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