ground/gcs/src/libs/eigen/blas/ztbmv.f

   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