extern "C" void magma_ssyr2k_mgpu( magma_int_t num_gpus, magma_uplo_t uplo, magma_trans_t trans, magma_int_t nb, magma_int_t n, magma_int_t k, float alpha, float **db, magma_int_t lddb, magma_int_t offset_b, float beta, float **dc, magma_int_t lddc, magma_int_t offset, magma_int_t num_streams, magma_queue_t stream[][10]) { #define dB(id, i, j) (db[(id)]+(j)*lddb + (i)+offset_b) #define dB1(id, i, j) (db[(id)]+(j)*lddb + (i)+offset_b)+k*lddb #define dC(id, i, j) (dc[(id)]+(j)*lddc + (i)) magma_int_t i, id, ib, ii, kk, n1; float c_one = MAGMA_S_ONE; magma_device_t orig_dev; magma_getdevice( &orig_dev ); magma_queue_t orig_stream; magmablasGetKernelStream( &orig_stream ); /* diagonal update */ for( i=0; i < n; i += nb ) { id = ((i+offset)/nb)%num_gpus; kk = (i/(nb*num_gpus))%num_streams; magma_setdevice(id); magmablasSetKernelStream(stream[id][kk]); ib = min(nb, n-i); ii = nb*((i+offset)/(nb*num_gpus)); /* ssyr2k on diagonal block */ trace_gpu_start( id, kk, "syr2k", "syr2k" ); magma_ssyr2k(uplo, trans, ib, k, alpha, dB1(id, i, 0 ), lddb, dB(id, i, 0 ), lddb, beta, dC(id, i+offset, ii), lddc); trace_gpu_end( id, kk ); } /* off-diagonal update */ if (uplo == MagmaUpper) { for( i=nb; i < n; i += nb ) { id = ((i+offset)/nb)%num_gpus; kk = (i/(nb*num_gpus))%num_streams; magma_setdevice(id); magmablasSetKernelStream(stream[id][kk]); ib = min(nb, n-i); ii = nb*((i+offset)/(nb*num_gpus)); magma_sgemm(MagmaNoTrans, MagmaConjTrans, i, ib, k, alpha, dB1(id, 0, 0 ), lddb, dB(id, i, 0 ), lddb, c_one, dC(id, 0, ii), lddc); } } else { for( i=0; i < n-nb; i += nb ) { id = ((i+offset)/nb)%num_gpus; kk = (i/(nb*num_gpus))%num_streams; magma_setdevice(id); magmablasSetKernelStream(stream[id][kk]); ib = min(nb, n-i); ii = nb*((i+offset)/(nb*num_gpus)); n1 = n-i-ib; // sgemm on off-diagonal blocks trace_gpu_start( id, kk, "gemm_up", "gemm_up" ); magma_sgemm(MagmaNoTrans, MagmaConjTrans, n1, ib, k, alpha, dB1(id, i+ib, 0 ), lddb, dB(id, i, 0 ), lddb, c_one, dC(id, i+offset+ib, ii), lddc); trace_gpu_end( id, kk ); } } if (uplo == MagmaUpper) { for( i=nb; i < n; i += nb ) { id = ((i+offset)/nb)%num_gpus; kk = (i/(nb*num_gpus))%num_streams; magma_setdevice(id); magmablasSetKernelStream(stream[id][kk]); ib = min(nb, n-i); ii = nb*((i+offset)/(nb*num_gpus)); magma_sgemm(MagmaNoTrans, MagmaConjTrans, i, ib, k, alpha, dB( id, 0, 0 ), lddb, dB1(id, i, 0 ), lddb, c_one, dC(id, 0, ii), lddc); } } else { for( i=0; i < n-nb; i += nb ) { id = ((i+offset)/nb)%num_gpus; kk = (i/(nb*num_gpus))%num_streams; magma_setdevice(id); magmablasSetKernelStream(stream[id][kk]); ib = min(nb, n-i); ii = nb*((i+offset)/(nb*num_gpus)); n1 = n-i-ib; /* sgemm on off-diagonal blocks */ trace_gpu_start( id, kk, "gemm_up", "gemm_up" ); magma_sgemm(MagmaNoTrans, MagmaConjTrans, n1, ib, k, alpha, dB(id, i+ib, 0 ), lddb, dB1(id, i, 0 ), lddb, c_one, dC(id, i+offset+ib, ii), lddc); trace_gpu_end( id, kk ); } } for( id=0; id < num_gpus; id++ ) { magma_setdevice(id); for( kk=0; kk < num_streams; kk++ ) { magma_queue_sync(stream[id][kk]); } } magma_setdevice( orig_dev ); magmablasSetKernelStream( orig_stream ); }
extern "C" magma_err_t magma_ssytrd(char uplo, magma_int_t n, float *a, magma_int_t lda, float *d, float *e, float *tau, float *work, magma_int_t lwork, magma_int_t *info, magma_queue_t queue) { /* -- clMAGMA (version 1.0.0) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver April 2012 Purpose ======= SSYTRD reduces a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation: Q**T * A * Q = T. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) REAL 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, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if UPLO = 'U', the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = 'L', the diagonal and first subdiagonal of A are over- written by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). D (output) REAL array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). E (output) REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. TAU (output) REAL array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= 1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Details =============== If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n-1) . . . H(2) H(1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in A(1:i-1,i+1), and tau in TAU(i). If UPLO = 'L', the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i). The contents of A on exit are illustrated by the following examples with n = 5: if UPLO = 'U': if UPLO = 'L': ( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d ) where d and e denote diagonal and off-diagonal elements of T, and vi denotes an element of the vector defining H(i). ===================================================================== */ char uplo_[2] = {uplo, 0}; magma_int_t ldda = lda; magma_int_t nb = magma_get_ssytrd_nb(n); float c_neg_one = MAGMA_S_NEG_ONE; float c_one = MAGMA_S_ONE; float d_one = MAGMA_D_ONE; magma_int_t kk, nx; magma_int_t i, j, i_n; magma_int_t iinfo; magma_int_t ldwork, lddwork, lwkopt; magma_int_t lquery; *info = 0; int upper = lapackf77_lsame(uplo_, "U"); lquery = lwork == -1; if (! upper && ! lapackf77_lsame(uplo_, "L")) { *info = -1; } else if (n < 0) { *info = -2; } else if (lda < max(1,n)) { *info = -4; } else if (lwork < nb*n && ! lquery) { *info = -9; } if (*info == 0) { /* Determine the block size. */ ldwork = lddwork = n; lwkopt = n * nb; // ACD // MAGMA_S_SET2REAL( work[0], lwkopt ); MAGMA_S_SET2REAL( work[0], (float) lwkopt ); } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) return *info; /* Quick return if possible */ if (n == 0) { work[0] = c_one; return *info; } magmaFloat_ptr da; size_t da_offset = 0; if (MAGMA_SUCCESS != magma_malloc( &da, (n*ldda + 2*n*nb )*sizeof(float))) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magmaFloat_ptr dwork = da; size_t dwork_offset = da_offset + (n)*ldda; if (n < 2048) nx = n; else nx = 512; if (upper) { /* Copy the matrix to the GPU */ magma_ssetmatrix( n, n, A(0, 0), 0, lda, dA(0, 0), ldda, queue ); /* Reduce the upper triangle of A. Columns 1:kk are handled by the unblocked method. */ kk = n - (n - nx + nb - 1) / nb * nb; for (i = n - nb; i >= kk; i -= nb) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the matrix W which is needed to update the unreduced part of the matrix */ /* Get the current panel (no need for the 1st iteration) */ if (i!=n-nb) magma_sgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), 0, lda, queue ); magma_slatrd(uplo, i+nb, nb, A(0, 0), lda, e, tau, work, ldwork, dA(0, 0), ldda, dwork, dwork_offset, lddwork, queue); /* Update the unreduced submatrix A(0:i-2,0:i-2), using an update of the form: A := A - V*W' - W*V' */ magma_ssetmatrix( i + nb, nb, work, 0, ldwork, dwork, dwork_offset, lddwork, queue ); magma_ssyr2k(magma_uplo_const(uplo), MagmaNoTrans, i, nb, c_neg_one, dA(0, i), ldda, dwork, dwork_offset, lddwork, d_one, dA(0, 0), ldda, queue); /* Copy superdiagonal elements back into A, and diagonal elements into D */ for (j = i; j < i+nb; ++j) { MAGMA_S_SET2REAL( *A(j-1, j), e[j - 1] ); d[j] = MAGMA_S_REAL( *A(j, j) ); } } magma_sgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), 0, lda, queue ); /* Use unblocked code to reduce the last or only block */ lapackf77_ssytd2(uplo_, &kk, A(0, 0), &lda, d, e, tau, &iinfo); } else { /* Copy the matrix to the GPU */ if (1<=n-nx) magma_ssetmatrix( n, n, A(0,0), 0, lda, dA(0,0), ldda, queue ); #ifdef FAST_SYMV // TODO this leaks memory from da, above magmaFloat_ptr dwork2; if (MAGMA_SUCCESS != magma_malloc( &dwork2, (n*n)*sizeof(float) )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } size_t dwork2_offset = 0; #endif /* Reduce the lower triangle of A */ for (i = 0; i < n-nx; i += nb) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the matrix W which is needed to update the unreduced part of the matrix */ /* Get the current panel (no need for the 1st iteration) */ if (i!=0) magma_sgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), 0, lda, queue ); #ifdef FAST_SYMV // unported magma_slatrd2(uplo, n-i, nb, A(i, i), lda, &e[i], &tau[i], work, ldwork, dA(i, i), ldda, dwork, lddwork, dwork2, n*n); #else magma_slatrd(uplo, n-i, nb, A(i, i), lda, &e[i], &tau[i], work, ldwork, dA(i, i), ldda, dwork, dwork_offset, lddwork, queue); #endif /* Update the unreduced submatrix A(i+ib:n,i+ib:n), using an update of the form: A := A - V*W' - W*V' */ magma_ssetmatrix( n-i, nb, work, 0, ldwork, dwork, dwork_offset, lddwork, queue ); magma_ssyr2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one, dA(i+nb, i), ldda, dwork, (dwork_offset+nb), lddwork, d_one, dA(i+nb, i+nb), ldda, queue); /* Copy subdiagonal elements back into A, and diagonal elements into D */ for (j = i; j < i+nb; ++j) { MAGMA_S_SET2REAL( *A(j+1, j), e[j] ); d[j] = MAGMA_S_REAL( *A(j, j) ); } } #ifdef FAST_SYMV magma_free( dwork2 ); #endif /* Use unblocked code to reduce the last or only block */ if (1<=n-nx) magma_sgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), 0, lda, queue ); i_n = n-i; lapackf77_ssytrd(uplo_, &i_n, A(i, i), &lda, &d[i], &e[i], &tau[i], work, &lwork, &iinfo); } magma_free( da ); // ACD // MAGMA_S_SET2REAL( work[0], lwkopt ); MAGMA_S_SET2REAL( work[0], (float) lwkopt ); return *info; } /* magma_ssytrd */
/** Purpose ------- SSYTRD2_GPU reduces a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T. This version passes a workspace that is used in an optimized GPU matrix-vector product. Arguments --------- @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] dA REAL 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, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = MagmaLower, the diagonal and first subdiagonal of A are over- written by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. @param[in] ldda INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[out] d REAL array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). @param[out] e REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower. @param[out] tau REAL array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). @param[out] wA (workspace) REAL array, dimension (LDA,N) On exit the diagonal, the upper part (UPLO=MagmaUpper) or the lower part (UPLO=MagmaLower) are copies of DA @param[in] ldwa INTEGER The leading dimension of the array wA. LDWA >= max(1,N). @param[out] work (workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. @param[in] lwork INTEGER The dimension of the array WORK. LWORK >= 1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. \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] dwork (workspace) REAL array on the GPU, dim (MAX(1,LDWORK)) @param[in] ldwork INTEGER The dimension of the array DWORK. LDWORK >= (n*n+64-1)/64 + 2*n*nb, where nb = magma_get_ssytrd_nb(n) @param[out] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value Further Details --------------- If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary reflectors Q = H(n-1) . . . H(2) H(1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in A(1:i-1,i+1), and tau in TAU(i). If UPLO = MagmaLower, the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i). The contents of A on exit are illustrated by the following examples with n = 5: if UPLO = MagmaUpper: if UPLO = MagmaLower: ( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d ) where d and e denote diagonal and off-diagonal elements of T, and vi denotes an element of the vector defining H(i). @ingroup magma_ssyev_comp ********************************************************************/ extern "C" magma_int_t magma_ssytrd2_gpu( magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, float *d, float *e, float *tau, float *wA, magma_int_t ldwa, float *work, magma_int_t lwork, magmaFloat_ptr dwork, magma_int_t ldwork, magma_int_t *info) { #define A(i, j) (wA + (j)*ldwa + (i)) #define dA(i, j) (dA + (j)*ldda + (i)) const char* uplo_ = lapack_uplo_const( uplo ); magma_int_t nb = magma_get_ssytrd_nb(n); float c_neg_one = MAGMA_S_NEG_ONE; float c_one = MAGMA_S_ONE; float d_one = MAGMA_D_ONE; magma_int_t kk, nx; magma_int_t i, j, i_n; magma_int_t iinfo; magma_int_t ldw, lddw, lwkopt; magma_int_t lquery; *info = 0; int upper = (uplo == MagmaUpper); lquery = (lwork == -1); if (! upper && uplo != MagmaLower) { *info = -1; } else if (n < 0) { *info = -2; } else if (ldda < max(1,n)) { *info = -4; } else if (ldwa < max(1,n)) { *info = -9; } else if (lwork < 1 && ! lquery) { *info = -11; } /* Determine the block size. */ ldw = lddw = n; lwkopt = n * nb; if (*info == 0) { work[0] = MAGMA_S_MAKE( lwkopt, 0 ); } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) return *info; /* Quick return if possible */ if (n == 0) { work[0] = c_one; return *info; } if (n < 1024) nx = n; else nx = 300; if (ldwork < (ldw*n+64-1)/64 + 2*ldw*nb) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } if (upper) { /* Reduce the upper triangle of A. Columns 1:kk are handled by the unblocked method. */ kk = n - (n - nx + nb - 1) / nb * nb; for (i = n - nb; i >= kk; i -= nb) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the matrix W which is needed to update the unreduced part of the matrix */ /* Get the current panel */ magma_sgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), ldwa ); magma_slatrd2(uplo, i+nb, nb, A(0, 0), ldwa, e, tau, work, ldw, dA(0, 0), ldda, dwork, lddw, dwork + 2*ldw*nb, ldwork - 2*ldw*nb); /* Update the unreduced submatrix A(0:i-2,0:i-2), using an update of the form: A := A - V*W' - W*V' */ magma_ssetmatrix( i + nb, nb, work, ldw, dwork, lddw ); magma_ssyr2k(uplo, MagmaNoTrans, i, nb, c_neg_one, dA(0, i), ldda, dwork, lddw, d_one, dA(0, 0), ldda); /* Copy superdiagonal elements back into A, and diagonal elements into D */ for (j = i; j < i+nb; ++j) { *A(j-1,j) = MAGMA_S_MAKE( e[j - 1], 0 ); d[j] = MAGMA_S_REAL( *A(j, j) ); } } magma_sgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), ldwa ); /* Use CPU code to reduce the last or only block */ lapackf77_ssytrd(uplo_, &kk, A(0, 0), &ldwa, d, e, tau, work, &lwork, &iinfo); magma_ssetmatrix( kk, kk, A(0, 0), ldwa, dA(0, 0), ldda ); } else { /* Reduce the lower triangle of A */ for (i = 0; i < n-nx; i += nb) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the matrix W which is needed to update the unreduced part of the matrix */ /* Get the current panel */ magma_sgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), ldwa ); magma_slatrd2(uplo, n-i, nb, A(i, i), ldwa, &e[i], &tau[i], work, ldw, dA(i, i), ldda, dwork, lddw, dwork + 2*ldw*nb, ldwork - 2*ldw*nb); /* Update the unreduced submatrix A(i+ib:n,i+ib:n), using an update of the form: A := A - V*W' - W*V' */ magma_ssetmatrix( n-i, nb, work, ldw, dwork, lddw ); magma_ssyr2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one, dA(i+nb, i), ldda, &dwork[nb], lddw, d_one, dA(i+nb, i+nb), ldda); /* Copy subdiagonal elements back into A, and diagonal elements into D */ for (j = i; j < i+nb; ++j) { *A(j+1,j) = MAGMA_S_MAKE( e[j], 0 ); d[j] = MAGMA_S_REAL( *A(j, j) ); } } /* Use unblocked code to reduce the last or only block */ magma_sgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), ldwa ); i_n = n-i; lapackf77_ssytrd(uplo_, &i_n, A(i, i), &ldwa, &d[i], &e[i], &tau[i], work, &lwork, &iinfo); magma_ssetmatrix( n-i, n-i, A(i, i), ldwa, dA(i, i), ldda ); } work[0] = MAGMA_S_MAKE( lwkopt, 0 ); return *info; } /* magma_ssytrd2_gpu */
/** Purpose ------- SSYTRD reduces a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T. Arguments --------- @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 REAL 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, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = MagmaLower, the diagonal and first subdiagonal of A are over- written by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. @param[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[out] d REAL array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). @param[out] e REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower. @param[out] tau REAL array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). @param[out] work (workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. @param[in] lwork INTEGER The dimension of the array WORK. LWORK >= N*NB, where NB is the optimal blocksize given by magma_get_ssytrd_nb(). \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] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value Further Details --------------- If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary reflectors Q = H(n-1) . . . H(2) H(1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in A(1:i-1,i+1), and tau in TAU(i). If UPLO = MagmaLower, the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i). The contents of A on exit are illustrated by the following examples with n = 5: if UPLO = MagmaUpper: if UPLO = MagmaLower: ( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d ) where d and e denote diagonal and off-diagonal elements of T, and vi denotes an element of the vector defining H(i). @ingroup magma_ssyev_comp ********************************************************************/ extern "C" magma_int_t magma_ssytrd(magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, float *d, float *e, float *tau, float *work, magma_int_t lwork, magma_int_t *info) { #define A(i, j) ( A + (j)*lda + (i)) #define dA(i, j) (dA + (j)*ldda + (i)) const char* uplo_ = lapack_uplo_const( uplo ); magma_int_t ldda = lda; magma_int_t nb = magma_get_ssytrd_nb(n); float c_neg_one = MAGMA_S_NEG_ONE; float c_one = MAGMA_S_ONE; float d_one = MAGMA_D_ONE; magma_int_t kk, nx; magma_int_t i, j, i_n; magma_int_t iinfo; magma_int_t ldwork, lddwork, lwkopt; magma_int_t lquery; *info = 0; int upper = (uplo == MagmaUpper); lquery = (lwork == -1); if (! upper && uplo != MagmaLower) { *info = -1; } else if (n < 0) { *info = -2; } else if (lda < max(1,n)) { *info = -4; } else if (lwork < nb*n && ! lquery) { *info = -9; } /* Determine the block size. */ ldwork = lddwork = n; lwkopt = n * nb; if (*info == 0) { work[0] = MAGMA_S_MAKE( lwkopt, 0 ); } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) return *info; /* Quick return if possible */ if (n == 0) { work[0] = c_one; return *info; } float *dA; if (MAGMA_SUCCESS != magma_smalloc( &dA, n*ldda + 2*n*nb )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } float *dwork = dA + n*ldda; if (n < 2048) nx = n; else nx = 512; if (upper) { /* Copy the matrix to the GPU */ magma_ssetmatrix( n, n, A(0, 0), lda, dA(0, 0), ldda ); /* Reduce the upper triangle of A. Columns 1:kk are handled by the unblocked method. */ kk = n - (n - nx + nb - 1) / nb * nb; for (i = n - nb; i >= kk; i -= nb) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the matrix W which is needed to update the unreduced part of the matrix */ /* Get the current panel (no need for the 1st iteration) */ if (i != n-nb) magma_sgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), lda ); magma_slatrd(uplo, i+nb, nb, A(0, 0), lda, e, tau, work, ldwork, dA(0, 0), ldda, dwork, lddwork); /* Update the unreduced submatrix A(0:i-2,0:i-2), using an update of the form: A := A - V*W' - W*V' */ magma_ssetmatrix( i + nb, nb, work, ldwork, dwork, lddwork ); magma_ssyr2k(uplo, MagmaNoTrans, i, nb, c_neg_one, dA(0, i), ldda, dwork, lddwork, d_one, dA(0, 0), ldda); /* Copy superdiagonal elements back into A, and diagonal elements into D */ for (j = i; j < i+nb; ++j) { *A(j-1,j) = MAGMA_S_MAKE( e[j - 1], 0 ); d[j] = MAGMA_S_REAL( *A(j, j) ); } } magma_sgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), lda ); /* Use unblocked code to reduce the last or only block */ lapackf77_ssytd2(uplo_, &kk, A(0, 0), &lda, d, e, tau, &iinfo); } else { /* Copy the matrix to the GPU */ if (1 <= n-nx) magma_ssetmatrix( n, n, A(0,0), lda, dA(0,0), ldda ); #ifdef FAST_HEMV // TODO this leaks memory from dA, above float *dwork2; if (MAGMA_SUCCESS != magma_smalloc( &dwork2, n*n )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } #endif /* Reduce the lower triangle of A */ for (i = 0; i < n-nx; i += nb) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the matrix W which is needed to update the unreduced part of the matrix */ /* Get the current panel (no need for the 1st iteration) */ if (i != 0) magma_sgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), lda ); #ifdef FAST_HEMV magma_slatrd2(uplo, n-i, nb, A(i, i), lda, &e[i], &tau[i], work, ldwork, dA(i, i), ldda, dwork, lddwork, dwork2, n*n); #else magma_slatrd(uplo, n-i, nb, A(i, i), lda, &e[i], &tau[i], work, ldwork, dA(i, i), ldda, dwork, lddwork); #endif /* Update the unreduced submatrix A(i+ib:n,i+ib:n), using an update of the form: A := A - V*W' - W*V' */ magma_ssetmatrix( n-i, nb, work, ldwork, dwork, lddwork ); magma_ssyr2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one, dA(i+nb, i), ldda, &dwork[nb], lddwork, d_one, dA(i+nb, i+nb), ldda); /* Copy subdiagonal elements back into A, and diagonal elements into D */ for (j = i; j < i+nb; ++j) { *A(j+1,j) = MAGMA_S_MAKE( e[j], 0 ); d[j] = MAGMA_S_REAL( *A(j, j) ); } } #ifdef FAST_HEMV magma_free( dwork2 ); #endif /* Use unblocked code to reduce the last or only block */ if (1 <= n-nx) magma_sgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), lda ); i_n = n-i; lapackf77_ssytrd(uplo_, &i_n, A(i, i), &lda, &d[i], &e[i], &tau[i], work, &lwork, &iinfo); } magma_free( dA ); work[0] = MAGMA_S_MAKE( lwkopt, 0 ); return *info; } /* magma_ssytrd */
int main( int argc, char** argv ) { TESTING_INIT(); real_Double_t gflops, t1, t2; float c_neg_one = MAGMA_S_NEG_ONE; magma_int_t ione = 1; const char trans[] = { 'N', 'C', 'T' }; const char uplo[] = { 'L', 'U' }; const char diag[] = { 'U', 'N' }; const char side[] = { 'L', 'R' }; float *A, *B, *C, *C2, *LU; float *dA, *dB, *dC1, *dC2; float alpha = MAGMA_S_MAKE( 0.5, 0.1 ); float beta = MAGMA_S_MAKE( 0.7, 0.2 ); float dalpha = 0.6; float dbeta = 0.8; float work[1], error, total_error; magma_int_t ISEED[4] = {0,0,0,1}; magma_int_t m, n, k, size, maxn, ld, info; magma_int_t *piv; magma_err_t err; magma_opts opts; parse_opts( argc, argv, &opts ); printf( "Compares magma wrapper function to cublas function; all diffs should be exactly 0.\n\n" ); total_error = 0.; for( int i = 0; i < opts.ntest; ++i ) { m = opts.msize[i]; n = opts.nsize[i]; k = opts.ksize[i]; printf("=========================================================================\n"); printf( "M %d, N %d, K %d\n", (int) m, (int) n, (int) k ); // allocate matrices // over-allocate so they can be any combination of {m,n,k} x {m,n,k}. maxn = max( max( m, n ), k ); ld = maxn; size = maxn*maxn; err = magma_malloc_cpu( (void**) &piv, maxn*sizeof(magma_int_t) ); assert( err == 0 ); err = magma_smalloc_pinned( &A, size ); assert( err == 0 ); err = magma_smalloc_pinned( &B, size ); assert( err == 0 ); err = magma_smalloc_pinned( &C, size ); assert( err == 0 ); err = magma_smalloc_pinned( &C2, size ); assert( err == 0 ); err = magma_smalloc_pinned( &LU, size ); assert( err == 0 ); err = magma_smalloc( &dA, size ); assert( err == 0 ); err = magma_smalloc( &dB, size ); assert( err == 0 ); err = magma_smalloc( &dC1, size ); assert( err == 0 ); err = magma_smalloc( &dC2, size ); assert( err == 0 ); // initialize matrices size = maxn*maxn; lapackf77_slarnv( &ione, ISEED, &size, A ); lapackf77_slarnv( &ione, ISEED, &size, B ); lapackf77_slarnv( &ione, ISEED, &size, C ); printf( "========== Level 1 BLAS ==========\n" ); // ----- test SSWAP // swap 2nd and 3rd columns of dA, then copy to C2 and compare with A assert( n >= 4 ); magma_ssetmatrix( m, n, A, ld, dA, ld ); magma_ssetmatrix( m, n, A, ld, dB, ld ); magma_sswap( m, dA(0,1), 1, dA(0,2), 1 ); magma_sswap( m, dB(0,1), 1, dB(0,2), 1 ); // check results, storing diff between magma and cuda calls in C2 cublasSaxpy( ld*n, c_neg_one, dA, 1, dB, 1 ); magma_sgetmatrix( m, n, dB, ld, C2, ld ); error = lapackf77_slange( "F", &m, &k, C2, &ld, work ); total_error += error; printf( "sswap diff %.2g\n", error ); // ----- test ISAMAX // get argmax of column of A magma_ssetmatrix( m, k, A, ld, dA, ld ); error = 0; for( int j = 0; j < k; ++j ) { magma_int_t i1 = magma_isamax( m, dA(0,j), 1 ); magma_int_t i2 = cublasIsamax( m, dA(0,j), 1 ); assert( i1 == i2 ); error += abs( i1 - i2 ); } total_error += error; gflops = (float)m * k / 1e9; printf( "isamax diff %.2g\n", error ); printf( "\n" ); printf( "========== Level 2 BLAS ==========\n" ); // ----- test SGEMV // c = alpha*A*b + beta*c, with A m*n; b,c m or n-vectors // try no-trans/trans for( int ia = 0; ia < 3; ++ia ) { magma_ssetmatrix( m, n, A, ld, dA, ld ); magma_ssetvector( maxn, B, 1, dB, 1 ); magma_ssetvector( maxn, C, 1, dC1, 1 ); magma_ssetvector( maxn, C, 1, dC2, 1 ); t1 = magma_sync_wtime( 0 ); magma_sgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC1, 1 ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasSgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC2, 1 ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 size = (trans[ia] == 'N' ? m : n); cublasSaxpy( size, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetvector( size, dC2, 1, C2, 1 ); error = lapackf77_slange( "F", &size, &ione, C2, &ld, work ); total_error += error; gflops = FLOPS_SGEMV( m, n ) / 1e9; printf( "sgemv( %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", trans[ia], error, gflops/t1, gflops/t2 ); } printf( "\n" ); // ----- test SSYMV // c = alpha*A*b + beta*c, with A m*m symmetric; b,c m-vectors // try upper/lower for( int iu = 0; iu < 2; ++iu ) { magma_ssetmatrix( m, m, A, ld, dA, ld ); magma_ssetvector( m, B, 1, dB, 1 ); magma_ssetvector( m, C, 1, dC1, 1 ); magma_ssetvector( m, C, 1, dC2, 1 ); t1 = magma_sync_wtime( 0 ); magma_ssymv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC1, 1 ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasSsymv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC2, 1 ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 cublasSaxpy( m, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetvector( m, dC2, 1, C2, 1 ); error = lapackf77_slange( "F", &m, &ione, C2, &ld, work ); total_error += error; gflops = FLOPS_SSYMV( m ) / 1e9; printf( "ssymv( %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", uplo[iu], error, gflops/t1, gflops/t2 ); } printf( "\n" ); // ----- test STRSV // solve A*c = c, with A m*m triangular; c m-vector // try upper/lower, no-trans/trans, unit/non-unit diag // Factor A into LU to get well-conditioned triangles, else solve yields garbage. // Still can give garbage if solves aren't consistent with LU factors, // e.g., using unit diag for U, so copy lower triangle to upper triangle. // Also used for trsm later. lapackf77_slacpy( "Full", &maxn, &maxn, A, &ld, LU, &ld ); lapackf77_sgetrf( &maxn, &maxn, LU, &ld, piv, &info ); for( int j = 0; j < maxn; ++j ) { for( int i = 0; i < j; ++i ) { *LU(i,j) = *LU(j,i); } } for( int iu = 0; iu < 2; ++iu ) { for( int it = 0; it < 3; ++it ) { for( int id = 0; id < 2; ++id ) { magma_ssetmatrix( m, m, LU, ld, dA, ld ); magma_ssetvector( m, C, 1, dC1, 1 ); magma_ssetvector( m, C, 1, dC2, 1 ); t1 = magma_sync_wtime( 0 ); magma_strsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC1, 1 ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasStrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC2, 1 ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 cublasSaxpy( m, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetvector( m, dC2, 1, C2, 1 ); error = lapackf77_slange( "F", &m, &ione, C2, &ld, work ); total_error += error; gflops = FLOPS_STRSM( MagmaLeft, m, 1 ) / 1e9; printf( "strsv( %c, %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", uplo[iu], trans[it], diag[id], error, gflops/t1, gflops/t2 ); }}} printf( "\n" ); printf( "========== Level 3 BLAS ==========\n" ); // ----- test SGEMM // C = alpha*A*B + beta*C, with A m*k or k*m; B k*n or n*k; C m*n // try combinations of no-trans/trans for( int ia = 0; ia < 3; ++ia ) { for( int ib = 0; ib < 3; ++ib ) { bool nta = (trans[ia] == 'N'); bool ntb = (trans[ib] == 'N'); magma_ssetmatrix( (nta ? m : k), (nta ? m : k), A, ld, dA, ld ); magma_ssetmatrix( (ntb ? k : n), (ntb ? n : k), B, ld, dB, ld ); magma_ssetmatrix( m, n, C, ld, dC1, ld ); magma_ssetmatrix( m, n, C, ld, dC2, ld ); t1 = magma_sync_wtime( 0 ); magma_sgemm( trans[ia], trans[ib], m, n, k, alpha, dA, ld, dB, ld, beta, dC1, ld ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasSgemm( trans[ia], trans[ib], m, n, k, alpha, dA, ld, dB, ld, beta, dC2, ld ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 cublasSaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetmatrix( m, n, dC2, ld, C2, ld ); error = lapackf77_slange( "F", &m, &n, C2, &ld, work ); total_error += error; gflops = FLOPS_SGEMM( m, n, k ) / 1e9; printf( "sgemm( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", trans[ia], trans[ib], error, gflops/t1, gflops/t2 ); }} printf( "\n" ); // ----- test SSYMM // C = alpha*A*B + beta*C (left) with A m*m symmetric; B,C m*n; or // C = alpha*B*A + beta*C (right) with A n*n symmetric; B,C m*n // try left/right, upper/lower for( int is = 0; is < 2; ++is ) { for( int iu = 0; iu < 2; ++iu ) { magma_ssetmatrix( m, m, A, ld, dA, ld ); magma_ssetmatrix( m, n, B, ld, dB, ld ); magma_ssetmatrix( m, n, C, ld, dC1, ld ); magma_ssetmatrix( m, n, C, ld, dC2, ld ); t1 = magma_sync_wtime( 0 ); magma_ssymm( side[is], uplo[iu], m, n, alpha, dA, ld, dB, ld, beta, dC1, ld ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasSsymm( side[is], uplo[iu], m, n, alpha, dA, ld, dB, ld, beta, dC2, ld ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 cublasSaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetmatrix( m, n, dC2, ld, C2, ld ); error = lapackf77_slange( "F", &m, &n, C2, &ld, work ); total_error += error; gflops = FLOPS_SSYMM( side[is], m, n ) / 1e9; printf( "ssymm( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", side[is], uplo[iu], error, gflops/t1, gflops/t2 ); }} printf( "\n" ); // ----- test SSYRK // C = alpha*A*A^H + beta*C (no-trans) with A m*k and C m*m symmetric; or // C = alpha*A^H*A + beta*C (trans) with A k*m and C m*m symmetric // try upper/lower, no-trans/trans for( int iu = 0; iu < 2; ++iu ) { for( int it = 0; it < 3; ++it ) { magma_ssetmatrix( n, k, A, ld, dA, ld ); magma_ssetmatrix( n, n, C, ld, dC1, ld ); magma_ssetmatrix( n, n, C, ld, dC2, ld ); t1 = magma_sync_wtime( 0 ); magma_ssyrk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC1, ld ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasSsyrk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC2, ld ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 cublasSaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetmatrix( n, n, dC2, ld, C2, ld ); error = lapackf77_slange( "F", &n, &n, C2, &ld, work ); total_error += error; gflops = FLOPS_SSYRK( k, n ) / 1e9; printf( "ssyrk( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", uplo[iu], trans[it], error, gflops/t1, gflops/t2 ); }} printf( "\n" ); // ----- test SSYR2K // C = alpha*A*B^H + ^alpha*B*A^H + beta*C (no-trans) with A,B n*k; C n*n symmetric; or // C = alpha*A^H*B + ^alpha*B^H*A + beta*C (trans) with A,B k*n; C n*n symmetric // try upper/lower, no-trans/trans for( int iu = 0; iu < 2; ++iu ) { for( int it = 0; it < 3; ++it ) { bool nt = (trans[it] == 'N'); magma_ssetmatrix( (nt ? n : k), (nt ? n : k), A, ld, dA, ld ); magma_ssetmatrix( n, n, C, ld, dC1, ld ); magma_ssetmatrix( n, n, C, ld, dC2, ld ); t1 = magma_sync_wtime( 0 ); magma_ssyr2k( uplo[iu], trans[it], n, k, alpha, dA, ld, dB, ld, dbeta, dC1, ld ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasSsyr2k( uplo[iu], trans[it], n, k, alpha, dA, ld, dB, ld, dbeta, dC2, ld ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 cublasSaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetmatrix( n, n, dC2, ld, C2, ld ); error = lapackf77_slange( "F", &n, &n, C2, &ld, work ); total_error += error; gflops = FLOPS_SSYR2K( k, n ) / 1e9; printf( "ssyr2k( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", uplo[iu], trans[it], error, gflops/t1, gflops/t2 ); }} printf( "\n" ); // ----- test STRMM // C = alpha*A*C (left) with A m*m triangular; C m*n; or // C = alpha*C*A (right) with A n*n triangular; C m*n // try left/right, upper/lower, no-trans/trans, unit/non-unit for( int is = 0; is < 2; ++is ) { for( int iu = 0; iu < 2; ++iu ) { for( int it = 0; it < 3; ++it ) { for( int id = 0; id < 2; ++id ) { bool left = (side[is] == 'L'); magma_ssetmatrix( (left ? m : n), (left ? m : n), A, ld, dA, ld ); magma_ssetmatrix( m, n, C, ld, dC1, ld ); magma_ssetmatrix( m, n, C, ld, dC2, ld ); t1 = magma_sync_wtime( 0 ); magma_strmm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasStrmm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC2, ld ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 cublasSaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetmatrix( m, n, dC2, ld, C2, ld ); error = lapackf77_slange( "F", &n, &n, C2, &ld, work ); total_error += error; gflops = FLOPS_STRMM( side[is], m, n ) / 1e9; printf( "strmm( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", uplo[iu], trans[it], error, gflops/t1, gflops/t2 ); }}}} printf( "\n" ); // ----- test STRSM // solve A*X = alpha*B (left) with A m*m triangular; B m*n; or // solve X*A = alpha*B (right) with A n*n triangular; B m*n // try left/right, upper/lower, no-trans/trans, unit/non-unit for( int is = 0; is < 2; ++is ) { for( int iu = 0; iu < 2; ++iu ) { for( int it = 0; it < 3; ++it ) { for( int id = 0; id < 2; ++id ) { bool left = (side[is] == 'L'); magma_ssetmatrix( (left ? m : n), (left ? m : n), LU, ld, dA, ld ); magma_ssetmatrix( m, n, C, ld, dC1, ld ); magma_ssetmatrix( m, n, C, ld, dC2, ld ); t1 = magma_sync_wtime( 0 ); magma_strsm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld ); t1 = magma_sync_wtime( 0 ) - t1; t2 = magma_sync_wtime( 0 ); cublasStrsm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC2, ld ); t2 = magma_sync_wtime( 0 ) - t2; // check results, storing diff between magma and cuda call in C2 cublasSaxpy( ld*n, c_neg_one, dC1, 1, dC2, 1 ); magma_sgetmatrix( m, n, dC2, ld, C2, ld ); error = lapackf77_slange( "F", &n, &n, C2, &ld, work ); total_error += error; gflops = FLOPS_STRSM( side[is], m, n ) / 1e9; printf( "strsm( %c, %c ) diff %.2g, Gflop/s %6.2f, %6.2f\n", uplo[iu], trans[it], error, gflops/t1, gflops/t2 ); }}}} printf( "\n" ); // cleanup magma_free_cpu( piv ); magma_free_pinned( A ); magma_free_pinned( B ); magma_free_pinned( C ); magma_free_pinned( C2 ); magma_free_pinned( LU ); magma_free( dA ); magma_free( dB ); magma_free( dC1 ); magma_free( dC2 ); } if ( total_error != 0. ) { printf( "total error %.2g -- ought to be 0 -- some test failed (see above).\n", total_error ); } else { printf( "all tests passed\n" ); } TESTING_FINALIZE(); return 0; }
extern "C" magma_int_t magma_ssytrd_sy2sb( char uplo, magma_int_t n, magma_int_t nb, float *a, magma_int_t lda, float *tau, float *work, magma_int_t lwork, float *dT, magma_int_t threads, magma_int_t *info) { /* -- MAGMA (version 1.3.0) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver November 2012 Purpose ======= SSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric band-diagonal form T by an orthogonal similarity transformation: Q**T * A * Q = T. This version stores the triangular matrices T used in the accumulated Householder transformations (I - V T V'). Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) REAL 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, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if UPLO = 'U', the Upper band-diagonal of A is overwritten by the corresponding elements of the band-diagonal matrix T, and the elements above the band diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = 'L', the the Lower band-diagonal of A is overwritten by the corresponding elements of the band-diagonal matrix T, and the elements below the band-diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). TAU (output) REAL array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= 1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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. dT (output) REAL array on the GPU, dimension N*NB, where NB is the optimal blocksize. On exit dT holds the upper triangular matrices T from the accumulated Householder transformations (I - V T V') used in the factorization. The nb x nb matrices T are ordered consecutively in memory one after another. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Details =============== If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n-1) . . . H(2) H(1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in A(1:i-1,i+1), and tau in TAU(i). If UPLO = 'L', the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i). The contents of A on exit are illustrated by the following examples with n = 5: if UPLO = 'U': if UPLO = 'L': ( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d ) where d and e denote diagonal and off-diagonal elements of T, and vi denotes an element of the vector defining H(i). ===================================================================== */ #define a_ref(a_1,a_2) ( a + ((a_2)-1)*( lda) + (a_1)-1) #define da_ref(a_1,a_2) (da + ((a_2)-1)*(ldda) + (a_1)-1) #define tau_ref(a_1) (tau + (a_1)-1) #define t_ref(a_1) (dT + ((a_1)-1)*(lddt)) char uplo_[2] = {uplo, 0}; int ldda = ((n+31)/32)*32; int lddt = nb; float c_neg_one = MAGMA_S_NEG_ONE; float c_neg_half = MAGMA_S_NEG_HALF; float c_one = MAGMA_S_ONE ; float c_zero = MAGMA_S_ZERO; float d_one = MAGMA_D_ONE; magma_int_t pm, pn, indi, indj, pk; magma_int_t pm_old=0, pn_old=0, indi_old=0, indj_old=0; int i; int lwkopt; int lquery; *info = 0; int upper = lapackf77_lsame(uplo_, "U"); lquery = lwork == -1; if (! upper && ! lapackf77_lsame(uplo_, "L")) { *info = -1; } else if (n < 0) { *info = -2; } else if (lda < max(1,n)) { *info = -4; } else if (lwork < 1 && ! lquery) { *info = -9; } if (*info == 0) { /* Determine the block size. */ lwkopt = n * nb; MAGMA_S_SET2REAL( work[0], lwkopt ); } if (*info != 0) return *info; else if (lquery) return *info; /* Quick return if possible */ if (n == 0) { work[0] = c_one; return *info; } float *da; if (MAGMA_SUCCESS != magma_smalloc( &da, (n + 2*nb)*ldda )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magma_int_t mklth = min(threads,12); #if defined(USEMKL) mkl_set_num_threads(mklth); #endif #if defined(USEACML) omp_set_num_threads(mklth); #endif /* Use the first panel of da as work space */ float *dwork = da+n*ldda; float *dW = dwork + nb*ldda; #ifdef TRACING char buf[80]; #endif cudaStream_t stream[3]; magma_queue_create( &stream[0] ); magma_queue_create( &stream[1] ); stream[2] = 0; // default stream trace_init( 1, 1, 3, stream ); float *hT = work + lwork - nb*nb; lwork -= nb*nb; memset( hT, 0, nb*nb*sizeof(float)); magmablasSetKernelStream( stream[0] ); cudaEvent_t Pupdate_event; cudaEventCreateWithFlags(&Pupdate_event,cudaEventDisableTiming); //cudaEventCreate(&Pupdate_event); if (upper) { printf("SSYTRD_HE2HB is not yet implemented for upper matrix storage. Exit.\n"); exit(1); }else { /* Copy the matrix to the GPU */ if (1 <= n-nb){ trace_gpu_start( 0, 0, "set", "set A" ); magma_ssetmatrix_async( (n-nb), (n-nb), a_ref(nb+1, nb+1), lda, da_ref(nb+1, nb+1), ldda, stream[0] ); trace_gpu_end( 0, 0 ); } /* Reduce the lower triangle of A */ for (i = 1; i <= n-nb; i += nb) { indi = i+nb; indj = i; pm = n - i - nb + 1; //pn = min(i+nb-1, n-nb) -i + 1; pn = nb; /* Get the current panel (no need for the 1st iteration) */ if (i > 1 ){ // spanel_to_q copy the upper oof diagonal part of // the matrix to work to be restored later. acctually // the zero's and one's putted are not used this is only // because we don't have a function that copy only the // upper part of A to be restored after copying the // lookahead panel that has been computted from GPU to CPU. spanel_to_q(MagmaUpper, pn-1, a_ref(i, i+1), lda, work); trace_gpu_start( 0, 1, "get", "get panel" ); //magma_queue_sync( stream[0] ); cudaStreamWaitEvent(stream[1], Pupdate_event, 0); magma_sgetmatrix_async( (pm+pn), pn, da_ref( i, i), ldda, a_ref ( i, i), lda, stream[1] ); trace_gpu_end( 0, 1 ); trace_gpu_start( 0, 2, "syr2k", "syr2k" ); magma_ssyr2k(MagmaLower, MagmaNoTrans, pm_old-pn_old, pn_old, c_neg_one, da_ref(indi_old+pn_old, indj_old), ldda, dW + pn_old , pm_old, d_one, da_ref(indi_old+pn_old, indi_old+pn_old), ldda); trace_gpu_end( 0, 2 ); trace_cpu_start( 0, "sync", "sync on 1" ); magma_queue_sync( stream[1] ); trace_cpu_end( 0 ); sq_to_panel(MagmaUpper, pn-1, a_ref(i, i+1), lda, work); } /* ========================================================== QR factorization on a panel starting nb off of the diagonal. Prepare the V and T matrices. ========================================================== */ #ifdef TRACING snprintf( buf, sizeof(buf), "panel %d", i ); #endif trace_cpu_start( 0, "geqrf", buf ); lapackf77_sgeqrf(&pm, &pn, a_ref(indi, indj), &lda, tau_ref(i), work, &lwork, info); /* Form the matrix T */ pk=min(pm,pn); lapackf77_slarft( MagmaForwardStr, MagmaColumnwiseStr, &pm, &pk, a_ref(indi, indj), &lda, tau_ref(i), hT, &nb); /* Prepare V - put 0s in the upper triangular part of the panel (and 1s on the diagonal), temporaly storing the original in work */ spanel_to_q(MagmaUpper, pk, a_ref(indi, indj), lda, work); trace_cpu_end( 0 ); /* Send V from the CPU to the GPU */ trace_gpu_start( 0, 0, "set", "set V and T" ); magma_ssetmatrix_async( pm, pk, a_ref(indi, indj), lda, da_ref(indi, indj), ldda, stream[0] ); /* Send the triangular factor T to the GPU */ magma_ssetmatrix_async( pk, pk, hT, nb, t_ref(i), lddt, stream[0] ); trace_gpu_end( 0, 0 ); /* ========================================================== Compute W: 1. X = A (V T) 2. W = X - 0.5* V * (T' * (V' * X)) ========================================================== */ /* dwork = V T */ trace_cpu_start( 0, "sync", "sync on 0" ); // this sync is done here to be sure that the copy has been finished // because below we made a restore sq_to_panel and this restore need // to ensure that the copy has been finished. we did it here to allow // overlapp of restore with next gemm and symm. magma_queue_sync( stream[0] ); trace_cpu_end( 0 ); trace_gpu_start( 0, 2, "gemm", "work = V*T" ); magma_sgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk, c_one, da_ref(indi, indj), ldda, t_ref(i), lddt, c_zero, dwork, pm); trace_gpu_end( 0, 2 ); /* dW = X = A*V*T. dW = A*dwork */ trace_gpu_start( 0, 2, "symm", "X = A*work" ); magma_ssymm(MagmaLeft, uplo, pm, pk, c_one, da_ref(indi, indi), ldda, dwork, pm, c_zero, dW, pm); trace_gpu_end( 0, 2 ); /* restore the panel */ sq_to_panel(MagmaUpper, pk, a_ref(indi, indj), lda, work); /* dwork = V*T already ==> dwork' = T'*V' * compute T'*V'*X ==> dwork'*W ==> * dwork + pm*nb = ((T' * V') * X) = dwork' * X = dwork' * W */ trace_gpu_start( 0, 2, "gemm", "work = T'*V'*X" ); magma_sgemm(MagmaTrans, MagmaNoTrans, pk, pk, pm, c_one, dwork, pm, dW, pm, c_zero, dwork + pm*nb, nb); trace_gpu_end( 0, 2 ); /* W = X - 0.5 * V * T'*V'*X * = X - 0.5 * V * (dwork + pm*nb) = W - 0.5 * V * (dwork + pm*nb) */ trace_gpu_start( 0, 2, "gemm", "W = X - 0.5*V*(T'*V'*X)" ); magma_sgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk, c_neg_half, da_ref(indi, indj), ldda, dwork + pm*nb, nb, c_one, dW, pm); trace_gpu_end( 0, 2 ); /* ========================================================== Update the unreduced submatrix A(i+ib:n,i+ib:n), using an update of the form: A := A - V*W' - W*V' ========================================================== */ if (i + nb <= n-nb){ /* There would be next iteration; do lookahead - update the next panel */ trace_gpu_start( 0, 2, "gemm", "gemm 4 next panel left" ); magma_sgemm(MagmaNoTrans, MagmaTrans, pm, pn, pn, c_neg_one, da_ref(indi, indj), ldda, dW , pm, c_one, da_ref(indi, indi), ldda); trace_gpu_end( 0, 2 ); trace_gpu_start( 0, 2, "gemm", "gemm 5 next panel right" ); magma_sgemm(MagmaNoTrans, MagmaTrans, pm, pn, pn, c_neg_one, dW , pm, da_ref(indi, indj), ldda, c_one, da_ref(indi, indi), ldda); trace_gpu_end( 0, 2 ); cudaEventRecord(Pupdate_event, stream[0]); } else { /* no look-ahead as this is last iteration */ trace_gpu_start( 0, 2, "syr2k", "syr2k last iteration" ); magma_ssyr2k(MagmaLower, MagmaNoTrans, pk, pk, c_neg_one, da_ref(indi, indj), ldda, dW , pm, d_one, da_ref(indi, indi), ldda); trace_gpu_end( 0, 2 ); } indi_old = indi; indj_old = indj; pm_old = pm; pn_old = pn; } // end loop for(i) /* Send the last block to the CPU */ pk = min(pm,pn); if (1 <= n-nb){ spanel_to_q(MagmaUpper, pk-1, a_ref(n-pk+1, n-pk+2), lda, work); trace_gpu_start( 0, 2, "get", "get last block" ); magma_sgetmatrix( pk, pk, da_ref(n-pk+1, n-pk+1), ldda, a_ref(n-pk+1, n-pk+1), lda ); trace_gpu_end( 0, 2 ); sq_to_panel(MagmaUpper, pk-1, a_ref(n-pk+1, n-pk+2), lda, work); } }// end of LOWER trace_finalize( "ssytrd_sy2sb.svg", "trace.css" ); cudaEventDestroy(Pupdate_event); magma_queue_destroy( stream[0] ); magma_queue_destroy( stream[1] ); magma_free( da ); MAGMA_S_SET2REAL( work[0], lwkopt ); magmablasSetKernelStream( 0 ); #if defined(USEMKL) mkl_set_num_threads(1); #endif #if defined(USEACML) omp_set_num_threads(1); #endif return *info; } /* ssytrd_sy2sb_ */
/** Purpose ------- SSYTRD2_GPU reduces a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation: Q**H * A * Q = T. This version passes a workspace that is used in an optimized GPU matrix-vector product. Arguments --------- @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] dA REAL array on the GPU, dimension (LDDA,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, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if UPLO = MagmaUpper, the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors; if UPLO = MagmaLower, the diagonal and first subdiagonal of A are over- written by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. See Further Details. @param[in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,N). @param[out] d REAL array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). @param[out] e REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower. @param[out] tau REAL array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). @param[out] A (workspace) REAL array, dimension (LDA,N) On exit the diagonal, the upper part (if uplo=MagmaUpper) or the lower part (if uplo=MagmaLower) are copies of DA @param[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). @param[out] work (workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. @param[in] lwork INTEGER The dimension of the array WORK. LWORK >= N*NB, where NB is the optimal blocksize given by magma_get_ssytrd_nb(). \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] dwork (workspace) REAL array on the GPU, dim (MAX(1,LDWORK)) @param[in] ldwork INTEGER The dimension of the array DWORK. LDWORK >= ldda*ceil(n/64) + 2*ldda*nb, where nb = magma_get_ssytrd_nb(n), and 64 is for the blocksize of magmablas_ssymv. @param[out] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value Further Details --------------- If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary reflectors Q = H(n-1) . . . H(2) H(1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in A(1:i-1,i+1), and tau in TAU(i). If UPLO = MagmaLower, the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in TAU(i). The contents of A on exit are illustrated by the following examples with n = 5: if UPLO = MagmaUpper: if UPLO = MagmaLower: ( d e v2 v3 v4 ) ( d ) ( d e v3 v4 ) ( e d ) ( d e v4 ) ( v1 e d ) ( d e ) ( v1 v2 e d ) ( d ) ( v1 v2 v3 e d ) where d and e denote diagonal and off-diagonal elements of T, and vi denotes an element of the vector defining H(i). @ingroup magma_ssyev_comp ********************************************************************/ extern "C" magma_int_t magma_ssytrd2_gpu( magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, float *d, float *e, float *tau, float *A, magma_int_t lda, float *work, magma_int_t lwork, magmaFloat_ptr dwork, magma_int_t ldwork, magma_int_t *info) { #define A(i_, j_) ( A + (i_) + (j_)*lda ) #define dA(i_, j_) (dA + (i_) + (j_)*ldda) /* Constants */ const float c_zero = MAGMA_S_ZERO; const float c_neg_one = MAGMA_S_NEG_ONE; const float c_one = MAGMA_S_ONE; const float d_one = MAGMA_D_ONE; /* Local variables */ const char* uplo_ = lapack_uplo_const( uplo ); magma_int_t nb = magma_get_ssytrd_nb( n ); magma_int_t kk, nx; magma_int_t i, j, i_n; magma_int_t iinfo; magma_int_t ldw, lddw, lwkopt; magma_int_t lquery; *info = 0; bool upper = (uplo == MagmaUpper); lquery = (lwork == -1); if (! upper && uplo != MagmaLower) { *info = -1; } else if (n < 0) { *info = -2; } else if (ldda < max(1,n)) { *info = -4; } else if (lda < max(1,n)) { *info = -9; } else if (lwork < nb*n && ! lquery) { *info = -11; } else if (ldwork < ldda*magma_ceildiv(n,64) + 2*ldda*nb) { *info = -13; } /* Determine the block size. */ ldw = n; lddw = ldda; // hopefully ldda is rounded up to multiple of 32; ldwork is in terms of ldda, so lddw can't be > ldda. lwkopt = n * nb; if (*info == 0) { work[0] = magma_smake_lwork( lwkopt ); } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) return *info; /* Quick return if possible */ if (n == 0) { work[0] = c_one; return *info; } // nx <= n is required // use LAPACK for n < 3000, otherwise switch at 512 if (n < 3000) nx = n; else nx = 512; float *work2; if (MAGMA_SUCCESS != magma_smalloc_cpu( &work2, n )) { *info = MAGMA_ERR_HOST_ALLOC; return *info; } magma_queue_t queue = NULL; magma_device_t cdev; magma_getdevice( &cdev ); magma_queue_create( cdev, &queue ); // clear out dwork in case it has NANs (used as y in ssymv) // rest of dwork (used as work in magmablas_ssymv) doesn't need to be cleared magmablas_slaset( MagmaFull, n, nb, c_zero, c_zero, dwork, lddw, queue ); if (upper) { /* Reduce the upper triangle of A. Columns 1:kk are handled by the unblocked method. */ kk = n - magma_roundup( n - nx, nb ); for (i = n - nb; i >= kk; i -= nb) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the matrix W which is needed to update the unreduced part of the matrix */ /* Get the current panel */ magma_sgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), lda, queue ); magma_slatrd2( uplo, i+nb, nb, A(0, 0), lda, e, tau, work, ldw, work2, n, dA(0, 0), ldda, dwork, lddw, dwork + 2*lddw*nb, ldwork - 2*lddw*nb, queue ); /* Update the unreduced submatrix A(0:i-2,0:i-2), using an update of the form: A := A - V*W' - W*V' */ magma_ssetmatrix( i + nb, nb, work, ldw, dwork, lddw, queue ); magma_ssyr2k( uplo, MagmaNoTrans, i, nb, c_neg_one, dA(0, i), ldda, dwork, lddw, d_one, dA(0, 0), ldda, queue ); /* Copy superdiagonal elements back into A, and diagonal elements into D */ for (j = i; j < i+nb; ++j) { *A(j-1,j) = MAGMA_S_MAKE( e[j - 1], 0 ); d[j] = MAGMA_S_REAL( *A(j, j) ); } } magma_sgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), lda, queue ); /* Use CPU code to reduce the last or only block */ lapackf77_ssytrd( uplo_, &kk, A(0, 0), &lda, d, e, tau, work, &lwork, &iinfo ); magma_ssetmatrix( kk, kk, A(0, 0), lda, dA(0, 0), ldda, queue ); } else { /* Reduce the lower triangle of A */ for (i = 0; i < n-nx; i += nb) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the matrix W which is needed to update the unreduced part of the matrix */ /* Get the current panel */ magma_sgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), lda, queue ); magma_slatrd2( uplo, n-i, nb, A(i, i), lda, &e[i], &tau[i], work, ldw, work2, n, dA(i, i), ldda, dwork, lddw, dwork + 2*lddw*nb, ldwork - 2*lddw*nb, queue ); /* Update the unreduced submatrix A(i+ib:n,i+ib:n), using an update of the form: A := A - V*W' - W*V' */ magma_ssetmatrix( n-i, nb, work, ldw, dwork, lddw, queue ); // cublas 6.5 crashes here if lddw % 32 != 0, e.g., N=250. magma_ssyr2k( MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one, dA(i+nb, i), ldda, &dwork[nb], lddw, d_one, dA(i+nb, i+nb), ldda, queue ); /* Copy subdiagonal elements back into A, and diagonal elements into D */ for (j = i; j < i+nb; ++j) { *A(j+1,j) = MAGMA_S_MAKE( e[j], 0 ); d[j] = MAGMA_S_REAL( *A(j, j) ); } } /* Use CPU code to reduce the last or only block */ magma_sgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), lda, queue ); i_n = n-i; lapackf77_ssytrd( uplo_, &i_n, A(i, i), &lda, &d[i], &e[i], &tau[i], work, &lwork, &iinfo ); magma_ssetmatrix( n-i, n-i, A(i, i), lda, dA(i, i), ldda, queue ); } magma_free_cpu( work2 ); magma_queue_destroy( queue ); work[0] = magma_smake_lwork( lwkopt ); return *info; } /* magma_ssytrd2_gpu */