*> \brief \b CTPQRT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CTPQRT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, * INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDB, LDT, N, M, L, NB * .. * .. Array Arguments .. * COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CTPQRT computes a blocked QR factorization of a complex *> "triangular-pentagonal" matrix C, which is composed of a *> triangular block A and pentagonal block B, using the compact *> WY representation for Q. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix B. *> M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix B, and the order of the *> triangular matrix A. *> N >= 0. *> \endverbatim *> *> \param[in] L *> \verbatim *> L is INTEGER *> The number of rows of the upper trapezoidal part of B. *> MIN(M,N) >= L >= 0. See Further Details. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> The block size to be used in the blocked QR. N >= NB >= 1. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX array, dimension (LDA,N) *> On entry, the upper triangular N-by-N matrix A. *> On exit, the elements on and above the diagonal of the array *> contain the upper triangular matrix R. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX array, dimension (LDB,N) *> On entry, the pentagonal M-by-N matrix B. The first M-L rows *> are rectangular, and the last L rows are upper trapezoidal. *> On exit, B contains the pentagonal matrix V. See Further Details. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,M). *> \endverbatim *> *> \param[out] T *> \verbatim *> T is COMPLEX array, dimension (LDT,N) *> The upper triangular block reflectors stored in compact form *> as a sequence of upper triangular blocks. See Further Details. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= NB. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension (NB*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complexOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The input matrix C is a (N+M)-by-N matrix *> *> C = [ A ] *> [ B ] *> *> where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal *> matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N *> upper trapezoidal matrix B2: *> *> B = [ B1 ] <- (M-L)-by-N rectangular *> [ B2 ] <- L-by-N upper trapezoidal. *> *> The upper trapezoidal matrix B2 consists of the first L rows of a *> N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0, *> B is rectangular M-by-N; if M=L=N, B is upper triangular. *> *> The matrix W stores the elementary reflectors H(i) in the i-th column *> below the diagonal (of A) in the (N+M)-by-N input matrix C *> *> C = [ A ] <- upper triangular N-by-N *> [ B ] <- M-by-N pentagonal *> *> so that W can be represented as *> *> W = [ I ] <- identity, N-by-N *> [ V ] <- M-by-N, same form as B. *> *> Thus, all of information needed for W is contained on exit in B, which *> we call V above. Note that V has the same form as B; that is, *> *> V = [ V1 ] <- (M-L)-by-N rectangular *> [ V2 ] <- L-by-N upper trapezoidal. *> *> The columns of V represent the vectors which define the H(i)'s. *> *> The number of blocks is B = ceiling(N/NB), where each *> block is of order NB except for the last block, which is of order *> IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block *> reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB *> for the last block) T's are stored in the NB-by-N matrix T as *> *> T = [T1 T2 ... TB]. *> \endverbatim *> * ===================================================================== SUBROUTINE CTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, \$ INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INFO, LDA, LDB, LDT, N, M, L, NB * .. * .. Array Arguments .. COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. INTEGER I, IB, LB, MB, IINFO * .. * .. External Subroutines .. EXTERNAL CTPQRT2, CTPRFB, XERBLA * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN INFO = -3 ELSE IF( NB.LT.1 .OR. (NB.GT.N .AND. N.GT.0)) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN INFO = -8 ELSE IF( LDT.LT.NB ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CTPQRT', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) RETURN * DO I = 1, N, NB * * Compute the QR factorization of the current block * IB = MIN( N-I+1, NB ) MB = MIN( M-L+I+IB-1, M ) IF( I.GE.L ) THEN LB = 0 ELSE LB = MB-M+L-I+1 END IF * CALL CTPQRT2( MB, IB, LB, A(I,I), LDA, B( 1, I ), LDB, \$ T(1, I ), LDT, IINFO ) * * Update by applying H**H to B(:,I+IB:N) from the left * IF( I+IB.LE.N ) THEN CALL CTPRFB( 'L', 'C', 'F', 'C', MB, N-I-IB+1, IB, LB, \$ B( 1, I ), LDB, T( 1, I ), LDT, \$ A( I, I+IB ), LDA, B( 1, I+IB ), LDB, \$ WORK, IB ) END IF END DO RETURN * * End of CTPQRT * END