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 SUBROUTINE DLARFT