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| 1 | 1 | equemene | SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) |
|---|---|---|---|
| 2 | 1 | equemene | * .. Scalar Arguments .. |
| 3 | 1 | equemene | INTEGER INCX,K,LDA,N |
| 4 | 1 | equemene | CHARACTER DIAG,TRANS,UPLO |
| 5 | 1 | equemene | * .. |
| 6 | 1 | equemene | * .. Array Arguments .. |
| 7 | 1 | equemene | COMPLEX A(LDA,*),X(*) |
| 8 | 1 | equemene | * .. |
| 9 | 1 | equemene | * |
| 10 | 1 | equemene | * Purpose |
| 11 | 1 | equemene | * ======= |
| 12 | 1 | equemene | * |
| 13 | 1 | equemene | * CTBSV solves one of the systems of equations |
| 14 | 1 | equemene | * |
| 15 | 1 | equemene | * A*x = b, or A'*x = b, or conjg( A' )*x = b, |
| 16 | 1 | equemene | * |
| 17 | 1 | equemene | * where b and x are n element vectors and A is an n by n unit, or |
| 18 | 1 | equemene | * non-unit, upper or lower triangular band matrix, with ( k + 1 ) |
| 19 | 1 | equemene | * diagonals. |
| 20 | 1 | equemene | * |
| 21 | 1 | equemene | * No test for singularity or near-singularity is included in this |
| 22 | 1 | equemene | * routine. Such tests must be performed before calling this routine. |
| 23 | 1 | equemene | * |
| 24 | 1 | equemene | * Arguments |
| 25 | 1 | equemene | * ========== |
| 26 | 1 | equemene | * |
| 27 | 1 | equemene | * UPLO - CHARACTER*1. |
| 28 | 1 | equemene | * On entry, UPLO specifies whether the matrix is an upper or |
| 29 | 1 | equemene | * lower triangular matrix as follows: |
| 30 | 1 | equemene | * |
| 31 | 1 | equemene | * UPLO = 'U' or 'u' A is an upper triangular matrix. |
| 32 | 1 | equemene | * |
| 33 | 1 | equemene | * UPLO = 'L' or 'l' A is a lower triangular matrix. |
| 34 | 1 | equemene | * |
| 35 | 1 | equemene | * Unchanged on exit. |
| 36 | 1 | equemene | * |
| 37 | 1 | equemene | * TRANS - CHARACTER*1. |
| 38 | 1 | equemene | * On entry, TRANS specifies the equations to be solved as |
| 39 | 1 | equemene | * follows: |
| 40 | 1 | equemene | * |
| 41 | 1 | equemene | * TRANS = 'N' or 'n' A*x = b. |
| 42 | 1 | equemene | * |
| 43 | 1 | equemene | * TRANS = 'T' or 't' A'*x = b. |
| 44 | 1 | equemene | * |
| 45 | 1 | equemene | * TRANS = 'C' or 'c' conjg( A' )*x = b. |
| 46 | 1 | equemene | * |
| 47 | 1 | equemene | * Unchanged on exit. |
| 48 | 1 | equemene | * |
| 49 | 1 | equemene | * DIAG - CHARACTER*1. |
| 50 | 1 | equemene | * On entry, DIAG specifies whether or not A is unit |
| 51 | 1 | equemene | * triangular as follows: |
| 52 | 1 | equemene | * |
| 53 | 1 | equemene | * DIAG = 'U' or 'u' A is assumed to be unit triangular. |
| 54 | 1 | equemene | * |
| 55 | 1 | equemene | * DIAG = 'N' or 'n' A is not assumed to be unit |
| 56 | 1 | equemene | * triangular. |
| 57 | 1 | equemene | * |
| 58 | 1 | equemene | * Unchanged on exit. |
| 59 | 1 | equemene | * |
| 60 | 1 | equemene | * N - INTEGER. |
| 61 | 1 | equemene | * On entry, N specifies the order of the matrix A. |
| 62 | 1 | equemene | * N must be at least zero. |
| 63 | 1 | equemene | * Unchanged on exit. |
| 64 | 1 | equemene | * |
| 65 | 1 | equemene | * K - INTEGER. |
| 66 | 1 | equemene | * On entry with UPLO = 'U' or 'u', K specifies the number of |
| 67 | 1 | equemene | * super-diagonals of the matrix A. |
| 68 | 1 | equemene | * On entry with UPLO = 'L' or 'l', K specifies the number of |
| 69 | 1 | equemene | * sub-diagonals of the matrix A. |
| 70 | 1 | equemene | * K must satisfy 0 .le. K. |
| 71 | 1 | equemene | * Unchanged on exit. |
| 72 | 1 | equemene | * |
| 73 | 1 | equemene | * A - COMPLEX array of DIMENSION ( LDA, n ). |
| 74 | 1 | equemene | * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) |
| 75 | 1 | equemene | * by n part of the array A must contain the upper triangular |
| 76 | 1 | equemene | * band part of the matrix of coefficients, supplied column by |
| 77 | 1 | equemene | * column, with the leading diagonal of the matrix in row |
| 78 | 1 | equemene | * ( k + 1 ) of the array, the first super-diagonal starting at |
| 79 | 1 | equemene | * position 2 in row k, and so on. The top left k by k triangle |
| 80 | 1 | equemene | * of the array A is not referenced. |
| 81 | 1 | equemene | * The following program segment will transfer an upper |
| 82 | 1 | equemene | * triangular band matrix from conventional full matrix storage |
| 83 | 1 | equemene | * to band storage: |
| 84 | 1 | equemene | * |
| 85 | 1 | equemene | * DO 20, J = 1, N |
| 86 | 1 | equemene | * M = K + 1 - J |
| 87 | 1 | equemene | * DO 10, I = MAX( 1, J - K ), J |
| 88 | 1 | equemene | * A( M + I, J ) = matrix( I, J ) |
| 89 | 1 | equemene | * 10 CONTINUE |
| 90 | 1 | equemene | * 20 CONTINUE |
| 91 | 1 | equemene | * |
| 92 | 1 | equemene | * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) |
| 93 | 1 | equemene | * by n part of the array A must contain the lower triangular |
| 94 | 1 | equemene | * band part of the matrix of coefficients, supplied column by |
| 95 | 1 | equemene | * column, with the leading diagonal of the matrix in row 1 of |
| 96 | 1 | equemene | * the array, the first sub-diagonal starting at position 1 in |
| 97 | 1 | equemene | * row 2, and so on. The bottom right k by k triangle of the |
| 98 | 1 | equemene | * array A is not referenced. |
| 99 | 1 | equemene | * The following program segment will transfer a lower |
| 100 | 1 | equemene | * triangular band matrix from conventional full matrix storage |
| 101 | 1 | equemene | * to band storage: |
| 102 | 1 | equemene | * |
| 103 | 1 | equemene | * DO 20, J = 1, N |
| 104 | 1 | equemene | * M = 1 - J |
| 105 | 1 | equemene | * DO 10, I = J, MIN( N, J + K ) |
| 106 | 1 | equemene | * A( M + I, J ) = matrix( I, J ) |
| 107 | 1 | equemene | * 10 CONTINUE |
| 108 | 1 | equemene | * 20 CONTINUE |
| 109 | 1 | equemene | * |
| 110 | 1 | equemene | * Note that when DIAG = 'U' or 'u' the elements of the array A |
| 111 | 1 | equemene | * corresponding to the diagonal elements of the matrix are not |
| 112 | 1 | equemene | * referenced, but are assumed to be unity. |
| 113 | 1 | equemene | * Unchanged on exit. |
| 114 | 1 | equemene | * |
| 115 | 1 | equemene | * LDA - INTEGER. |
| 116 | 1 | equemene | * On entry, LDA specifies the first dimension of A as declared |
| 117 | 1 | equemene | * in the calling (sub) program. LDA must be at least |
| 118 | 1 | equemene | * ( k + 1 ). |
| 119 | 1 | equemene | * Unchanged on exit. |
| 120 | 1 | equemene | * |
| 121 | 1 | equemene | * X - COMPLEX array of dimension at least |
| 122 | 1 | equemene | * ( 1 + ( n - 1 )*abs( INCX ) ). |
| 123 | 1 | equemene | * Before entry, the incremented array X must contain the n |
| 124 | 1 | equemene | * element right-hand side vector b. On exit, X is overwritten |
| 125 | 1 | equemene | * with the solution vector x. |
| 126 | 1 | equemene | * |
| 127 | 1 | equemene | * INCX - INTEGER. |
| 128 | 1 | equemene | * On entry, INCX specifies the increment for the elements of |
| 129 | 1 | equemene | * X. INCX must not be zero. |
| 130 | 1 | equemene | * Unchanged on exit. |
| 131 | 1 | equemene | * |
| 132 | 1 | equemene | * |
| 133 | 1 | equemene | * Level 2 Blas routine. |
| 134 | 1 | equemene | * |
| 135 | 1 | equemene | * -- Written on 22-October-1986. |
| 136 | 1 | equemene | * Jack Dongarra, Argonne National Lab. |
| 137 | 1 | equemene | * Jeremy Du Croz, Nag Central Office. |
| 138 | 1 | equemene | * Sven Hammarling, Nag Central Office. |
| 139 | 1 | equemene | * Richard Hanson, Sandia National Labs. |
| 140 | 1 | equemene | * |
| 141 | 1 | equemene | * |
| 142 | 1 | equemene | * .. Parameters .. |
| 143 | 1 | equemene | COMPLEX ZERO |
| 144 | 1 | equemene | PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
| 145 | 1 | equemene | * .. |
| 146 | 1 | equemene | * .. Local Scalars .. |
| 147 | 1 | equemene | COMPLEX TEMP |
| 148 | 1 | equemene | INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L |
| 149 | 1 | equemene | LOGICAL NOCONJ,NOUNIT |
| 150 | 1 | equemene | * .. |
| 151 | 1 | equemene | * .. External Functions .. |
| 152 | 1 | equemene | LOGICAL LSAME |
| 153 | 1 | equemene | EXTERNAL LSAME |
| 154 | 1 | equemene | * .. |
| 155 | 1 | equemene | * .. External Subroutines .. |
| 156 | 1 | equemene | EXTERNAL XERBLA |
| 157 | 1 | equemene | * .. |
| 158 | 1 | equemene | * .. Intrinsic Functions .. |
| 159 | 1 | equemene | INTRINSIC CONJG,MAX,MIN |
| 160 | 1 | equemene | * .. |
| 161 | 1 | equemene | * |
| 162 | 1 | equemene | * Test the input parameters. |
| 163 | 1 | equemene | * |
| 164 | 1 | equemene | INFO = 0 |
| 165 | 1 | equemene | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
| 166 | 1 | equemene | INFO = 1 |
| 167 | 1 | equemene | ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. |
| 168 | 1 | equemene | + .NOT.LSAME(TRANS,'C')) THEN |
| 169 | 1 | equemene | INFO = 2 |
| 170 | 1 | equemene | ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN |
| 171 | 1 | equemene | INFO = 3 |
| 172 | 1 | equemene | ELSE IF (N.LT.0) THEN |
| 173 | 1 | equemene | INFO = 4 |
| 174 | 1 | equemene | ELSE IF (K.LT.0) THEN |
| 175 | 1 | equemene | INFO = 5 |
| 176 | 1 | equemene | ELSE IF (LDA.LT. (K+1)) THEN |
| 177 | 1 | equemene | INFO = 7 |
| 178 | 1 | equemene | ELSE IF (INCX.EQ.0) THEN |
| 179 | 1 | equemene | INFO = 9 |
| 180 | 1 | equemene | END IF |
| 181 | 1 | equemene | IF (INFO.NE.0) THEN |
| 182 | 1 | equemene | CALL XERBLA('CTBSV ',INFO)
|
| 183 | 1 | equemene | RETURN |
| 184 | 1 | equemene | END IF |
| 185 | 1 | equemene | * |
| 186 | 1 | equemene | * Quick return if possible. |
| 187 | 1 | equemene | * |
| 188 | 1 | equemene | IF (N.EQ.0) RETURN |
| 189 | 1 | equemene | * |
| 190 | 1 | equemene | NOCONJ = LSAME(TRANS,'T') |
| 191 | 1 | equemene | NOUNIT = LSAME(DIAG,'N') |
| 192 | 1 | equemene | * |
| 193 | 1 | equemene | * Set up the start point in X if the increment is not unity. This |
| 194 | 1 | equemene | * will be ( N - 1 )*INCX too small for descending loops. |
| 195 | 1 | equemene | * |
| 196 | 1 | equemene | IF (INCX.LE.0) THEN |
| 197 | 1 | equemene | KX = 1 - (N-1)*INCX |
| 198 | 1 | equemene | ELSE IF (INCX.NE.1) THEN |
| 199 | 1 | equemene | KX = 1 |
| 200 | 1 | equemene | END IF |
| 201 | 1 | equemene | * |
| 202 | 1 | equemene | * Start the operations. In this version the elements of A are |
| 203 | 1 | equemene | * accessed by sequentially with one pass through A. |
| 204 | 1 | equemene | * |
| 205 | 1 | equemene | IF (LSAME(TRANS,'N')) THEN |
| 206 | 1 | equemene | * |
| 207 | 1 | equemene | * Form x := inv( A )*x. |
| 208 | 1 | equemene | * |
| 209 | 1 | equemene | IF (LSAME(UPLO,'U')) THEN |
| 210 | 1 | equemene | KPLUS1 = K + 1 |
| 211 | 1 | equemene | IF (INCX.EQ.1) THEN |
| 212 | 1 | equemene | DO 20 J = N,1,-1 |
| 213 | 1 | equemene | IF (X(J).NE.ZERO) THEN |
| 214 | 1 | equemene | L = KPLUS1 - J |
| 215 | 1 | equemene | IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J) |
| 216 | 1 | equemene | TEMP = X(J) |
| 217 | 1 | equemene | DO 10 I = J - 1,MAX(1,J-K),-1 |
| 218 | 1 | equemene | X(I) = X(I) - TEMP*A(L+I,J) |
| 219 | 1 | equemene | 10 CONTINUE |
| 220 | 1 | equemene | END IF |
| 221 | 1 | equemene | 20 CONTINUE |
| 222 | 1 | equemene | ELSE |
| 223 | 1 | equemene | KX = KX + (N-1)*INCX |
| 224 | 1 | equemene | JX = KX |
| 225 | 1 | equemene | DO 40 J = N,1,-1 |
| 226 | 1 | equemene | KX = KX - INCX |
| 227 | 1 | equemene | IF (X(JX).NE.ZERO) THEN |
| 228 | 1 | equemene | IX = KX |
| 229 | 1 | equemene | L = KPLUS1 - J |
| 230 | 1 | equemene | IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J) |
| 231 | 1 | equemene | TEMP = X(JX) |
| 232 | 1 | equemene | DO 30 I = J - 1,MAX(1,J-K),-1 |
| 233 | 1 | equemene | X(IX) = X(IX) - TEMP*A(L+I,J) |
| 234 | 1 | equemene | IX = IX - INCX |
| 235 | 1 | equemene | 30 CONTINUE |
| 236 | 1 | equemene | END IF |
| 237 | 1 | equemene | JX = JX - INCX |
| 238 | 1 | equemene | 40 CONTINUE |
| 239 | 1 | equemene | END IF |
| 240 | 1 | equemene | ELSE |
| 241 | 1 | equemene | IF (INCX.EQ.1) THEN |
| 242 | 1 | equemene | DO 60 J = 1,N |
| 243 | 1 | equemene | IF (X(J).NE.ZERO) THEN |
| 244 | 1 | equemene | L = 1 - J |
| 245 | 1 | equemene | IF (NOUNIT) X(J) = X(J)/A(1,J) |
| 246 | 1 | equemene | TEMP = X(J) |
| 247 | 1 | equemene | DO 50 I = J + 1,MIN(N,J+K) |
| 248 | 1 | equemene | X(I) = X(I) - TEMP*A(L+I,J) |
| 249 | 1 | equemene | 50 CONTINUE |
| 250 | 1 | equemene | END IF |
| 251 | 1 | equemene | 60 CONTINUE |
| 252 | 1 | equemene | ELSE |
| 253 | 1 | equemene | JX = KX |
| 254 | 1 | equemene | DO 80 J = 1,N |
| 255 | 1 | equemene | KX = KX + INCX |
| 256 | 1 | equemene | IF (X(JX).NE.ZERO) THEN |
| 257 | 1 | equemene | IX = KX |
| 258 | 1 | equemene | L = 1 - J |
| 259 | 1 | equemene | IF (NOUNIT) X(JX) = X(JX)/A(1,J) |
| 260 | 1 | equemene | TEMP = X(JX) |
| 261 | 1 | equemene | DO 70 I = J + 1,MIN(N,J+K) |
| 262 | 1 | equemene | X(IX) = X(IX) - TEMP*A(L+I,J) |
| 263 | 1 | equemene | IX = IX + INCX |
| 264 | 1 | equemene | 70 CONTINUE |
| 265 | 1 | equemene | END IF |
| 266 | 1 | equemene | JX = JX + INCX |
| 267 | 1 | equemene | 80 CONTINUE |
| 268 | 1 | equemene | END IF |
| 269 | 1 | equemene | END IF |
| 270 | 1 | equemene | ELSE |
| 271 | 1 | equemene | * |
| 272 | 1 | equemene | * Form x := inv( A' )*x or x := inv( conjg( A') )*x. |
| 273 | 1 | equemene | * |
| 274 | 1 | equemene | IF (LSAME(UPLO,'U')) THEN |
| 275 | 1 | equemene | KPLUS1 = K + 1 |
| 276 | 1 | equemene | IF (INCX.EQ.1) THEN |
| 277 | 1 | equemene | DO 110 J = 1,N |
| 278 | 1 | equemene | TEMP = X(J) |
| 279 | 1 | equemene | L = KPLUS1 - J |
| 280 | 1 | equemene | IF (NOCONJ) THEN |
| 281 | 1 | equemene | DO 90 I = MAX(1,J-K),J - 1 |
| 282 | 1 | equemene | TEMP = TEMP - A(L+I,J)*X(I) |
| 283 | 1 | equemene | 90 CONTINUE |
| 284 | 1 | equemene | IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) |
| 285 | 1 | equemene | ELSE |
| 286 | 1 | equemene | DO 100 I = MAX(1,J-K),J - 1 |
| 287 | 1 | equemene | TEMP = TEMP - CONJG(A(L+I,J))*X(I) |
| 288 | 1 | equemene | 100 CONTINUE |
| 289 | 1 | equemene | IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J)) |
| 290 | 1 | equemene | END IF |
| 291 | 1 | equemene | X(J) = TEMP |
| 292 | 1 | equemene | 110 CONTINUE |
| 293 | 1 | equemene | ELSE |
| 294 | 1 | equemene | JX = KX |
| 295 | 1 | equemene | DO 140 J = 1,N |
| 296 | 1 | equemene | TEMP = X(JX) |
| 297 | 1 | equemene | IX = KX |
| 298 | 1 | equemene | L = KPLUS1 - J |
| 299 | 1 | equemene | IF (NOCONJ) THEN |
| 300 | 1 | equemene | DO 120 I = MAX(1,J-K),J - 1 |
| 301 | 1 | equemene | TEMP = TEMP - A(L+I,J)*X(IX) |
| 302 | 1 | equemene | IX = IX + INCX |
| 303 | 1 | equemene | 120 CONTINUE |
| 304 | 1 | equemene | IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) |
| 305 | 1 | equemene | ELSE |
| 306 | 1 | equemene | DO 130 I = MAX(1,J-K),J - 1 |
| 307 | 1 | equemene | TEMP = TEMP - CONJG(A(L+I,J))*X(IX) |
| 308 | 1 | equemene | IX = IX + INCX |
| 309 | 1 | equemene | 130 CONTINUE |
| 310 | 1 | equemene | IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J)) |
| 311 | 1 | equemene | END IF |
| 312 | 1 | equemene | X(JX) = TEMP |
| 313 | 1 | equemene | JX = JX + INCX |
| 314 | 1 | equemene | IF (J.GT.K) KX = KX + INCX |
| 315 | 1 | equemene | 140 CONTINUE |
| 316 | 1 | equemene | END IF |
| 317 | 1 | equemene | ELSE |
| 318 | 1 | equemene | IF (INCX.EQ.1) THEN |
| 319 | 1 | equemene | DO 170 J = N,1,-1 |
| 320 | 1 | equemene | TEMP = X(J) |
| 321 | 1 | equemene | L = 1 - J |
| 322 | 1 | equemene | IF (NOCONJ) THEN |
| 323 | 1 | equemene | DO 150 I = MIN(N,J+K),J + 1,-1 |
| 324 | 1 | equemene | TEMP = TEMP - A(L+I,J)*X(I) |
| 325 | 1 | equemene | 150 CONTINUE |
| 326 | 1 | equemene | IF (NOUNIT) TEMP = TEMP/A(1,J) |
| 327 | 1 | equemene | ELSE |
| 328 | 1 | equemene | DO 160 I = MIN(N,J+K),J + 1,-1 |
| 329 | 1 | equemene | TEMP = TEMP - CONJG(A(L+I,J))*X(I) |
| 330 | 1 | equemene | 160 CONTINUE |
| 331 | 1 | equemene | IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J)) |
| 332 | 1 | equemene | END IF |
| 333 | 1 | equemene | X(J) = TEMP |
| 334 | 1 | equemene | 170 CONTINUE |
| 335 | 1 | equemene | ELSE |
| 336 | 1 | equemene | KX = KX + (N-1)*INCX |
| 337 | 1 | equemene | JX = KX |
| 338 | 1 | equemene | DO 200 J = N,1,-1 |
| 339 | 1 | equemene | TEMP = X(JX) |
| 340 | 1 | equemene | IX = KX |
| 341 | 1 | equemene | L = 1 - J |
| 342 | 1 | equemene | IF (NOCONJ) THEN |
| 343 | 1 | equemene | DO 180 I = MIN(N,J+K),J + 1,-1 |
| 344 | 1 | equemene | TEMP = TEMP - A(L+I,J)*X(IX) |
| 345 | 1 | equemene | IX = IX - INCX |
| 346 | 1 | equemene | 180 CONTINUE |
| 347 | 1 | equemene | IF (NOUNIT) TEMP = TEMP/A(1,J) |
| 348 | 1 | equemene | ELSE |
| 349 | 1 | equemene | DO 190 I = MIN(N,J+K),J + 1,-1 |
| 350 | 1 | equemene | TEMP = TEMP - CONJG(A(L+I,J))*X(IX) |
| 351 | 1 | equemene | IX = IX - INCX |
| 352 | 1 | equemene | 190 CONTINUE |
| 353 | 1 | equemene | IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J)) |
| 354 | 1 | equemene | END IF |
| 355 | 1 | equemene | X(JX) = TEMP |
| 356 | 1 | equemene | JX = JX - INCX |
| 357 | 1 | equemene | IF ((N-J).GE.K) KX = KX - INCX |
| 358 | 1 | equemene | 200 CONTINUE |
| 359 | 1 | equemene | END IF |
| 360 | 1 | equemene | END IF |
| 361 | 1 | equemene | END IF |
| 362 | 1 | equemene | * |
| 363 | 1 | equemene | RETURN |
| 364 | 1 | equemene | * |
| 365 | 1 | equemene | * End of CTBSV . |
| 366 | 1 | equemene | * |
| 367 | 1 | equemene | END |