dtplqt2()

subroutine dtplqt2	(	integer	m,
		integer	n,
		integer	l,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( ldb, * )	b,
		integer	ldb,
		double precision, dimension( ldt, * )	t,
		integer	ldt,
		integer	info )

DTPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Download DTPLQT2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> DTPLQT2 computes a LQ a factorization of a real 
!> matrix C, which is composed of a triangular block A and pentagonal block B,
!> using the compact WY representation for Q.
!> 

Parameters

[in]	M	!> M is INTEGER !> The total number of rows of the matrix B. !> M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix B, and the order of !> the triangular matrix A. !> N >= 0. !>
[in]	L	!> L is INTEGER !> The number of rows of the lower trapezoidal part of B. !> MIN(M,N) >= L >= 0. See Further Details. !>
[in,out]	A	!> A is DOUBLE PRECISION array, dimension (LDA,M) !> On entry, the lower triangular M-by-M matrix A. !> On exit, the elements on and below the diagonal of the array !> contain the lower triangular matrix L. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[in,out]	B	!> B is DOUBLE PRECISION 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. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,M). !>
[out]	T	!> T is DOUBLE PRECISION array, dimension (LDT,M) !> The N-by-N upper triangular factor T of the block reflector. !> See Further Details. !>
[in]	LDT	!> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,M) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  The input matrix C is a M-by-(M+N) matrix
!>
!>               C = [ A ][ B ]
!>
!>
!>  where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
!>  matrix consisting of a M-by-(N-L) rectangular matrix B1 left of a M-by-L
!>  upper trapezoidal matrix B2:
!>
!>               B = [ B1 ][ B2 ]
!>                   [ B1 ]  <-     M-by-(N-L) rectangular
!>                   [ B2 ]  <-     M-by-L lower 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 M-by-M
!>                   [ B ]  <- M-by-N pentagonal
!>
!>  so that W can be represented as
!>
!>               W = [ I ][ V ]
!>                   [ I ]  <- identity, M-by-M
!>                   [ 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,
!>
!>               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by
!>
!>               H = I - W**T * T * W
!>
!>  where W^H is the conjugate transpose of W and T is the upper triangular
!>  factor of the block reflector.
!> 

Definition at line 174 of file dtplqt2.f.

*
*  -- 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
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), T( LDT, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION  ONE, ZERO
      parameter( one = 1.0, zero = 0.0 )
*     ..
*     .. Local Scalars ..
      INTEGER   I, J, P, MP, NP
      DOUBLE PRECISION   ALPHA
*     ..
*     .. External Subroutines ..
      EXTERNAL  dlarfg, dgemv, dger, dtrmv, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC max, min
*     ..
*     .. 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) ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -5
      ELSE IF( ldb.LT.max( 1, m ) ) THEN
         info = -7
      ELSE IF( ldt.LT.max( 1, m ) ) THEN
         info = -9
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DTPLQT2', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 .OR. m.EQ.0 ) RETURN
*
      DO i = 1, m
*
*        Generate elementary reflector H(I) to annihilate B(I,:)
*
         p = n-l+min( l, i )
         CALL dlarfg( p+1, a( i, i ), b( i, 1 ), ldb, t( 1, i ) )
         IF( i.LT.m ) THEN
*
*           W(M-I:1) := C(I+1:M,I:N) * C(I,I:N) [use W = T(M,:)]
*
            DO j = 1, m-i
               t( m, j ) = (a( i+j, i ))
            END DO
            CALL dgemv( 'N', m-i, p, one, b( i+1, 1 ), ldb,
     $                  b( i, 1 ), ldb, one, t( m, 1 ), ldt )
*
*           C(I+1:M,I:N) = C(I+1:M,I:N) + alpha * C(I,I:N)*W(M-1:1)^H
*
            alpha = -(t( 1, i ))
            DO j = 1, m-i
               a( i+j, i ) = a( i+j, i ) + alpha*(t( m, j ))
            END DO
            CALL dger( m-i, p, alpha,  t( m, 1 ), ldt,
     $          b( i, 1 ), ldb, b( i+1, 1 ), ldb )
         END IF
      END DO
*
      DO i = 2, m
*
*        T(I,1:I-1) := C(I:I-1,1:N) * (alpha * C(I,I:N)^H)
*
         alpha = -t( 1, i )
 
         DO j = 1, i-1
            t( i, j ) = zero
         END DO
         p = min( i-1, l )
         np = min( n-l+1, n )
         mp = min( p+1, m )
*
*        Triangular part of B2
*
         DO j = 1, p
            t( i, j ) = alpha*b( i, n-l+j )
         END DO
         CALL dtrmv( 'L', 'N', 'N', p, b( 1, np ), ldb,
     $               t( i, 1 ), ldt )
*
*        Rectangular part of B2
*
         CALL dgemv( 'N', i-1-p, l,  alpha, b( mp, np ), ldb,
     $               b( i, np ), ldb, zero, t( i,mp ), ldt )
*
*        B1
*
         CALL dgemv( 'N', i-1, n-l, alpha, b, ldb, b( i, 1 ), ldb,
     $               one, t( i, 1 ), ldt )
*
*        T(1:I-1,I) := T(1:I-1,1:I-1) * T(I,1:I-1)
*
        CALL dtrmv( 'L', 'T', 'N', i-1, t, ldt, t( i, 1 ), ldt )
*
*        T(I,I) = tau(I)
*
         t( i, i ) = t( 1, i )
         t( 1, i ) = zero
      END DO
      DO i=1,m
         DO j= i+1,m
            t(i,j)=t(j,i)
            t(j,i)= zero
         END DO
      END DO
 
*
*     End of DTPLQT2
*

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