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