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