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SUBROUTINE <a name="ZLARFB.1"></a><a href="zlarfb.f.html#ZLARFB.1">ZLARFB</a>( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV,
$ T, LDT, C, LDC, WORK, LDWORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary 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 DIRECT, SIDE, STOREV, TRANS
INTEGER K, LDC, LDT, LDV, LDWORK, M, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ),
$ WORK( LDWORK, * )
<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="ZLARFB.20"></a><a href="zlarfb.f.html#ZLARFB.1">ZLARFB</a> applies a complex block reflector H or its transpose H' to a
</span><span class="comment">*</span><span class="comment"> complex M-by-N matrix C, from either the left or the right.
</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': apply H or H' from the Left
</span><span class="comment">*</span><span class="comment"> = 'R': apply H or H' from the Right
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': apply H (No transpose)
</span><span class="comment">*</span><span class="comment"> = 'C': apply H' (Conjugate transpose)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DIRECT (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Indicates how H is formed from a product of elementary
</span><span class="comment">*</span><span class="comment"> reflectors
</span><span class="comment">*</span><span class="comment"> = 'F': H = H(1) H(2) . . . H(k) (Forward)
</span><span class="comment">*</span><span class="comment"> = 'B': H = H(k) . . . H(2) H(1) (Backward)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> STOREV (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Indicates how the vectors which define the elementary
</span><span class="comment">*</span><span class="comment"> reflectors are stored:
</span><span class="comment">*</span><span class="comment"> = 'C': Columnwise
</span><span class="comment">*</span><span class="comment"> = 'R': Rowwise
</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"> K (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix T (= the number of elementary
</span><span class="comment">*</span><span class="comment"> reflectors whose product defines the block reflector).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> V (input) COMPLEX*16 array, dimension
</span><span class="comment">*</span><span class="comment"> (LDV,K) if STOREV = 'C'
</span><span class="comment">*</span><span class="comment"> (LDV,M) if STOREV = 'R' and SIDE = 'L'
</span><span class="comment">*</span><span class="comment"> (LDV,N) if STOREV = 'R' and SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> The matrix V. See further details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDV (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array V.
</span><span class="comment">*</span><span class="comment"> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
</span><span class="comment">*</span><span class="comment"> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
</span><span class="comment">*</span><span class="comment"> if STOREV = 'R', LDV >= K.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> T (input) COMPLEX*16 array, dimension (LDT,K)
</span><span class="comment">*</span><span class="comment"> The triangular K-by-K matrix T in the representation of the
</span><span class="comment">*</span><span class="comment"> block reflector.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDT (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array T. LDT >= K.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input/output) COMPLEX*16 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 H*C or H'*C or C*H or C*H'.
</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) COMPLEX*16 array, dimension (LDWORK,K)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array WORK.
</span><span class="comment">*</span><span class="comment"> If SIDE = 'L', LDWORK >= max(1,N);
</span><span class="comment">*</span><span class="comment"> if SIDE = 'R', LDWORK >= max(1,M).
</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> COMPLEX*16 ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> CHARACTER TRANST
INTEGER I, J
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.100"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.101"></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"> .. External Subroutines ..
</span> EXTERNAL ZCOPY, ZGEMM, <a name="ZLACGV.104"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>, ZTRMM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC DCONJG
<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><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
<span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.116"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> ) ) THEN
TRANST = <span class="string">'C'</span>
ELSE
TRANST = <span class="string">'N'</span>
END IF
<span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.122"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( STOREV, <span class="string">'C'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.124"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIRECT, <span class="string">'F'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Let V = ( V1 ) (first K rows)
</span><span class="comment">*</span><span class="comment"> ( V2 )
</span><span class="comment">*</span><span class="comment"> where V1 is unit lower triangular.
</span><span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.130"></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 or H' * C where C = ( C1 )
</span><span class="comment">*</span><span class="comment"> ( C2 )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W := C1'
</span><span class="comment">*</span><span class="comment">
</span> DO 10 J = 1, K
CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
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