(PRECISION_s) || defined(PRECISION_d)
tol2 = 0;
#endif
}
if ( error > tol2 && norm[inorm] == MagmaInfNorm && uplo[iuplo] == MagmaLower ) {
mkl_warning = true;
}
printf("%5d %4c %4c %7.2f (%7.2f) %7.2f (%7.2f) %#9.3g %s\n",
(int) N,
lapacke_norm_const( norm[inorm] ),
lapacke_uplo_const( uplo[iuplo] ),
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
error, (error <= tol2 ? "ok" : "failed") );
status += ! (error <= tol2);
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_work );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_work );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
} // end iuplo, inorm, iter
printf( "\n" );
}
if ( mkl_warning ) {
printf("* Some versions of MKL (e.g., 11.1.0) have a bug in dlansy with uplo=L\n"
" and multiple threads. Try again with MKL_NUM_THREADS=1.\n" );
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgetrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
float error;
magmaFloatComplex *h_A, *h_R;
magmaFloatComplex *d_A;
magma_int_t *ipiv;
magma_int_t M, N, n2, lda, ldda, info, min_mn;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
printf(" M N CPU GFlop/s (ms) GPU GFlop/s (ms) ||PA-LU||/(||A||*N)\n");
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = FLOPS_CGETRF( M, N ) / 1e9;
if ( N > 512 ) {
printf( "%5d %5d skipping because cgetf2 does not support N > 512\n", (int) M, (int) N );
continue;
}
TESTING_MALLOC_CPU( ipiv, magma_int_t, min_mn );
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, n2 );
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, n2 );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*N );
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
lapackf77_clacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_csetmatrix( M, N, h_R, lda, d_A, ldda );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_cgetrf(&M, &N, h_A, &lda, ipiv, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_cgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_cgetf2_gpu( M, N, d_A, ldda, ipiv, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_cgetf2_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) M, (int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000. );
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f)",
(int) M, (int) N, gpu_perf, gpu_time*1000. );
}
if ( opts.check ) {
magma_cgetmatrix( M, N, d_A, ldda, h_A, lda );
error = get_LU_error( M, N, h_R, lda, h_A, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
}
else {
printf(" --- \n");
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgels
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double gpu_error, cpu_error, error, Anorm, work[1];
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_A2, *h_B, *h_X, *h_R, *tau, *h_work, tmp[1];
magmaDouble_ptr d_A, d_B;
magma_int_t M, N, size, nrhs, lda, ldb, ldda, lddb, min_mn, max_mn, nb, info;
magma_int_t lworkgpu, lhwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
opts.parse_opts( argc, argv );
magma_int_t status = 0;
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
printf("%% ||b-Ax|| / (N||A||) ||dx-x||/(N||A||)\n");
printf("%% M N NRHS CPU Gflop/s (sec) GPU Gflop/s (sec) CPU GPU \n");
printf("%%==================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
if ( M < N ) {
printf( "%5d %5d %5d skipping because M < N is not yet supported.\n", (int) M, (int) N, (int) nrhs );
continue;
}
min_mn = min(M, N);
max_mn = max(M, N);
lda = M;
ldb = max_mn;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
lddb = magma_roundup( max_mn, opts.align ); // multiple of 32 by default
nb = magma_get_dgeqrf_nb( M, N );
gflops = (FLOPS_DGEQRF( M, N ) + FLOPS_DGEQRS( M, N, nrhs )) / 1e9;
lworkgpu = (M - N + nb)*(nrhs + nb) + nrhs*nb;
// query for workspace size
lhwork = -1;
lapackf77_dgels( MagmaNoTransStr, &M, &N, &nrhs,
NULL, &lda, NULL, &ldb, tmp, &lhwork, &info );
lhwork = (magma_int_t) MAGMA_D_REAL( tmp[0] );
lhwork = max( lhwork, lworkgpu );
TESTING_MALLOC_CPU( tau, double, min_mn );
TESTING_MALLOC_CPU( h_A, double, lda*N );
TESTING_MALLOC_CPU( h_A2, double, lda*N );
TESTING_MALLOC_CPU( h_B, double, ldb*nrhs );
TESTING_MALLOC_CPU( h_X, double, ldb*nrhs );
TESTING_MALLOC_CPU( h_R, double, ldb*nrhs );
TESTING_MALLOC_CPU( h_work, double, lhwork );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
TESTING_MALLOC_DEV( d_B, double, lddb*nrhs );
/* Initialize the matrices */
size = lda*N;
lapackf77_dlarnv( &ione, ISEED, &size, h_A );
lapackf77_dlacpy( MagmaFullStr, &M, &N, h_A, &lda, h_A2, &lda );
// make random RHS
size = ldb*nrhs;
lapackf77_dlarnv( &ione, ISEED, &size, h_B );
lapackf77_dlacpy( MagmaFullStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
// make consistent RHS
//size = N*nrhs;
//lapackf77_dlarnv( &ione, ISEED, &size, h_X );
//blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
// &c_one, h_A, &lda,
// h_X, &ldb,
// &c_zero, h_B, &ldb );
//lapackf77_dlacpy( MagmaFullStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_dsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_dsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
gpu_time = magma_wtime();
magma_dgels_gpu( MagmaNoTrans, M, N, nrhs, d_A, ldda,
d_B, lddb, h_work, lworkgpu, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dgels_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
// compute the residual
magma_dgetmatrix( N, nrhs, d_B, lddb, h_X, ldb );
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A, &lda,
h_X, &ldb,
&c_one, h_R, &ldb );
Anorm = lapackf77_dlange("f", &M, &N, h_A, &lda, work);
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
lapackf77_dlacpy( MagmaFullStr, &M, &nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_dgels( MagmaNoTransStr, &M, &N, &nrhs,
h_A, &lda, h_X, &ldb, h_work, &lhwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_dgels returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A2, &lda,
h_X, &ldb,
&c_one, h_B, &ldb );
cpu_error = lapackf77_dlange("f", &M, &nrhs, h_B, &ldb, work) / (min_mn*Anorm);
gpu_error = lapackf77_dlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*Anorm);
// error relative to LAPACK
size = M*nrhs;
blasf77_daxpy( &size, &c_neg_one, h_B, &ione, h_R, &ione );
error = lapackf77_dlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*Anorm);
printf("%5d %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %8.2e",
(int) M, (int) N, (int) nrhs,
cpu_perf, cpu_time, gpu_perf, gpu_time, cpu_error, gpu_error, error );
bool okay;
if ( M == N ) {
okay = (gpu_error < tol && error < tol);
}
else {
okay = (error < tol);
}
status += ! okay;
printf( " %s\n", (okay ? "ok" : "failed"));
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_A2 );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( h_R );
TESTING_FREE_CPU( h_work );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgetrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
double error;
double *h_A;
magmaDouble_ptr d_A;
magma_int_t *ipiv;
magma_int_t M, N, n2, lda, ldda, info, min_mn;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
if ( opts.check == 2 ) {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |Ax-b|/(N*|A|*|x|)\n");
}
else {
printf(" M N CPU GFlop/s (sec) GPU GFlop/s (sec) |PA-LU|/(N*|A|)\n");
}
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = FLOPS_DGETRF( M, N ) / 1e9;
TESTING_MALLOC_CPU( ipiv, magma_int_t, min_mn );
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
init_matrix( M, N, h_A, lda );
cpu_time = magma_wtime();
lapackf77_dgetrf(&M, &N, h_A, &lda, ipiv, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_dgetrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
init_matrix( M, N, h_A, lda );
magma_dsetmatrix( M, N, h_A, lda, d_A, ldda );
gpu_time = magma_wtime();
magma_dgetrf_gpu( M, N, d_A, ldda, ipiv, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_dgetrf_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) M, (int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f)",
(int) M, (int) N, gpu_perf, gpu_time );
}
if ( opts.check == 2 ) {
magma_dgetmatrix( M, N, d_A, ldda, h_A, lda );
error = get_residual( M, N, h_A, lda, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else if ( opts.check ) {
magma_dgetmatrix( M, N, d_A, ldda, h_A, lda );
error = get_LU_error( M, N, h_A, lda, ipiv );
printf(" %8.2e %s\n", error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else {
printf(" --- \n");
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( h_A );
TESTING_FREE_DEV( d_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zgetrf
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A, *h_R, *work;
magmaDoubleComplex_ptr d_A, dwork;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t N, n2, lda, ldda, info, lwork, ldwork;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magmaDoubleComplex tmp;
double error, rwork[1];
magma_int_t *ipiv;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
// need looser bound (3000*eps instead of 30*eps) for tests
// TODO: should compute ||I - A*A^{-1}|| / (n*||A||*||A^{-1}||)
opts.tolerance = max( 3000., opts.tolerance );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R||_F / (N*||A||_F)\n");
printf("=================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N;
ldda = ((N+31)/32)*32;
ldwork = N * magma_get_zgetri_nb( N );
gflops = FLOPS_ZGETRI( N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_zgetri( &N, NULL, &lda, NULL, &tmp, &lwork, &info );
if (info != 0)
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lwork = int( MAGMA_Z_REAL( tmp ));
TESTING_MALLOC_CPU( ipiv, magma_int_t, N );
TESTING_MALLOC_CPU( work, magmaDoubleComplex, lwork );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_PIN( h_R, magmaDoubleComplex, n2 );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( dwork, magmaDoubleComplex, ldwork );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
error = lapackf77_zlange( "f", &N, &N, h_A, &lda, rwork ); // norm(A)
/* Factor the matrix. Both MAGMA and LAPACK will use this factor. */
magma_zsetmatrix( N, N, h_A, lda, d_A, 0, ldda, opts.queue );
magma_zgetrf_gpu( N, N, d_A, 0, ldda, ipiv, opts.queue, &info );
magma_zgetmatrix( N, N, d_A, 0, ldda, h_A, lda, opts.queue );
if ( info != 0 )
printf("magma_zgetrf_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// check for exact singularity
//h_A[ 10 + 10*lda ] = MAGMA_Z_MAKE( 0.0, 0.0 );
//magma_zsetmatrix( N, N, h_A, lda, d_A, 0, ldda, opts.queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zgetri_gpu( N, d_A, 0, ldda, ipiv, dwork, 0, ldwork, opts.queues2, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zgetri_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
magma_zgetmatrix( N, N, d_A, 0, ldda, h_R, lda, opts.queue );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_zgetri( &N, h_A, &lda, ipiv, work, &lwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgetri returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
blasf77_zaxpy( &n2, &c_neg_one, h_A, &ione, h_R, &ione );
error = lapackf77_zlange( "f", &N, &N, h_R, &lda, rwork ) / (N*error);
printf( "%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
}
else {
printf( "%5d --- ( --- ) %7.2f (%7.2f) ---\n",
(int) N, gpu_perf, gpu_time );
}
TESTING_FREE_CPU( ipiv );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( dwork );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgesv_gpu
*/
int main(int argc, char **argv)
{
TESTING_INIT();
real_Double_t gflops, cpu_perf, cpu_time, gpu_perf, gpu_time;
double error, Rnorm, Anorm, Xnorm, *work;
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_B, *h_X;
magmaDouble_ptr d_A, d_B;
magma_int_t *ipiv;
magma_int_t N, nrhs, lda, ldb, ldda, lddb, info, sizeA, sizeB;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
printf("%% N NRHS CPU Gflop/s (sec) GPU Gflop/s (sec) ||B - AX|| / N*||A||*||X||\n");
printf("%%===============================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
ldb = lda;
ldda = magma_roundup( N, opts.align ); // multiple of 32 by default
lddb = ldda;
gflops = ( FLOPS_DGETRF( N, N ) + FLOPS_DGETRS( N, nrhs ) ) / 1e9;
TESTING_MALLOC_CPU( h_A, double, lda*N );
TESTING_MALLOC_CPU( h_B, double, ldb*nrhs );
TESTING_MALLOC_CPU( h_X, double, ldb*nrhs );
TESTING_MALLOC_CPU( work, double, N );
TESTING_MALLOC_CPU( ipiv, magma_int_t, N );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
TESTING_MALLOC_DEV( d_B, double, lddb*nrhs );
/* Initialize the matrices */
sizeA = lda*N;
sizeB = ldb*nrhs;
lapackf77_dlarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_dlarnv( &ione, ISEED, &sizeB, h_B );
magma_dsetmatrix( N, N, h_A, lda, d_A, ldda, opts.queue );
magma_dsetmatrix( N, nrhs, h_B, ldb, d_B, lddb, opts.queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_dgesv_gpu( N, nrhs, d_A, ldda, ipiv, d_B, lddb, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dgesv_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
//=====================================================================
// Residual
//=====================================================================
magma_dgetmatrix( N, nrhs, d_B, lddb, h_X, ldb, opts.queue );
Anorm = lapackf77_dlange("I", &N, &N, h_A, &lda, work);
Xnorm = lapackf77_dlange("I", &N, &nrhs, h_X, &ldb, work);
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &N, &nrhs, &N,
&c_one, h_A, &lda,
h_X, &ldb,
&c_neg_one, h_B, &ldb);
Rnorm = lapackf77_dlange("I", &N, &nrhs, h_B, &ldb, work);
error = Rnorm/(N*Anorm*Xnorm);
status += ! (error < tol);
/* ====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_dgesv( &N, &nrhs, h_A, &lda, ipiv, h_B, &ldb, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_dgesv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
printf( "%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) N, (int) nrhs, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
}
else {
printf( "%5d %5d --- ( --- ) %7.2f (%7.2f) %8.2e %s\n",
(int) N, (int) nrhs, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed"));
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( work );
TESTING_FREE_CPU( ipiv );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing sgeqrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
const float d_neg_one = MAGMA_D_NEG_ONE;
const float d_one = MAGMA_D_ONE;
const float c_neg_one = MAGMA_S_NEG_ONE;
const float c_one = MAGMA_S_ONE;
const float c_zero = MAGMA_S_ZERO;
const magma_int_t ione = 1;
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf=0, cpu_time=0;
float Anorm, error=0, error2=0;
float *h_A, *h_R, *tau, *h_work, tmp[1];
magmaFloat_ptr d_A, dT;
magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn, nb, size;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
opts.parse_opts( argc, argv );
magma_int_t status = 0;
float tol = opts.tolerance * lapackf77_slamch("E");
// version 3 can do either check
if (opts.check == 1 && opts.version == 1) {
opts.check = 2;
printf( "%% version 1 requires check 2 (solve A*x=b)\n" );
}
if (opts.check == 2 && opts.version == 2) {
opts.check = 1;
printf( "%% version 2 requires check 1 (R - Q^H*A)\n" );
}
printf( "%% version %d\n", (int) opts.version );
if ( opts.check == 1 ) {
printf("%% M N CPU Gflop/s (sec) GPU Gflop/s (sec) |R - Q^H*A| |I - Q^H*Q|\n");
printf("%%==============================================================================\n");
}
else {
printf("%% M N CPU Gflop/s (sec) GPU Gflop/s (sec) |b - A*x|\n");
printf("%%===============================================================\n");
}
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
min_mn = min( M, N );
lda = M;
n2 = lda*N;
ldda = magma_roundup( M, opts.align ); // multiple of 32 by default
nb = magma_get_sgeqrf_nb( M, N );
gflops = FLOPS_SGEQRF( M, N ) / 1e9;
// query for workspace size
lwork = -1;
lapackf77_sgeqrf( &M, &N, NULL, &M, NULL, tmp, &lwork, &info );
lwork = (magma_int_t)MAGMA_S_REAL( tmp[0] );
TESTING_MALLOC_CPU( tau, float, min_mn );
TESTING_MALLOC_CPU( h_A, float, n2 );
TESTING_MALLOC_CPU( h_work, float, lwork );
TESTING_MALLOC_PIN( h_R, float, n2 );
TESTING_MALLOC_DEV( d_A, float, ldda*N );
if ( opts.version == 1 || opts.version == 3 ) {
size = (2*min(M, N) + magma_roundup( N, 32 ) )*nb;
TESTING_MALLOC_DEV( dT, float, size );
magmablas_slaset( MagmaFull, size, 1, c_zero, c_zero, dT, size );
}
/* Initialize the matrix */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
lapackf77_slacpy( MagmaFullStr, &M, &N, h_A, &lda, h_R, &lda );
magma_ssetmatrix( M, N, h_R, lda, d_A, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
nb = magma_get_sgeqrf_nb( M, N );
gpu_time = magma_wtime();
if ( opts.version == 1 ) {
// stores dT, V blocks have zeros, R blocks inverted & stored in dT
magma_sgeqrf_gpu( M, N, d_A, ldda, tau, dT, &info );
}
else if ( opts.version == 2 ) {
// LAPACK complaint arguments
magma_sgeqrf2_gpu( M, N, d_A, ldda, tau, &info );
}
#ifdef HAVE_CUBLAS
else if ( opts.version == 3 ) {
// stores dT, V blocks have zeros, R blocks stored in dT
magma_sgeqrf3_gpu( M, N, d_A, ldda, tau, dT, &info );
}
#endif
else {
printf( "Unknown version %d\n", (int) opts.version );
return -1;
}
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_sgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
if ( opts.check == 1 && (opts.version == 2 || opts.version == 3) ) {
if ( opts.version == 3 ) {
// copy diagonal blocks of R back to A
for( int i=0; i < min_mn-nb; i += nb ) {
magma_int_t ib = min( min_mn-i, nb );
magmablas_slacpy( MagmaUpper, ib, ib, &dT[min_mn*nb + i*nb], nb, &d_A[ i + i*ldda ], ldda );
}
}
/* =====================================================================
Check the result, following zqrt01 except using the reduced Q.
This works for any M,N (square, tall, wide).
Only for version 2, which has LAPACK complaint output.
Or for version 3, after restoring diagonal blocks of A above.
=================================================================== */
magma_sgetmatrix( M, N, d_A, ldda, h_R, lda );
magma_int_t ldq = M;
magma_int_t ldr = min_mn;
float *Q, *R;
float *work;
TESTING_MALLOC_CPU( Q, float, ldq*min_mn ); // M by K
TESTING_MALLOC_CPU( R, float, ldr*N ); // K by N
TESTING_MALLOC_CPU( work, float, min_mn );
// generate M by K matrix Q, where K = min(M,N)
lapackf77_slacpy( "Lower", &M, &min_mn, h_R, &lda, Q, &ldq );
lapackf77_sorgqr( &M, &min_mn, &min_mn, Q, &ldq, tau, h_work, &lwork, &info );
assert( info == 0 );
// copy K by N matrix R
lapackf77_slaset( "Lower", &min_mn, &N, &c_zero, &c_zero, R, &ldr );
lapackf77_slacpy( "Upper", &min_mn, &N, h_R, &lda, R, &ldr );
// error = || R - Q^H*A || / (N * ||A||)
blasf77_sgemm( "Conj", "NoTrans", &min_mn, &N, &M,
&c_neg_one, Q, &ldq, h_A, &lda, &c_one, R, &ldr );
Anorm = lapackf77_slange( "1", &M, &N, h_A, &lda, work );
error = lapackf77_slange( "1", &min_mn, &N, R, &ldr, work );
if ( N > 0 && Anorm > 0 )
error /= (N*Anorm);
// set R = I (K by K identity), then R = I - Q^H*Q
// error = || I - Q^H*Q || / N
lapackf77_slaset( "Upper", &min_mn, &min_mn, &c_zero, &c_one, R, &ldr );
blasf77_ssyrk( "Upper", "Conj", &min_mn, &M, &d_neg_one, Q, &ldq, &d_one, R, &ldr );
error2 = safe_lapackf77_slansy( "1", "Upper", &min_mn, R, &ldr, work );
if ( N > 0 )
error2 /= N;
TESTING_FREE_CPU( Q ); Q = NULL;
TESTING_FREE_CPU( R ); R = NULL;
TESTING_FREE_CPU( work ); work = NULL;
}
else if ( opts.check == 2 && M >= N && (opts.version == 1 || opts.version == 3) ) {
/* =====================================================================
Check the result by solving consistent linear system, A*x = b.
Only for versions 1 & 3 with M >= N.
=================================================================== */
magma_int_t lwork2;
float *x, *b, *hwork;
magmaFloat_ptr d_B;
// initialize RHS, b = A*random
TESTING_MALLOC_CPU( x, float, N );
TESTING_MALLOC_CPU( b, float, M );
lapackf77_slarnv( &ione, ISEED, &N, x );
blasf77_sgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_zero, b, &ione );
// copy to GPU
TESTING_MALLOC_DEV( d_B, float, M );
magma_ssetvector( M, b, 1, d_B, 1 );
if ( opts.version == 1 ) {
// allocate hwork
magma_sgeqrs_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, tmp, -1, &info );
lwork2 = (magma_int_t)MAGMA_S_REAL( tmp[0] );
TESTING_MALLOC_CPU( hwork, float, lwork2 );
// solve linear system
magma_sgeqrs_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, hwork, lwork2, &info );
if (info != 0) {
printf("magma_sgeqrs returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
TESTING_FREE_CPU( hwork );
}
#ifdef HAVE_CUBLAS
else if ( opts.version == 3 ) {
// allocate hwork
magma_sgeqrs3_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, tmp, -1, &info );
lwork2 = (magma_int_t)MAGMA_S_REAL( tmp[0] );
TESTING_MALLOC_CPU( hwork, float, lwork2 );
// solve linear system
magma_sgeqrs3_gpu( M, N, 1,
d_A, ldda, tau, dT,
d_B, M, hwork, lwork2, &info );
if (info != 0) {
printf("magma_sgeqrs3 returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
TESTING_FREE_CPU( hwork );
}
#endif
else {
printf( "Unknown version %d\n", (int) opts.version );
return -1;
}
magma_sgetvector( N, d_B, 1, x, 1 );
// compute r = Ax - b, saved in b
blasf77_sgemv( "Notrans", &M, &N, &c_one, h_A, &lda, x, &ione, &c_neg_one, b, &ione );
// compute residual |Ax - b| / (max(m,n)*|A|*|x|)
float norm_x, norm_A, norm_r, work[1];
norm_A = lapackf77_slange( "F", &M, &N, h_A, &lda, work );
norm_r = lapackf77_slange( "F", &M, &ione, b, &M, work );
norm_x = lapackf77_slange( "F", &N, &ione, x, &N, work );
TESTING_FREE_CPU( x );
TESTING_FREE_CPU( b );
TESTING_FREE_DEV( d_B );
error = norm_r / (max(M,N) * norm_A * norm_x);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_sgeqrf( &M, &N, h_A, &lda, tau, h_work, &lwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_sgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
}
/* =====================================================================
Print performance and error.
=================================================================== */
printf("%5d %5d ", (int) M, (int) N );
if ( opts.lapack ) {
printf( "%7.2f (%7.2f)", cpu_perf, cpu_time );
}
else {
printf(" --- ( --- )" );
}
printf( " %7.2f (%7.2f) ", gpu_perf, gpu_time );
if ( opts.check == 1 ) {
bool okay = (error < tol && error2 < tol);
status += ! okay;
printf( "%11.2e %11.2e %s\n", error, error2, (okay ? "ok" : "failed") );
}
else if ( opts.check == 2 ) {
if ( M >= N ) {
bool okay = (error < tol);
status += ! okay;
printf( "%10.2e %s\n", error, (okay ? "ok" : "failed") );
}
else {
printf( "(error check only for M >= N)\n" );
}
}
else {
printf( " ---\n" );
}
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_work );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
if ( opts.version == 1 || opts.version == 3 ) {
TESTING_FREE_DEV( dT );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgeqrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex *h_A, *h_R, *tau, *dtau, *h_work, tmp[1];
magmaFloatComplex *d_A;
float *dwork;
magma_int_t M, N, n2, lda, ldda, lwork, info, min_mn;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
printf(" M N CPU GFlop/s (ms) GPU GFlop/s (ms) ||R||_F / ||A||_F\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];
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = FLOPS_CGEQRF( M, N ) / 1e9;
lwork = -1;
lapackf77_cgeqrf(&M, &N, h_A, &M, tau, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_C_REAL( tmp[0] );
TESTING_MALLOC( tau, magmaFloatComplex, min_mn );
TESTING_MALLOC( h_A, magmaFloatComplex, n2 );
TESTING_HOSTALLOC( h_R, magmaFloatComplex, n2 );
TESTING_DEVALLOC( d_A, magmaFloatComplex, ldda*N );
TESTING_DEVALLOC( dtau, magmaFloatComplex, min_mn );
TESTING_DEVALLOC(dwork, float, min_mn );
TESTING_MALLOC( h_work, magmaFloatComplex, lwork );
/* Initialize the matrix */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
lapackf77_clacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_csetmatrix( M, N, h_R, lda, d_A, ldda );
// warmup
magma_cgeqr2_gpu( M, N, d_A, ldda, dtau, dwork, &info );
magma_csetmatrix( M, N, h_R, lda, d_A, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_sync_wtime( 0 );
magma_cgeqr2_gpu( M, N, d_A, ldda, dtau, dwork, &info );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_cgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.lapack ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_cgeqrf(&M, &N, h_A, &lda, tau, h_work, &lwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_cgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
magma_cgetmatrix( M, N, d_A, ldda, h_R, M );
error = lapackf77_clange("f", &M, &N, h_A, &lda, work);
blasf77_caxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_clange("f", &M, &N, h_R, &lda, work) / error;
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e\n",
(int) M, (int) N, cpu_perf, 1000.*cpu_time, gpu_perf, 1000.*gpu_time, error );
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, 1000.*gpu_time );
}
TESTING_FREE( tau );
TESTING_FREE( h_A );
TESTING_FREE( h_work );
TESTING_HOSTFREE( h_R );
TESTING_DEVFREE( d_A );
TESTING_DEVFREE( dtau );
TESTING_DEVFREE( dwork );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ssygvdx
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time /*cpu_time*/;
float *h_A, *h_R, *h_B, *h_S, *h_work;
float *w1, *w2, vl=0, vu=0;
float result[2] = {0};
magma_int_t *iwork;
magma_int_t N, n2, info, il, iu, m1, m2, nb, lwork, liwork;
float c_zero = MAGMA_S_ZERO;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
#if defined(PRECISION_z) || defined(PRECISION_c)
float *rwork;
magma_int_t lrwork;
#endif
//float d_one = 1.;
//float d_ten = 10.;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
float tolulp = opts.tolerance * lapackf77_slamch("P");
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf(" N M GPU Time (sec)\n");
printf("============================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
n2 = N*N;
nb = magma_get_ssytrd_nb(N);
#if defined(PRECISION_z) || defined(PRECISION_c)
lwork = 2*N*nb + N*N;
lrwork = 1 + 5*N +2*N*N;
#else
lwork = 1 + 6*N*nb + 2* N*N;
#endif
liwork = 3 + 5*N;
if ( opts.fraction == 0 ) {
il = N / 10;
iu = N / 5+il;
}
else {
il = 1;
iu = (int) (opts.fraction*N);
if (iu < 1) iu = 1;
}
TESTING_MALLOC( h_A, float, n2 );
TESTING_MALLOC( h_B, float, n2 );
TESTING_MALLOC( w1, float, N );
TESTING_MALLOC( w2, float, N );
TESTING_MALLOC( iwork, magma_int_t, liwork );
TESTING_HOSTALLOC( h_R, float, n2 );
TESTING_HOSTALLOC( h_S, float, n2 );
TESTING_HOSTALLOC( h_work, float, lwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_HOSTALLOC( rwork, float, lrwork);
#endif
/* Initialize the matrix */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
lapackf77_slarnv( &ione, ISEED, &n2, h_B );
/* increase the diagonal */
for(int i=0; i<N; i++) {
MAGMA_S_SET2REAL( h_B[i*N+i], ( MAGMA_S_REAL(h_B[i*N+i]) + 1.*N ) );
MAGMA_S_SET2REAL( h_A[i*N+i], MAGMA_S_REAL(h_A[i*N+i]) );
}
// ==================================================================
// Warmup using MAGMA
// ==================================================================
if(opts.warmup){
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_ssygvdx( opts.itype, opts.jobz, 'I', opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info );
if (info != 0)
printf("magma_ssygvdx returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
gpu_time = magma_wtime();
magma_ssygvdx( opts.itype, opts.jobz, 'I', opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m1, w1,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info );
gpu_time = magma_wtime() - gpu_time;
if (info != 0)
printf("magma_ssygvdx returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.check ) {
/* =====================================================================
Check the results following the LAPACK's [zc]hegvdx routine.
A x = lambda B x is solved
and the following 3 tests computed:
(1) | A Z - B Z D | / ( |A||Z| N ) (itype = 1)
| A B Z - Z D | / ( |A||Z| N ) (itype = 2)
| B A Z - Z D | / ( |A||Z| N ) (itype = 3)
(2) | S(with V) - S(w/o V) | / | S |
=================================================================== */
#if defined(PRECISION_d) || defined(PRECISION_s)
float *rwork = h_work + N*N;
#endif
float temp1, temp2;
result[0] = 1.;
result[0] /= lapackf77_slansy("1", &opts.uplo, &N, h_A, &N, rwork);
result[0] /= lapackf77_slange("1", &N, &m1, h_R, &N, rwork);
if (opts.itype == 1) {
blasf77_ssymm("L", &opts.uplo, &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i < m1; ++i)
blasf77_sscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_ssymm("L", &opts.uplo, &N, &m1, &c_neg_one, h_B, &N, h_R, &N, &c_one, h_work, &N);
result[0] *= lapackf77_slange("1", &N, &m1, h_work, &N, rwork)/N;
}
else if (opts.itype == 2) {
blasf77_ssymm("L", &opts.uplo, &N, &m1, &c_one, h_B, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i < m1; ++i)
blasf77_sscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_ssymm("L", &opts.uplo, &N, &m1, &c_one, h_A, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_slange("1", &N, &m1, h_R, &N, rwork)/N;
}
else if (opts.itype == 3) {
blasf77_ssymm("L", &opts.uplo, &N, &m1, &c_one, h_A, &N, h_R, &N, &c_zero, h_work, &N);
for(int i=0; i < m1; ++i)
blasf77_sscal(&N, &w1[i], &h_R[i*N], &ione);
blasf77_ssymm("L", &opts.uplo, &N, &m1, &c_one, h_B, &N, h_work, &N, &c_neg_one, h_R, &N);
result[0] *= lapackf77_slange("1", &N, &m1, h_R, &N, rwork)/N;
}
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &N, h_R, &N );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_B, &N, h_S, &N );
magma_ssygvdx( opts.itype, 'N', 'I', opts.uplo,
N, h_R, N, h_S, N, vl, vu, il, iu, &m2, w2,
h_work, lwork,
#if defined(PRECISION_z) || defined(PRECISION_c)
rwork, lrwork,
#endif
iwork, liwork,
&info );
if (info != 0)
printf("magma_ssygvdx returned error %d: %s.\n",
(int) info, magma_strerror( info ));
temp1 = temp2 = 0;
for(int j=0; j < m2; j++) {
temp1 = max(temp1, absv(w1[j]));
temp1 = max(temp1, absv(w2[j]));
temp2 = max(temp2, absv(w1[j]-w2[j]));
}
result[1] = temp2 / (((float)m2)*temp1);
}
/* =====================================================================
Print execution time
=================================================================== */
printf("%5d %5d %7.2f\n",
(int) N, (int) m1, gpu_time);
if ( opts.check ) {
printf("Testing the eigenvalues and eigenvectors for correctness:\n");
if (opts.itype==1)
printf("(1) | A Z - B Z D | / (|A| |Z| N) = %8.2e%s\n", result[0], (result[0] < tol ? "" : " failed"));
else if (opts.itype==2)
printf("(1) | A B Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result[0], (result[0] < tol ? "" : " failed"));
else if (opts.itype==3)
printf("(1) | B A Z - Z D | / (|A| |Z| N) = %8.2e%s\n", result[0], (result[0] < tol ? "" : " failed"));
printf( "(2) | D(w/ Z) - D(w/o Z) | / |D| = %8.2e%s\n\n", result[1], (result[1] < tolulp ? "" : " failed"));
}
TESTING_FREE( h_A );
TESTING_FREE( h_B );
TESTING_FREE( w1 );
TESTING_FREE( w2 );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_HOSTFREE( rwork);
#endif
TESTING_FREE( iwork );
TESTING_HOSTFREE( h_work );
TESTING_HOSTFREE( h_R );
TESTING_HOSTFREE( h_S );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dsyevd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gpu_time, cpu_time;
double *h_A, *h_R, *h_work;
double *w1, *w2;
magma_int_t *iwork;
magma_int_t N, n2, info, lwork, liwork, lda, aux_iwork[1];
magma_int_t izero = 0;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
double result[3], eps, aux_work[1];
eps = lapackf77_dlamch( "E" );
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
double tolulp = opts.tolerance * lapackf77_dlamch("P");
if ( opts.check && opts.jobz == MagmaNoVec ) {
fprintf( stderr, "checking results requires vectors; setting jobz=V (option -JV)\n" );
opts.jobz = MagmaVec;
}
printf("using: jobz = %s, uplo = %s\n",
lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo));
printf(" N CPU Time (sec) GPU Time (sec)\n");
printf("=======================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
n2 = N*N;
lda = N;
// query for workspace sizes
magma_dsyevd( opts.jobz, opts.uplo,
N, NULL, lda, NULL,
aux_work, -1,
aux_iwork, -1,
opts.queue, &info );
lwork = (magma_int_t) aux_work[0];
liwork = aux_iwork[0];
/* Allocate host memory for the matrix */
TESTING_MALLOC_CPU( h_A, double, N*lda );
TESTING_MALLOC_CPU( w1, double, N );
TESTING_MALLOC_CPU( w2, double, N );
TESTING_MALLOC_CPU( iwork, magma_int_t, liwork );
TESTING_MALLOC_PIN( h_R, double, N*lda );
TESTING_MALLOC_PIN( h_work, double, lwork );
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* warm up run */
if ( opts.warmup ) {
magma_dsyevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
iwork, liwork,
opts.queue, &info );
if (info != 0)
printf("magma_dsyevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_dsyevd( opts.jobz, opts.uplo,
N, h_R, lda, w1,
h_work, lwork,
iwork, liwork,
opts.queue, &info );
gpu_time = magma_wtime() - gpu_time;
if (info != 0)
printf("magma_dsyevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.check ) {
/* =====================================================================
Check the results following the LAPACK's [zcds]drvst routine.
A is factored as A = U S U' and the following 3 tests computed:
(1) | A - U S U' | / ( |A| N )
(2) | I - U'U | / ( N )
(3) | S(with U) - S(w/o U) | / | S |
=================================================================== */
double temp1, temp2;
// tau=NULL is unused since itype=1
lapackf77_dsyt21( &ione, lapack_uplo_const(opts.uplo), &N, &izero,
h_A, &lda,
w1, h_work,
h_R, &lda,
h_R, &lda,
NULL, h_work, &result[0] );
lapackf77_dlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
magma_dsyevd( MagmaNoVec, opts.uplo,
N, h_R, lda, w2,
h_work, lwork,
iwork, liwork,
opts.queue, &info );
if (info != 0)
printf("magma_dsyevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
temp1 = temp2 = 0;
for( int j=0; j<N; j++ ) {
temp1 = max(temp1, fabs(w1[j]));
temp1 = max(temp1, fabs(w2[j]));
temp2 = max(temp2, fabs(w1[j]-w2[j]));
}
result[2] = temp2 / (((double)N)*temp1);
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_dsyevd( lapack_vec_const(opts.jobz), lapack_uplo_const(opts.uplo),
&N, h_A, &lda, w2,
h_work, &lwork,
iwork, &liwork,
&info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0)
printf("lapackf77_dsyevd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
printf("%5d %7.2f %7.2f\n",
(int) N, cpu_time, gpu_time);
}
else {
printf("%5d --- %7.2f\n",
(int) N, gpu_time);
}
/* =====================================================================
Print execution time
=================================================================== */
if ( opts.check ) {
printf("Testing the factorization A = U S U' for correctness:\n");
printf("(1) | A - U S U' | / (|A| N) = %8.2e %s\n", result[0]*eps, (result[0]*eps < tol ? "ok" : "failed") );
printf("(2) | I - U'U | / N = %8.2e %s\n", result[1]*eps, (result[1]*eps < tol ? "ok" : "failed") );
printf("(3) | S(w/ U) - S(w/o U) | / |S| = %8.2e %s\n\n", result[2] , (result[2] < tolulp ? "ok" : "failed") );
status += ! (result[0]*eps < tol && result[1]*eps < tol && result[2] < tolulp);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( w1 );
TESTING_FREE_CPU( w2 );
TESTING_FREE_CPU( iwork );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dgeqrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
double error, work[1];
double c_neg_one = MAGMA_D_NEG_ONE;
double *h_A, *h_T, *h_R, *tau, *h_work, tmp[1];
double *d_A, *d_T, *ddA, *dtau;
double *d_A2, *d_T2, *ddA2, *dtau2;
double *dwork, *dwork2;
magma_int_t M, N, lda, ldda, lwork, n2, info, min_mn;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
#define BLOCK_SIZE 64
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = 10. * opts.tolerance * lapackf77_dlamch("E");
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
printf("version %d\n", (int) opts.version );
printf(" M N CPU GFlop/s (ms) GPU GFlop/s (ms) ||R||_F/||A||_F ||R_T||\n");
printf("=============================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
if (N > 128) {
printf("%5d %5d skipping because dgeqr2x requires N <= 128\n",
(int) M, (int) N);
continue;
}
if (M < N) {
printf("%5d %5d skipping because dgeqr2x requires M >= N\n",
(int) M, (int) N);
continue;
}
min_mn = min(M, N);
lda = M;
n2 = lda*N;
ldda = ((M+31)/32)*32;
gflops = (FLOPS_DGEQRF( M, N ) + FLOPS_DGEQRT( M, N )) / 1e9;
/* Allocate memory for the matrix */
TESTING_MALLOC_CPU( tau, double, min_mn );
TESTING_MALLOC_CPU( h_A, double, n2 );
TESTING_MALLOC_CPU( h_T, double, N*N );
TESTING_MALLOC_PIN( h_R, double, n2 );
TESTING_MALLOC_DEV( d_A, double, ldda*N );
TESTING_MALLOC_DEV( d_T, double, N*N );
TESTING_MALLOC_DEV( ddA, double, N*N );
TESTING_MALLOC_DEV( dtau, double, min_mn );
TESTING_MALLOC_DEV( d_A2, double, ldda*N );
TESTING_MALLOC_DEV( d_T2, double, N*N );
TESTING_MALLOC_DEV( ddA2, double, N*N );
TESTING_MALLOC_DEV( dtau2, double, min_mn );
TESTING_MALLOC_DEV( dwork, double, max(5*min_mn, (BLOCK_SIZE*2+2)*min_mn) );
TESTING_MALLOC_DEV( dwork2, double, max(5*min_mn, (BLOCK_SIZE*2+2)*min_mn) );
// todo replace with magma_dlaset
cudaMemset(ddA, 0, N*N*sizeof(double));
cudaMemset(d_T, 0, N*N*sizeof(double));
cudaMemset(ddA2, 0, N*N*sizeof(double));
cudaMemset(d_T2, 0, N*N*sizeof(double));
lwork = -1;
lapackf77_dgeqrf(&M, &N, NULL, &M, NULL, tmp, &lwork, &info);
lwork = (magma_int_t)MAGMA_D_REAL( tmp[0] );
lwork = max(lwork, N*N);
TESTING_MALLOC_CPU( h_work, double, lwork );
/* Initialize the matrix */
lapackf77_dlarnv( &ione, ISEED, &n2, h_A );
lapackf77_dlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_R, &lda );
magma_dsetmatrix( M, N, h_R, lda, d_A, ldda );
magma_dsetmatrix( M, N, h_R, lda, d_A2, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_sync_wtime(0);
if (opts.version == 1)
magma_dgeqr2x_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info);
else if (opts.version == 2)
magma_dgeqr2x2_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info);
else if (opts.version == 3)
magma_dgeqr2x3_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info);
else {
printf( "call magma_dgeqr2x4_gpu\n" );
/*
Going through NULL stream is faster
Going through any stream is slower
Doing two streams in parallel is slower than doing them sequentially
Queuing happens on the NULL stream - user defined buffers are smaller?
*/
magma_dgeqr2x4_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info, NULL);
//magma_dgeqr2x4_gpu(M, N, d_A, ldda, dtau, d_T, ddA, dwork, &info, stream[1]);
//magma_dgeqr2x4_gpu(M, N, d_A2, ldda, dtau2, d_T2, ddA2, dwork2, &info, stream[0]);
//magma_dgeqr2x4_gpu(M, N, d_A2, ldda, dtau2, d_T2, ddA2, dwork2, &info, NULL);
//gflops *= 2;
}
gpu_time = magma_sync_wtime(0) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dgeqr2x_gpu version %d returned error %d: %s.\n",
(int) opts.version, (int) info, magma_strerror( info ));
}
else {
if ( opts.check ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_dgeqrf(&M, &N, h_A, &lda, tau, h_work, &lwork, &info);
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&M, &N, h_A, &lda, tau, h_work, &N);
//magma_dgeqr2(&M, &N, h_A, &lda, tau, h_work, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_dgeqrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
magma_dgetmatrix( M, N, d_A, ldda, h_R, M );
magma_dgetmatrix( N, N, ddA, N, h_T, N );
// Restore the upper triangular part of A before the check
for(int col=0; col < N; col++){
for(int row=0; row <= col; row++)
h_R[row + col*M] = h_T[row + col*N];
}
error = lapackf77_dlange("M", &M, &N, h_A, &lda, work);
blasf77_daxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_dlange("M", &M, &N, h_R, &lda, work) / (N * error);
// Check if T is the same
magma_dgetmatrix( N, N, d_T, N, h_T, N );
double terr = 0.;
for(int col=0; col < N; col++)
for(int row=0; row <= col; row++)
terr += ( MAGMA_D_ABS(h_work[row + col*N] - h_T[row + col*N])*
MAGMA_D_ABS(h_work[row + col*N] - h_T[row + col*N]) );
terr = magma_dsqrt(terr);
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %s\n",
(int) M, (int) N, cpu_perf, 1000.*cpu_time, gpu_perf, 1000.*gpu_time,
error, terr, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
}
else {
printf("%5d %5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) M, (int) N, gpu_perf, 1000.*gpu_time);
}
}
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_T );
TESTING_FREE_CPU( h_work );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_T );
TESTING_FREE_DEV( ddA );
TESTING_FREE_DEV( dtau );
TESTING_FREE_DEV( dwork );
TESTING_FREE_DEV( d_A2 );
TESTING_FREE_DEV( d_T2 );
TESTING_FREE_DEV( ddA2 );
TESTING_FREE_DEV( dtau2 );
TESTING_FREE_DEV( dwork2 );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zcgeqrsv
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time, gpu_perfd, gpu_perfs;
double error, gpu_error, cpu_error, Anorm, work[1];
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *h_A, *h_A2, *h_B, *h_X, *h_R;
magmaDoubleComplex_ptr d_A, d_B, d_X, d_T;
magmaFloatComplex *d_SA, *d_SB;
magmaDoubleComplex *h_workd, *tau, tmp[1];
magmaFloatComplex *h_works;
magma_int_t lda, ldb, lhwork, lworkgpu;
magma_int_t ldda, lddb, lddx;
magma_int_t M, N, nrhs, qrsv_iters, info, size, min_mn, max_mn, nb;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
printf("Epsilon(double): %8.6e\n"
"Epsilon(single): %8.6e\n\n",
lapackf77_dlamch("Epsilon"), lapackf77_slamch("Epsilon") );
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
nrhs = opts.nrhs;
printf(" CPU Gflop/s GPU Gflop/s |b-Ax|| / (N||A||) ||dx-x||/(N||A||)\n");
printf(" M N NRHS double double single mixed Iter CPU GPU \n");
printf("=============================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
if ( M < N ) {
printf( "%5d %5d %5d skipping because M < N is not yet supported.\n", (int) M, (int) N, (int) nrhs );
continue;
}
min_mn = min(M, N);
max_mn = max(M, N);
lda = M;
ldb = max_mn;
ldda = ((M+31)/32) * 32;
lddb = ((max_mn+31)/32)*32;
lddx = ((N+31)/32) * 32;
nb = max( magma_get_zgeqrf_nb( M ), magma_get_cgeqrf_nb( M ) );
gflops = (FLOPS_ZGEQRF( M, N ) + FLOPS_ZGEQRS( M, N, nrhs )) / 1e9;
lworkgpu = (M - N + nb)*(nrhs + nb) + nrhs*nb;
// query for workspace size
lhwork = -1;
lapackf77_zgels( MagmaNoTransStr, &M, &N, &nrhs,
NULL, &lda, NULL, &ldb, tmp, &lhwork, &info );
lhwork = (magma_int_t) MAGMA_Z_REAL( tmp[0] );
lhwork = max( lhwork, lworkgpu );
TESTING_MALLOC_CPU( tau, magmaDoubleComplex, min_mn );
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( h_A2, magmaDoubleComplex, lda*N );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( h_X, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( h_R, magmaDoubleComplex, ldb*nrhs );
TESTING_MALLOC_CPU( h_workd, magmaDoubleComplex, lhwork );
h_works = (magmaFloatComplex*)h_workd;
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( d_B, magmaDoubleComplex, lddb*nrhs );
TESTING_MALLOC_DEV( d_X, magmaDoubleComplex, lddx*nrhs );
TESTING_MALLOC_DEV( d_T, magmaDoubleComplex, ( 2*min_mn + (N+31)/32*32 )*nb );
/* Initialize the matrices */
size = lda*N;
lapackf77_zlarnv( &ione, ISEED, &size, h_A );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &N, h_A, &lda, h_A2, &lda );
// make random RHS
size = ldb*nrhs;
lapackf77_zlarnv( &ione, ISEED, &size, h_B );
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_R, &ldb );
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
//=====================================================================
// Mixed Precision Iterative Refinement - GPU
//=====================================================================
gpu_time = magma_wtime();
magma_zcgeqrsv_gpu( M, N, nrhs,
d_A, ldda, d_B, lddb,
d_X, lddx, &qrsv_iters, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zcgeqrsv returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute the residual
magma_zgetmatrix( N, nrhs, d_X, lddx, h_X, ldb );
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A, &lda,
h_X, &ldb,
&c_one, h_R, &ldb);
Anorm = lapackf77_zlange("f", &M, &N, h_A, &lda, work);
//=====================================================================
// Double Precision Solve
//=====================================================================
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
gpu_time = magma_wtime();
magma_zgels_gpu( MagmaNoTrans, M, N, nrhs, d_A, ldda,
d_B, lddb, h_workd, lworkgpu, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perfd = gflops / gpu_time;
//=====================================================================
// Single Precision Solve
//=====================================================================
magma_zsetmatrix( M, N, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, nrhs, h_B, ldb, d_B, lddb );
/* The allocation of d_SA and d_SB is done here to avoid
* to double the memory used on GPU with zcgeqrsv */
TESTING_MALLOC_DEV( d_SA, magmaFloatComplex, ldda*N );
TESTING_MALLOC_DEV( d_SB, magmaFloatComplex, lddb*nrhs );
magmablas_zlag2c( M, N, d_A, ldda, d_SA, ldda, &info );
magmablas_zlag2c( N, nrhs, d_B, lddb, d_SB, lddb, &info );
gpu_time = magma_wtime();
magma_cgels_gpu( MagmaNoTrans, M, N, nrhs, d_SA, ldda,
d_SB, lddb, h_works, lhwork, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perfs = gflops / gpu_time;
TESTING_FREE_DEV( d_SA );
TESTING_FREE_DEV( d_SB );
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
lapackf77_zlacpy( MagmaUpperLowerStr, &M, &nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_zgels( MagmaNoTransStr, &M, &N, &nrhs,
h_A, &lda, h_X, &ldb, h_workd, &lhwork, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zgels returned error %d: %s.\n",
(int) info, magma_strerror( info ));
blasf77_zgemm( MagmaNoTransStr, MagmaNoTransStr, &M, &nrhs, &N,
&c_neg_one, h_A2, &lda,
h_X, &ldb,
&c_one, h_B, &ldb );
cpu_error = lapackf77_zlange("f", &M, &nrhs, h_B, &ldb, work) / (min_mn*Anorm);
gpu_error = lapackf77_zlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*Anorm);
// error relative to LAPACK
size = M*nrhs;
blasf77_zaxpy( &size, &c_neg_one, h_B, &ione, h_R, &ione );
error = lapackf77_zlange("f", &M, &nrhs, h_R, &ldb, work) / (min_mn*Anorm);
printf("%5d %5d %5d %7.2f %7.2f %7.2f %7.2f %4d %8.2e %8.2e %8.2e %s\n",
(int) M, (int) N, (int) nrhs,
cpu_perf, gpu_perfd, gpu_perfs, gpu_perf,
(int) qrsv_iters,
cpu_error, gpu_error, error, (error < tol ? "ok" : "failed"));
status += ! (error < tol);
TESTING_FREE_CPU( tau );
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_A2 );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( h_R );
TESTING_FREE_CPU( h_workd );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
TESTING_FREE_DEV( d_X );
TESTING_FREE_DEV( d_T );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
int main( int argc, char** argv )
{
magma_init();
cublasHandle_t handle;
cudaSetDevice( 0 );
cublasCreate( &handle );
double *A, *B, *C;
double *dA, *dB, *dC;
double error, work[1];
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = { 1, 2, 3, 4 };
magma_int_t n = 10;
magma_int_t lda = n;
magma_int_t ldda = ((n+31)/32)*32;
magma_int_t size = lda*n;
magma_int_t info;
magma_dmalloc_cpu( &A, lda*n );
magma_dmalloc_cpu( &B, lda*n );
magma_dmalloc_cpu( &C, lda*n );
magma_dmalloc( &dA, ldda*n );
magma_dmalloc( &dB, ldda*n );
magma_dmalloc( &dC, ldda*n );
// initialize matrices
lapackf77_dlarnv( &ione, ISEED, &size, A );
lapackf77_dlarnv( &ione, ISEED, &size, B );
lapackf77_dlarnv( &ione, ISEED, &size, C );
// increase diagonal to be SPD
for( int i=0; i < n; ++i ) {
C[i+i*lda] = MAGMA_D_ADD( C[i+i*lda], MAGMA_D_MAKE( n*n, 0 ));
}
magma_dsetmatrix( n, n, A, lda, dA, ldda );
magma_dsetmatrix( n, n, B, lda, dB, ldda );
magma_dsetmatrix( n, n, C, lda, dC, ldda );
// compute with cublas
cublasDgemm( handle, CUBLAS_OP_N, CUBLAS_OP_N, n, n, n,
&c_neg_one, dA, ldda, dB, ldda, &c_one, dC, ldda );
magma_dpotrf_gpu( MagmaLower, n, dC, ldda, &info );
if (info != 0)
printf("magma_dpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute with LAPACK
blasf77_dgemm( MagmaNoTransStr, MagmaNoTransStr, &n, &n, &n,
&c_neg_one, A, &lda, B, &lda, &c_one, C, &lda );
lapackf77_dpotrf( MagmaLowerStr, &n, C, &lda, &info );
if (info != 0)
printf("lapackf77_dpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
// compute difference
magma_dgetmatrix( n, n, dC, ldda, A, lda );
blasf77_daxpy( &size, &c_neg_one, C, &ione, A, &ione );
error = lapackf77_dlange( "F", &n, &n, A, &lda, work );
printf( "n %d, error %8.2e\n", n, error );
magma_free( dA );
magma_free( dB );
magma_free( dC );
magma_free_cpu( A );
magma_free_cpu( B );
magma_free_cpu( C );
cublasDestroy( handle );
magma_finalize();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cgehrd
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaFloatComplex *h_A, *h_R, *h_Q, *h_work, *tau, *twork;
magmaFloatComplex_ptr dT;
#if defined(PRECISION_z) || defined(PRECISION_c)
float *rwork;
#endif
float eps, result[2];
magma_int_t N, n2, lda, nb, lwork, ltwork, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
eps = lapackf77_slamch( "E" );
magma_opts opts;
parse_opts( argc, argv, &opts );
float tol = opts.tolerance * lapackf77_slamch("E");
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) |A-QHQ'|/N|A| |I-QQ'|/N\n");
printf("=========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N;
nb = magma_get_cgehrd_nb(N);
/* We suppose the magma nb is bigger than lapack nb */
lwork = N*nb;
gflops = FLOPS_CGEHRD( N ) / 1e9;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, n2 );
TESTING_MALLOC_CPU( tau, magmaFloatComplex, N );
TESTING_MALLOC_PIN( h_R, magmaFloatComplex, n2 );
TESTING_MALLOC_PIN( h_work, magmaFloatComplex, lwork );
TESTING_MALLOC_DEV( dT, magmaFloatComplex, nb*N );
/* Initialize the matrices */
lapackf77_clarnv( &ione, ISEED, &n2, h_A );
lapackf77_clacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_cgehrd( N, ione, N, h_R, lda, tau, h_work, lwork, dT, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_cgehrd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.check ) {
ltwork = 2*(N*N);
TESTING_MALLOC_PIN( h_Q, magmaFloatComplex, lda*N );
TESTING_MALLOC_CPU( twork, magmaFloatComplex, ltwork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_MALLOC_CPU( rwork, float, N );
#endif
lapackf77_clacpy(MagmaUpperLowerStr, &N, &N, h_R, &lda, h_Q, &lda);
for( int j = 0; j < N-1; ++j )
for( int i = j+2; i < N; ++i )
h_R[i+j*lda] = MAGMA_C_ZERO;
magma_cunghr(N, ione, N, h_Q, lda, tau, dT, nb, &info);
if (info != 0) {
printf("magma_cunghr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
exit(1);
}
#if defined(PRECISION_z) || defined(PRECISION_c)
lapackf77_chst01(&N, &ione, &N,
h_A, &lda, h_R, &lda,
h_Q, &lda, twork, <work, rwork, result);
#else
lapackf77_chst01(&N, &ione, &N,
h_A, &lda, h_R, &lda,
h_Q, &lda, twork, <work, result);
#endif
TESTING_FREE_PIN( h_Q );
TESTING_FREE_CPU( twork );
#if defined(PRECISION_z) || defined(PRECISION_c)
TESTING_FREE_CPU( rwork );
#endif
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_cgehrd(&N, &ione, &N, h_R, &lda, tau, h_work, &lwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_cgehrd returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Print performance and error.
=================================================================== */
if ( opts.lapack ) {
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f)",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5d --- ( --- ) %7.2f (%7.2f)",
(int) N, gpu_perf, gpu_time );
}
if ( opts.check ) {
printf(" %8.2e %8.2e %s\n",
result[0]*eps, result[1]*eps,
( ( (result[0]*eps < tol) && (result[1]*eps < tol) ) ? "ok" : "failed") );
status += ! (result[0]*eps < tol);
status += ! (result[1]*eps < tol);
}
else {
printf(" --- ---\n");
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( tau );
TESTING_FREE_PIN( h_R );
TESTING_FREE_PIN( h_work );
TESTING_FREE_DEV( dT );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zpotrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A, *h_R;
magma_int_t N, n2, lda, info;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
double work[1], error;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("ngpu %d, uplo %c\n", (int) opts.ngpu, opts.uplo );
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R_magma - R_lapack||_F / ||R_lapack||_F\n");
printf("========================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
lda = N;
n2 = lda*N;
gflops = FLOPS_ZPOTRF( N ) / 1e9;
TESTING_MALLOC( h_A, magmaDoubleComplex, n2 );
TESTING_HOSTALLOC( h_R, magmaDoubleComplex, n2 );
/* Initialize the matrix */
lapackf77_zlarnv( &ione, ISEED, &n2, h_A );
magma_zmake_hpd( N, h_A, lda );
lapackf77_zlacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_zpotrf( opts.uplo, N, h_R, lda, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_zpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.lapack ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_zpotrf( &opts.uplo, &N, h_A, &lda, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_zpotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
error = lapackf77_zlange("f", &N, &N, h_A, &lda, work);
blasf77_zaxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_zlange("f", &N, &N, h_R, &lda, work) / error;
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e%s\n",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "" : " failed") );
status |= ! (error < tol);
}
else {
printf("%5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) N, gpu_perf, gpu_time );
}
TESTING_FREE( h_A );
TESTING_HOSTFREE( h_R );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing zlanhe
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gbytes, gpu_perf, gpu_time, cpu_perf, cpu_time;
magmaDoubleComplex *h_A;
double *h_work;
magmaDoubleComplex_ptr d_A;
magmaDouble_ptr d_work;
magma_int_t i, j, N, n2, lda, ldda;
magma_int_t idist = 3; // normal distribution (otherwise max norm is always ~ 1)
magma_int_t ISEED[4] = {0,0,0,1};
double error, norm_magma, norm_lapack;
magma_int_t status = 0;
magma_int_t lapack_nan_fail = 0;
magma_int_t lapack_inf_fail = 0;
bool mkl_warning = false;
magma_opts opts;
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
double tol2;
magma_uplo_t uplo[] = { MagmaLower, MagmaUpper };
magma_norm_t norm[] = { MagmaInfNorm, MagmaOneNorm, MagmaMaxNorm, MagmaFrobeniusNorm };
// Double-Complex inf-norm not supported on Tesla (CUDA arch 1.x)
#if defined(PRECISION_z)
magma_int_t arch = magma_getdevice_arch();
if ( arch < 200 ) {
printf("!!!! NOTE: Double-Complex %s and %s norm are not supported\n"
"!!!! on CUDA architecture %d; requires arch >= 200.\n"
"!!!! It should report \"parameter number 1 had an illegal value\" below.\n\n",
MagmaInfNormStr, MagmaOneNormStr, (int) arch );
for( int inorm = 0; inorm < 2; ++inorm ) {
for( int iuplo = 0; iuplo < 2; ++iuplo ) {
printf( "Testing that magmablas_zlanhe( %s, %s, ... ) returns -1 error...\n",
lapack_norm_const( norm[inorm] ),
lapack_uplo_const( uplo[iuplo] ));
norm_magma = magmablas_zlanhe( norm[inorm], uplo[iuplo], 1, NULL, 1, NULL, 1 );
if ( norm_magma != -1 ) {
printf( "expected magmablas_zlanhe to return -1 error, but got %f\n", norm_magma );
status = 1;
}
}}
printf( "...return values %s\n\n", (status == 0 ? "ok" : "failed") );
}
#endif
#ifdef MAGMA_WITH_MKL
// MKL 11.1 has bug in multi-threaded zlanhe; use single thread to work around.
// MKL 11.2 corrects it for inf, one, max norm.
// MKL 11.2 still segfaults for Frobenius norm, which is not tested here
// because MAGMA doesn't implement Frobenius norm yet.
MKLVersion mkl_version;
mkl_get_version( &mkl_version );
magma_int_t la_threads = magma_get_lapack_numthreads();
bool mkl_single_thread = (mkl_version.MajorVersion <= 11 && mkl_version.MinorVersion < 2);
if ( mkl_single_thread ) {
printf( "\nNote: using single thread to work around MKL zlanhe bug.\n\n" );
}
#endif
printf("%% N norm uplo CPU GByte/s (ms) GPU GByte/s (ms) error nan inf\n");
printf("%%=================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int inorm = 0; inorm < 3; ++inorm ) { /* < 4 for Frobenius */
for( int iuplo = 0; iuplo < 2; ++iuplo ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
n2 = lda*N;
ldda = magma_roundup( N, opts.align );
// read upper or lower triangle
gbytes = 0.5*(N+1)*N*sizeof(magmaDoubleComplex) / 1e9;
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, n2 );
TESTING_MALLOC_CPU( h_work, double, N );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*N );
TESTING_MALLOC_DEV( d_work, double, N );
/* Initialize the matrix */
lapackf77_zlarnv( &idist, ISEED, &n2, h_A );
magma_zsetmatrix( N, N, h_A, lda, d_A, ldda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
norm_magma = magmablas_zlanhe( norm[inorm], uplo[iuplo], N, d_A, ldda, d_work, N );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gbytes / gpu_time;
if (norm_magma == -1) {
printf( "%5d %4c skipped because %s norm isn't supported\n",
(int) N, lapacke_norm_const( norm[inorm] ), lapack_norm_const( norm[inorm] ));
goto cleanup;
}
else if (norm_magma < 0) {
printf("magmablas_zlanhe returned error %f: %s.\n",
norm_magma, magma_strerror( (int) norm_magma ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
#ifdef MAGMA_WITH_MKL
if ( mkl_single_thread ) {
// work around MKL bug in multi-threaded zlanhe
magma_set_lapack_numthreads( 1 );
}
#endif
cpu_time = magma_wtime();
norm_lapack = lapackf77_zlanhe(
lapack_norm_const( norm[inorm] ),
lapack_uplo_const( uplo[iuplo] ),
&N, h_A, &lda, h_work );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
if (norm_lapack < 0) {
printf("lapackf77_zlanhe returned error %f: %s.\n",
norm_lapack, magma_strerror( (int) norm_lapack ));
}
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
error = fabs( norm_magma - norm_lapack ) / norm_lapack;
tol2 = tol;
if ( norm[inorm] == MagmaMaxNorm ) {
// max-norm depends on only one element, so for Real precisions,
// MAGMA and LAPACK should exactly agree (tol2 = 0),
// while Complex precisions incur roundoff in cuCabs.
#ifdef REAL
tol2 = 0;
#endif
}
bool okay; okay = (error <= tol2);
status += ! okay;
mkl_warning |= ! okay;
/* ====================================================================
Check for NAN and INF propagation
=================================================================== */
#define h_A(i_, j_) (h_A + (i_) + (j_)*lda)
#define d_A(i_, j_) (d_A + (i_) + (j_)*ldda)
i = rand() % N;
j = rand() % N;
magma_int_t tmp;
if ( uplo[iuplo] == MagmaLower && i < j ) {
tmp = i;
i = j;
j = tmp;
}
else if ( uplo[iuplo] == MagmaUpper && i > j ) {
tmp = i;
i = j;
j = tmp;
}
*h_A(i,j) = MAGMA_Z_NAN;
magma_zsetvector( 1, h_A(i,j), 1, d_A(i,j), 1 );
norm_magma = magmablas_zlanhe( norm[inorm], uplo[iuplo], N, d_A, ldda, d_work, N );
norm_lapack = lapackf77_zlanhe( lapack_norm_const( norm[inorm] ),
lapack_uplo_const( uplo[iuplo] ),
&N, h_A, &lda, h_work );
bool nan_okay; nan_okay = isnan(norm_magma);
bool la_nan_okay; la_nan_okay = isnan(norm_lapack);
lapack_nan_fail += ! la_nan_okay;
status += ! nan_okay;
*h_A(i,j) = MAGMA_Z_INF;
magma_zsetvector( 1, h_A(i,j), 1, d_A(i,j), 1 );
norm_magma = magmablas_zlanhe( norm[inorm], uplo[iuplo], N, d_A, ldda, d_work, N );
norm_lapack = lapackf77_zlanhe( lapack_norm_const( norm[inorm] ),
lapack_uplo_const( uplo[iuplo] ),
&N, h_A, &lda, h_work );
bool inf_okay; inf_okay = isinf(norm_magma);
bool la_inf_okay; la_inf_okay = isinf(norm_lapack);
lapack_inf_fail += ! la_inf_okay;
status += ! inf_okay;
#ifdef MAGMA_WITH_MKL
if ( mkl_single_thread ) {
// end single thread to work around MKL bug
magma_set_lapack_numthreads( la_threads );
}
#endif
printf("%5d %4c %4c %7.2f (%7.2f) %7.2f (%7.2f) %#9.3g %-6s %6s%1s %6s%1s\n",
(int) N,
lapacke_norm_const( norm[inorm] ),
lapacke_uplo_const( uplo[iuplo] ),
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
error,
(okay ? "ok" : "failed"),
(nan_okay ? "ok" : "failed"), (la_nan_okay ? " " : "*"),
(inf_okay ? "ok" : "failed"), (la_inf_okay ? " " : "*"));
cleanup:
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_work );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_work );
fflush( stdout );
} // end iter
if ( opts.niter > 1 ) {
printf( "\n" );
}
}} // end iuplo, inorm
printf( "\n" );
}
// don't print "failed" here because then run_tests.py thinks MAGMA failed
if ( lapack_nan_fail ) {
printf( "* Warning: LAPACK did not pass NAN propagation test; upgrade to LAPACK version >= 3.4.2 (Sep. 2012)\n" );
}
if ( lapack_inf_fail ) {
printf( "* Warning: LAPACK did not pass INF propagation test\n" );
}
if ( mkl_warning ) {
printf("* MKL (e.g., 11.1) has a bug in zlanhe with multiple threads;\n"
" corrected in 11.2 for one, inf, max norms, but still in Frobenius norm.\n"
" Try again with MKL_NUM_THREADS=1.\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
