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+ SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
+*
+* -- LAPACK auxiliary routine (version 3.1) --
+* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+* November 2006
+*
+* .. Scalar Arguments ..
+ CHARACTER DIRECT, STOREV
+ INTEGER K, LDT, LDV, N
+* ..
+* .. Array Arguments ..
+ DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
+* ..
+*
+* Purpose
+* =======
+*
+* DLARFT forms the triangular factor T of a real block reflector H
+* of order n, which is defined as a product of k elementary reflectors.
+*
+* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
+*
+* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
+*
+* If STOREV = 'C', the vector which defines the elementary reflector
+* H(i) is stored in the i-th column of the array V, and
+*
+* H = I - V * T * V'
+*
+* If STOREV = 'R', the vector which defines the elementary reflector
+* H(i) is stored in the i-th row of the array V, and
+*
+* H = I - V' * T * V
+*
+* Arguments
+* =========
+*
+* DIRECT (input) CHARACTER*1
+* Specifies the order in which the elementary reflectors are
+* multiplied to form the block reflector:
+* = 'F': H = H(1) H(2) . . . H(k) (Forward)
+* = 'B': H = H(k) . . . H(2) H(1) (Backward)
+*
+* STOREV (input) CHARACTER*1
+* Specifies how the vectors which define the elementary
+* reflectors are stored (see also Further Details):
+* = 'C': columnwise
+* = 'R': rowwise
+*
+* N (input) INTEGER
+* The order of the block reflector H. N >= 0.
+*
+* K (input) INTEGER
+* The order of the triangular factor T (= the number of
+* elementary reflectors). K >= 1.
+*
+* V (input/output) DOUBLE PRECISION array, dimension
+* (LDV,K) if STOREV = 'C'
+* (LDV,N) if STOREV = 'R'
+* The matrix V. See further details.
+*
+* LDV (input) INTEGER
+* The leading dimension of the array V.
+* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
+*
+* TAU (input) DOUBLE PRECISION array, dimension (K)
+* TAU(i) must contain the scalar factor of the elementary
+* reflector H(i).
+*
+* T (output) DOUBLE PRECISION array, dimension (LDT,K)
+* The k by k triangular factor T of the block reflector.
+* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
+* lower triangular. The rest of the array is not used.
+*
+* LDT (input) INTEGER
+* The leading dimension of the array T. LDT >= K.
+*
+* Further Details
+* ===============
+*
+* The shape of the matrix V and the storage of the vectors which define
+* the H(i) is best illustrated by the following example with n = 5 and
+* k = 3. The elements equal to 1 are not stored; the corresponding
+* array elements are modified but restored on exit. The rest of the
+* array is not used.
+*
+* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
+*
+* V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
+* ( v1 1 ) ( 1 v2 v2 v2 )
+* ( v1 v2 1 ) ( 1 v3 v3 )
+* ( v1 v2 v3 )
+* ( v1 v2 v3 )
+*
+* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
+*
+* V = ( v1 v2 v3 ) V = ( v1 v1 1 )
+* ( v1 v2 v3 ) ( v2 v2 v2 1 )
+* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
+* ( 1 v3 )
+* ( 1 )
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ONE, ZERO
+ PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, J
+ DOUBLE PRECISION VII
+* ..
+* .. External Subroutines ..
+ EXTERNAL DGEMV, DTRMV
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. Executable Statements ..
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 )
+ $ RETURN
+*
+ IF( LSAME( DIRECT, 'F' ) ) THEN
+ DO 20 I = 1, K
+ IF( TAU( I ).EQ.ZERO ) THEN
+*
+* H(i) = I
+*
+ DO 10 J = 1, I
+ T( J, I ) = ZERO
+ 10 CONTINUE
+ ELSE
+*
+* general case
+*
+ VII = V( I, I )
+ V( I, I ) = ONE
+ IF( LSAME( STOREV, 'C' ) ) THEN
+*
+* T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i)
+*
+ CALL DGEMV( 'Transpose', N-I+1, I-1, -TAU( I ),
+ $ V( I, 1 ), LDV, V( I, I ), 1, ZERO,
+ $ T( 1, I ), 1 )
+ ELSE
+*
+* T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)'
+*
+ CALL DGEMV( 'No transpose', I-1, N-I+1, -TAU( I ),
+ $ V( 1, I ), LDV, V( I, I ), LDV, ZERO,
+ $ T( 1, I ), 1 )
+ END IF
+ V( I, I ) = VII
+*
+* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
+*
+ CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,
+ $ LDT, T( 1, I ), 1 )
+ T( I, I ) = TAU( I )
+ END IF
+ 20 CONTINUE
+ ELSE
+ DO 40 I = K, 1, -1
+ IF( TAU( I ).EQ.ZERO ) THEN
+*
+* H(i) = I
+*
+ DO 30 J = I, K
+ T( J, I ) = ZERO
+ 30 CONTINUE
+ ELSE
+*
+* general case
+*
+ IF( I.LT.K ) THEN
+ IF( LSAME( STOREV, 'C' ) ) THEN
+ VII = V( N-K+I, I )
+ V( N-K+I, I ) = ONE
+*
+* T(i+1:k,i) :=
+* - tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i)
+*
+ CALL DGEMV( 'Transpose', N-K+I, K-I, -TAU( I ),
+ $ V( 1, I+1 ), LDV, V( 1, I ), 1, ZERO,
+ $ T( I+1, I ), 1 )
+ V( N-K+I, I ) = VII
+ ELSE
+ VII = V( I, N-K+I )
+ V( I, N-K+I ) = ONE
+*
+* T(i+1:k,i) :=
+* - tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)'
+*
+ CALL DGEMV( 'No transpose', K-I, N-K+I, -TAU( I ),
+ $ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
+ $ T( I+1, I ), 1 )
+ V( I, N-K+I ) = VII
+ END IF
+*
+* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)
+*
+ CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
+ $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
+ END IF
+ T( I, I ) = TAU( I )
+ END IF
+ 40 CONTINUE
+ END IF
+ RETURN
+*
+* End of DLARFT
+*
+ END