*> \brief \b DLATZM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLATZM + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK ) * * .. Scalar Arguments .. * CHARACTER SIDE * INTEGER INCV, LDC, M, N * DOUBLE PRECISION TAU * .. * .. Array Arguments .. * DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> This routine is deprecated and has been replaced by routine DORMRZ. *> *> DLATZM applies a Householder matrix generated by DTZRQF to a matrix. *> *> Let P = I - tau*u*u**T, u = ( 1 ), *> ( v ) *> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if *> SIDE = 'R'. *> *> If SIDE equals 'L', let *> C = [ C1 ] 1 *> [ C2 ] m-1 *> n *> Then C is overwritten by P*C. *> *> If SIDE equals 'R', let *> C = [ C1, C2 ] m *> 1 n-1 *> Then C is overwritten by C*P. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': form P * C *> = 'R': form C * P *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is DOUBLE PRECISION array, dimension *> (1 + (M-1)*abs(INCV)) if SIDE = 'L' *> (1 + (N-1)*abs(INCV)) if SIDE = 'R' *> The vector v in the representation of P. V is not used *> if TAU = 0. *> \endverbatim *> *> \param[in] INCV *> \verbatim *> INCV is INTEGER *> The increment between elements of v. INCV <> 0 *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION *> The value tau in the representation of P. *> \endverbatim *> *> \param[in,out] C1 *> \verbatim *> C1 is DOUBLE PRECISION array, dimension *> (LDC,N) if SIDE = 'L' *> (M,1) if SIDE = 'R' *> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 *> if SIDE = 'R'. *> *> On exit, the first row of P*C if SIDE = 'L', or the first *> column of C*P if SIDE = 'R'. *> \endverbatim *> *> \param[in,out] C2 *> \verbatim *> C2 is DOUBLE PRECISION array, dimension *> (LDC, N) if SIDE = 'L' *> (LDC, N-1) if SIDE = 'R' *> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the *> m x (n - 1) matrix C2 if SIDE = 'R'. *> *> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P *> if SIDE = 'R'. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the arrays C1 and C2. LDC >= (1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension *> (N) if SIDE = 'L' *> (M) if SIDE = 'R' *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2011 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK ) * * -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2011 * * .. Scalar Arguments .. CHARACTER SIDE INTEGER INCV, LDC, M, N DOUBLE PRECISION TAU * .. * .. Array Arguments .. DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. External Subroutines .. EXTERNAL DAXPY, DCOPY, DGEMV, DGER * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( ( MIN( M, N ).EQ.0 ) .OR. ( TAU.EQ.ZERO ) ) $ RETURN * IF( LSAME( SIDE, 'L' ) ) THEN * * w := (C1 + v**T * C2)**T * CALL DCOPY( N, C1, LDC, WORK, 1 ) CALL DGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE, $ WORK, 1 ) * * [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T * [ C2 ] [ C2 ] [ v ] * CALL DAXPY( N, -TAU, WORK, 1, C1, LDC ) CALL DGER( M-1, N, -TAU, V, INCV, WORK, 1, C2, LDC ) * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * w := C1 + C2 * v * CALL DCOPY( M, C1, 1, WORK, 1 ) CALL DGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE, $ WORK, 1 ) * * [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T] * CALL DAXPY( M, -TAU, WORK, 1, C1, 1 ) CALL DGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC ) END IF * RETURN * * End of DLATZM * END