218 lines
7 KiB
Fortran
218 lines
7 KiB
Fortran
SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
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*
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* -- LAPACK auxiliary routine (version 2.0) --
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* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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* Courant Institute, Argonne National Lab, and Rice University
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* February 29, 1992
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*
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* .. Scalar Arguments ..
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CHARACTER DIRECT, STOREV
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INTEGER K, LDT, LDV, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
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* ..
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*
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* Purpose
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* =======
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*
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* DLARFT forms the triangular factor T of a real block reflector H
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* of order n, which is defined as a product of k elementary reflectors.
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*
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* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
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*
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* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
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*
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* If STOREV = 'C', the vector which defines the elementary reflector
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* H(i) is stored in the i-th column of the array V, and
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*
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* H = I - V * T * V'
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*
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* If STOREV = 'R', the vector which defines the elementary reflector
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* H(i) is stored in the i-th row of the array V, and
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*
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* H = I - V' * T * V
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*
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* Arguments
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* =========
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*
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* DIRECT (input) CHARACTER*1
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* Specifies the order in which the elementary reflectors are
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* multiplied to form the block reflector:
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* = 'F': H = H(1) H(2) . . . H(k) (Forward)
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* = 'B': H = H(k) . . . H(2) H(1) (Backward)
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*
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* STOREV (input) CHARACTER*1
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* Specifies how the vectors which define the elementary
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* reflectors are stored (see also Further Details):
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* = 'C': columnwise
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* = 'R': rowwise
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*
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* N (input) INTEGER
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* The order of the block reflector H. N >= 0.
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*
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* K (input) INTEGER
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* The order of the triangular factor T (= the number of
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* elementary reflectors). K >= 1.
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*
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* V (input/output) DOUBLE PRECISION array, dimension
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* (LDV,K) if STOREV = 'C'
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* (LDV,N) if STOREV = 'R'
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* The matrix V. See further details.
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*
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* LDV (input) INTEGER
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* The leading dimension of the array V.
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* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
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*
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* TAU (input) DOUBLE PRECISION array, dimension (K)
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* TAU(i) must contain the scalar factor of the elementary
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* reflector H(i).
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*
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* T (output) DOUBLE PRECISION array, dimension (LDT,K)
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* The k by k triangular factor T of the block reflector.
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* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
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* lower triangular. The rest of the array is not used.
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*
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* LDT (input) INTEGER
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* The leading dimension of the array T. LDT >= K.
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*
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* Further Details
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* ===============
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*
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* The shape of the matrix V and the storage of the vectors which define
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* the H(i) is best illustrated by the following example with n = 5 and
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* k = 3. The elements equal to 1 are not stored; the corresponding
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* array elements are modified but restored on exit. The rest of the
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* array is not used.
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*
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* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
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*
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* V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
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* ( v1 1 ) ( 1 v2 v2 v2 )
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* ( v1 v2 1 ) ( 1 v3 v3 )
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* ( v1 v2 v3 )
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* ( v1 v2 v3 )
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*
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* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
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*
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* V = ( v1 v2 v3 ) V = ( v1 v1 1 )
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* ( v1 v2 v3 ) ( v2 v2 v2 1 )
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* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
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* ( 1 v3 )
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* ( 1 )
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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DOUBLE PRECISION VII
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* ..
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* .. External Subroutines ..
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EXTERNAL DGEMV, DTRMV
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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IF( LSAME( DIRECT, 'F' ) ) THEN
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DO 20 I = 1, K
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IF( TAU( I ).EQ.ZERO ) THEN
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*
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* H(i) = I
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*
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DO 10 J = 1, I
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T( J, I ) = ZERO
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10 CONTINUE
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ELSE
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*
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* general case
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*
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VII = V( I, I )
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V( I, I ) = ONE
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IF( LSAME( STOREV, 'C' ) ) THEN
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*
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* T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i)
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*
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CALL DGEMV( 'Transpose', N-I+1, I-1, -TAU( I ),
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$ V( I, 1 ), LDV, V( I, I ), 1, ZERO,
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$ T( 1, I ), 1 )
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ELSE
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*
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* T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)'
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*
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CALL DGEMV( 'No transpose', I-1, N-I+1, -TAU( I ),
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$ V( 1, I ), LDV, V( I, I ), LDV, ZERO,
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$ T( 1, I ), 1 )
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END IF
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V( I, I ) = VII
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*
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* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
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*
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CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T,
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$ LDT, T( 1, I ), 1 )
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T( I, I ) = TAU( I )
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END IF
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20 CONTINUE
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ELSE
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DO 40 I = K, 1, -1
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IF( TAU( I ).EQ.ZERO ) THEN
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*
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* H(i) = I
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*
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DO 30 J = I, K
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T( J, I ) = ZERO
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30 CONTINUE
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ELSE
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*
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* general case
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*
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IF( I.LT.K ) THEN
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IF( LSAME( STOREV, 'C' ) ) THEN
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VII = V( N-K+I, I )
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V( N-K+I, I ) = ONE
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*
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* T(i+1:k,i) :=
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* - tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i)
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*
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CALL DGEMV( 'Transpose', N-K+I, K-I, -TAU( I ),
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$ V( 1, I+1 ), LDV, V( 1, I ), 1, ZERO,
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$ T( I+1, I ), 1 )
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V( N-K+I, I ) = VII
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ELSE
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VII = V( I, N-K+I )
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V( I, N-K+I ) = ONE
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*
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* T(i+1:k,i) :=
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* - tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)'
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*
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CALL DGEMV( 'No transpose', K-I, N-K+I, -TAU( I ),
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$ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
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$ T( I+1, I ), 1 )
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V( I, N-K+I ) = VII
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END IF
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*
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* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)
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*
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CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
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$ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
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END IF
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T( I, I ) = TAU( I )
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END IF
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40 CONTINUE
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END IF
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RETURN
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*
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* End of DLARFT
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*
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END
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