Move LAPACK trunk into position.

1 files changed, 186 insertions, 0 deletions

diff --git a/SRC/zlarzt.f b/SRC/zlarzt.f
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+      SUBROUTINE ZLARZT( 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 ..
+      COMPLEX*16         T( LDT, * ), TAU( * ), V( LDV, * )
+*     ..
+*
+*  Purpose
+*  =======
+*
+*  ZLARZT forms the triangular factor T of a complex 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) COMPLEX*16 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) COMPLEX*16 array, dimension (K)
+*          TAU(i) must contain the scalar factor of the elementary
+*          reflector H(i).
+*
+*  T       (output) COMPLEX*16 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 ..
+      COMPLEX*16         ZERO
+      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            I, INFO, J
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA, ZGEMV, ZLACGV, ZTRMV
+*     ..
+*     .. 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( 'ZLARZT', -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 ZLACGV( N, V( I, 1 ), LDV )
+               CALL ZGEMV( 'No transpose', K-I, N, -TAU( I ),
+     $                     V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
+     $                     T( I+1, I ), 1 )
+               CALL ZLACGV( N, V( I, 1 ), LDV )
+*
+*              T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
+*
+               CALL ZTRMV( '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 ZLARZT
+*
+      END