*> \brief \b STPLQT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download STPLQT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE STPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, * INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDB, LDT, N, M, L, MB * .. * .. Array Arguments .. * REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STPLQT computes a blocked LQ factorization of a real *> "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, and the order of the *> triangular matrix A. *> M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix B. *> N >= 0. *> \endverbatim *> *> \param[in] L *> \verbatim *> L is INTEGER *> The number of rows of the lower trapezoidal part of B. *> MIN(M,N) >= L >= 0. See Further Details. *> \endverbatim *> *> \param[in] MB *> \verbatim *> MB is INTEGER *> The block size to be used in the blocked QR. M >= MB >= 1. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> On entry, the lower triangular N-by-N matrix A. *> On exit, the elements on and below the diagonal of the array *> contain the lower triangular matrix L. *> \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 REAL array, dimension (LDB,N) *> On entry, the pentagonal M-by-N matrix B. The first N-L columns *> are rectangular, and the last L columns are lower 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 REAL array, dimension (LDT,N) *> The lower 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 >= MB. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (MB*M) *> \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 doubleOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The input matrix C is a M-by-(M+N) matrix *> *> C = [ A ] [ B ] *> *> *> where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal *> matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L *> upper trapezoidal matrix B2: *> [ B ] = [ B1 ] [ B2 ] *> [ B1 ] <- M-by-(N-L) rectangular *> [ B2 ] <- M-by-L upper trapezoidal. *> *> The lower trapezoidal matrix B2 consists of the first L columns of a *> N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0, *> B is rectangular M-by-N; if M=L=N, B is lower triangular. *> *> The matrix W stores the elementary reflectors H(i) in the i-th row *> above the diagonal (of A) in the M-by-(M+N) input matrix C *> [ C ] = [ A ] [ B ] *> [ A ] <- lower triangular N-by-N *> [ B ] <- M-by-N pentagonal *> *> so that W can be represented as *> [ W ] = [ I ] [ V ] *> [ 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 ] [ V2 ] *> [ V1 ] <- M-by-(N-L) rectangular *> [ V2 ] <- M-by-L lower trapezoidal. *> *> The rows of V represent the vectors which define the H(i)'s. *> *> The number of blocks is B = ceiling(M/MB), where each *> block is of order MB except for the last block, which is of order *> IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block *> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB *> for the last block) T's are stored in the MB-by-N matrix T as *> *> T = [T1 T2 ... TB]. *> \endverbatim *> * ===================================================================== SUBROUTINE STPLQT( M, N, L, MB, 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, MB * .. * .. Array Arguments .. REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. INTEGER I, IB, LB, NB, IINFO * .. * .. External Subroutines .. EXTERNAL STPLQT2, STPRFB, 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( MB.LT.1 .OR. (MB.GT.M .AND. M.GT.0)) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -6 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN INFO = -8 ELSE IF( LDT.LT.MB ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'STPLQT', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) RETURN * DO I = 1, M, MB * * Compute the QR factorization of the current block * IB = MIN( M-I+1, MB ) NB = MIN( N-L+I+IB-1, N ) IF( I.GE.L ) THEN LB = 0 ELSE LB = NB-N+L-I+1 END IF * CALL STPLQT2( IB, NB, LB, A(I,I), LDA, B( I, 1 ), LDB, \$ T(1, I ), LDT, IINFO ) * * Update by applying H**T to B(I+IB:M,:) from the right * IF( I+IB.LE.M ) THEN CALL STPRFB( 'R', 'N', 'F', 'R', M-I-IB+1, NB, IB, LB, \$ B( I, 1 ), LDB, T( 1, I ), LDT, \$ A( I+IB, I ), LDA, B( I+IB, 1 ), LDB, \$ WORK, M-I-IB+1) END IF END DO RETURN * * End of STPLQT * END