|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 |
SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
$ WORK, INFO ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, L, LDA, LDC, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * DORMR3 overwrites the general real m by n matrix C with * * Q * C if SIDE = 'L' and TRANS = 'N', or * * Q**T* C if SIDE = 'L' and TRANS = 'C', or * * C * Q if SIDE = 'R' and TRANS = 'N', or * * C * Q**T if SIDE = 'R' and TRANS = 'C', * * where Q is a real orthogonal matrix defined as the product of k * elementary reflectors * * Q = H(1) H(2) . . . H(k) * * as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n * if SIDE = 'R'. * * Arguments * ========= * * SIDE (input) CHARACTER*1 * = 'L': apply Q or Q**T from the Left * = 'R': apply Q or Q**T from the Right * * TRANS (input) CHARACTER*1 * = 'N': apply Q (No transpose) * = 'T': apply Q**T (Transpose) * * M (input) INTEGER * The number of rows of the matrix C. M >= 0. * * N (input) INTEGER * The number of columns of the matrix C. N >= 0. * * K (input) INTEGER * The number of elementary reflectors whose product defines * the matrix Q. * If SIDE = 'L', M >= K >= 0; * if SIDE = 'R', N >= K >= 0. * * L (input) INTEGER * The number of columns of the matrix A containing * the meaningful part of the Householder reflectors. * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. * * A (input) DOUBLE PRECISION array, dimension * (LDA,M) if SIDE = 'L', * (LDA,N) if SIDE = 'R' * The i-th row must contain the vector which defines the * elementary reflector H(i), for i = 1,2,...,k, as returned by * DTZRZF in the last k rows of its array argument A. * A is modified by the routine but restored on exit. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,K). * * TAU (input) DOUBLE PRECISION array, dimension (K) * TAU(i) must contain the scalar factor of the elementary * reflector H(i), as returned by DTZRZF. * * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) * On entry, the m-by-n matrix C. * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. * * LDC (input) INTEGER * The leading dimension of the array C. LDC >= max(1,M). * * WORK (workspace) DOUBLE PRECISION array, dimension * (N) if SIDE = 'L', * (M) if SIDE = 'R' * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * Further Details * =============== * * Based on contributions by * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA * * ===================================================================== * * .. Local Scalars .. LOGICAL LEFT, NOTRAN INTEGER I, I1, I2, I3, IC, JA, JC, MI, NI, NQ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DLARZ, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) * * NQ is the order of Q * IF( LEFT ) THEN NQ = M ELSE NQ = N END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR. $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN INFO = -6 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN INFO = -8 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMR3', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) $ RETURN * IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN I1 = 1 I2 = K I3 = 1 ELSE I1 = K I2 = 1 I3 = -1 END IF * IF( LEFT ) THEN NI = N JA = M - L + 1 JC = 1 ELSE MI = M JA = N - L + 1 IC = 1 END IF * DO 10 I = I1, I2, I3 IF( LEFT ) THEN * * H(i) or H(i)**T is applied to C(i:m,1:n) * MI = M - I + 1 IC = I ELSE * * H(i) or H(i)**T is applied to C(1:m,i:n) * NI = N - I + 1 JC = I END IF * * Apply H(i) or H(i)**T * CALL DLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ), $ C( IC, JC ), LDC, WORK ) * 10 CONTINUE * RETURN * * End of DORMR3 * END |