root / src / lapack / double / dormqr.f @ 1
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| 1 | 1 | equemene | SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
|---|---|---|---|
| 2 | 1 | equemene | $ WORK, LWORK, INFO ) |
| 3 | 1 | equemene | * |
| 4 | 1 | equemene | * -- LAPACK routine (version 3.2) -- |
| 5 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 6 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 7 | 1 | equemene | * November 2006 |
| 8 | 1 | equemene | * |
| 9 | 1 | equemene | * .. Scalar Arguments .. |
| 10 | 1 | equemene | CHARACTER SIDE, TRANS |
| 11 | 1 | equemene | INTEGER INFO, K, LDA, LDC, LWORK, M, N |
| 12 | 1 | equemene | * .. |
| 13 | 1 | equemene | * .. Array Arguments .. |
| 14 | 1 | equemene | DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
| 15 | 1 | equemene | * .. |
| 16 | 1 | equemene | * |
| 17 | 1 | equemene | * Purpose |
| 18 | 1 | equemene | * ======= |
| 19 | 1 | equemene | * |
| 20 | 1 | equemene | * DORMQR overwrites the general real M-by-N matrix C with |
| 21 | 1 | equemene | * |
| 22 | 1 | equemene | * SIDE = 'L' SIDE = 'R' |
| 23 | 1 | equemene | * TRANS = 'N': Q * C C * Q |
| 24 | 1 | equemene | * TRANS = 'T': Q**T * C C * Q**T |
| 25 | 1 | equemene | * |
| 26 | 1 | equemene | * where Q is a real orthogonal matrix defined as the product of k |
| 27 | 1 | equemene | * elementary reflectors |
| 28 | 1 | equemene | * |
| 29 | 1 | equemene | * Q = H(1) H(2) . . . H(k) |
| 30 | 1 | equemene | * |
| 31 | 1 | equemene | * as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N |
| 32 | 1 | equemene | * if SIDE = 'R'. |
| 33 | 1 | equemene | * |
| 34 | 1 | equemene | * Arguments |
| 35 | 1 | equemene | * ========= |
| 36 | 1 | equemene | * |
| 37 | 1 | equemene | * SIDE (input) CHARACTER*1 |
| 38 | 1 | equemene | * = 'L': apply Q or Q**T from the Left; |
| 39 | 1 | equemene | * = 'R': apply Q or Q**T from the Right. |
| 40 | 1 | equemene | * |
| 41 | 1 | equemene | * TRANS (input) CHARACTER*1 |
| 42 | 1 | equemene | * = 'N': No transpose, apply Q; |
| 43 | 1 | equemene | * = 'T': Transpose, apply Q**T. |
| 44 | 1 | equemene | * |
| 45 | 1 | equemene | * M (input) INTEGER |
| 46 | 1 | equemene | * The number of rows of the matrix C. M >= 0. |
| 47 | 1 | equemene | * |
| 48 | 1 | equemene | * N (input) INTEGER |
| 49 | 1 | equemene | * The number of columns of the matrix C. N >= 0. |
| 50 | 1 | equemene | * |
| 51 | 1 | equemene | * K (input) INTEGER |
| 52 | 1 | equemene | * The number of elementary reflectors whose product defines |
| 53 | 1 | equemene | * the matrix Q. |
| 54 | 1 | equemene | * If SIDE = 'L', M >= K >= 0; |
| 55 | 1 | equemene | * if SIDE = 'R', N >= K >= 0. |
| 56 | 1 | equemene | * |
| 57 | 1 | equemene | * A (input) DOUBLE PRECISION array, dimension (LDA,K) |
| 58 | 1 | equemene | * The i-th column must contain the vector which defines the |
| 59 | 1 | equemene | * elementary reflector H(i), for i = 1,2,...,k, as returned by |
| 60 | 1 | equemene | * DGEQRF in the first k columns of its array argument A. |
| 61 | 1 | equemene | * A is modified by the routine but restored on exit. |
| 62 | 1 | equemene | * |
| 63 | 1 | equemene | * LDA (input) INTEGER |
| 64 | 1 | equemene | * The leading dimension of the array A. |
| 65 | 1 | equemene | * If SIDE = 'L', LDA >= max(1,M); |
| 66 | 1 | equemene | * if SIDE = 'R', LDA >= max(1,N). |
| 67 | 1 | equemene | * |
| 68 | 1 | equemene | * TAU (input) DOUBLE PRECISION array, dimension (K) |
| 69 | 1 | equemene | * TAU(i) must contain the scalar factor of the elementary |
| 70 | 1 | equemene | * reflector H(i), as returned by DGEQRF. |
| 71 | 1 | equemene | * |
| 72 | 1 | equemene | * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) |
| 73 | 1 | equemene | * On entry, the M-by-N matrix C. |
| 74 | 1 | equemene | * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. |
| 75 | 1 | equemene | * |
| 76 | 1 | equemene | * LDC (input) INTEGER |
| 77 | 1 | equemene | * The leading dimension of the array C. LDC >= max(1,M). |
| 78 | 1 | equemene | * |
| 79 | 1 | equemene | * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
| 80 | 1 | equemene | * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
| 81 | 1 | equemene | * |
| 82 | 1 | equemene | * LWORK (input) INTEGER |
| 83 | 1 | equemene | * The dimension of the array WORK. |
| 84 | 1 | equemene | * If SIDE = 'L', LWORK >= max(1,N); |
| 85 | 1 | equemene | * if SIDE = 'R', LWORK >= max(1,M). |
| 86 | 1 | equemene | * For optimum performance LWORK >= N*NB if SIDE = 'L', and |
| 87 | 1 | equemene | * LWORK >= M*NB if SIDE = 'R', where NB is the optimal |
| 88 | 1 | equemene | * blocksize. |
| 89 | 1 | equemene | * |
| 90 | 1 | equemene | * If LWORK = -1, then a workspace query is assumed; the routine |
| 91 | 1 | equemene | * only calculates the optimal size of the WORK array, returns |
| 92 | 1 | equemene | * this value as the first entry of the WORK array, and no error |
| 93 | 1 | equemene | * message related to LWORK is issued by XERBLA. |
| 94 | 1 | equemene | * |
| 95 | 1 | equemene | * INFO (output) INTEGER |
| 96 | 1 | equemene | * = 0: successful exit |
| 97 | 1 | equemene | * < 0: if INFO = -i, the i-th argument had an illegal value |
| 98 | 1 | equemene | * |
| 99 | 1 | equemene | * ===================================================================== |
| 100 | 1 | equemene | * |
| 101 | 1 | equemene | * .. Parameters .. |
| 102 | 1 | equemene | INTEGER NBMAX, LDT |
| 103 | 1 | equemene | PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) |
| 104 | 1 | equemene | * .. |
| 105 | 1 | equemene | * .. Local Scalars .. |
| 106 | 1 | equemene | LOGICAL LEFT, LQUERY, NOTRAN |
| 107 | 1 | equemene | INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK, |
| 108 | 1 | equemene | $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW |
| 109 | 1 | equemene | * .. |
| 110 | 1 | equemene | * .. Local Arrays .. |
| 111 | 1 | equemene | DOUBLE PRECISION T( LDT, NBMAX ) |
| 112 | 1 | equemene | * .. |
| 113 | 1 | equemene | * .. External Functions .. |
| 114 | 1 | equemene | LOGICAL LSAME |
| 115 | 1 | equemene | INTEGER ILAENV |
| 116 | 1 | equemene | EXTERNAL LSAME, ILAENV |
| 117 | 1 | equemene | * .. |
| 118 | 1 | equemene | * .. External Subroutines .. |
| 119 | 1 | equemene | EXTERNAL DLARFB, DLARFT, DORM2R, XERBLA |
| 120 | 1 | equemene | * .. |
| 121 | 1 | equemene | * .. Intrinsic Functions .. |
| 122 | 1 | equemene | INTRINSIC MAX, MIN |
| 123 | 1 | equemene | * .. |
| 124 | 1 | equemene | * .. Executable Statements .. |
| 125 | 1 | equemene | * |
| 126 | 1 | equemene | * Test the input arguments |
| 127 | 1 | equemene | * |
| 128 | 1 | equemene | INFO = 0 |
| 129 | 1 | equemene | LEFT = LSAME( SIDE, 'L' ) |
| 130 | 1 | equemene | NOTRAN = LSAME( TRANS, 'N' ) |
| 131 | 1 | equemene | LQUERY = ( LWORK.EQ.-1 ) |
| 132 | 1 | equemene | * |
| 133 | 1 | equemene | * NQ is the order of Q and NW is the minimum dimension of WORK |
| 134 | 1 | equemene | * |
| 135 | 1 | equemene | IF( LEFT ) THEN |
| 136 | 1 | equemene | NQ = M |
| 137 | 1 | equemene | NW = N |
| 138 | 1 | equemene | ELSE |
| 139 | 1 | equemene | NQ = N |
| 140 | 1 | equemene | NW = M |
| 141 | 1 | equemene | END IF |
| 142 | 1 | equemene | IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN |
| 143 | 1 | equemene | INFO = -1 |
| 144 | 1 | equemene | ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN |
| 145 | 1 | equemene | INFO = -2 |
| 146 | 1 | equemene | ELSE IF( M.LT.0 ) THEN |
| 147 | 1 | equemene | INFO = -3 |
| 148 | 1 | equemene | ELSE IF( N.LT.0 ) THEN |
| 149 | 1 | equemene | INFO = -4 |
| 150 | 1 | equemene | ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN |
| 151 | 1 | equemene | INFO = -5 |
| 152 | 1 | equemene | ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN |
| 153 | 1 | equemene | INFO = -7 |
| 154 | 1 | equemene | ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
| 155 | 1 | equemene | INFO = -10 |
| 156 | 1 | equemene | ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN |
| 157 | 1 | equemene | INFO = -12 |
| 158 | 1 | equemene | END IF |
| 159 | 1 | equemene | * |
| 160 | 1 | equemene | IF( INFO.EQ.0 ) THEN |
| 161 | 1 | equemene | * |
| 162 | 1 | equemene | * Determine the block size. NB may be at most NBMAX, where NBMAX |
| 163 | 1 | equemene | * is used to define the local array T. |
| 164 | 1 | equemene | * |
| 165 | 1 | equemene | NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K, |
| 166 | 1 | equemene | $ -1 ) ) |
| 167 | 1 | equemene | LWKOPT = MAX( 1, NW )*NB |
| 168 | 1 | equemene | WORK( 1 ) = LWKOPT |
| 169 | 1 | equemene | END IF |
| 170 | 1 | equemene | * |
| 171 | 1 | equemene | IF( INFO.NE.0 ) THEN |
| 172 | 1 | equemene | CALL XERBLA( 'DORMQR', -INFO ) |
| 173 | 1 | equemene | RETURN |
| 174 | 1 | equemene | ELSE IF( LQUERY ) THEN |
| 175 | 1 | equemene | RETURN |
| 176 | 1 | equemene | END IF |
| 177 | 1 | equemene | * |
| 178 | 1 | equemene | * Quick return if possible |
| 179 | 1 | equemene | * |
| 180 | 1 | equemene | IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN |
| 181 | 1 | equemene | WORK( 1 ) = 1 |
| 182 | 1 | equemene | RETURN |
| 183 | 1 | equemene | END IF |
| 184 | 1 | equemene | * |
| 185 | 1 | equemene | NBMIN = 2 |
| 186 | 1 | equemene | LDWORK = NW |
| 187 | 1 | equemene | IF( NB.GT.1 .AND. NB.LT.K ) THEN |
| 188 | 1 | equemene | IWS = NW*NB |
| 189 | 1 | equemene | IF( LWORK.LT.IWS ) THEN |
| 190 | 1 | equemene | NB = LWORK / LDWORK |
| 191 | 1 | equemene | NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K, |
| 192 | 1 | equemene | $ -1 ) ) |
| 193 | 1 | equemene | END IF |
| 194 | 1 | equemene | ELSE |
| 195 | 1 | equemene | IWS = NW |
| 196 | 1 | equemene | END IF |
| 197 | 1 | equemene | * |
| 198 | 1 | equemene | IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN |
| 199 | 1 | equemene | * |
| 200 | 1 | equemene | * Use unblocked code |
| 201 | 1 | equemene | * |
| 202 | 1 | equemene | CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, |
| 203 | 1 | equemene | $ IINFO ) |
| 204 | 1 | equemene | ELSE |
| 205 | 1 | equemene | * |
| 206 | 1 | equemene | * Use blocked code |
| 207 | 1 | equemene | * |
| 208 | 1 | equemene | IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. |
| 209 | 1 | equemene | $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN |
| 210 | 1 | equemene | I1 = 1 |
| 211 | 1 | equemene | I2 = K |
| 212 | 1 | equemene | I3 = NB |
| 213 | 1 | equemene | ELSE |
| 214 | 1 | equemene | I1 = ( ( K-1 ) / NB )*NB + 1 |
| 215 | 1 | equemene | I2 = 1 |
| 216 | 1 | equemene | I3 = -NB |
| 217 | 1 | equemene | END IF |
| 218 | 1 | equemene | * |
| 219 | 1 | equemene | IF( LEFT ) THEN |
| 220 | 1 | equemene | NI = N |
| 221 | 1 | equemene | JC = 1 |
| 222 | 1 | equemene | ELSE |
| 223 | 1 | equemene | MI = M |
| 224 | 1 | equemene | IC = 1 |
| 225 | 1 | equemene | END IF |
| 226 | 1 | equemene | * |
| 227 | 1 | equemene | DO 10 I = I1, I2, I3 |
| 228 | 1 | equemene | IB = MIN( NB, K-I+1 ) |
| 229 | 1 | equemene | * |
| 230 | 1 | equemene | * Form the triangular factor of the block reflector |
| 231 | 1 | equemene | * H = H(i) H(i+1) . . . H(i+ib-1) |
| 232 | 1 | equemene | * |
| 233 | 1 | equemene | CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ), |
| 234 | 1 | equemene | $ LDA, TAU( I ), T, LDT ) |
| 235 | 1 | equemene | IF( LEFT ) THEN |
| 236 | 1 | equemene | * |
| 237 | 1 | equemene | * H or H' is applied to C(i:m,1:n) |
| 238 | 1 | equemene | * |
| 239 | 1 | equemene | MI = M - I + 1 |
| 240 | 1 | equemene | IC = I |
| 241 | 1 | equemene | ELSE |
| 242 | 1 | equemene | * |
| 243 | 1 | equemene | * H or H' is applied to C(1:m,i:n) |
| 244 | 1 | equemene | * |
| 245 | 1 | equemene | NI = N - I + 1 |
| 246 | 1 | equemene | JC = I |
| 247 | 1 | equemene | END IF |
| 248 | 1 | equemene | * |
| 249 | 1 | equemene | * Apply H or H' |
| 250 | 1 | equemene | * |
| 251 | 1 | equemene | CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI, |
| 252 | 1 | equemene | $ IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, |
| 253 | 1 | equemene | $ WORK, LDWORK ) |
| 254 | 1 | equemene | 10 CONTINUE |
| 255 | 1 | equemene | END IF |
| 256 | 1 | equemene | WORK( 1 ) = LWKOPT |
| 257 | 1 | equemene | RETURN |
| 258 | 1 | equemene | * |
| 259 | 1 | equemene | * End of DORMQR |
| 260 | 1 | equemene | * |
| 261 | 1 | equemene | END |