root / src / lapack / double / dorml2.f @ 10
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| 1 | 1 | pfleura2 | SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
|---|---|---|---|
| 2 | 1 | pfleura2 | $ WORK, INFO ) |
| 3 | 1 | pfleura2 | * |
| 4 | 1 | pfleura2 | * -- LAPACK routine (version 3.2) -- |
| 5 | 1 | pfleura2 | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 6 | 1 | pfleura2 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 7 | 1 | pfleura2 | * November 2006 |
| 8 | 1 | pfleura2 | * |
| 9 | 1 | pfleura2 | * .. Scalar Arguments .. |
| 10 | 1 | pfleura2 | CHARACTER SIDE, TRANS |
| 11 | 1 | pfleura2 | INTEGER INFO, K, LDA, LDC, M, N |
| 12 | 1 | pfleura2 | * .. |
| 13 | 1 | pfleura2 | * .. Array Arguments .. |
| 14 | 1 | pfleura2 | DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
| 15 | 1 | pfleura2 | * .. |
| 16 | 1 | pfleura2 | * |
| 17 | 1 | pfleura2 | * Purpose |
| 18 | 1 | pfleura2 | * ======= |
| 19 | 1 | pfleura2 | * |
| 20 | 1 | pfleura2 | * DORML2 overwrites the general real m by n matrix C with |
| 21 | 1 | pfleura2 | * |
| 22 | 1 | pfleura2 | * Q * C if SIDE = 'L' and TRANS = 'N', or |
| 23 | 1 | pfleura2 | * |
| 24 | 1 | pfleura2 | * Q'* C if SIDE = 'L' and TRANS = 'T', or |
| 25 | 1 | pfleura2 | * |
| 26 | 1 | pfleura2 | * C * Q if SIDE = 'R' and TRANS = 'N', or |
| 27 | 1 | pfleura2 | * |
| 28 | 1 | pfleura2 | * C * Q' if SIDE = 'R' and TRANS = 'T', |
| 29 | 1 | pfleura2 | * |
| 30 | 1 | pfleura2 | * where Q is a real orthogonal matrix defined as the product of k |
| 31 | 1 | pfleura2 | * elementary reflectors |
| 32 | 1 | pfleura2 | * |
| 33 | 1 | pfleura2 | * Q = H(k) . . . H(2) H(1) |
| 34 | 1 | pfleura2 | * |
| 35 | 1 | pfleura2 | * as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n |
| 36 | 1 | pfleura2 | * if SIDE = 'R'. |
| 37 | 1 | pfleura2 | * |
| 38 | 1 | pfleura2 | * Arguments |
| 39 | 1 | pfleura2 | * ========= |
| 40 | 1 | pfleura2 | * |
| 41 | 1 | pfleura2 | * SIDE (input) CHARACTER*1 |
| 42 | 1 | pfleura2 | * = 'L': apply Q or Q' from the Left |
| 43 | 1 | pfleura2 | * = 'R': apply Q or Q' from the Right |
| 44 | 1 | pfleura2 | * |
| 45 | 1 | pfleura2 | * TRANS (input) CHARACTER*1 |
| 46 | 1 | pfleura2 | * = 'N': apply Q (No transpose) |
| 47 | 1 | pfleura2 | * = 'T': apply Q' (Transpose) |
| 48 | 1 | pfleura2 | * |
| 49 | 1 | pfleura2 | * M (input) INTEGER |
| 50 | 1 | pfleura2 | * The number of rows of the matrix C. M >= 0. |
| 51 | 1 | pfleura2 | * |
| 52 | 1 | pfleura2 | * N (input) INTEGER |
| 53 | 1 | pfleura2 | * The number of columns of the matrix C. N >= 0. |
| 54 | 1 | pfleura2 | * |
| 55 | 1 | pfleura2 | * K (input) INTEGER |
| 56 | 1 | pfleura2 | * The number of elementary reflectors whose product defines |
| 57 | 1 | pfleura2 | * the matrix Q. |
| 58 | 1 | pfleura2 | * If SIDE = 'L', M >= K >= 0; |
| 59 | 1 | pfleura2 | * if SIDE = 'R', N >= K >= 0. |
| 60 | 1 | pfleura2 | * |
| 61 | 1 | pfleura2 | * A (input) DOUBLE PRECISION array, dimension |
| 62 | 1 | pfleura2 | * (LDA,M) if SIDE = 'L', |
| 63 | 1 | pfleura2 | * (LDA,N) if SIDE = 'R' |
| 64 | 1 | pfleura2 | * The i-th row must contain the vector which defines the |
| 65 | 1 | pfleura2 | * elementary reflector H(i), for i = 1,2,...,k, as returned by |
| 66 | 1 | pfleura2 | * DGELQF in the first k rows of its array argument A. |
| 67 | 1 | pfleura2 | * A is modified by the routine but restored on exit. |
| 68 | 1 | pfleura2 | * |
| 69 | 1 | pfleura2 | * LDA (input) INTEGER |
| 70 | 1 | pfleura2 | * The leading dimension of the array A. LDA >= max(1,K). |
| 71 | 1 | pfleura2 | * |
| 72 | 1 | pfleura2 | * TAU (input) DOUBLE PRECISION array, dimension (K) |
| 73 | 1 | pfleura2 | * TAU(i) must contain the scalar factor of the elementary |
| 74 | 1 | pfleura2 | * reflector H(i), as returned by DGELQF. |
| 75 | 1 | pfleura2 | * |
| 76 | 1 | pfleura2 | * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) |
| 77 | 1 | pfleura2 | * On entry, the m by n matrix C. |
| 78 | 1 | pfleura2 | * On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q. |
| 79 | 1 | pfleura2 | * |
| 80 | 1 | pfleura2 | * LDC (input) INTEGER |
| 81 | 1 | pfleura2 | * The leading dimension of the array C. LDC >= max(1,M). |
| 82 | 1 | pfleura2 | * |
| 83 | 1 | pfleura2 | * WORK (workspace) DOUBLE PRECISION array, dimension |
| 84 | 1 | pfleura2 | * (N) if SIDE = 'L', |
| 85 | 1 | pfleura2 | * (M) if SIDE = 'R' |
| 86 | 1 | pfleura2 | * |
| 87 | 1 | pfleura2 | * INFO (output) INTEGER |
| 88 | 1 | pfleura2 | * = 0: successful exit |
| 89 | 1 | pfleura2 | * < 0: if INFO = -i, the i-th argument had an illegal value |
| 90 | 1 | pfleura2 | * |
| 91 | 1 | pfleura2 | * ===================================================================== |
| 92 | 1 | pfleura2 | * |
| 93 | 1 | pfleura2 | * .. Parameters .. |
| 94 | 1 | pfleura2 | DOUBLE PRECISION ONE |
| 95 | 1 | pfleura2 | PARAMETER ( ONE = 1.0D+0 ) |
| 96 | 1 | pfleura2 | * .. |
| 97 | 1 | pfleura2 | * .. Local Scalars .. |
| 98 | 1 | pfleura2 | LOGICAL LEFT, NOTRAN |
| 99 | 1 | pfleura2 | INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ |
| 100 | 1 | pfleura2 | DOUBLE PRECISION AII |
| 101 | 1 | pfleura2 | * .. |
| 102 | 1 | pfleura2 | * .. External Functions .. |
| 103 | 1 | pfleura2 | LOGICAL LSAME |
| 104 | 1 | pfleura2 | EXTERNAL LSAME |
| 105 | 1 | pfleura2 | * .. |
| 106 | 1 | pfleura2 | * .. External Subroutines .. |
| 107 | 1 | pfleura2 | EXTERNAL DLARF, XERBLA |
| 108 | 1 | pfleura2 | * .. |
| 109 | 1 | pfleura2 | * .. Intrinsic Functions .. |
| 110 | 1 | pfleura2 | INTRINSIC MAX |
| 111 | 1 | pfleura2 | * .. |
| 112 | 1 | pfleura2 | * .. Executable Statements .. |
| 113 | 1 | pfleura2 | * |
| 114 | 1 | pfleura2 | * Test the input arguments |
| 115 | 1 | pfleura2 | * |
| 116 | 1 | pfleura2 | INFO = 0 |
| 117 | 1 | pfleura2 | LEFT = LSAME( SIDE, 'L' ) |
| 118 | 1 | pfleura2 | NOTRAN = LSAME( TRANS, 'N' ) |
| 119 | 1 | pfleura2 | * |
| 120 | 1 | pfleura2 | * NQ is the order of Q |
| 121 | 1 | pfleura2 | * |
| 122 | 1 | pfleura2 | IF( LEFT ) THEN |
| 123 | 1 | pfleura2 | NQ = M |
| 124 | 1 | pfleura2 | ELSE |
| 125 | 1 | pfleura2 | NQ = N |
| 126 | 1 | pfleura2 | END IF |
| 127 | 1 | pfleura2 | IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN |
| 128 | 1 | pfleura2 | INFO = -1 |
| 129 | 1 | pfleura2 | ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN |
| 130 | 1 | pfleura2 | INFO = -2 |
| 131 | 1 | pfleura2 | ELSE IF( M.LT.0 ) THEN |
| 132 | 1 | pfleura2 | INFO = -3 |
| 133 | 1 | pfleura2 | ELSE IF( N.LT.0 ) THEN |
| 134 | 1 | pfleura2 | INFO = -4 |
| 135 | 1 | pfleura2 | ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN |
| 136 | 1 | pfleura2 | INFO = -5 |
| 137 | 1 | pfleura2 | ELSE IF( LDA.LT.MAX( 1, K ) ) THEN |
| 138 | 1 | pfleura2 | INFO = -7 |
| 139 | 1 | pfleura2 | ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
| 140 | 1 | pfleura2 | INFO = -10 |
| 141 | 1 | pfleura2 | END IF |
| 142 | 1 | pfleura2 | IF( INFO.NE.0 ) THEN |
| 143 | 1 | pfleura2 | CALL XERBLA( 'DORML2', -INFO ) |
| 144 | 1 | pfleura2 | RETURN |
| 145 | 1 | pfleura2 | END IF |
| 146 | 1 | pfleura2 | * |
| 147 | 1 | pfleura2 | * Quick return if possible |
| 148 | 1 | pfleura2 | * |
| 149 | 1 | pfleura2 | IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) |
| 150 | 1 | pfleura2 | $ RETURN |
| 151 | 1 | pfleura2 | * |
| 152 | 1 | pfleura2 | IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) |
| 153 | 1 | pfleura2 | $ THEN |
| 154 | 1 | pfleura2 | I1 = 1 |
| 155 | 1 | pfleura2 | I2 = K |
| 156 | 1 | pfleura2 | I3 = 1 |
| 157 | 1 | pfleura2 | ELSE |
| 158 | 1 | pfleura2 | I1 = K |
| 159 | 1 | pfleura2 | I2 = 1 |
| 160 | 1 | pfleura2 | I3 = -1 |
| 161 | 1 | pfleura2 | END IF |
| 162 | 1 | pfleura2 | * |
| 163 | 1 | pfleura2 | IF( LEFT ) THEN |
| 164 | 1 | pfleura2 | NI = N |
| 165 | 1 | pfleura2 | JC = 1 |
| 166 | 1 | pfleura2 | ELSE |
| 167 | 1 | pfleura2 | MI = M |
| 168 | 1 | pfleura2 | IC = 1 |
| 169 | 1 | pfleura2 | END IF |
| 170 | 1 | pfleura2 | * |
| 171 | 1 | pfleura2 | DO 10 I = I1, I2, I3 |
| 172 | 1 | pfleura2 | IF( LEFT ) THEN |
| 173 | 1 | pfleura2 | * |
| 174 | 1 | pfleura2 | * H(i) is applied to C(i:m,1:n) |
| 175 | 1 | pfleura2 | * |
| 176 | 1 | pfleura2 | MI = M - I + 1 |
| 177 | 1 | pfleura2 | IC = I |
| 178 | 1 | pfleura2 | ELSE |
| 179 | 1 | pfleura2 | * |
| 180 | 1 | pfleura2 | * H(i) is applied to C(1:m,i:n) |
| 181 | 1 | pfleura2 | * |
| 182 | 1 | pfleura2 | NI = N - I + 1 |
| 183 | 1 | pfleura2 | JC = I |
| 184 | 1 | pfleura2 | END IF |
| 185 | 1 | pfleura2 | * |
| 186 | 1 | pfleura2 | * Apply H(i) |
| 187 | 1 | pfleura2 | * |
| 188 | 1 | pfleura2 | AII = A( I, I ) |
| 189 | 1 | pfleura2 | A( I, I ) = ONE |
| 190 | 1 | pfleura2 | CALL DLARF( SIDE, MI, NI, A( I, I ), LDA, TAU( I ), |
| 191 | 1 | pfleura2 | $ C( IC, JC ), LDC, WORK ) |
| 192 | 1 | pfleura2 | A( I, I ) = AII |
| 193 | 1 | pfleura2 | 10 CONTINUE |
| 194 | 1 | pfleura2 | RETURN |
| 195 | 1 | pfleura2 | * |
| 196 | 1 | pfleura2 | * End of DORML2 |
| 197 | 1 | pfleura2 | * |
| 198 | 1 | pfleura2 | END |