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SUBROUTINE <a name="SLARZ.1"></a><a href="slarz.f.html#SLARZ.1">SLARZ</a>( SIDE, M, N, L, V, INCV, TAU, C, 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, L, LDC, M, N
REAL TAU
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL C( 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"> <a name="SLARZ.19"></a><a href="slarz.f.html#SLARZ.1">SLARZ</a> applies a real elementary reflector H to a real M-by-N
</span><span class="comment">*</span><span class="comment"> matrix C, from either the left or the right. H is represented in the
</span><span class="comment">*</span><span class="comment"> form
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> H = I - tau * v * v'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where tau is a real scalar and v is a real vector.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If tau = 0, then H is taken to be the unit matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> H is a product of k elementary reflectors as returned by <a name="STZRZF.30"></a><a href="stzrzf.f.html#STZRZF.1">STZRZF</a>.
</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 H * C
</span><span class="comment">*</span><span class="comment"> = 'R': form C * H
</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"> L (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of entries of the vector V containing
</span><span class="comment">*</span><span class="comment"> the meaningful part of the Householder vectors.
</span><span class="comment">*</span><span class="comment"> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> V (input) REAL array, dimension (1+(L-1)*abs(INCV))
</span><span class="comment">*</span><span class="comment"> The vector v in the representation of H as returned by
</span><span class="comment">*</span><span class="comment"> <a name="STZRZF.52"></a><a href="stzrzf.f.html#STZRZF.1">STZRZF</a>. V is not used 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) REAL
</span><span class="comment">*</span><span class="comment"> The value tau in the representation of H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input/output) REAL array, dimension (LDC,N)
</span><span class="comment">*</span><span class="comment"> On entry, the M-by-N matrix C.
</span><span class="comment">*</span><span class="comment"> On exit, C is overwritten by the matrix H * C if SIDE = 'L',
</span><span class="comment">*</span><span class="comment"> or C * H 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 array C. LDC >= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) REAL array, dimension
</span><span class="comment">*</span><span class="comment"> (N) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment"> or (M) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Based on contributions by
</span><span class="comment">*</span><span class="comment"> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
</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> REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL SAXPY, SCOPY, SGEMV, SGER
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.88"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.89"></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"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.93"></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"> Form H * C
</span><span class="comment">*</span><span class="comment">
</span> IF( TAU.NE.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> w( 1:n ) = C( 1, 1:n )
</span><span class="comment">*</span><span class="comment">
</span> CALL SCOPY( N, C, LDC, WORK, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l )
</span><span class="comment">*</span><span class="comment">
</span> CALL SGEMV( <span class="string">'Transpose'</span>, L, N, ONE, C( M-L+1, 1 ), LDC, V,
$ INCV, ONE, WORK, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
</span><span class="comment">*</span><span class="comment">
</span> CALL SAXPY( N, -TAU, WORK, 1, C, LDC )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
</span><span class="comment">*</span><span class="comment"> tau * v( 1:l ) * w( 1:n )'
</span><span class="comment">*</span><span class="comment">
</span> CALL SGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
$ LDC )
END IF
<span class="comment">*</span><span class="comment">
</span> ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Form C * H
</span><span class="comment">*</span><span class="comment">
</span> IF( TAU.NE.ZERO ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> w( 1:m ) = C( 1:m, 1 )
</span><span class="comment">*</span><span class="comment">
</span> CALL SCOPY( M, C, 1, WORK, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
</span><span class="comment">*</span><span class="comment">
</span> CALL SGEMV( <span class="string">'No transpose'</span>, M, L, ONE, C( 1, N-L+1 ), LDC,
$ V, INCV, ONE, WORK, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
</span><span class="comment">*</span><span class="comment">
</span> CALL SAXPY( M, -TAU, WORK, 1, C, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
</span><span class="comment">*</span><span class="comment"> tau * w( 1:m ) * v( 1:l )'
</span><span class="comment">*</span><span class="comment">
</span> CALL SGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
$ LDC )
<span class="comment">*</span><span class="comment">
</span> END IF
<span class="comment">*</span><span class="comment">
</span> 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="SLARZ.150"></a><a href="slarz.f.html#SLARZ.1">SLARZ</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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