extern "C" magma_int_t magma_cgehrd(magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magmaFloatComplex *dT, magma_int_t *info) { /* -- MAGMA (version 1.4.0) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver August 2013 Purpose ======= CGEHRD reduces a COMPLEX general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H . This version stores the triangular matrices used in the factorization so that they can be applied directly (i.e., without being recomputed) later. As a result, the application of Q is much faster. Arguments ========= N (input) INTEGER The order of the matrix A. N >= 0. ILO (input) INTEGER IHI (input) INTEGER It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a previous call to CGEBAL; otherwise they should be set to 1 and N respectively. See Further Details. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. A (input/output) COMPLEX array, dimension (LDA,N) On entry, the N-by-N general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, 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). TAU (output) COMPLEX array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to zero. WORK (workspace/output) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The length of the array WORK. LWORK >= max(1,N). 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) COMPLEX array on the GPU, dimension NB*N, where NB is the optimal blocksize. It stores the NB*NB blocks of the triangular T matrices used in the reduction. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. Further Details =============== The matrix Q is represented as a product of (ihi-ilo) elementary reflectors Q = H(ilo) H(ilo+1) . . . H(ihi-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in TAU(i). The contents of A are illustrated by the following example, with n = 7, ilo = 2 and ihi = 6: on entry, on exit, ( a a a a a a a ) ( a a h h h h a ) ( a a a a a a ) ( a h h h h a ) ( a a a a a a ) ( h h h h h h ) ( a a a a a a ) ( v2 h h h h h ) ( a a a a a a ) ( v2 v3 h h h h ) ( a a a a a a ) ( v2 v3 v4 h h h ) ( a ) ( a ) where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i). This implementation follows the hybrid algorithm and notations described in S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009. This version stores the T matrices in dT, for later use in magma_cunghr. ===================================================================== */ #define A( i, j ) ( A + (i) + (j)*lda) #define dA( i, j ) (dA + (i) + (j-ilo)*ldda) magmaFloatComplex c_one = MAGMA_C_ONE; magmaFloatComplex c_zero = MAGMA_C_ZERO; magma_int_t nb = magma_get_cgehrd_nb(n); magma_int_t ldda = n; // assumed in clahru magma_int_t nh, iws; magma_int_t iinfo; magma_int_t ldwork; magma_int_t lquery; *info = 0; iws = n*nb; MAGMA_C_SET2REAL( work[0], (float) iws ); lquery = lwork == -1; if (n < 0) { *info = -1; } else if (ilo < 1 || ilo > max(1,n)) { *info = -2; } else if (ihi < min(ilo,n) || ihi > n) { *info = -3; } else if (lda < max(1,n)) { *info = -5; } else if (lwork < max(1,n) && ! lquery) { *info = -8; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) return *info; // Adjust from 1-based indexing ilo -= 1; // Quick return if possible nh = ihi - ilo; if (nh <= 1) { work[0] = c_one; return *info; } // GPU workspace is: // nb*ldda for dwork for clahru // nb*ldda for dV // n*ldda for dA magmaFloatComplex *dwork; if (MAGMA_SUCCESS != magma_cmalloc( &dwork, 2*nb*ldda + n*ldda )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magmaFloatComplex *dV = dwork + nb*ldda; magmaFloatComplex *dA = dwork + nb*ldda*2; ldwork = n; magma_int_t i; magmaFloatComplex *T, *dTi; magma_cmalloc_cpu( &T, nb*nb ); if ( T == NULL ) { magma_free( dwork ); *info = MAGMA_ERR_HOST_ALLOC; return *info; } // zero first block of V, which is lower triangular czero_nbxnb_block(nb, dV, ldda); // Set elements 0:ILO-1 and IHI-1:N-2 of TAU to zero for(i = 0; i < ilo; ++i) tau[i] = c_zero; for(i = max(0,ihi-1); i < n-1; ++i) tau[i] = c_zero; for(i=0; i < nb*nb; i += 4) T[i] = T[i+1] = T[i+2] = T[i+3] = c_zero; magmablas_claset( 'F', nb, n, dT, nb ); // If not enough workspace, use unblocked code if ( lwork < iws ) { nb = 1; } if (nb == 1 || nb > nh) { // Use unblocked code below i = ilo; } else { // Use blocked code // Copy the matrix to the GPU magma_csetmatrix( n, n-ilo, A(0,ilo), lda, dA, ldda ); for (i = ilo; i < ihi-1 - nb; i += nb) { // Reduce columns i:i+nb-1 to Hessenberg form, returning the // matrices V and T of the block reflector H = I - V*T*V' // which performs the reduction, and also the matrix Y = A*V*T // Get the current panel (no need for the 1st iteration) magma_cgetmatrix( ihi-i, nb, dA(i,i), ldda, A (i,i), lda ); // add 1 to i for 1-based index magma_clahr2( ihi, i+1, nb, dA(0,i), dV, A (0,i), lda, &tau[i], T, nb, work, ldwork); // Copy T from the CPU to dT on the GPU dTi = dT + (i - ilo)*nb; magma_csetmatrix( nb, nb, T, nb, dTi, nb ); magma_clahru( n, ihi, i, nb, A (0,i), lda, dA(0,i), // dA dA(i,i), // dY, stored over current panel dV, dTi, dwork ); } // Copy remainder to host magma_cgetmatrix( n, n-i, dA(0,i), ldda, A (0,i), lda ); } // Use unblocked code to reduce the rest of the matrix // add 1 to i for 1-based index i += 1; lapackf77_cgehd2(&n, &i, &ihi, A, &lda, tau, work, &iinfo); MAGMA_C_SET2REAL( work[0], (float) iws ); magma_free( dwork ); magma_free_cpu( T ); return *info; } /* magma_cgehrd */
/** Purpose ------- CGEHRD reduces a COMPLEX general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H . This version stores the triangular matrices used in the factorization so that they can be applied directly (i.e., without being recomputed) later. As a result, the application of Q is much faster. Arguments --------- @param[in] n INTEGER The order of the matrix A. N >= 0. @param[in] ilo INTEGER @param[in] ihi INTEGER It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a previous call to CGEBAL; otherwise they should be set to 1 and N respectively. See Further Details. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. @param[in,out] A COMPLEX array, dimension (LDA,N) On entry, the N-by-N general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, 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] tau COMPLEX array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to zero. @param[out] work (workspace) COMPLEX 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,N). 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] dT COMPLEX array on the GPU, dimension NB*N, where NB is the optimal blocksize. It stores the NB*NB blocks of the triangular T matrices used in the reduction. @param[out] info INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value. Further Details --------------- The matrix Q is represented as a product of (ihi-ilo) elementary reflectors Q = H(ilo) H(ilo+1) . . . H(ihi-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in TAU(i). The contents of A are illustrated by the following example, with n = 7, ilo = 2 and ihi = 6: @verbatim on entry, on exit, ( a a a a a a a ) ( a a h h h h a ) ( a a a a a a ) ( a h h h h a ) ( a a a a a a ) ( h h h h h h ) ( a a a a a a ) ( v2 h h h h h ) ( a a a a a a ) ( v2 v3 h h h h ) ( a a a a a a ) ( v2 v3 v4 h h h ) ( a ) ( a ) @endverbatim where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i). This implementation follows the hybrid algorithm and notations described in S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009. This version stores the T matrices in dT, for later use in magma_cunghr. @ingroup magma_cgeev_comp ********************************************************************/ extern "C" magma_int_t magma_cgehrd( magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magmaFloatComplex_ptr dT, magma_int_t *info) { #define A(i_,j_) ( A + (i_) + (j_)*lda) #define dA(i_,j_) (dA + (i_) + (j_)*ldda) magmaFloatComplex c_one = MAGMA_C_ONE; magmaFloatComplex c_zero = MAGMA_C_ZERO; magma_int_t nb = magma_get_cgehrd_nb(n); magma_int_t ldda = ((n+31)/32)*32; magma_int_t i, nh, iws; magma_int_t iinfo; magma_int_t lquery; *info = 0; iws = n*nb; work[0] = MAGMA_C_MAKE( iws, 0 ); lquery = (lwork == -1); if (n < 0) { *info = -1; } else if (ilo < 1 || ilo > max(1,n)) { *info = -2; } else if (ihi < min(ilo,n) || ihi > n) { *info = -3; } else if (lda < max(1,n)) { *info = -5; } else if (lwork < max(1,n) && ! lquery) { *info = -8; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) return *info; // Adjust from 1-based indexing ilo -= 1; // Quick return if possible nh = ihi - ilo; if (nh <= 1) { work[0] = c_one; return *info; } // If not enough workspace, use unblocked code if ( lwork < iws ) { nb = 1; } if (nb == 1 || nb > nh) { // Use unblocked code below i = ilo; } else { // Use blocked code // GPU workspace is: // nb*ldda for dwork for clahru // nb*ldda for dV // n*ldda for dA magmaFloatComplex *dwork; if (MAGMA_SUCCESS != magma_cmalloc( &dwork, 2*nb*ldda + n*ldda )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magmaFloatComplex *dV = dwork + nb*ldda; magmaFloatComplex *dA = dwork + nb*ldda*2; magmaFloatComplex *dTi; magmaFloatComplex *T; magma_cmalloc_cpu( &T, nb*nb ); if ( T == NULL ) { magma_free( dwork ); *info = MAGMA_ERR_HOST_ALLOC; return *info; } // zero first block of V, which is lower triangular magmablas_claset( MagmaFull, nb, nb, c_zero, c_zero, dV, ldda ); // Set elements 0:ILO-1 and IHI-1:N-2 of TAU to zero for (i = 0; i < ilo; ++i) tau[i] = c_zero; for (i = max(0,ihi-1); i < n-1; ++i) tau[i] = c_zero; assert( nb % 4 == 0 ); for (i=0; i < nb*nb; i += 4) T[i] = T[i+1] = T[i+2] = T[i+3] = c_zero; magmablas_claset( MagmaFull, nb, n, c_zero, c_zero, dT, nb ); // Copy the matrix to the GPU magma_csetmatrix( n, n-ilo, A(0,ilo), lda, dA, ldda ); for (i = ilo; i < ihi-1 - nb; i += nb) { // Reduce columns i:i+nb-1 to Hessenberg form, returning the // matrices V and T of the block reflector H = I - V*T*V' // which performs the reduction, and also the matrix Y = A*V*T // Get the current panel (no need for the 1st iteration) magma_cgetmatrix( ihi-i, nb, dA(i,i-ilo), ldda, A(i,i), lda ); // add 1 to i for 1-based index magma_clahr2( ihi, i+1, nb, dA(0,i-ilo), ldda, dV, ldda, A(0,i), lda, &tau[i], T, nb, work, n); // Copy T from the CPU to dT on the GPU dTi = dT + (i - ilo)*nb; magma_csetmatrix( nb, nb, T, nb, dTi, nb ); magma_clahru( n, ihi, i, nb, A(0,i), lda, dA(0,i-ilo), ldda, // dA dA(i,i-ilo), ldda, // dY, stored over current panel dV, ldda, dTi, dwork ); } // Copy remainder to host magma_cgetmatrix( n, n-i, dA(0,i-ilo), ldda, A(0,i), lda ); magma_free( dwork ); magma_free_cpu( T ); } // Use unblocked code to reduce the rest of the matrix // add 1 to i for 1-based index i += 1; lapackf77_cgehd2(&n, &i, &ihi, A, &lda, tau, work, &iinfo); work[0] = MAGMA_C_MAKE( iws, 0 ); return *info; } /* magma_cgehrd */
extern "C" magma_int_t magma_cgehrd2(magma_int_t n, magma_int_t ilo, magma_int_t ihi, magmaFloatComplex *a, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info) { /* -- MAGMA (version 1.4.0) -- Univ. of Tennessee, Knoxville Univ. of California, Berkeley Univ. of Colorado, Denver August 2013 Purpose ======= CGEHRD2 reduces a COMPLEX general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H . Arguments ========= N (input) INTEGER The order of the matrix A. N >= 0. ILO (input) INTEGER IHI (input) INTEGER It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a previous call to CGEBAL; otherwise they should be set to 1 and N respectively. See Further Details. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. A (input/output) COMPLEX array, dimension (LDA,N) On entry, the N-by-N general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, 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). TAU (output) COMPLEX array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to zero. WORK (workspace/output) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The length of the array WORK. LWORK >= max(1,N). 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 =============== The matrix Q is represented as a product of (ihi-ilo) elementary reflectors Q = H(ilo) H(ilo+1) . . . H(ihi-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in TAU(i). The contents of A are illustrated by the following example, with n = 7, ilo = 2 and ihi = 6: on entry, on exit, ( a a a a a a a ) ( a a h h h h a ) ( a a a a a a ) ( a h h h h a ) ( a a a a a a ) ( h h h h h h ) ( a a a a a a ) ( v2 h h h h h ) ( a a a a a a ) ( v2 v3 h h h h ) ( a a a a a a ) ( v2 v3 v4 h h h ) ( a ) ( a ) where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i). This implementation follows the hybrid algorithm and notations described in S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009. ===================================================================== */ magmaFloatComplex c_one = MAGMA_C_ONE; magmaFloatComplex c_zero = MAGMA_C_ZERO; magma_int_t nb = magma_get_cgehrd_nb(n); magma_int_t N = n, ldda = n; magma_int_t ib; magma_int_t nh, iws; magma_int_t nbmin, iinfo; magma_int_t ldwork; magma_int_t lquery; --tau; *info = 0; MAGMA_C_SET2REAL( work[0], (float) n * nb ); lquery = lwork == -1; if (n < 0) { *info = -1; } else if (ilo < 1 || ilo > max(1,n)) { *info = -2; } else if (ihi < min(ilo,n) || ihi > n) { *info = -3; } else if (lda < max(1,n)) { *info = -5; } else if (lwork < max(1,n) && ! lquery) { *info = -8; } if (*info != 0) { magma_xerbla( __func__, -(*info) ); return *info; } else if (lquery) return *info; /* Quick return if possible */ nh = ihi - ilo + 1; if (nh <= 1) { work[0] = c_one; return *info; } magmaFloatComplex *da; if (MAGMA_SUCCESS != magma_cmalloc( &da, N*ldda + 2*N*nb + nb*nb )) { *info = MAGMA_ERR_DEVICE_ALLOC; return *info; } magmaFloatComplex *d_A = da; magmaFloatComplex *d_work = da + (N+nb)*ldda; magma_int_t i__; magmaFloatComplex *t, *d_t; magma_cmalloc_cpu( &t, nb*nb ); if ( t == NULL ) { magma_free( da ); *info = MAGMA_ERR_HOST_ALLOC; return *info; } d_t = d_work + nb * ldda; czero_nbxnb_block(nb, d_A+N*ldda, ldda); /* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */ for (i__ = 1; i__ < ilo; ++i__) tau[i__] = c_zero; for (i__ = max(1,ihi); i__ < n; ++i__) tau[i__] = c_zero; for(i__=0; i__< nb*nb; i__+=4) t[i__] = t[i__+1] = t[i__+2] = t[i__+3] = c_zero; nbmin = 2; iws = 1; if (nb > 1 && nb < nh) { /* Determine when to cross over from blocked to unblocked code (last block is always handled by unblocked code) */ if (nb < nh) { /* Determine if workspace is large enough for blocked code */ iws = n * nb; if (lwork < iws) { /* Not enough workspace to use optimal NB: determine the minimum value of NB, and reduce NB or force use of unblocked code */ nbmin = nb; if (lwork >= n * nbmin) nb = lwork / n; else nb = 1; } } } ldwork = n; if (nb < nbmin || nb >= nh) { /* Use unblocked code below */ i__ = ilo; } else { /* Use blocked code */ /* Copy the matrix to the GPU */ magma_csetmatrix( N, N-ilo+1, a+(ilo-1)*(lda), lda, d_A, ldda ); for (i__ = ilo; i__ < ihi - nb; i__ += nb) { /* Computing MIN */ ib = min(nb, ihi - i__); /* Reduce columns i:i+ib-1 to Hessenberg form, returning the matrices V and T of the block reflector H = I - V*T*V' which performs the reduction, and also the matrix Y = A*V*T */ /* Get the current panel (no need for the 1st iteration) */ magma_cgetmatrix( ihi-i__+1, ib, d_A + (i__ - ilo)*ldda + i__ - 1, ldda, a + (i__ - 1 )*lda + i__ - 1, lda ); magma_clahr2(ihi, i__, ib, d_A + (i__ - ilo)*ldda, d_A + N*ldda + 1, a + (i__ - 1 )*(lda) , lda, &tau[i__], t, nb, work, ldwork); /* Copy T from the CPU to D_T on the GPU */ magma_csetmatrix( nb, nb, t, nb, d_t, nb ); magma_clahru(n, ihi, i__ - 1, ib, a + (i__ - 1 )*(lda), lda, d_A + (i__ - ilo)*ldda, d_A + (i__ - ilo)*ldda + i__ - 1, d_A + N*ldda, d_t, d_work); } } /* Use unblocked code to reduce the rest of the matrix */ if (!(nb < nbmin || nb >= nh)) { magma_cgetmatrix( n, n-i__+1, d_A+ (i__-ilo)*ldda, ldda, a + (i__-1)*(lda), lda ); } lapackf77_cgehd2(&n, &i__, &ihi, a, &lda, &tau[1], work, &iinfo); MAGMA_C_SET2REAL( work[0], (float) iws ); magma_free( da ); magma_free_cpu(t); return *info; } /* magma_cgehrd2 */