root / src / lapack / double / dlarzt.f @ 2
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| 1 | 1 | equemene | SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) |
|---|---|---|---|
| 2 | 1 | equemene | * |
| 3 | 1 | equemene | * -- LAPACK routine (version 3.2) -- |
| 4 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 5 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 6 | 1 | equemene | * November 2006 |
| 7 | 1 | equemene | * |
| 8 | 1 | equemene | * .. Scalar Arguments .. |
| 9 | 1 | equemene | CHARACTER DIRECT, STOREV |
| 10 | 1 | equemene | INTEGER K, LDT, LDV, N |
| 11 | 1 | equemene | * .. |
| 12 | 1 | equemene | * .. Array Arguments .. |
| 13 | 1 | equemene | DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) |
| 14 | 1 | equemene | * .. |
| 15 | 1 | equemene | * |
| 16 | 1 | equemene | * Purpose |
| 17 | 1 | equemene | * ======= |
| 18 | 1 | equemene | * |
| 19 | 1 | equemene | * DLARZT forms the triangular factor T of a real block reflector |
| 20 | 1 | equemene | * H of order > n, which is defined as a product of k elementary |
| 21 | 1 | equemene | * reflectors. |
| 22 | 1 | equemene | * |
| 23 | 1 | equemene | * If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; |
| 24 | 1 | equemene | * |
| 25 | 1 | equemene | * If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. |
| 26 | 1 | equemene | * |
| 27 | 1 | equemene | * If STOREV = 'C', the vector which defines the elementary reflector |
| 28 | 1 | equemene | * H(i) is stored in the i-th column of the array V, and |
| 29 | 1 | equemene | * |
| 30 | 1 | equemene | * H = I - V * T * V' |
| 31 | 1 | equemene | * |
| 32 | 1 | equemene | * If STOREV = 'R', the vector which defines the elementary reflector |
| 33 | 1 | equemene | * H(i) is stored in the i-th row of the array V, and |
| 34 | 1 | equemene | * |
| 35 | 1 | equemene | * H = I - V' * T * V |
| 36 | 1 | equemene | * |
| 37 | 1 | equemene | * Currently, only STOREV = 'R' and DIRECT = 'B' are supported. |
| 38 | 1 | equemene | * |
| 39 | 1 | equemene | * Arguments |
| 40 | 1 | equemene | * ========= |
| 41 | 1 | equemene | * |
| 42 | 1 | equemene | * DIRECT (input) CHARACTER*1 |
| 43 | 1 | equemene | * Specifies the order in which the elementary reflectors are |
| 44 | 1 | equemene | * multiplied to form the block reflector: |
| 45 | 1 | equemene | * = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) |
| 46 | 1 | equemene | * = 'B': H = H(k) . . . H(2) H(1) (Backward) |
| 47 | 1 | equemene | * |
| 48 | 1 | equemene | * STOREV (input) CHARACTER*1 |
| 49 | 1 | equemene | * Specifies how the vectors which define the elementary |
| 50 | 1 | equemene | * reflectors are stored (see also Further Details): |
| 51 | 1 | equemene | * = 'C': columnwise (not supported yet) |
| 52 | 1 | equemene | * = 'R': rowwise |
| 53 | 1 | equemene | * |
| 54 | 1 | equemene | * N (input) INTEGER |
| 55 | 1 | equemene | * The order of the block reflector H. N >= 0. |
| 56 | 1 | equemene | * |
| 57 | 1 | equemene | * K (input) INTEGER |
| 58 | 1 | equemene | * The order of the triangular factor T (= the number of |
| 59 | 1 | equemene | * elementary reflectors). K >= 1. |
| 60 | 1 | equemene | * |
| 61 | 1 | equemene | * V (input/output) DOUBLE PRECISION array, dimension |
| 62 | 1 | equemene | * (LDV,K) if STOREV = 'C' |
| 63 | 1 | equemene | * (LDV,N) if STOREV = 'R' |
| 64 | 1 | equemene | * The matrix V. See further details. |
| 65 | 1 | equemene | * |
| 66 | 1 | equemene | * LDV (input) INTEGER |
| 67 | 1 | equemene | * The leading dimension of the array V. |
| 68 | 1 | equemene | * If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. |
| 69 | 1 | equemene | * |
| 70 | 1 | equemene | * TAU (input) DOUBLE PRECISION array, dimension (K) |
| 71 | 1 | equemene | * TAU(i) must contain the scalar factor of the elementary |
| 72 | 1 | equemene | * reflector H(i). |
| 73 | 1 | equemene | * |
| 74 | 1 | equemene | * T (output) DOUBLE PRECISION array, dimension (LDT,K) |
| 75 | 1 | equemene | * The k by k triangular factor T of the block reflector. |
| 76 | 1 | equemene | * If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is |
| 77 | 1 | equemene | * lower triangular. The rest of the array is not used. |
| 78 | 1 | equemene | * |
| 79 | 1 | equemene | * LDT (input) INTEGER |
| 80 | 1 | equemene | * The leading dimension of the array T. LDT >= K. |
| 81 | 1 | equemene | * |
| 82 | 1 | equemene | * Further Details |
| 83 | 1 | equemene | * =============== |
| 84 | 1 | equemene | * |
| 85 | 1 | equemene | * Based on contributions by |
| 86 | 1 | equemene | * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
| 87 | 1 | equemene | * |
| 88 | 1 | equemene | * The shape of the matrix V and the storage of the vectors which define |
| 89 | 1 | equemene | * the H(i) is best illustrated by the following example with n = 5 and |
| 90 | 1 | equemene | * k = 3. The elements equal to 1 are not stored; the corresponding |
| 91 | 1 | equemene | * array elements are modified but restored on exit. The rest of the |
| 92 | 1 | equemene | * array is not used. |
| 93 | 1 | equemene | * |
| 94 | 1 | equemene | * DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': |
| 95 | 1 | equemene | * |
| 96 | 1 | equemene | * ______V_____ |
| 97 | 1 | equemene | * ( v1 v2 v3 ) / \ |
| 98 | 1 | equemene | * ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 ) |
| 99 | 1 | equemene | * V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 ) |
| 100 | 1 | equemene | * ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 ) |
| 101 | 1 | equemene | * ( v1 v2 v3 ) |
| 102 | 1 | equemene | * . . . |
| 103 | 1 | equemene | * . . . |
| 104 | 1 | equemene | * 1 . . |
| 105 | 1 | equemene | * 1 . |
| 106 | 1 | equemene | * 1 |
| 107 | 1 | equemene | * |
| 108 | 1 | equemene | * DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': |
| 109 | 1 | equemene | * |
| 110 | 1 | equemene | * ______V_____ |
| 111 | 1 | equemene | * 1 / \ |
| 112 | 1 | equemene | * . 1 ( 1 . . . . v1 v1 v1 v1 v1 ) |
| 113 | 1 | equemene | * . . 1 ( . 1 . . . v2 v2 v2 v2 v2 ) |
| 114 | 1 | equemene | * . . . ( . . 1 . . v3 v3 v3 v3 v3 ) |
| 115 | 1 | equemene | * . . . |
| 116 | 1 | equemene | * ( v1 v2 v3 ) |
| 117 | 1 | equemene | * ( v1 v2 v3 ) |
| 118 | 1 | equemene | * V = ( v1 v2 v3 ) |
| 119 | 1 | equemene | * ( v1 v2 v3 ) |
| 120 | 1 | equemene | * ( v1 v2 v3 ) |
| 121 | 1 | equemene | * |
| 122 | 1 | equemene | * ===================================================================== |
| 123 | 1 | equemene | * |
| 124 | 1 | equemene | * .. Parameters .. |
| 125 | 1 | equemene | DOUBLE PRECISION ZERO |
| 126 | 1 | equemene | PARAMETER ( ZERO = 0.0D+0 ) |
| 127 | 1 | equemene | * .. |
| 128 | 1 | equemene | * .. Local Scalars .. |
| 129 | 1 | equemene | INTEGER I, INFO, J |
| 130 | 1 | equemene | * .. |
| 131 | 1 | equemene | * .. External Subroutines .. |
| 132 | 1 | equemene | EXTERNAL DGEMV, DTRMV, XERBLA |
| 133 | 1 | equemene | * .. |
| 134 | 1 | equemene | * .. External Functions .. |
| 135 | 1 | equemene | LOGICAL LSAME |
| 136 | 1 | equemene | EXTERNAL LSAME |
| 137 | 1 | equemene | * .. |
| 138 | 1 | equemene | * .. Executable Statements .. |
| 139 | 1 | equemene | * |
| 140 | 1 | equemene | * Check for currently supported options |
| 141 | 1 | equemene | * |
| 142 | 1 | equemene | INFO = 0 |
| 143 | 1 | equemene | IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN |
| 144 | 1 | equemene | INFO = -1 |
| 145 | 1 | equemene | ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN |
| 146 | 1 | equemene | INFO = -2 |
| 147 | 1 | equemene | END IF |
| 148 | 1 | equemene | IF( INFO.NE.0 ) THEN |
| 149 | 1 | equemene | CALL XERBLA( 'DLARZT', -INFO ) |
| 150 | 1 | equemene | RETURN |
| 151 | 1 | equemene | END IF |
| 152 | 1 | equemene | * |
| 153 | 1 | equemene | DO 20 I = K, 1, -1 |
| 154 | 1 | equemene | IF( TAU( I ).EQ.ZERO ) THEN |
| 155 | 1 | equemene | * |
| 156 | 1 | equemene | * H(i) = I |
| 157 | 1 | equemene | * |
| 158 | 1 | equemene | DO 10 J = I, K |
| 159 | 1 | equemene | T( J, I ) = ZERO |
| 160 | 1 | equemene | 10 CONTINUE |
| 161 | 1 | equemene | ELSE |
| 162 | 1 | equemene | * |
| 163 | 1 | equemene | * general case |
| 164 | 1 | equemene | * |
| 165 | 1 | equemene | IF( I.LT.K ) THEN |
| 166 | 1 | equemene | * |
| 167 | 1 | equemene | * T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)' |
| 168 | 1 | equemene | * |
| 169 | 1 | equemene | CALL DGEMV( 'No transpose', K-I, N, -TAU( I ), |
| 170 | 1 | equemene | $ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO, |
| 171 | 1 | equemene | $ T( I+1, I ), 1 ) |
| 172 | 1 | equemene | * |
| 173 | 1 | equemene | * T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i) |
| 174 | 1 | equemene | * |
| 175 | 1 | equemene | CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, |
| 176 | 1 | equemene | $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) |
| 177 | 1 | equemene | END IF |
| 178 | 1 | equemene | T( I, I ) = TAU( I ) |
| 179 | 1 | equemene | END IF |
| 180 | 1 | equemene | 20 CONTINUE |
| 181 | 1 | equemene | RETURN |
| 182 | 1 | equemene | * |
| 183 | 1 | equemene | * End of DLARZT |
| 184 | 1 | equemene | * |
| 185 | 1 | equemene | END |