1 SUBROUTINE ZTBMV(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 DOUBLE COMPLEX A(LDA,*),X(*) 8 * .. 9 * 10 * Purpose 11 * ======= 12 * 13 * ZTBMV 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*16 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*16 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 * Further Details 129 * =============== 130 * 131 * Level 2 Blas routine. 132 * 133 * -- Written on 22-October-1986. 134 * Jack Dongarra, Argonne National Lab. 135 * Jeremy Du Croz, Nag Central Office. 136 * Sven Hammarling, Nag Central Office. 137 * Richard Hanson, Sandia National Labs. 138 * 139 * ===================================================================== 140 * 141 * .. Parameters .. 142 DOUBLE COMPLEX ZERO 143 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 144 * .. 145 * .. Local Scalars .. 146 DOUBLE COMPLEX TEMP 147 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L 148 LOGICAL NOCONJ,NOUNIT 149 * .. 150 * .. External Functions .. 151 LOGICAL LSAME 152 EXTERNAL LSAME 153 * .. 154 * .. External Subroutines .. 155 EXTERNAL XERBLA 156 * .. 157 * .. Intrinsic Functions .. 158 INTRINSIC DCONJG,MAX,MIN 159 * .. 160 * 161 * Test the input parameters. 162 * 163 INFO = 0 164 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 165 INFO = 1 166 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 167 + .NOT.LSAME(TRANS,'C')) THEN 168 INFO = 2 169 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 170 INFO = 3 171 ELSE IF (N.LT.0) THEN 172 INFO = 4 173 ELSE IF (K.LT.0) THEN 174 INFO = 5 175 ELSE IF (LDA.LT. (K+1)) THEN 176 INFO = 7 177 ELSE IF (INCX.EQ.0) THEN 178 INFO = 9 179 END IF 180 IF (INFO.NE.0) THEN 181 CALL XERBLA('ZTBMV ',INFO) 182 RETURN 183 END IF 184 * 185 * Quick return if possible. 186 * 187 IF (N.EQ.0) RETURN 188 * 189 NOCONJ = LSAME(TRANS,'T') 190 NOUNIT = LSAME(DIAG,'N') 191 * 192 * Set up the start point in X if the increment is not unity. This 193 * will be ( N - 1 )*INCX too small for descending loops. 194 * 195 IF (INCX.LE.0) THEN 196 KX = 1 - (N-1)*INCX 197 ELSE IF (INCX.NE.1) THEN 198 KX = 1 199 END IF 200 * 201 * Start the operations. In this version the elements of A are 202 * accessed sequentially with one pass through A. 203 * 204 IF (LSAME(TRANS,'N')) THEN 205 * 206 * Form x := A*x. 207 * 208 IF (LSAME(UPLO,'U')) THEN 209 KPLUS1 = K + 1 210 IF (INCX.EQ.1) THEN 211 DO 20 J = 1,N 212 IF (X(J).NE.ZERO) THEN 213 TEMP = X(J) 214 L = KPLUS1 - J 215 DO 10 I = MAX(1,J-K),J - 1 216 X(I) = X(I) + TEMP*A(L+I,J) 217 10 CONTINUE 218 IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) 219 END IF 220 20 CONTINUE 221 ELSE 222 JX = KX 223 DO 40 J = 1,N 224 IF (X(JX).NE.ZERO) THEN 225 TEMP = X(JX) 226 IX = KX 227 L = KPLUS1 - J 228 DO 30 I = MAX(1,J-K),J - 1 229 X(IX) = X(IX) + TEMP*A(L+I,J) 230 IX = IX + INCX 231 30 CONTINUE 232 IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) 233 END IF 234 JX = JX + INCX 235 IF (J.GT.K) KX = KX + INCX 236 40 CONTINUE 237 END IF 238 ELSE 239 IF (INCX.EQ.1) THEN 240 DO 60 J = N,1,-1 241 IF (X(J).NE.ZERO) THEN 242 TEMP = X(J) 243 L = 1 - J 244 DO 50 I = MIN(N,J+K),J + 1,-1 245 X(I) = X(I) + TEMP*A(L+I,J) 246 50 CONTINUE 247 IF (NOUNIT) X(J) = X(J)*A(1,J) 248 END IF 249 60 CONTINUE 250 ELSE 251 KX = KX + (N-1)*INCX 252 JX = KX 253 DO 80 J = N,1,-1 254 IF (X(JX).NE.ZERO) THEN 255 TEMP = X(JX) 256 IX = KX 257 L = 1 - J 258 DO 70 I = MIN(N,J+K),J + 1,-1 259 X(IX) = X(IX) + TEMP*A(L+I,J) 260 IX = IX - INCX 261 70 CONTINUE 262 IF (NOUNIT) X(JX) = X(JX)*A(1,J) 263 END IF 264 JX = JX - INCX 265 IF ((N-J).GE.K) KX = KX - INCX 266 80 CONTINUE 267 END IF 268 END IF 269 ELSE 270 * 271 * Form x := A'*x or x := conjg( A' )*x. 272 * 273 IF (LSAME(UPLO,'U')) THEN 274 KPLUS1 = K + 1 275 IF (INCX.EQ.1) THEN 276 DO 110 J = N,1,-1 277 TEMP = X(J) 278 L = KPLUS1 - J 279 IF (NOCONJ) THEN 280 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) 281 DO 90 I = J - 1,MAX(1,J-K),-1 282 TEMP = TEMP + A(L+I,J)*X(I) 283 90 CONTINUE 284 ELSE 285 IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) 286 DO 100 I = J - 1,MAX(1,J-K),-1 287 TEMP = TEMP + DCONJG(A(L+I,J))*X(I) 288 100 CONTINUE 289 END IF 290 X(J) = TEMP 291 110 CONTINUE 292 ELSE 293 KX = KX + (N-1)*INCX 294 JX = KX 295 DO 140 J = N,1,-1 296 TEMP = X(JX) 297 KX = KX - INCX 298 IX = KX 299 L = KPLUS1 - J 300 IF (NOCONJ) THEN 301 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) 302 DO 120 I = J - 1,MAX(1,J-K),-1 303 TEMP = TEMP + A(L+I,J)*X(IX) 304 IX = IX - INCX 305 120 CONTINUE 306 ELSE 307 IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) 308 DO 130 I = J - 1,MAX(1,J-K),-1 309 TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) 310 IX = IX - INCX 311 130 CONTINUE 312 END IF 313 X(JX) = TEMP 314 JX = JX - INCX 315 140 CONTINUE 316 END IF 317 ELSE 318 IF (INCX.EQ.1) THEN 319 DO 170 J = 1,N 320 TEMP = X(J) 321 L = 1 - J 322 IF (NOCONJ) THEN 323 IF (NOUNIT) TEMP = TEMP*A(1,J) 324 DO 150 I = J + 1,MIN(N,J+K) 325 TEMP = TEMP + A(L+I,J)*X(I) 326 150 CONTINUE 327 ELSE 328 IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) 329 DO 160 I = J + 1,MIN(N,J+K) 330 TEMP = TEMP + DCONJG(A(L+I,J))*X(I) 331 160 CONTINUE 332 END IF 333 X(J) = TEMP 334 170 CONTINUE 335 ELSE 336 JX = KX 337 DO 200 J = 1,N 338 TEMP = X(JX) 339 KX = KX + INCX 340 IX = KX 341 L = 1 - J 342 IF (NOCONJ) THEN 343 IF (NOUNIT) TEMP = TEMP*A(1,J) 344 DO 180 I = J + 1,MIN(N,J+K) 345 TEMP = TEMP + A(L+I,J)*X(IX) 346 IX = IX + INCX 347 180 CONTINUE 348 ELSE 349 IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) 350 DO 190 I = J + 1,MIN(N,J+K) 351 TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) 352 IX = IX + INCX 353 190 CONTINUE 354 END IF 355 X(JX) = TEMP 356 JX = JX + INCX 357 200 CONTINUE 358 END IF 359 END IF 360 END IF 361 * 362 RETURN 363 * 364 * End of ZTBMV . 365 * 366 END 367
