/** Purpose ------- ZLAQPS computes a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3. It tries to factorize NB columns from A starting from the row OFFSET+1, and updates all of the matrix with Blas-3 xGEMM. In some cases, due to catastrophic cancellations, it cannot factorize NB columns. Hence, the actual number of factorized columns is returned in KB. Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. Arguments --------- @param[in] m INTEGER The number of rows of the matrix A. M >= 0. @param[in] n INTEGER The number of columns of the matrix A. N >= 0 @param[in] offset INTEGER The number of rows of A that have been factorized in previous steps. @param[in] nb INTEGER The number of columns to factorize. @param[out] kb INTEGER The number of columns actually factorized. @param[in,out] A COMPLEX_16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, block A(OFFSET+1:M,1:KB) is the triangular factor obtained and block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated. @param[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,M). @param[in,out] jpvt INTEGER array, dimension (N) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP. @param[out] tau COMPLEX_16 array, dimension (KB) The scalar factors of the elementary reflectors. @param[in,out] vn1 DOUBLE PRECISION array, dimension (N) The vector with the partial column norms. @param[in,out] vn2 DOUBLE PRECISION array, dimension (N) The vector with the exact column norms. @param[in,out] auxv COMPLEX_16 array, dimension (NB) Auxiliar vector. @param[in,out] F COMPLEX_16 array, dimension (LDF,NB) Matrix F' = L*Y'*A. @param[in] ldf INTEGER The leading dimension of the array F. LDF >= max(1,N). @ingroup magma_zgeqp3_aux ********************************************************************/ extern "C" magma_int_t magma_zlaqps( magma_int_t m, magma_int_t n, magma_int_t offset, magma_int_t nb, magma_int_t *kb, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *jpvt, magmaDoubleComplex *tau, double *vn1, double *vn2, magmaDoubleComplex *auxv, magmaDoubleComplex *F, magma_int_t ldf, magmaDoubleComplex_ptr dF, magma_int_t lddf) { #define A(i, j) (A + (i) + (j)*(lda )) #define dA(i, j) (dA + (i) + (j)*(ldda)) #define F(i, j) (F + (i) + (j)*(ldf )) #define dF(i, j) (dF + (i) + (j)*(lddf)) magmaDoubleComplex c_zero = MAGMA_Z_MAKE( 0.,0.); magmaDoubleComplex c_one = MAGMA_Z_MAKE( 1.,0.); magmaDoubleComplex c_neg_one = MAGMA_Z_MAKE(-1.,0.); magma_int_t ione = 1; magma_int_t i__1, i__2; double d__1; magmaDoubleComplex z__1; magma_int_t j, k, rk; magmaDoubleComplex Akk; magma_int_t pvt; double temp, temp2, tol3z; magma_int_t itemp; magma_int_t lsticc; magma_int_t lastrk; lastrk = min( m, n + offset ); tol3z = magma_dsqrt( lapackf77_dlamch("Epsilon")); magma_queue_t queue; magma_device_t cdev; magma_getdevice( &cdev ); magma_queue_create( cdev, &queue ); lsticc = 0; k = 0; while( k < nb && lsticc == 0 ) { rk = offset + k; /* Determine ith pivot column and swap if necessary */ // subtract 1 from Fortran idamax; pvt, k are 0-based. i__1 = n-k; pvt = k + blasf77_idamax( &i__1, &vn1[k], &ione ) - 1; if (pvt != k) { if (pvt >= nb) { /* 1. Start copy from GPU */ magma_zgetmatrix_async( m - offset - nb, 1, dA(offset + nb, pvt), ldda, A (offset + nb, pvt), lda, queue ); } /* F gets swapped so F must be sent at the end to GPU */ i__1 = k; blasf77_zswap( &i__1, F(pvt,0), &ldf, F(k,0), &ldf ); itemp = jpvt[pvt]; jpvt[pvt] = jpvt[k]; jpvt[k] = itemp; vn1[pvt] = vn1[k]; vn2[pvt] = vn2[k]; if (pvt < nb) { /* no need of transfer if pivot is within the panel */ blasf77_zswap( &m, A(0, pvt), &ione, A(0, k), &ione ); } else { /* 1. Finish copy from GPU */ magma_queue_sync( queue ); /* 2. Swap as usual on CPU */ blasf77_zswap(&m, A(0, pvt), &ione, A(0, k), &ione); /* 3. Restore the GPU */ magma_zsetmatrix_async( m - offset - nb, 1, A (offset + nb, pvt), lda, dA(offset + nb, pvt), ldda, queue ); } } /* Apply previous Householder reflectors to column K: A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'. Optimization: multiply with beta=0; wait for vector and subtract */ if (k > 0) { #ifdef COMPLEX for (j = 0; j < k; ++j) { *F(k,j) = MAGMA_Z_CONJ( *F(k,j) ); } #endif i__1 = m - rk; i__2 = k; blasf77_zgemv( MagmaNoTransStr, &i__1, &i__2, &c_neg_one, A(rk, 0), &lda, F(k, 0), &ldf, &c_one, A(rk, k), &ione ); #ifdef COMPLEX for (j = 0; j < k; ++j) { *F(k,j) = MAGMA_Z_CONJ( *F(k,j) ); } #endif } /* Generate elementary reflector H(k). */ if (rk < m-1) { i__1 = m - rk; lapackf77_zlarfg( &i__1, A(rk, k), A(rk + 1, k), &ione, &tau[k] ); } else { lapackf77_zlarfg( &ione, A(rk, k), A(rk, k), &ione, &tau[k] ); } Akk = *A(rk, k); *A(rk, k) = c_one; /* Compute Kth column of F: Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K) on the GPU */ if (k < n-1) { i__1 = m - rk; i__2 = n - k - 1; /* Send the vector to the GPU */ magma_zsetmatrix( i__1, 1, A(rk, k), lda, dA(rk,k), ldda, queue ); /* Multiply on GPU */ // was CALL ZGEMV( 'Conjugate transpose', M-RK+1, N-K, // TAU( K ), A( RK, K+1 ), LDA, // A( RK, K ), 1, // CZERO, F( K+1, K ), 1 ) magma_int_t i__3 = nb-k-1; magma_int_t i__4 = i__2 - i__3; magma_int_t i__5 = nb-k; magma_zgemv( MagmaConjTrans, i__1 - i__5, i__2 - i__3, tau[k], dA(rk +i__5, k+1+i__3), ldda, dA(rk +i__5, k ), ione, c_zero, dF(k+1+i__3, k ), ione, queue ); magma_zgetmatrix_async( i__2-i__3, 1, dF(k + 1 +i__3, k), i__2, F (k + 1 +i__3, k), i__2, queue ); blasf77_zgemv( MagmaConjTransStr, &i__1, &i__3, &tau[k], A(rk, k+1), &lda, A(rk, k ), &ione, &c_zero, F(k+1, k ), &ione ); magma_queue_sync( queue ); blasf77_zgemv( MagmaConjTransStr, &i__5, &i__4, &tau[k], A(rk, k+1+i__3), &lda, A(rk, k ), &ione, &c_one, F(k+1+i__3, k ), &ione ); } /* Padding F(1:K,K) with zeros. */ for (j = 0; j < k; ++j) { *F(j, k) = c_zero; } /* Incremental updating of F: F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'*A(RK:M,K). */ if (k > 0) { i__1 = m - rk; i__2 = k; z__1 = MAGMA_Z_NEGATE( tau[k] ); blasf77_zgemv( MagmaConjTransStr, &i__1, &i__2, &z__1, A(rk, 0), &lda, A(rk, k), &ione, &c_zero, auxv, &ione ); i__1 = k; blasf77_zgemv( MagmaNoTransStr, &n, &i__1, &c_one, F(0,0), &ldf, auxv, &ione, &c_one, F(0,k), &ione ); } /* Optimization: On the last iteration start sending F back to the GPU */ /* Update the current row of A: A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. */ if (k < n-1) { i__1 = n - k - 1; i__2 = k + 1; blasf77_zgemm( MagmaNoTransStr, MagmaConjTransStr, &ione, &i__1, &i__2, &c_neg_one, A(rk, 0 ), &lda, F(k+1,0 ), &ldf, &c_one, A(rk, k+1), &lda ); } /* Update partial column norms. */ if (rk < lastrk) { for (j = k + 1; j < n; ++j) { if (vn1[j] != 0.) { /* NOTE: The following 4 lines follow from the analysis in Lapack Working Note 176. */ temp = MAGMA_Z_ABS( *A(rk,j) ) / vn1[j]; temp = max( 0., ((1. + temp) * (1. - temp)) ); d__1 = vn1[j] / vn2[j]; temp2 = temp * (d__1 * d__1); if (temp2 <= tol3z) { vn2[j] = (double) lsticc; lsticc = j; } else { vn1[j] *= magma_dsqrt(temp); } } } } *A(rk, k) = Akk; ++k; } // leave k as the last column done --k; *kb = k + 1; rk = offset + *kb - 1; /* Apply the block reflector to the rest of the matrix: A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)' */ if (*kb < min(n, m - offset)) { i__1 = m - rk - 1; i__2 = n - *kb; /* Send F to the GPU */ magma_zsetmatrix( i__2, *kb, F (*kb, 0), ldf, dF(*kb, 0), i__2, queue ); magma_zgemm( MagmaNoTrans, MagmaConjTrans, i__1, i__2, *kb, c_neg_one, dA(rk+1, 0 ), ldda, dF(*kb, 0 ), i__2, c_one, dA(rk+1, *kb), ldda, queue ); } /* Recomputation of difficult columns. */ while( lsticc > 0 ) { itemp = (magma_int_t)(vn2[lsticc] >= 0. ? floor(vn2[lsticc] + .5) : -floor(.5 - vn2[lsticc])); i__1 = m - rk - 1; if (lsticc <= nb) { vn1[lsticc] = magma_cblas_dznrm2( i__1, A(rk+1,lsticc), ione ); } else { /* Where is the data, CPU or GPU ? */ double r1, r2; r1 = magma_cblas_dznrm2( nb-k, A(rk+1,lsticc), ione ); r2 = magma_dznrm2( m-offset-nb, dA(offset + nb + 1, lsticc), ione, queue ); //vn1[lsticc] = magma_dznrm2( i__1, dA(rk + 1, lsticc), ione, queue ); vn1[lsticc] = magma_dsqrt(r1*r1 + r2*r2); } /* NOTE: The computation of VN1( LSTICC ) relies on the fact that SNRM2 does not fail on vectors with norm below the value of SQRT(DLAMCH('S')) */ vn2[lsticc] = vn1[lsticc]; lsticc = itemp; } magma_queue_destroy( queue ); return MAGMA_SUCCESS; } /* magma_zlaqps */
/* //////////////////////////////////////////////////////////////////////////// -- Testing zswap, zswapblk, zlaswp, zlaswpx */ int main( int argc, char** argv) { TESTING_INIT(); // OpenCL use: cl_mem , offset (two arguments); // else use: pointer + offset (one argument). #ifdef HAVE_clBLAS #define d_A1(i_, j_) d_A1 , (i_) + (j_)*ldda #define d_A2(i_, j_) d_A2 , (i_) + (j_)*ldda #define d_ipiv(i_) d_ipiv , (i_) #else #define d_A1(i_, j_) (d_A1 + (i_) + (j_)*ldda) #define d_A2(i_, j_) (d_A2 + (i_) + (j_)*ldda) #define d_ipiv(i_) (d_ipiv + (i_)) #endif #define h_A1(i_, j_) (h_A1 + (i_) + (j_)*lda) #define h_A2(i_, j_) (h_A2 + (i_) + (j_)*lda) magmaDoubleComplex *h_A1, *h_A2; magmaDoubleComplex *h_R1, *h_R2; magmaDoubleComplex_ptr d_A1, d_A2; // row-major and column-major performance real_Double_t row_perf0 = MAGMA_D_NAN, col_perf0 = MAGMA_D_NAN; real_Double_t row_perf1 = MAGMA_D_NAN, col_perf1 = MAGMA_D_NAN; real_Double_t row_perf2 = MAGMA_D_NAN, col_perf2 = MAGMA_D_NAN; real_Double_t row_perf4 = MAGMA_D_NAN; real_Double_t row_perf5 = MAGMA_D_NAN, col_perf5 = MAGMA_D_NAN; real_Double_t row_perf6 = MAGMA_D_NAN, col_perf6 = MAGMA_D_NAN; real_Double_t row_perf7 = MAGMA_D_NAN; real_Double_t cpu_perf = MAGMA_D_NAN; real_Double_t time, gbytes; magma_int_t N, lda, ldda, nb, j; magma_int_t ione = 1; magma_int_t *ipiv, *ipiv2; magmaInt_ptr d_ipiv; magma_int_t status = 0; magma_opts opts; opts.parse_opts( argc, argv ); printf("%% %8s zswap zswap zswapblk zlaswp zlaswp2 zlaswpx zcopymatrix CPU (all in )\n", g_platform_str ); printf("%% N nb row-maj/col-maj row-maj/col-maj row-maj/col-maj row-maj row-maj row-maj/col-maj row-blk/col-blk zlaswp (GByte/s)\n"); printf("%%========================================================================================================================================\n"); for( int itest = 0; itest < opts.ntest; ++itest ) { for( int iter = 0; iter < opts.niter; ++iter ) { // For an N x N matrix, swap nb rows or nb columns using various methods. // Each test is assigned one bit in the 'check' bitmask; bit=1 indicates failure. // The variable 'shift' keeps track of which bit is for current test magma_int_t shift = 1; magma_int_t check = 0; N = opts.nsize[itest]; lda = N; ldda = magma_roundup( N, opts.align ); // multiple of 32 by default nb = (opts.nb > 0 ? opts.nb : magma_get_zgetrf_nb( N, N )); nb = min( N, nb ); // each swap does 2N loads and 2N stores, for nb swaps gbytes = sizeof(magmaDoubleComplex) * 4.*N*nb / 1e9; TESTING_MALLOC_PIN( h_A1, magmaDoubleComplex, lda*N ); TESTING_MALLOC_PIN( h_A2, magmaDoubleComplex, lda*N ); TESTING_MALLOC_PIN( h_R1, magmaDoubleComplex, lda*N ); TESTING_MALLOC_PIN( h_R2, magmaDoubleComplex, lda*N ); TESTING_MALLOC_CPU( ipiv, magma_int_t, nb ); TESTING_MALLOC_CPU( ipiv2, magma_int_t, nb ); TESTING_MALLOC_DEV( d_ipiv, magma_int_t, nb ); TESTING_MALLOC_DEV( d_A1, magmaDoubleComplex, ldda*N ); TESTING_MALLOC_DEV( d_A2, magmaDoubleComplex, ldda*N ); // getrf always makes ipiv[j] >= j+1, where ipiv is one based and j is zero based // some implementations (e.g., MacOS dlaswp) assume this for( j=0; j < nb; j++ ) { ipiv[j] = (rand() % (N-j)) + j + 1; assert( ipiv[j] >= j+1 ); assert( ipiv[j] <= N ); } /* ===================================================================== * cublas / clBLAS / Xeon Phi zswap, row-by-row (2 matrices) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2(0,0), ldda ); magmablasSetKernelStream( opts.queue ); // opts.handle also uses opts.queue time = magma_sync_wtime( opts.queue ); for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { #ifdef HAVE_CUBLAS cublasZswap( opts.handle, N, d_A1(0,j), 1, d_A2(0,ipiv[j]-1), 1 ); #else magma_zswap( N, d_A1(0,j), 1, d_A2(0,ipiv[j]-1), 1, opts.queue ); #endif } } time = magma_sync_wtime( opts.queue ) - time; row_perf0 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1(0,j), &ione, h_A2(0,ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2(0,0), ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* Column Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2(0,0), ldda ); time = magma_sync_wtime( opts.queue ); for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { #ifdef HAVE_CUBLAS cublasZswap( opts.handle, N, d_A1(j,0), ldda, d_A2(ipiv[j]-1,0), ldda ); #else magma_zswap( N, d_A1(j,0), ldda, d_A2(ipiv[j]-1,0), ldda, opts.queue ); #endif } } time = magma_sync_wtime( opts.queue ) - time; col_perf0 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+j, &lda, h_A2+(ipiv[j]-1), &lda); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2(0,0), ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* ===================================================================== * zswap, row-by-row (2 matrices) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2(0,0), ldda ); time = magma_sync_wtime( opts.queue ); for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { magmablas_zswap( N, d_A1(0,j), 1, d_A2(0,ipiv[j]-1), 1); } } time = magma_sync_wtime( opts.queue ) - time; row_perf1 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1(0,j), &ione, h_A2(0,ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2(0,0), ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* Column Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2(0,0), ldda ); time = magma_sync_wtime( opts.queue ); for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { magmablas_zswap( N, d_A1(j,0), ldda, d_A2(ipiv[j]-1,0), ldda ); } } time = magma_sync_wtime( opts.queue ) - time; col_perf1 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+j, &lda, h_A2+(ipiv[j]-1), &lda); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2(0,0), ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* ===================================================================== * zswapblk, blocked version (2 matrices) */ #ifdef HAVE_CUBLAS /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2(0,0), ldda ); time = magma_sync_wtime( opts.queue ); magmablas_zswapblk( MagmaRowMajor, N, d_A1(0,0), ldda, d_A2(0,0), ldda, 1, nb, ipiv, 1, 0); time = magma_sync_wtime( opts.queue ) - time; row_perf2 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1(0,j), &ione, h_A2(0,ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2(0,0), ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* Column Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2(0,0), ldda ); time = magma_sync_wtime( opts.queue ); magmablas_zswapblk( MagmaColMajor, N, d_A1(0,0), ldda, d_A2(0,0), ldda, 1, nb, ipiv, 1, 0); time = magma_sync_wtime( opts.queue ) - time; col_perf2 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1(j,0), &lda, h_A2(ipiv[j]-1,0), &lda); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2(0,0), ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; #endif /* ===================================================================== * LAPACK-style zlaswp (1 matrix) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); time = magma_sync_wtime( opts.queue ); magmablas_zlaswp( N, d_A1(0,0), ldda, 1, nb, ipiv, 1); time = magma_sync_wtime( opts.queue ) - time; row_perf4 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1(0,j), &ione, h_A1(0,ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* ===================================================================== * LAPACK-style zlaswp (1 matrix) - d_ipiv on GPU */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); time = magma_sync_wtime( opts.queue ); magma_setvector( nb, sizeof(magma_int_t), ipiv, 1, d_ipiv(0), 1 ); magmablas_zlaswp2( N, d_A1(0,0), ldda, 1, nb, d_ipiv(0), 1 ); time = magma_sync_wtime( opts.queue ) - time; row_perf7 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1(0,j), &ione, h_A1(0,ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* ===================================================================== * LAPACK-style zlaswpx (extended for row- and col-major) (1 matrix) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); time = magma_sync_wtime( opts.queue ); magmablas_zlaswpx( N, d_A1(0,0), ldda, 1, 1, nb, ipiv, 1); time = magma_sync_wtime( opts.queue ) - time; row_perf5 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1(0,j), &ione, h_A1(0,ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* Col Major */ init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1(0,0), ldda ); time = magma_sync_wtime( opts.queue ); magmablas_zlaswpx( N, d_A1(0,0), 1, ldda, 1, nb, ipiv, 1); time = magma_sync_wtime( opts.queue ) - time; col_perf5 = gbytes / time; /* LAPACK swap on CPU for comparison */ time = magma_wtime(); lapackf77_zlaswp( &N, h_A1, &lda, &ione, &nb, ipiv, &ione); time = magma_wtime() - time; cpu_perf = gbytes / time; magma_zgetmatrix( N, N, d_A1(0,0), ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* ===================================================================== * Copy matrix. */ time = magma_sync_wtime( opts.queue ); magma_zcopymatrix( N, nb, d_A1(0,0), ldda, d_A2(0,0), ldda ); time = magma_sync_wtime( opts.queue ) - time; // copy reads 1 matrix and writes 1 matrix, so has half gbytes of swap col_perf6 = 0.5 * gbytes / time; time = magma_sync_wtime( opts.queue ); magma_zcopymatrix( nb, N, d_A1(0,0), ldda, d_A2(0,0), ldda ); time = magma_sync_wtime( opts.queue ) - time; // copy reads 1 matrix and writes 1 matrix, so has half gbytes of swap row_perf6 = 0.5 * gbytes / time; printf("%5d %3d %6.2f%c/ %6.2f%c %6.2f%c/ %6.2f%c %6.2f%c/ %6.2f%c %6.2f%c %6.2f%c %6.2f%c/ %6.2f%c %6.2f / %6.2f %6.2f %10s\n", (int) N, (int) nb, row_perf0, ((check & 0x001) != 0 ? '*' : ' '), col_perf0, ((check & 0x002) != 0 ? '*' : ' '), row_perf1, ((check & 0x004) != 0 ? '*' : ' '), col_perf1, ((check & 0x008) != 0 ? '*' : ' '), row_perf2, ((check & 0x010) != 0 ? '*' : ' '), col_perf2, ((check & 0x020) != 0 ? '*' : ' '), row_perf4, ((check & 0x040) != 0 ? '*' : ' '), row_perf7, ((check & 0x080) != 0 ? '*' : ' '), row_perf5, ((check & 0x100) != 0 ? '*' : ' '), col_perf5, ((check & 0x200) != 0 ? '*' : ' '), row_perf6, col_perf6, cpu_perf, (check == 0 ? "ok" : "* failed") ); status += ! (check == 0); TESTING_FREE_PIN( h_A1 ); TESTING_FREE_PIN( h_A2 ); TESTING_FREE_PIN( h_R1 ); TESTING_FREE_PIN( h_R2 ); TESTING_FREE_CPU( ipiv ); TESTING_FREE_CPU( ipiv2 ); TESTING_FREE_DEV( d_ipiv ); TESTING_FREE_DEV( d_A1 ); TESTING_FREE_DEV( d_A2 ); fflush( stdout ); } if ( opts.niter > 1 ) { printf( "\n" ); } } opts.cleanup(); TESTING_FINALIZE(); return status; }
/** Purpose ------- ZHEEVR computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. Whenever possible, ZHEEVR calls ZSTEGR to compute the eigenspectrum using Relatively Robust Representations. ZSTEGR computes eigenvalues by the dqds algorithm, while orthogonal eigenvectors are computed from various "good" L D L^T representations (also known as Relatively Robust Representations). Gram-Schmidt orthogonalization is avoided as far as possible. More specifically, the various steps of the algorithm are as follows. For the i-th unreduced block of T, 1. Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation, 2. Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high relative accuracy by the dqds algorithm, 3. If there is a cluster of close eigenvalues, "choose" sigma_i close to the cluster, and go to step (a), 4. Given the approximate eigenvalue lambda_j of L_i D_i L_i^T, compute the corresponding eigenvector by forming a rank-revealing twisted factorization. The desired accuracy of the output can be specified by the input parameter ABSTOL. For more details, see "A new O(n^2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon, Computer Science Division Technical Report No. UCB//CSD-97-971, UC Berkeley, May 1997. Note 1 : ZHEEVR calls ZSTEGR when the full spectrum is requested on machines which conform to the ieee-754 floating point standard. ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and when partial spectrum requests are made. Normal execution of ZSTEGR may create NaNs and infinities and hence may abort due to a floating point exception in environments which do not handle NaNs and infinities in the ieee standard default manner. Arguments --------- @param[in] jobz magma_vec_t - = MagmaNoVec: Compute eigenvalues only; - = MagmaVec: Compute eigenvalues and eigenvectors. @param[in] range magma_range_t - = MagmaRangeAll: all eigenvalues will be found. - = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU] will be found. - = MagmaRangeI: the IL-th through IU-th eigenvalues will be found. @param[in] uplo magma_uplo_t - = MagmaUpper: Upper triangle of A is stored; - = MagmaLower: Lower triangle of A is stored. @param[in] n INTEGER The order of the matrix A. N >= 0. @param[in,out] A COMPLEX_16 array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=MagmaLower) or the upper triangle (if UPLO=MagmaUpper) of A, including the diagonal, is destroyed. @param[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[in] vl DOUBLE PRECISION @param[in] vu DOUBLE PRECISION If RANGE=MagmaRangeV, the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = MagmaRangeAll or MagmaRangeI. @param[in] il INTEGER @param[in] iu INTEGER If RANGE=MagmaRangeI, the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = MagmaRangeAll or MagmaRangeV. @param[in] abstol DOUBLE PRECISION The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ), \n where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. \n See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. \n If high relative accuracy is important, set ABSTOL to DLAMCH( 'Safe minimum' ). Doing so will guarantee that eigenvalues are computed to high relative accuracy when possible in future releases. The current code does not make any guarantees about high relative accuracy, but furutre releases will. See J. Barlow and J. Demmel, "Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices", LAPACK Working Note #7, for a discussion of which matrices define their eigenvalues to high relative accuracy. @param[out] m INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1. @param[out] w DOUBLE PRECISION array, dimension (N) The first M elements contain the selected eigenvalues in ascending order. @param[out] Z COMPLEX_16 array, dimension (LDZ, max(1,M)) If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = MagmaNoVec, then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M is not known in advance and an upper bound must be used. @param[in] ldz INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = MagmaVec, LDZ >= max(1,N). @param[out] isuppz INTEGER ARRAY, dimension ( 2*max(1,M) ) The support of the eigenvectors in Z, i.e., the indices indicating the nonzero elements in Z. The i-th eigenvector is nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i ). __Implemented only for__ RANGE = MagmaRangeAll or MagmaRangeI and IU - IL = N - 1 @param[out] work (workspace) COMPLEX_16 array, dimension (LWORK) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. @param[in] lwork INTEGER The length of the array WORK. LWORK >= max(1,2*N). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the max of the blocksize for ZHETRD and for ZUNMTR as returned by ILAENV. \n If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. @param[out] rwork (workspace) DOUBLE PRECISION array, dimension (LRWORK) On exit, if INFO = 0, RWORK[0] returns the optimal (and minimal) LRWORK. @param[in] lrwork INTEGER The length of the array RWORK. LRWORK >= max(1,24*N). \n If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the RWORK array, returns this value as the first entry of the RWORK array, and no error message related to LRWORK is issued by XERBLA. @param[out] iwork (workspace) INTEGER array, dimension (LIWORK) On exit, if INFO = 0, IWORK[0] returns the optimal (and minimal) LIWORK. @param[in] liwork INTEGER The dimension of the array IWORK. LIWORK >= max(1,10*N). \n If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to 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: Internal error Further Details --------------- Based on contributions by Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USA Ken Stanley, Computer Science Division, University of California at Berkeley, USA @ingroup magma_zheev_driver ********************************************************************/ extern "C" magma_int_t magma_zheevr( magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, double vl, double vu, magma_int_t il, magma_int_t iu, double abstol, magma_int_t *m, double *w, magmaDoubleComplex *Z, magma_int_t ldz, magma_int_t *isuppz, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t lrwork, magma_int_t *iwork, magma_int_t liwork, magma_int_t *info) { /* Constants */ const magma_int_t izero = 0; const magma_int_t ione = 1; const float szero = 0.; const float sone = 1.; /* Local variables */ const char* uplo_ = lapack_uplo_const( uplo ); const char* jobz_ = lapack_vec_const( jobz ); const char* range_ = lapack_range_const( range ); magma_int_t indrd, indre; magma_int_t imax; magma_int_t lopt, itmp1, indree, indrdd; magma_int_t tryrac; magma_int_t i, j, jj, i__1; magma_int_t iscale, indibl, indifl; magma_int_t indiwo, indisp, indtau; magma_int_t indrwk, indwk; magma_int_t llwork, llrwork, nsplit; magma_int_t ieeeok; magma_int_t iinfo; magma_int_t lwmin, lrwmin, liwmin; double safmin; double bignum; double smlnum; double eps, tmp1; double anrm; double sigma, d__1; double rmin, rmax; bool lower = (uplo == MagmaLower); bool wantz = (jobz == MagmaVec); bool alleig = (range == MagmaRangeAll); bool valeig = (range == MagmaRangeV); bool indeig = (range == MagmaRangeI); bool lquery = (lwork == -1 || lrwork == -1 || liwork == -1); *info = 0; if (! (wantz || (jobz == MagmaNoVec))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *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 (ldz < 1 || (wantz && ldz < n)) { *info = -15; } else { if (valeig) { if (n > 0 && vu <= vl) { *info = -8; } } else if (indeig) { if (il < 1 || il > max(1,n)) { *info = -9; } else if (iu < min(n,il) || iu > n) { *info = -10; } } } magma_int_t nb = magma_get_zhetrd_nb(n); lwmin = n * (nb + 1); lrwmin = 24 * n; liwmin = 10 * n; work[0] = magma_zmake_lwork( lwmin ); rwork[0] = magma_dmake_lwork( lrwmin ); iwork[0] = liwmin; if (lwork < lwmin && ! lquery) { *info = -18; } else if ((lrwork < lrwmin) && ! lquery) { *info = -20; } else if ((liwork < liwmin) && ! lquery) { *info = -22; } if (*info != 0) { magma_xerbla(__func__, -(*info)); return *info; } else if (lquery) { return *info; } *m = 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_zheevr(jobz_, range_, uplo_, &n, A, &lda, &vl, &vu, &il, &iu, &abstol, m, w, Z, &ldz, isuppz, work, &lwork, rwork, &lrwork, iwork, &liwork, info); return *info; } --w; --work; --rwork; --iwork; --isuppz; /* Get machine constants. */ safmin = lapackf77_dlamch("Safe minimum"); eps = lapackf77_dlamch("Precision"); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = magma_dsqrt(smlnum); rmax = magma_dsqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = lapackf77_zlanhe("M", uplo_, &n, A, &lda, &rwork[1]); iscale = 0; if (anrm > 0. && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { d__1 = 1.; lapackf77_zlascl(uplo_, &izero, &izero, &d__1, &sigma, &n, &n, A, &lda, info); if (abstol > 0.) { abstol *= sigma; } if (valeig) { vl *= sigma; vu *= sigma; } } /* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ indtau = 1; indwk = indtau + n; indre = 1; indrd = indre + n; indree = indrd + n; indrdd = indree + n; indrwk = indrdd + n; llwork = lwork - indwk + 1; llrwork = lrwork - indrwk + 1; indifl = 1; indibl = indifl + n; indisp = indibl + n; indiwo = indisp + n; magma_zhetrd(uplo, n, A, lda, &rwork[indrd], &rwork[indre], &work[indtau], &work[indwk], llwork, &iinfo); lopt = n + (magma_int_t)MAGMA_Z_REAL(work[indwk]); /* If all eigenvalues are desired and ABSTOL is less than or equal to zero, then call DSTERF or ZUNGTR and ZSTEQR. If this fails for some eigenvalue, then try DSTEBZ. */ ieeeok = lapackf77_ieeeck( &ione, &szero, &sone); /* If only the eigenvalues are required call DSTERF for all or DSTEBZ for a part */ if (! wantz) { blasf77_dcopy(&n, &rwork[indrd], &ione, &w[1], &ione); i__1 = n - 1; if (alleig || (indeig && il == 1 && iu == n)) { lapackf77_dsterf(&n, &w[1], &rwork[indre], info); *m = n; } else { lapackf77_dstebz(range_, "E", &n, &vl, &vu, &il, &iu, &abstol, &rwork[indrd], &rwork[indre], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &rwork[indrwk], &iwork[indiwo], info); } /* Otherwise call ZSTEMR if infinite and NaN arithmetic is supported */ } else if (ieeeok == 1) { i__1 = n - 1; blasf77_dcopy(&i__1, &rwork[indre], &ione, &rwork[indree], &ione); blasf77_dcopy(&n, &rwork[indrd], &ione, &rwork[indrdd], &ione); if (abstol < 2*n*eps) tryrac = 1; else tryrac = 0; lapackf77_zstemr(jobz_, range_, &n, &rwork[indrdd], &rwork[indree], &vl, &vu, &il, &iu, m, &w[1], Z, &ldz, &n, &isuppz[1], &tryrac, &rwork[indrwk], &llrwork, &iwork[1], &liwork, info); if (*info == 0 && wantz) { magma_zunmtr(MagmaLeft, uplo, MagmaNoTrans, n, *m, A, lda, &work[indtau], Z, ldz, &work[indwk], llwork, &iinfo); } } /* Call DSTEBZ and ZSTEIN if infinite and NaN arithmetic is not supported or ZSTEMR didn't converge. */ if (wantz && (ieeeok == 0 || *info != 0)) { *info = 0; lapackf77_dstebz(range_, "B", &n, &vl, &vu, &il, &iu, &abstol, &rwork[indrd], &rwork[indre], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &rwork[indrwk], &iwork[indiwo], info); lapackf77_zstein(&n, &rwork[indrd], &rwork[indre], m, &w[1], &iwork[indibl], &iwork[indisp], Z, &ldz, &rwork[indrwk], &iwork[indiwo], &iwork[indifl], info); /* Apply unitary matrix used in reduction to tridiagonal form to eigenvectors returned by ZSTEIN. */ magma_zunmtr(MagmaLeft, uplo, MagmaNoTrans, n, *m, A, lda, &work[indtau], Z, ldz, &work[indwk], llwork, &iinfo); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } d__1 = 1. / sigma; blasf77_dscal(&imax, &d__1, &w[1], &ione); } /* If eigenvalues are not in order, then sort them, along with eigenvectors. */ if (wantz) { for (j = 1; j <= *m-1; ++j) { i = 0; tmp1 = w[j]; for (jj = j + 1; jj <= *m; ++jj) { if (w[jj] < tmp1) { i = jj; tmp1 = w[jj]; } } if (i != 0) { itmp1 = iwork[indibl + i - 1]; w[i] = w[j]; iwork[indibl + i - 1] = iwork[indibl + j - 1]; w[j] = tmp1; iwork[indibl + j - 1] = itmp1; blasf77_zswap(&n, Z + (i-1)*ldz, &ione, Z + (j-1)*ldz, &ione); } } } /* Set WORK[0] to optimal complex workspace size. */ work[1] = magma_zmake_lwork( lopt ); rwork[1] = magma_dmake_lwork( lrwmin ); iwork[1] = liwmin; return *info; } /* magma_zheevr */
/* //////////////////////////////////////////////////////////////////////////// -- Testing zswap, zswapblk, zpermute, zlaswp, zlaswpx */ int main( int argc, char** argv) { TESTING_INIT(); magmaDoubleComplex *h_A1, *h_A2; magmaDoubleComplex *d_A1, *d_A2; magmaDoubleComplex *h_R1, *h_R2; // row-major and column-major performance real_Double_t row_perf0, col_perf0; real_Double_t row_perf1, col_perf1; real_Double_t row_perf2, col_perf2; real_Double_t row_perf3; real_Double_t row_perf4; real_Double_t row_perf5, col_perf5; real_Double_t row_perf6, col_perf6; real_Double_t row_perf7; real_Double_t cpu_perf; real_Double_t time, gbytes; magma_int_t N, lda, ldda, nb, j; magma_int_t ione = 1; magma_int_t *ipiv, *ipiv2; magma_int_t *d_ipiv; magma_int_t status = 0; magma_opts opts; parse_opts( argc, argv, &opts ); magma_queue_t queue = 0; printf(" cublasZswap zswap zswapblk zlaswp zpermute zlaswp2 zlaswpx zcopymatrix CPU (all in )\n"); printf(" N nb row-maj/col-maj row-maj/col-maj row-maj/col-maj row-maj row-maj row-maj row-maj/col-maj row-blk/col-blk zlaswp (GByte/s)\n"); printf("==================================================================================================================================================\n"); for( int itest = 0; itest < opts.ntest; ++itest ) { for( int iter = 0; iter < opts.niter; ++iter ) { // For an N x N matrix, swap nb rows or nb columns using various methods. // Each test is assigned one bit in the 'check' bitmask; bit=1 indicates failure. // The variable 'shift' keeps track of which bit is for current test int shift = 1; int check = 0; N = opts.nsize[itest]; lda = N; ldda = ((N+31)/32)*32; nb = (opts.nb > 0 ? opts.nb : magma_get_zgetrf_nb( N )); nb = min( N, nb ); // each swap does 2N loads and 2N stores, for nb swaps gbytes = sizeof(magmaDoubleComplex) * 4.*N*nb / 1e9; TESTING_MALLOC_PIN( h_A1, magmaDoubleComplex, lda*N ); TESTING_MALLOC_PIN( h_A2, magmaDoubleComplex, lda*N ); TESTING_MALLOC_PIN( h_R1, magmaDoubleComplex, lda*N ); TESTING_MALLOC_PIN( h_R2, magmaDoubleComplex, lda*N ); TESTING_MALLOC_CPU( ipiv, magma_int_t, nb ); TESTING_MALLOC_CPU( ipiv2, magma_int_t, nb ); TESTING_MALLOC_DEV( d_ipiv, magma_int_t, nb ); TESTING_MALLOC_DEV( d_A1, magmaDoubleComplex, ldda*N ); TESTING_MALLOC_DEV( d_A2, magmaDoubleComplex, ldda*N ); for( j=0; j < nb; j++ ) { ipiv[j] = (magma_int_t) ((rand()*1.*N) / (RAND_MAX * 1.)) + 1; } /* ===================================================================== * cublasZswap, row-by-row (2 matrices) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2, ldda ); time = magma_sync_wtime( queue ); for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { cublasZswap( N, d_A1+ldda*j, 1, d_A2+ldda*(ipiv[j]-1), 1); } } time = magma_sync_wtime( queue ) - time; row_perf0 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+lda*j, &ione, h_A2+lda*(ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2, ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* Column Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2, ldda ); time = magma_sync_wtime( queue ); for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { cublasZswap( N, d_A1+j, ldda, d_A2+ipiv[j]-1, ldda); } } time = magma_sync_wtime( queue ) - time; col_perf0 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+j, &lda, h_A2+(ipiv[j]-1), &lda); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2, ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* ===================================================================== * zswap, row-by-row (2 matrices) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2, ldda ); time = magma_sync_wtime( queue ); for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { magmablas_zswap( N, d_A1+ldda*j, 1, d_A2+ldda*(ipiv[j]-1), 1); } } time = magma_sync_wtime( queue ) - time; row_perf1 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+lda*j, &ione, h_A2+lda*(ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2, ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* Column Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2, ldda ); time = magma_sync_wtime( queue ); for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { magmablas_zswap( N, d_A1+j, ldda, d_A2+ipiv[j]-1, ldda ); } } time = magma_sync_wtime( queue ) - time; col_perf1 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+j, &lda, h_A2+(ipiv[j]-1), &lda); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2, ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* ===================================================================== * zswapblk, blocked version (2 matrices) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2, ldda ); time = magma_sync_wtime( queue ); magmablas_zswapblk( MagmaRowMajor, N, d_A1, ldda, d_A2, ldda, 1, nb, ipiv, 1, 0); time = magma_sync_wtime( queue ) - time; row_perf2 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+lda*j, &ione, h_A2+lda*(ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2, ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* Column Major */ init_matrix( N, N, h_A1, lda, 0 ); init_matrix( N, N, h_A2, lda, 100 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); magma_zsetmatrix( N, N, h_A2, lda, d_A2, ldda ); time = magma_sync_wtime( queue ); magmablas_zswapblk( MagmaColMajor, N, d_A1, ldda, d_A2, ldda, 1, nb, ipiv, 1, 0); time = magma_sync_wtime( queue ) - time; col_perf2 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+j, &lda, h_A2+(ipiv[j]-1), &lda); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); magma_zgetmatrix( N, N, d_A2, ldda, h_R2, lda ); check += (diff_matrix( N, N, h_A1, lda, h_R1, lda ) || diff_matrix( N, N, h_A2, lda, h_R2, lda ))*shift; shift *= 2; /* ===================================================================== * zpermute_long (1 matrix) */ /* Row Major */ memcpy( ipiv2, ipiv, nb*sizeof(magma_int_t) ); // zpermute updates ipiv2 init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); time = magma_sync_wtime( queue ); magmablas_zpermute_long2( N, d_A1, ldda, ipiv2, nb, 0 ); time = magma_sync_wtime( queue ) - time; row_perf3 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+lda*j, &ione, h_A1+lda*(ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* ===================================================================== * LAPACK-style zlaswp (1 matrix) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); time = magma_sync_wtime( queue ); magmablas_zlaswp( N, d_A1, ldda, 1, nb, ipiv, 1); time = magma_sync_wtime( queue ) - time; row_perf4 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+lda*j, &ione, h_A1+lda*(ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* ===================================================================== * LAPACK-style zlaswp (1 matrix) - d_ipiv on GPU */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); time = magma_sync_wtime( queue ); magma_setvector( nb, sizeof(magma_int_t), ipiv, 1, d_ipiv, 1 ); magmablas_zlaswp2( N, d_A1, ldda, 1, nb, d_ipiv ); time = magma_sync_wtime( queue ) - time; row_perf7 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+lda*j, &ione, h_A1+lda*(ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* ===================================================================== * LAPACK-style zlaswpx (extended for row- and col-major) (1 matrix) */ /* Row Major */ init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); time = magma_sync_wtime( queue ); magmablas_zlaswpx( N, d_A1, ldda, 1, 1, nb, ipiv, 1); time = magma_sync_wtime( queue ) - time; row_perf5 = gbytes / time; for( j=0; j < nb; j++) { if ( j != (ipiv[j]-1)) { blasf77_zswap( &N, h_A1+lda*j, &ione, h_A1+lda*(ipiv[j]-1), &ione); } } magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* Col Major */ init_matrix( N, N, h_A1, lda, 0 ); magma_zsetmatrix( N, N, h_A1, lda, d_A1, ldda ); time = magma_sync_wtime( queue ); magmablas_zlaswpx( N, d_A1, 1, ldda, 1, nb, ipiv, 1); time = magma_sync_wtime( queue ) - time; col_perf5 = gbytes / time; time = magma_wtime(); lapackf77_zlaswp( &N, h_A1, &lda, &ione, &nb, ipiv, &ione); time = magma_wtime() - time; cpu_perf = gbytes / time; magma_zgetmatrix( N, N, d_A1, ldda, h_R1, lda ); check += diff_matrix( N, N, h_A1, lda, h_R1, lda )*shift; shift *= 2; /* ===================================================================== * Copy matrix. */ time = magma_sync_wtime( queue ); magma_zcopymatrix( N, nb, d_A1, ldda, d_A2, ldda ); time = magma_sync_wtime( queue ) - time; // copy reads 1 matrix and writes 1 matrix, so has half gbytes of swap col_perf6 = 0.5 * gbytes / time; time = magma_sync_wtime( queue ); magma_zcopymatrix( nb, N, d_A1, ldda, d_A2, ldda ); time = magma_sync_wtime( queue ) - time; // copy reads 1 matrix and writes 1 matrix, so has half gbytes of swap row_perf6 = 0.5 * gbytes / time; printf("%5d %3d %6.2f%c/ %6.2f%c %6.2f%c/ %6.2f%c %6.2f%c/ %6.2f%c %6.2f%c %6.2f%c %6.2f%c %6.2f%c/ %6.2f%c %6.2f / %6.2f %6.2f %10s\n", (int) N, (int) nb, row_perf0, ((check & 0x001) != 0 ? '*' : ' '), col_perf0, ((check & 0x002) != 0 ? '*' : ' '), row_perf1, ((check & 0x004) != 0 ? '*' : ' '), col_perf1, ((check & 0x008) != 0 ? '*' : ' '), row_perf2, ((check & 0x010) != 0 ? '*' : ' '), col_perf2, ((check & 0x020) != 0 ? '*' : ' '), row_perf3, ((check & 0x040) != 0 ? '*' : ' '), row_perf4, ((check & 0x080) != 0 ? '*' : ' '), row_perf7, ((check & 0x100) != 0 ? '*' : ' '), row_perf5, ((check & 0x200) != 0 ? '*' : ' '), col_perf5, ((check & 0x400) != 0 ? '*' : ' '), row_perf6, col_perf6, cpu_perf, (check == 0 ? "ok" : "* failed") ); status += ! (check == 0); TESTING_FREE_PIN( h_A1 ); TESTING_FREE_PIN( h_A2 ); TESTING_FREE_PIN( h_R1 ); TESTING_FREE_PIN( h_R2 ); TESTING_FREE_CPU( ipiv ); TESTING_FREE_CPU( ipiv2 ); TESTING_FREE_DEV( d_ipiv ); TESTING_FREE_DEV( d_A1 ); TESTING_FREE_DEV( d_A2 ); fflush( stdout ); } if ( opts.niter > 1 ) { printf( "\n" ); } } TESTING_FINALIZE(); return status; }