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SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
* -- LAPACK 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
* =======
*
* DLARZT 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
*
* Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
*
* 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, not supported yet)
* = '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 (not supported yet)
* = '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
* ===============
*
* Based on contributions by
* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
* 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_____
* ( v1 v2 v3 ) / \
* ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )
* V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )
* ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )
* ( v1 v2 v3 )
* . . .
* . . .
* 1 . .
* 1 .
* 1
*
* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
*
* ______V_____
* 1 / \
* . 1 ( 1 . . . . v1 v1 v1 v1 v1 )
* . . 1 ( . 1 . . . v2 v2 v2 v2 v2 )
* . . . ( . . 1 . . v3 v3 v3 v3 v3 )
* . . .
* ( v1 v2 v3 )
* ( v1 v2 v3 )
* V = ( v1 v2 v3 )
* ( v1 v2 v3 )
* ( v1 v2 v3 )
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
* ..
* .. External Subroutines ..
EXTERNAL DGEMV, DTRMV, XERBLA
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
* Check for currently supported options
*
INFO = 0
IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLARZT', -INFO )
RETURN
END IF
*
DO 20 I = K, 1, -1
IF( TAU( I ).EQ.ZERO ) THEN
*
* H(i) = I
*
DO 10 J = I, K
T( J, I ) = ZERO
10 CONTINUE
ELSE
*
* general case
*
IF( I.LT.K ) THEN
*
* T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
*
CALL DGEMV( 'No transpose', K-I, N, -TAU( I ),
$ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
$ T( I+1, I ), 1 )
*
* 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
20 CONTINUE
RETURN
*
* End of DLARZT
*
END
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