void magmaf_dsyevd_gpu( magma_vec_t *jobz, magma_uplo_t *uplo, magma_int_t *n, devptr_t *da, magma_int_t *ldda, double *w, double *wa, magma_int_t *ldwa, double *work, magma_int_t *lwork, magma_int_t *iwork, magma_int_t *liwork, magma_int_t *info ) { magma_dsyevd_gpu( *jobz, *uplo, *n, magma_ddevptr(da), *ldda, w, wa, *ldwa, work, *lwork, iwork, *liwork, info ); }
extern "C" magma_int_t magma_dlobpcg( magma_d_sparse_matrix A, magma_d_solver_par *solver_par ){ #define residualNorms(i,iter) ( residualNorms + (i) + (iter)*n ) #define magmablas_swap(x, y) { pointer = x; x = y; y = pointer; } #define hresidualNorms(i,iter) (hresidualNorms + (i) + (iter)*n ) #define gramA( m, n) (gramA + (m) + (n)*ldgram) #define gramB( m, n) (gramB + (m) + (n)*ldgram) #define gevectors(m, n) (gevectors + (m) + (n)*ldgram) #define h_gramB( m, n) (h_gramB + (m) + (n)*ldgram) #define magma_d_bspmv_tuned(m, n, alpha, A, X, beta, AX) { \ magmablas_dtranspose( m, n, X, m, blockW, n ); \ magma_d_vector x, ax; \ x.memory_location = Magma_DEV; x.num_rows = m*n; x.nnz = m*n; x.val = blockW; \ ax.memory_location= Magma_DEV; ax.num_rows = m*n; ax.nnz = m*n; ax.val = AX; \ magma_d_spmv(alpha, A, x, beta, ax ); \ magmablas_dtranspose( n, m, blockW, n, X, m ); \ } //************************************************************** // Memory allocation for the eigenvectors, eigenvalues, and workspace solver_par->solver = Magma_LOBPCG; magma_int_t m = A.num_rows; magma_int_t n =(solver_par->num_eigenvalues); double *blockX = solver_par->eigenvectors; double *evalues = solver_par->eigenvalues; double *dwork, *hwork; double *blockP, *blockAP, *blockR, *blockAR, *blockAX, *blockW; double *gramA, *gramB, *gramM; double *gevectors, *h_gramB; double *pointer, *origX = blockX; double *eval_gpu; magma_int_t lwork = max( 2*n+n*magma_get_dsytrd_nb(n), 1 + 6*3*n + 2* 3*n* 3*n); magma_dmalloc_pinned( &hwork , lwork ); magma_dmalloc( &blockAX , m*n ); magma_dmalloc( &blockAR , m*n ); magma_dmalloc( &blockAP , m*n ); magma_dmalloc( &blockR , m*n ); magma_dmalloc( &blockP , m*n ); magma_dmalloc( &blockW , m*n ); magma_dmalloc( &dwork , m*n ); magma_dmalloc( &eval_gpu , 3*n ); //**********************************************************+ magma_int_t verbosity = 1; magma_int_t *iwork, liwork = 15*n+9; // === Set solver parameters === double residualTolerance = solver_par->epsilon; magma_int_t maxIterations = solver_par->maxiter; // === Set some constants & defaults === double c_one = MAGMA_D_ONE, c_zero = MAGMA_D_ZERO; double *residualNorms, *condestGhistory, condestG; double *gevalues; magma_int_t *activeMask; // === Check some parameters for possible quick exit === solver_par->info = 0; if (m < 2) solver_par->info = -1; else if (n > m) solver_par->info = -2; if (solver_par->info != 0) { magma_xerbla( __func__, -(solver_par->info) ); return solver_par->info; } magma_int_t *info = &(solver_par->info); // local info variable; // === Allocate GPU memory for the residual norms' history === magma_dmalloc(&residualNorms, (maxIterations+1) * n); magma_malloc( (void **)&activeMask, (n+1) * sizeof(magma_int_t) ); // === Allocate CPU work space === magma_dmalloc_cpu(&condestGhistory, maxIterations+1); magma_dmalloc_cpu(&gevalues, 3 * n); magma_malloc_cpu((void **)&iwork, liwork * sizeof(magma_int_t)); double *hW; magma_dmalloc_pinned(&hW, n*n); magma_dmalloc_pinned(&gevectors, 9*n*n); magma_dmalloc_pinned(&h_gramB , 9*n*n); // === Allocate GPU workspace === magma_dmalloc(&gramM, n * n); magma_dmalloc(&gramA, 9 * n * n); magma_dmalloc(&gramB, 9 * n * n); #if defined(PRECISION_z) || defined(PRECISION_c) double *rwork; magma_int_t lrwork = 1 + 5*(3*n) + 2*(3*n)*(3*n); magma_dmalloc_cpu(&rwork, lrwork); #endif // === Set activemask to one === for(int k =0; k<n; k++) iwork[k]=1; magma_setmatrix(n, 1, sizeof(magma_int_t), iwork, n ,activeMask, n); magma_int_t gramDim, ldgram = 3*n, ikind = 4; // === Make the initial vectors orthonormal === magma_dgegqr_gpu(ikind, m, n, blockX, m, dwork, hwork, info ); //magma_dorthomgs( m, n, blockX ); magma_d_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX ); // === Compute the Gram matrix = (X, AX) & its eigenstates === magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, blockX, m, blockAX, m, c_zero, gramM, n); magma_dsyevd_gpu( MagmaVec, MagmaUpper, n, gramM, n, evalues, hW, n, hwork, lwork, #if defined(PRECISION_z) || defined(PRECISION_c) rwork, lrwork, #endif iwork, liwork, info ); // === Update X = X * evectors === magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n, c_one, blockX, m, gramM, n, c_zero, blockW, m); magmablas_swap(blockW, blockX); // === Update AX = AX * evectors === magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n, c_one, blockAX, m, gramM, n, c_zero, blockW, m); magmablas_swap(blockW, blockAX); condestGhistory[1] = 7.82; magma_int_t iterationNumber, cBlockSize, restart = 1, iter; //Chronometry real_Double_t tempo1, tempo2; magma_device_sync(); tempo1=magma_wtime(); // === Main LOBPCG loop ============================================================ for(iterationNumber = 1; iterationNumber < maxIterations; iterationNumber++) { // === compute the residuals (R = Ax - x evalues ) magmablas_dlacpy( MagmaUpperLower, m, n, blockAX, m, blockR, m); /* for(int i=0; i<n; i++){ magma_daxpy(m, MAGMA_D_MAKE(-evalues[i],0), blockX+i*m, 1, blockR+i*m, 1); } */ #if defined(PRECISION_z) || defined(PRECISION_d) magma_dsetmatrix( 3*n, 1, evalues, 3*n, eval_gpu, 3*n ); #else magma_ssetmatrix( 3*n, 1, evalues, 3*n, eval_gpu, 3*n ); #endif magma_dlobpcg_res( m, n, eval_gpu, blockX, blockR, eval_gpu); magmablas_dnrm2_cols(m, n, blockR, m, residualNorms(0, iterationNumber)); // === remove the residuals corresponding to already converged evectors magma_dcompact(m, n, blockR, m, residualNorms(0, iterationNumber), residualTolerance, activeMask, &cBlockSize); if (cBlockSize == 0) break; // === apply a preconditioner P to the active residulas: R_new = P R_old // === for now set P to be identity (no preconditioner => nothing to be done ) // magmablas_dlacpy( MagmaUpperLower, m, cBlockSize, blockR, m, blockW, m); /* // === make the preconditioned residuals orthogonal to X magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, cBlockSize, m, c_one, blockX, m, blockR, m, c_zero, gramB(0,0), ldgram); magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n, c_mone, blockX, m, gramB(0,0), ldgram, c_one, blockR, m); */ // === make the active preconditioned residuals orthonormal magma_dgegqr_gpu(ikind, m, cBlockSize, blockR, m, dwork, hwork, info ); //magma_dorthomgs( m, cBlockSize, blockR ); // === compute AR magma_d_bspmv_tuned(m, cBlockSize, c_one, A, blockR, c_zero, blockAR ); if (!restart) { // === compact P & AP as well magma_dcompactActive(m, n, blockP, m, activeMask); magma_dcompactActive(m, n, blockAP, m, activeMask); /* // === make P orthogonal to X ? magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, cBlockSize, m, c_one, blockX, m, blockP, m, c_zero, gramB(0,0), ldgram); magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n, c_mone, blockX, m, gramB(0,0), ldgram, c_one, blockP, m); // === make P orthogonal to R ? magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m, c_one, blockR, m, blockP, m, c_zero, gramB(0,0), ldgram); magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, cBlockSize, cBlockSize, c_mone, blockR, m, gramB(0,0), ldgram, c_one, blockP, m); */ // === Make P orthonormal & properly change AP (without multiplication by A) magma_dgegqr_gpu(ikind, m, cBlockSize, blockP, m, dwork, hwork, info ); //magma_dorthomgs( m, cBlockSize, blockP ); //magma_d_bspmv_tuned(m, cBlockSize, c_one, A, blockP, c_zero, blockAP ); magma_dsetmatrix( cBlockSize, cBlockSize, hwork, cBlockSize, dwork, cBlockSize); // magma_dtrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, // m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m); // replacement according to Stan #if defined(PRECISION_s) || defined(PRECISION_d) magmablas_dtrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m); #else magma_dtrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m); #endif } iter = max(1,iterationNumber-10- (int)(log(1.*cBlockSize))); double condestGmean = 0.; for(int i = 0; i<iterationNumber-iter+1; i++) condestGmean += condestGhistory[i]; condestGmean = condestGmean / (iterationNumber-iter+1); if (restart) gramDim = n+cBlockSize; else gramDim = n+2*cBlockSize; /* --- The Raileight-Ritz method for [X R P] ----------------------- [ X R P ]' [AX AR AP] y = evalues [ X R P ]' [ X R P ], i.e., GramA GramB / X'AX X'AR X'AP \ / X'X X'R X'P \ | R'AX R'AR R'AP | y = evalues | R'X R'R R'P | \ P'AX P'AR P'AP / \ P'X P'R P'P / ----------------------------------------------------------------- */ // === assemble GramB; first, set it to I magmablas_dlaset(MagmaFull, ldgram, ldgram, c_zero, c_one, gramB, ldgram); // identity if (!restart) { magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m, c_one, blockP, m, blockX, m, c_zero, gramB(n+cBlockSize,0), ldgram); magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m, c_one, blockP, m, blockR, m, c_zero, gramB(n+cBlockSize,n), ldgram); } magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m, c_one, blockR, m, blockX, m, c_zero, gramB(n,0), ldgram); // === get GramB from the GPU to the CPU and compute its eigenvalues only magma_dgetmatrix(gramDim, gramDim, gramB, ldgram, h_gramB, ldgram); lapackf77_dsyev("N", "L", &gramDim, h_gramB, &ldgram, gevalues, hwork, &lwork, #if defined(PRECISION_z) || defined(PRECISION_c) rwork, #endif info); // === check stability criteria if we need to restart condestG = log10( gevalues[gramDim-1]/gevalues[0] ) + 1.; if ((condestG/condestGmean>2 && condestG>2) || condestG>8) { // Steepest descent restart for stability restart=1; printf("restart at step #%d\n", (int) iterationNumber); } // === assemble GramA; first, set it to I magmablas_dlaset(MagmaFull, ldgram, ldgram, c_zero, c_one, gramA, ldgram); // identity magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m, c_one, blockR, m, blockAX, m, c_zero, gramA(n,0), ldgram); magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m, c_one, blockR, m, blockAR, m, c_zero, gramA(n,n), ldgram); if (!restart) { magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m, c_one, blockP, m, blockAX, m, c_zero, gramA(n+cBlockSize,0), ldgram); magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m, c_one, blockP, m, blockAR, m, c_zero, gramA(n+cBlockSize,n), ldgram); magma_dgemm(MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m, c_one, blockP, m, blockAP, m, c_zero, gramA(n+cBlockSize,n+cBlockSize), ldgram); } /* // === Compute X' AX or just use the eigenvalues below ? magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, blockX, m, blockAX, m, c_zero, gramA(0,0), ldgram); */ if (restart==0) { magma_dgetmatrix(gramDim, gramDim, gramA, ldgram, gevectors, ldgram); } else { gramDim = n+cBlockSize; magma_dgetmatrix(gramDim, gramDim, gramA, ldgram, gevectors, ldgram); } for(int k=0; k<n; k++) *gevectors(k,k) = MAGMA_D_MAKE(evalues[k], 0); // === the previous eigensolver destroyed what is in h_gramB => must copy it again magma_dgetmatrix(gramDim, gramDim, gramB, ldgram, h_gramB, ldgram); magma_int_t itype = 1; lapackf77_dsygvd(&itype, "V", "L", &gramDim, gevectors, &ldgram, h_gramB, &ldgram, gevalues, hwork, &lwork, #if defined(PRECISION_z) || defined(PRECISION_c) rwork, &lrwork, #endif iwork, &liwork, info); for(int k =0; k<n; k++) evalues[k] = gevalues[k]; // === copy back the result to gramA on the GPU and use it for the updates magma_dsetmatrix(gramDim, gramDim, gevectors, ldgram, gramA, ldgram); if (restart == 0) { // === contribution from P to the new X (in new search direction P) magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize, c_one, blockP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m); magmablas_swap(dwork, blockP); // === contribution from R to the new X (in new search direction P) magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize, c_one, blockR, m, gramA(n,0), ldgram, c_one, blockP, m); // === corresponding contribution from AP to the new AX (in AP) magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize, c_one, blockAP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m); magmablas_swap(dwork, blockAP); // === corresponding contribution from AR to the new AX (in AP) magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize, c_one, blockAR, m, gramA(n,0), ldgram, c_one, blockAP, m); } else { // === contribution from R (only) to the new X magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize, c_one, blockR, m, gramA(n,0), ldgram, c_zero, blockP, m); // === corresponding contribution from AR (only) to the new AX magma_dgemm(MagmaNoTrans, MagmaNoTrans,m, n, cBlockSize, c_one, blockAR, m, gramA(n,0), ldgram, c_zero, blockAP, m); } // === contribution from old X to the new X + the new search direction P magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n, c_one, blockX, m, gramA, ldgram, c_zero, dwork, m); magmablas_swap(dwork, blockX); //magma_daxpy(m*n, c_one, blockP, 1, blockX, 1); magma_dlobpcg_maxpy( m, n, blockP, blockX ); // === corresponding contribution from old AX to new AX + AP magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n, c_one, blockAX, m, gramA, ldgram, c_zero, dwork, m); magmablas_swap(dwork, blockAX); //magma_daxpy(m*n, c_one, blockAP, 1, blockAX, 1); magma_dlobpcg_maxpy( m, n, blockAP, blockAX ); condestGhistory[iterationNumber+1]=condestG; if (verbosity==1) { // double res; // magma_dgetmatrix(1, 1, // (double*)residualNorms(0, iterationNumber), 1, // (double*)&res, 1); // // printf("Iteration %4d, CBS %4d, Residual: %10.7f\n", // iterationNumber, cBlockSize, res); printf("%4d-%2d ", (int) iterationNumber, (int) cBlockSize); magma_dprint_gpu(1, n, residualNorms(0, iterationNumber), 1); } restart = 0; } // === end for iterationNumber = 1,maxIterations ======================= // fill solver info magma_device_sync(); tempo2=magma_wtime(); solver_par->runtime = (real_Double_t) tempo2-tempo1; solver_par->numiter = iterationNumber; if( solver_par->numiter < solver_par->maxiter){ solver_par->info = 0; }else if( solver_par->init_res > solver_par->final_res ) solver_par->info = -2; else solver_par->info = -1; // ============================================================================= // === postprocessing; // ============================================================================= // === compute the real AX and corresponding eigenvalues magma_d_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX ); magma_dgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, blockX, m, blockAX, m, c_zero, gramM, n); magma_dsyevd_gpu( MagmaVec, MagmaUpper, n, gramM, n, gevalues, dwork, n, hwork, lwork, #if defined(PRECISION_z) || defined(PRECISION_c) rwork, lrwork, #endif iwork, liwork, info ); for(int k =0; k<n; k++) evalues[k] = gevalues[k]; // === update X = X * evectors magmablas_swap(blockX, dwork); magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n, c_one, dwork, m, gramM, n, c_zero, blockX, m); // === update AX = AX * evectors to compute the final residual magmablas_swap(blockAX, dwork); magma_dgemm(MagmaNoTrans, MagmaNoTrans, m, n, n, c_one, dwork, m, gramM, n, c_zero, blockAX, m); // === compute R = AX - evalues X magmablas_dlacpy( MagmaUpperLower, m, n, blockAX, m, blockR, m); for(int i=0; i<n; i++) magma_daxpy(m, MAGMA_D_MAKE(-evalues[i], 0), blockX+i*m, 1, blockR+i*m, 1); // === residualNorms[iterationNumber] = || R || magmablas_dnrm2_cols(m, n, blockR, m, residualNorms(0, iterationNumber)); // === restore blockX if needed if (blockX != origX) magmablas_dlacpy( MagmaUpperLower, m, n, blockX, m, origX, m); printf("Eigenvalues:\n"); for(int i =0; i<n; i++) printf("%e ", evalues[i]); printf("\n\n"); printf("Final residuals:\n"); magma_dprint_gpu(1, n, residualNorms(0, iterationNumber), 1); printf("\n\n"); //=== Print residual history in a file for plotting ==== double *hresidualNorms; magma_dmalloc_cpu(&hresidualNorms, (iterationNumber+1) * n); magma_dgetmatrix(n, iterationNumber, (double*)residualNorms, n, (double*)hresidualNorms, n); printf("Residuals are stored in file residualNorms\n"); printf("Plot the residuals using: myplot \n"); FILE *residuals_file; residuals_file = fopen("residualNorms", "w"); for(int i =1; i<iterationNumber; i++) { for(int j = 0; j<n; j++) fprintf(residuals_file, "%f ", *hresidualNorms(j,i)); fprintf(residuals_file, "\n"); } fclose(residuals_file); magma_free_cpu(hresidualNorms); // === free work space magma_free( residualNorms ); magma_free_cpu( condestGhistory ); magma_free_cpu( gevalues ); magma_free_cpu( iwork ); magma_free_pinned( hW ); magma_free_pinned( gevectors ); magma_free_pinned( h_gramB ); magma_free( gramM ); magma_free( gramA ); magma_free( gramB ); magma_free( activeMask ); magma_free( blockAX ); magma_free( blockAR ); magma_free( blockAP ); magma_free( blockR ); magma_free( blockP ); magma_free( blockW ); magma_free( dwork ); magma_free( eval_gpu ); magma_free_pinned( hwork ); #if defined(PRECISION_z) || defined(PRECISION_c) magma_free_cpu( rwork ); #endif return MAGMA_SUCCESS; }
/* //////////////////////////////////////////////////////////////////////////// -- Testing dsyevd */ int main( int argc, char** argv) { TESTING_INIT(); real_Double_t gpu_time, cpu_time; double *h_A, *h_R, *d_R, *h_work; double *w1, *w2; magma_int_t *iwork; magma_int_t N, n2, info, lwork, liwork, lda, ldda, 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_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(" N CPU Time (sec) 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; lda = N; ldda = ((N + 31)/32)*32; // query for workspace sizes magma_dsyevd_gpu( opts.jobz, opts.uplo, N, NULL, ldda, NULL, NULL, lda, aux_work, -1, aux_iwork, -1, &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 ); TESTING_MALLOC_DEV( d_R, double, N*ldda ); /* Initialize the matrix */ lapackf77_dlarnv( &ione, ISEED, &n2, h_A ); magma_dsetmatrix( N, N, h_A, lda, d_R, ldda ); /* warm up run */ if ( opts.warmup ) { magma_dsyevd_gpu( opts.jobz, opts.uplo, N, d_R, ldda, w1, h_R, lda, h_work, lwork, iwork, liwork, &info ); if (info != 0) printf("magma_dsyevd_gpu returned error %d: %s.\n", (int) info, magma_strerror( info )); magma_dsetmatrix( N, N, h_A, lda, d_R, ldda ); } /* ==================================================================== Performs operation using MAGMA =================================================================== */ gpu_time = magma_wtime(); magma_dsyevd_gpu( opts.jobz, opts.uplo, N, d_R, ldda, w1, h_R, lda, h_work, lwork, iwork, liwork, &info ); gpu_time = magma_wtime() - gpu_time; if (info != 0) printf("magma_dsyevd_gpu 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 magma_dgetmatrix( N, N, d_R, ldda, h_R, lda ); lapackf77_dsyt21( &ione, &opts.uplo, &N, &izero, h_A, &lda, w1, h_work, h_R, &lda, h_R, &lda, NULL, h_work, &result[0] ); magma_dsetmatrix( N, N, h_A, lda, d_R, ldda ); magma_dsyevd_gpu( MagmaNoVec, opts.uplo, N, d_R, ldda, w2, h_R, lda, h_work, lwork, iwork, liwork, &info ); if (info != 0) printf("magma_dsyevd_gpu returned error %d: %s.\n", (int) info, magma_strerror( info )); temp1 = temp2 = 0; for( int j=0; j<N; j++ ) { temp1 = max(temp1, absv(w1[j])); temp1 = max(temp1, absv(w2[j])); temp2 = max(temp2, absv(w1[j]-w2[j])); } result[2] = temp2 / (((double)N)*temp1); } /* ===================================================================== Performs operation using LAPACK =================================================================== */ if ( opts.lapack ) { cpu_time = magma_wtime(); lapackf77_dsyevd( &opts.jobz, &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 ? "" : " failed") ); printf("(2) | I - U'U | / N = %8.2e%s\n", result[1]*eps, (result[1]*eps < tol ? "" : " failed") ); printf("(3) | S(w/ U) - S(w/o U) | / |S| = %8.2e%s\n\n", result[2] , (result[2] < tolulp ? "" : " failed") ); } 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 ); TESTING_FREE_DEV( d_R ); } if ( opts.niter > 1 ) { printf( "\n" ); } } TESTING_FINALIZE(); return 0; }
/** Purpose ------- DSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments --------- @param[in] itype INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x @param[in] jobz magma_vec_t - = MagmaNoVec: Compute eigenvalues only; - = MagmaVec: Compute eigenvalues and eigenvectors. @param[in] uplo magma_uplo_t - = MagmaUpper: Upper triangles of A and B are stored; - = MagmaLower: Lower triangles of A and B are stored. @param[in] n INTEGER The order of the matrices A and B. N >= 0. @param[in,out] A DOUBLE PRECISION array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. \n On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T * B * Z = I; if ITYPE = 3, Z**T * inv(B) * Z = I. If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper) or the lower triangle (if UPLO=MagmaLower) of A, including the diagonal, is destroyed. @param[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[in,out] B DOUBLE PRECISION array, dimension (LDB, N) On entry, the symmetric matrix B. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = MagmaLower, the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. \n On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T * U or B = L * L**T. @param[in] ldb INTEGER The leading dimension of the array B. LDB >= max(1,N). @param[out] w DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. @param[out] work (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. @param[in] lwork INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LWORK >= 2*N + N*NB. If JOBZ = MagmaVec and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_dsytrd_nb(N). \n If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. @param[out] iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. @param[in] liwork INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1. If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N. \n If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. @param[out] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value - > 0: DPOTRF or DSYEVD returned an error code: <= N: if INFO = i and JOBZ = MagmaNoVec, then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = MagmaVec, then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1); > N: if INFO = N + i, for 1 <= i <= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. Further Details --------------- Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA Modified so that no backsubstitution is performed if DSYEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A - reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05. @ingroup magma_dsygv_driver ********************************************************************/ extern "C" magma_int_t magma_dsygvd( magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n, double *A, magma_int_t lda, double *B, magma_int_t ldb, double *w, double *work, magma_int_t lwork, #ifdef COMPLEX double *rwork, magma_int_t lrwork, #endif magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) { const char* uplo_ = lapack_uplo_const( uplo ); const char* jobz_ = lapack_vec_const( jobz ); double d_one = MAGMA_D_ONE; double *dA=NULL, *dB=NULL; magma_int_t ldda = n; magma_int_t lddb = n; magma_int_t lower; magma_trans_t trans; magma_int_t wantz, lquery; magma_int_t lwmin, liwmin; magma_queue_t stream; magma_queue_create( &stream ); wantz = (jobz == MagmaVec); lower = (uplo == MagmaLower); lquery = (lwork == -1 || liwork == -1); *info = 0; if (itype < 1 || itype > 3) { *info = -1; } else if (! (wantz || (jobz == MagmaNoVec))) { *info = -2; } else if (! (lower || (uplo == MagmaUpper))) { *info = -3; } else if (n < 0) { *info = -4; } else if (lda < max(1,n)) { *info = -6; } else if (ldb < max(1,n)) { *info = -8; } magma_int_t nb = magma_get_dsytrd_nb( n ); if ( n <= 1 ) { lwmin = 1; liwmin = 1; } else if ( wantz ) { lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n ); liwmin = 3 + 5*n; } else { lwmin = 2*n + n*nb; liwmin = 1; } // multiply by 1+eps (in Double!) to ensure length gets rounded up, // if it cannot be exactly represented in floating point. real_Double_t one_eps = 1. + lapackf77_dlamch("Epsilon"); work[0] = lwmin * one_eps; iwork[0] = liwmin; if (lwork < lwmin && ! lquery) { *info = -11; } else if (liwork < liwmin && ! lquery) { *info = -13; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) { return *info; } /* Quick return if possible */ if (n == 0) { return *info; } /* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */ if (n <= 128) { #ifdef ENABLE_DEBUG printf("--------------------------------------------------------------\n"); printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb); printf("--------------------------------------------------------------\n"); #endif lapackf77_dsygvd(&itype, jobz_, uplo_, &n, A, &lda, B, &ldb, w, work, &lwork, iwork, &liwork, info); return *info; } if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda ) || MAGMA_SUCCESS != magma_dmalloc( &dB, n*lddb )) { magma_free( dA ); magma_free( dB ); *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } /* Form a Cholesky factorization of B. */ magma_dsetmatrix( n, n, B, ldb, dB, lddb ); magma_dsetmatrix_async( n, n, A, lda, dA, ldda, stream ); magma_timer_t time=0; timer_start( time ); magma_dpotrf_gpu(uplo, n, dB, lddb, info); if (*info != 0) { *info = n + *info; return *info; } timer_stop( time ); timer_printf( "time dpotrf_gpu = %6.2f\n", time ); magma_queue_sync( stream ); magma_dgetmatrix_async( n, n, dB, lddb, B, ldb, stream ); timer_start( time ); /* Transform problem to standard eigenvalue problem and solve. */ magma_dsygst_gpu(itype, uplo, n, dA, ldda, dB, lddb, info); timer_stop( time ); timer_printf( "time dsygst_gpu = %6.2f\n", time ); /* simple fix to be able to run bigger size. * need to have a dwork here that will be used * as dB and then passed to dsyevd. * */ if (n > 5000) { magma_queue_sync( stream ); magma_free( dB ); } timer_start( time ); magma_dsyevd_gpu(jobz, uplo, n, dA, ldda, w, A, lda, work, lwork, iwork, liwork, info); timer_stop( time ); timer_printf( "time dsyevd_gpu = %6.2f\n", time ); if (wantz && *info == 0) { timer_start( time ); /* allocate and copy dB back */ if (n > 5000) { if (MAGMA_SUCCESS != magma_dmalloc( &dB, n*lddb ) ) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_dsetmatrix( n, n, B, ldb, dB, lddb ); } /* Backtransform eigenvectors to the original problem. */ if (itype == 1 || itype == 2) { /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ if (lower) { trans = MagmaTrans; } else { trans = MagmaNoTrans; } magma_dtrsm(MagmaLeft, uplo, trans, MagmaNonUnit, n, n, d_one, dB, lddb, dA, ldda); } else if (itype == 3) { /* For B*A*x=(lambda)*x; backtransform eigenvectors: x = L*y or U'*y */ if (lower) { trans = MagmaNoTrans; } else { trans = MagmaTrans; } magma_dtrmm(MagmaLeft, uplo, trans, MagmaNonUnit, n, n, d_one, dB, lddb, dA, ldda); } magma_dgetmatrix( n, n, dA, ldda, A, lda ); /* free dB */ if (n > 5000) { magma_free( dB ); } timer_stop( time ); timer_printf( "time dtrsm/mm + getmatrix = %6.2f\n", time ); } magma_queue_sync( stream ); magma_queue_destroy( stream ); work[0] = lwmin * one_eps; // round up iwork[0] = liwmin; magma_free( dA ); if (n <= 5000) { magma_free( dB ); } return *info; } /* magma_dsygvd */
extern "C" magma_int_t magma_dsygvd(magma_int_t itype, char jobz, char uplo, magma_int_t n, double *a, magma_int_t lda, double *b, magma_int_t ldb, double *w, double *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) { /* -- MAGMA (version 1.4.0) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver August 2013 Purpose ======= DSYGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments ========= ITYPE (input) INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. N (input) INTEGER The order of the matrices A and B. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T * B * Z = I; if ITYPE = 3, Z**T * inv(B) * Z = I. If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input/output) COMPLEX*16 array, dimension (LDB, N) On entry, the symmetric matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T * U or B = L * L**T. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). W (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. WORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. LWORK (input) INTEGER The length of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N + N*NB. If JOBZ = 'V' and N > 1, LWORK >= max( 2*N + N*NB, 1 + 6*N + 2*N**2 ). NB can be obtained through magma_get_dsytrd_nb(N). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK. LIWORK (input) INTEGER The dimension of the array IWORK. If N <= 1, LIWORK >= 1. If JOBZ = 'N' and N > 1, LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: DPOTRF or DSYEVD returned an error code: <= N: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1); > N: if INFO = N + i, for 1 <= i <= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. Further Details =============== Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA Modified so that no backsubstitution is performed if DSYEVD fails to converge (NEIG in old code could be greater than N causing out of bounds reference to A - reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05. ===================================================================== */ char uplo_[2] = {uplo, 0}; char jobz_[2] = {jobz, 0}; double d_one = MAGMA_D_ONE; double *da; double *db; magma_int_t ldda = n; magma_int_t lddb = n; magma_int_t lower; char trans[1]; magma_int_t wantz, lquery; magma_int_t lwmin, liwmin; magma_queue_t stream; magma_queue_create( &stream ); wantz = lapackf77_lsame(jobz_, MagmaVecStr); lower = lapackf77_lsame(uplo_, MagmaLowerStr); lquery = lwork == -1 || liwork == -1; *info = 0; if (itype < 1 || itype > 3) { *info = -1; } else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVecStr))) { *info = -2; } else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) { *info = -3; } else if (n < 0) { *info = -4; } else if (lda < max(1,n)) { *info = -6; } else if (ldb < max(1,n)) { *info = -8; } magma_int_t nb = magma_get_dsytrd_nb( n ); if ( n <= 1 ) { lwmin = 1; liwmin = 1; } else if ( wantz ) { lwmin = max( 2*n + n*nb, 1 + 6*n + 2*n*n ); liwmin = 3 + 5*n; } else { lwmin = 2*n + n*nb; liwmin = 1; } // multiply by 1+eps to ensure length gets rounded up, // if it cannot be exactly represented in floating point. work[0] = lwmin * (1. + lapackf77_dlamch("Epsilon")); iwork[0] = liwmin; if (lwork < lwmin && ! lquery) { *info = -11; } else if (liwork < liwmin && ! lquery) { *info = -13; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return MAGMA_ERR_ILLEGAL_VALUE; } else if (lquery) { return MAGMA_SUCCESS; } /* Quick return if possible */ if (n == 0) { return 0; } /* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */ if (n <= 128){ #ifdef ENABLE_DEBUG printf("--------------------------------------------------------------\n"); printf(" warning matrix too small N=%d NB=%d, calling lapack on CPU \n", (int) n, (int) nb); printf("--------------------------------------------------------------\n"); #endif lapackf77_dsygvd(&itype, jobz_, uplo_, &n, a, &lda, b, &ldb, w, work, &lwork, iwork, &liwork, info); return *info; } if (MAGMA_SUCCESS != magma_dmalloc( &da, n*ldda ) || MAGMA_SUCCESS != magma_dmalloc( &db, n*lddb )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } /* Form a Cholesky factorization of B. */ magma_dsetmatrix( n, n, b, ldb, db, lddb ); magma_dsetmatrix_async( n, n, a, lda, da, ldda, stream ); #ifdef ENABLE_TIMER magma_timestr_t start, end; start = get_current_time(); #endif magma_dpotrf_gpu(uplo, n, db, lddb, info); if (*info != 0) { *info = n + *info; return 0; } #ifdef ENABLE_TIMER end = get_current_time(); printf("time dpotrf_gpu = %6.2f\n", GetTimerValue(start,end)/1000.); #endif magma_queue_sync( stream ); magma_dgetmatrix_async( n, n, db, lddb, b, ldb, stream ); #ifdef ENABLE_TIMER start = get_current_time(); #endif /* Transform problem to standard eigenvalue problem and solve. */ magma_dsygst_gpu(itype, uplo, n, da, ldda, db, lddb, info); #ifdef ENABLE_TIMER end = get_current_time(); printf("time dsygst_gpu = %6.2f\n", GetTimerValue(start,end)/1000.); #endif /* simple fix to be able to run bigger size. * need to have a dwork here that will be used * a db and then passed to dsyevd. * */ if(n > 5000){ magma_queue_sync( stream ); magma_free( db ); } #ifdef ENABLE_TIMER start = get_current_time(); #endif magma_dsyevd_gpu(jobz, uplo, n, da, ldda, w, a, lda, work, lwork, iwork, liwork, info); #ifdef ENABLE_TIMER end = get_current_time(); printf("time dsyevd_gpu = %6.2f\n", GetTimerValue(start,end)/1000.); #endif if (wantz && *info == 0) { #ifdef ENABLE_TIMER start = get_current_time(); #endif /* allocate and copy db back */ if(n > 5000){ if (MAGMA_SUCCESS != magma_dmalloc( &db, n*lddb ) ){ *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_dsetmatrix( n, n, b, ldb, db, lddb ); } /* Backtransform eigenvectors to the original problem. */ if (itype == 1 || itype == 2) { /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ if (lower) { *(unsigned char *)trans = MagmaTrans; } else { *(unsigned char *)trans = MagmaNoTrans; } magma_dtrsm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, n, d_one, db, lddb, da, ldda); } else if (itype == 3) { /* For B*A*x=(lambda)*x; backtransform eigenvectors: x = L*y or U'*y */ if (lower) { *(unsigned char *)trans = MagmaNoTrans; } else { *(unsigned char *)trans = MagmaTrans; } magma_dtrmm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, n, d_one, db, lddb, da, ldda); } magma_dgetmatrix( n, n, da, ldda, a, lda ); #ifdef ENABLE_TIMER end = get_current_time(); printf("time dtrsm/mm + getmatrix = %6.2f\n", GetTimerValue(start,end)/1000.); #endif /* free db */ if(n > 5000){ magma_free( db ); } } magma_queue_sync( stream ); magma_queue_destroy( stream ); work[0] = lwmin * (1. + lapackf77_dlamch("Epsilon")); // round up iwork[0] = liwmin; magma_free( da ); if(n <= 5000){ magma_free( db ); } return MAGMA_SUCCESS; } /* magma_dsygvd */