dlatzm.f.html
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SUBROUTINE <a name="DLATZM.1"></a><a href="dlatzm.f.html#DLATZM.1">DLATZM</a>( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER SIDE
INTEGER INCV, LDC, M, N
DOUBLE PRECISION TAU
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This routine is deprecated and has been replaced by routine <a name="DORMRZ.19"></a><a href="dormrz.f.html#DORMRZ.1">DORMRZ</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DLATZM.21"></a><a href="dlatzm.f.html#DLATZM.1">DLATZM</a> applies a Householder matrix generated by <a name="DTZRQF.21"></a><a href="dtzrqf.f.html#DTZRQF.1">DTZRQF</a> to a matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Let P = I - tau*u*u', u = ( 1 ),
</span><span class="comment">*</span><span class="comment"> ( v )
</span><span class="comment">*</span><span class="comment"> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
</span><span class="comment">*</span><span class="comment"> SIDE = 'R'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If SIDE equals 'L', let
</span><span class="comment">*</span><span class="comment"> C = [ C1 ] 1
</span><span class="comment">*</span><span class="comment"> [ C2 ] m-1
</span><span class="comment">*</span><span class="comment"> n
</span><span class="comment">*</span><span class="comment"> Then C is overwritten by P*C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If SIDE equals 'R', let
</span><span class="comment">*</span><span class="comment"> C = [ C1, C2 ] m
</span><span class="comment">*</span><span class="comment"> 1 n-1
</span><span class="comment">*</span><span class="comment"> Then C is overwritten by C*P.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SIDE (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'L': form P * C
</span><span class="comment">*</span><span class="comment"> = 'R': form C * P
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of rows of the matrix C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of columns of the matrix C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> V (input) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment"> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment"> (1 + (N-1)*abs(INCV)) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> The vector v in the representation of P. V is not used
</span><span class="comment">*</span><span class="comment"> if TAU = 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INCV (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The increment between elements of v. INCV <> 0
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TAU (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> The value tau in the representation of P.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C1 (input/output) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment"> (LDC,N) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment"> (M,1) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
</span><span class="comment">*</span><span class="comment"> if SIDE = 'R'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, the first row of P*C if SIDE = 'L', or the first
</span><span class="comment">*</span><span class="comment"> column of C*P if SIDE = 'R'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C2 (input/output) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment"> (LDC, N) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment"> (LDC, N-1) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
</span><span class="comment">*</span><span class="comment"> m x (n - 1) matrix C2 if SIDE = 'R'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
</span><span class="comment">*</span><span class="comment"> if SIDE = 'R'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDC (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the arrays C1 and C2. LDC >= (1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment"> (N) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment"> (M) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL DAXPY, DCOPY, DGEMV, DGER
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.99"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.100"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MIN
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span> IF( ( MIN( M, N ).EQ.0 ) .OR. ( TAU.EQ.ZERO ) )
$ RETURN
<span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.110"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'L'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> w := C1 + v' * C2
</span><span class="comment">*</span><span class="comment">
</span> CALL DCOPY( N, C1, LDC, WORK, 1 )
CALL DGEMV( <span class="string">'Transpose'</span>, M-1, N, ONE, C2, LDC, V, INCV, ONE,
$ WORK, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
</span><span class="comment">*</span><span class="comment"> [ C2 ] [ C2 ] [ v ]
</span><span class="comment">*</span><span class="comment">
</span> CALL DAXPY( N, -TAU, WORK, 1, C1, LDC )
CALL DGER( M-1, N, -TAU, V, INCV, WORK, 1, C2, LDC )
<span class="comment">*</span><span class="comment">
</span> ELSE IF( <a name="LSAME.124"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SIDE, <span class="string">'R'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> w := C1 + C2 * v
</span><span class="comment">*</span><span class="comment">
</span> CALL DCOPY( M, C1, 1, WORK, 1 )
CALL DGEMV( <span class="string">'No transpose'</span>, M, N-1, ONE, C2, LDC, V, INCV, ONE,
$ WORK, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v']
</span><span class="comment">*</span><span class="comment">
</span> CALL DAXPY( M, -TAU, WORK, 1, C1, 1 )
CALL DGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
END IF
<span class="comment">*</span><span class="comment">
</span> RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="DLATZM.140"></a><a href="dlatzm.f.html#DLATZM.1">DLATZM</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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