LAPACK 3.3.1 Linear Algebra PACKage

# clarzt.f

Go to the documentation of this file.
```00001       SUBROUTINE CLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
00002 *
00003 *  -- LAPACK routine (version 3.3.1) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *  -- April 2011                                                      --
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          DIRECT, STOREV
00010       INTEGER            K, LDT, LDV, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       COMPLEX            T( LDT, * ), TAU( * ), V( LDV, * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  CLARZT forms the triangular factor T of a complex block reflector
00020 *  H of order > n, which is defined as a product of k elementary
00021 *  reflectors.
00022 *
00023 *  If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
00024 *
00025 *  If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
00026 *
00027 *  If STOREV = 'C', the vector which defines the elementary reflector
00028 *  H(i) is stored in the i-th column of the array V, and
00029 *
00030 *     H  =  I - V * T * V**H
00031 *
00032 *  If STOREV = 'R', the vector which defines the elementary reflector
00033 *  H(i) is stored in the i-th row of the array V, and
00034 *
00035 *     H  =  I - V**H * T * V
00036 *
00037 *  Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
00038 *
00039 *  Arguments
00040 *  =========
00041 *
00042 *  DIRECT  (input) CHARACTER*1
00043 *          Specifies the order in which the elementary reflectors are
00044 *          multiplied to form the block reflector:
00045 *          = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
00046 *          = 'B': H = H(k) . . . H(2) H(1) (Backward)
00047 *
00048 *  STOREV  (input) CHARACTER*1
00049 *          Specifies how the vectors which define the elementary
00051 *          = 'C': columnwise                        (not supported yet)
00052 *          = 'R': rowwise
00053 *
00054 *  N       (input) INTEGER
00055 *          The order of the block reflector H. N >= 0.
00056 *
00057 *  K       (input) INTEGER
00058 *          The order of the triangular factor T (= the number of
00059 *          elementary reflectors). K >= 1.
00060 *
00061 *  V       (input/output) COMPLEX array, dimension
00062 *                               (LDV,K) if STOREV = 'C'
00063 *                               (LDV,N) if STOREV = 'R'
00064 *          The matrix V. See further details.
00065 *
00066 *  LDV     (input) INTEGER
00067 *          The leading dimension of the array V.
00068 *          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
00069 *
00070 *  TAU     (input) COMPLEX array, dimension (K)
00071 *          TAU(i) must contain the scalar factor of the elementary
00072 *          reflector H(i).
00073 *
00074 *  T       (output) COMPLEX array, dimension (LDT,K)
00075 *          The k by k triangular factor T of the block reflector.
00076 *          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
00077 *          lower triangular. The rest of the array is not used.
00078 *
00079 *  LDT     (input) INTEGER
00080 *          The leading dimension of the array T. LDT >= K.
00081 *
00082 *  Further Details
00083 *  ===============
00084 *
00085 *  Based on contributions by
00086 *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
00087 *
00088 *  The shape of the matrix V and the storage of the vectors which define
00089 *  the H(i) is best illustrated by the following example with n = 5 and
00090 *  k = 3. The elements equal to 1 are not stored; the corresponding
00091 *  array elements are modified but restored on exit. The rest of the
00092 *  array is not used.
00093 *
00094 *  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
00095 *
00096 *                                              ______V_____
00097 *         ( v1 v2 v3 )                        /            \
00098 *         ( v1 v2 v3 )                      ( v1 v1 v1 v1 v1 . . . . 1 )
00099 *     V = ( v1 v2 v3 )                      ( v2 v2 v2 v2 v2 . . . 1   )
00100 *         ( v1 v2 v3 )                      ( v3 v3 v3 v3 v3 . . 1     )
00101 *         ( v1 v2 v3 )
00102 *            .  .  .
00103 *            .  .  .
00104 *            1  .  .
00105 *               1  .
00106 *                  1
00107 *
00108 *  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
00109 *
00110 *                                                        ______V_____
00111 *            1                                          /            \
00112 *            .  1                           ( 1 . . . . v1 v1 v1 v1 v1 )
00113 *            .  .  1                        ( . 1 . . . v2 v2 v2 v2 v2 )
00114 *            .  .  .                        ( . . 1 . . v3 v3 v3 v3 v3 )
00115 *            .  .  .
00116 *         ( v1 v2 v3 )
00117 *         ( v1 v2 v3 )
00118 *     V = ( v1 v2 v3 )
00119 *         ( v1 v2 v3 )
00120 *         ( v1 v2 v3 )
00121 *
00122 *  =====================================================================
00123 *
00124 *     .. Parameters ..
00125       COMPLEX            ZERO
00126       PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ) )
00127 *     ..
00128 *     .. Local Scalars ..
00129       INTEGER            I, INFO, J
00130 *     ..
00131 *     .. External Subroutines ..
00132       EXTERNAL           CGEMV, CLACGV, CTRMV, XERBLA
00133 *     ..
00134 *     .. External Functions ..
00135       LOGICAL            LSAME
00136       EXTERNAL           LSAME
00137 *     ..
00138 *     .. Executable Statements ..
00139 *
00140 *     Check for currently supported options
00141 *
00142       INFO = 0
00143       IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
00144          INFO = -1
00145       ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
00146          INFO = -2
00147       END IF
00148       IF( INFO.NE.0 ) THEN
00149          CALL XERBLA( 'CLARZT', -INFO )
00150          RETURN
00151       END IF
00152 *
00153       DO 20 I = K, 1, -1
00154          IF( TAU( I ).EQ.ZERO ) THEN
00155 *
00156 *           H(i)  =  I
00157 *
00158             DO 10 J = I, K
00159                T( J, I ) = ZERO
00160    10       CONTINUE
00161          ELSE
00162 *
00163 *           general case
00164 *
00165             IF( I.LT.K ) THEN
00166 *
00167 *              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**H
00168 *
00169                CALL CLACGV( N, V( I, 1 ), LDV )
00170                CALL CGEMV( 'No transpose', K-I, N, -TAU( I ),
00171      \$                     V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
00172      \$                     T( I+1, I ), 1 )
00173                CALL CLACGV( N, V( I, 1 ), LDV )
00174 *
00175 *              T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
00176 *
00177                CALL CTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
00178      \$                     T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
00179             END IF
00180             T( I, I ) = TAU( I )
00181          END IF
00182    20 CONTINUE
00183       RETURN
00184 *
00185 *     End of CLARZT
00186 *
00187       END
```