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source: branches/2789_MathNetNumerics-Exploration/HeuristicLab.Algorithms.DataAnalysis.Experimental/sbart/chbmv.f @ 17185

Last change on this file since 17185 was 15457, checked in by gkronber, 7 years ago

#2789 added Finbarr O'Sullivan smoothing spline code

File size: 9.5 KB
Line 
1      SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
2*     .. Scalar Arguments ..
3      COMPLEX ALPHA,BETA
4      INTEGER INCX,INCY,K,LDA,N
5      CHARACTER UPLO
6*     ..
7*     .. Array Arguments ..
8      COMPLEX A(LDA,*),X(*),Y(*)
9*     ..
10*
11*  Purpose
12*  =======
13*
14*  CHBMV  performs the matrix-vector  operation
15*
16*     y := alpha*A*x + beta*y,
17*
18*  where alpha and beta are scalars, x and y are n element vectors and
19*  A is an n by n hermitian band matrix, with k super-diagonals.
20*
21*  Arguments
22*  ==========
23*
24*  UPLO   - CHARACTER*1.
25*           On entry, UPLO specifies whether the upper or lower
26*           triangular part of the band matrix A is being supplied as
27*           follows:
28*
29*              UPLO = 'U' or 'u'   The upper triangular part of A is
30*                                  being supplied.
31*
32*              UPLO = 'L' or 'l'   The lower triangular part of A is
33*                                  being supplied.
34*
35*           Unchanged on exit.
36*
37*  N      - INTEGER.
38*           On entry, N specifies the order of the matrix A.
39*           N must be at least zero.
40*           Unchanged on exit.
41*
42*  K      - INTEGER.
43*           On entry, K specifies the number of super-diagonals of the
44*           matrix A. K must satisfy  0 .le. K.
45*           Unchanged on exit.
46*
47*  ALPHA  - COMPLEX         .
48*           On entry, ALPHA specifies the scalar alpha.
49*           Unchanged on exit.
50*
51*  A      - COMPLEX          array of DIMENSION ( LDA, n ).
52*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
53*           by n part of the array A must contain the upper triangular
54*           band part of the hermitian matrix, supplied column by
55*           column, with the leading diagonal of the matrix in row
56*           ( k + 1 ) of the array, the first super-diagonal starting at
57*           position 2 in row k, and so on. The top left k by k triangle
58*           of the array A is not referenced.
59*           The following program segment will transfer the upper
60*           triangular part of a hermitian band matrix from conventional
61*           full matrix storage to band storage:
62*
63*                 DO 20, J = 1, N
64*                    M = K + 1 - J
65*                    DO 10, I = MAX( 1, J - K ), J
66*                       A( M + I, J ) = matrix( I, J )
67*              10    CONTINUE
68*              20 CONTINUE
69*
70*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
71*           by n part of the array A must contain the lower triangular
72*           band part of the hermitian matrix, supplied column by
73*           column, with the leading diagonal of the matrix in row 1 of
74*           the array, the first sub-diagonal starting at position 1 in
75*           row 2, and so on. The bottom right k by k triangle of the
76*           array A is not referenced.
77*           The following program segment will transfer the lower
78*           triangular part of a hermitian band matrix from conventional
79*           full matrix storage to band storage:
80*
81*                 DO 20, J = 1, N
82*                    M = 1 - J
83*                    DO 10, I = J, MIN( N, J + K )
84*                       A( M + I, J ) = matrix( I, J )
85*              10    CONTINUE
86*              20 CONTINUE
87*
88*           Note that the imaginary parts of the diagonal elements need
89*           not be set and are assumed to be zero.
90*           Unchanged on exit.
91*
92*  LDA    - INTEGER.
93*           On entry, LDA specifies the first dimension of A as declared
94*           in the calling (sub) program. LDA must be at least
95*           ( k + 1 ).
96*           Unchanged on exit.
97*
98*  X      - COMPLEX          array of DIMENSION at least
99*           ( 1 + ( n - 1 )*abs( INCX ) ).
100*           Before entry, the incremented array X must contain the
101*           vector x.
102*           Unchanged on exit.
103*
104*  INCX   - INTEGER.
105*           On entry, INCX specifies the increment for the elements of
106*           X. INCX must not be zero.
107*           Unchanged on exit.
108*
109*  BETA   - COMPLEX         .
110*           On entry, BETA specifies the scalar beta.
111*           Unchanged on exit.
112*
113*  Y      - COMPLEX          array of DIMENSION at least
114*           ( 1 + ( n - 1 )*abs( INCY ) ).
115*           Before entry, the incremented array Y must contain the
116*           vector y. On exit, Y is overwritten by the updated vector y.
117*
118*  INCY   - INTEGER.
119*           On entry, INCY specifies the increment for the elements of
120*           Y. INCY must not be zero.
121*           Unchanged on exit.
122*
123*
124*  Level 2 Blas routine.
125*
126*  -- Written on 22-October-1986.
127*     Jack Dongarra, Argonne National Lab.
128*     Jeremy Du Croz, Nag Central Office.
129*     Sven Hammarling, Nag Central Office.
130*     Richard Hanson, Sandia National Labs.
131*
132*
133*     .. Parameters ..
134      COMPLEX ONE
135      PARAMETER (ONE= (1.0E+0,0.0E+0))
136      COMPLEX ZERO
137      PARAMETER (ZERO= (0.0E+0,0.0E+0))
138*     ..
139*     .. Local Scalars ..
140      COMPLEX TEMP1,TEMP2
141      INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
142*     ..
143*     .. External Functions ..
144      LOGICAL LSAME
145      EXTERNAL LSAME
146*     ..
147*     .. External Subroutines ..
148      EXTERNAL XERBLA
149*     ..
150*     .. Intrinsic Functions ..
151      INTRINSIC CONJG,MAX,MIN,REAL
152*     ..
153*
154*     Test the input parameters.
155*
156      INFO = 0
157      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
158          INFO = 1
159      ELSE IF (N.LT.0) THEN
160          INFO = 2
161      ELSE IF (K.LT.0) THEN
162          INFO = 3
163      ELSE IF (LDA.LT. (K+1)) THEN
164          INFO = 6
165      ELSE IF (INCX.EQ.0) THEN
166          INFO = 8
167      ELSE IF (INCY.EQ.0) THEN
168          INFO = 11
169      END IF
170      IF (INFO.NE.0) THEN
171          CALL XERBLA('CHBMV ',INFO)
172          RETURN
173      END IF
174*
175*     Quick return if possible.
176*
177      IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
178*
179*     Set up the start points in  X  and  Y.
180*
181      IF (INCX.GT.0) THEN
182          KX = 1
183      ELSE
184          KX = 1 - (N-1)*INCX
185      END IF
186      IF (INCY.GT.0) THEN
187          KY = 1
188      ELSE
189          KY = 1 - (N-1)*INCY
190      END IF
191*
192*     Start the operations. In this version the elements of the array A
193*     are accessed sequentially with one pass through A.
194*
195*     First form  y := beta*y.
196*
197      IF (BETA.NE.ONE) THEN
198          IF (INCY.EQ.1) THEN
199              IF (BETA.EQ.ZERO) THEN
200                  DO 10 I = 1,N
201                      Y(I) = ZERO
202   10             CONTINUE
203              ELSE
204                  DO 20 I = 1,N
205                      Y(I) = BETA*Y(I)
206   20             CONTINUE
207              END IF
208          ELSE
209              IY = KY
210              IF (BETA.EQ.ZERO) THEN
211                  DO 30 I = 1,N
212                      Y(IY) = ZERO
213                      IY = IY + INCY
214   30             CONTINUE
215              ELSE
216                  DO 40 I = 1,N
217                      Y(IY) = BETA*Y(IY)
218                      IY = IY + INCY
219   40             CONTINUE
220              END IF
221          END IF
222      END IF
223      IF (ALPHA.EQ.ZERO) RETURN
224      IF (LSAME(UPLO,'U')) THEN
225*
226*        Form  y  when upper triangle of A is stored.
227*
228          KPLUS1 = K + 1
229          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
230              DO 60 J = 1,N
231                  TEMP1 = ALPHA*X(J)
232                  TEMP2 = ZERO
233                  L = KPLUS1 - J
234                  DO 50 I = MAX(1,J-K),J - 1
235                      Y(I) = Y(I) + TEMP1*A(L+I,J)
236                      TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(I)
237   50             CONTINUE
238                  Y(J) = Y(J) + TEMP1*REAL(A(KPLUS1,J)) + ALPHA*TEMP2
239   60         CONTINUE
240          ELSE
241              JX = KX
242              JY = KY
243              DO 80 J = 1,N
244                  TEMP1 = ALPHA*X(JX)
245                  TEMP2 = ZERO
246                  IX = KX
247                  IY = KY
248                  L = KPLUS1 - J
249                  DO 70 I = MAX(1,J-K),J - 1
250                      Y(IY) = Y(IY) + TEMP1*A(L+I,J)
251                      TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(IX)
252                      IX = IX + INCX
253                      IY = IY + INCY
254   70             CONTINUE
255                  Y(JY) = Y(JY) + TEMP1*REAL(A(KPLUS1,J)) + ALPHA*TEMP2
256                  JX = JX + INCX
257                  JY = JY + INCY
258                  IF (J.GT.K) THEN
259                      KX = KX + INCX
260                      KY = KY + INCY
261                  END IF
262   80         CONTINUE
263          END IF
264      ELSE
265*
266*        Form  y  when lower triangle of A is stored.
267*
268          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
269              DO 100 J = 1,N
270                  TEMP1 = ALPHA*X(J)
271                  TEMP2 = ZERO
272                  Y(J) = Y(J) + TEMP1*REAL(A(1,J))
273                  L = 1 - J
274                  DO 90 I = J + 1,MIN(N,J+K)
275                      Y(I) = Y(I) + TEMP1*A(L+I,J)
276                      TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(I)
277   90             CONTINUE
278                  Y(J) = Y(J) + ALPHA*TEMP2
279  100         CONTINUE
280          ELSE
281              JX = KX
282              JY = KY
283              DO 120 J = 1,N
284                  TEMP1 = ALPHA*X(JX)
285                  TEMP2 = ZERO
286                  Y(JY) = Y(JY) + TEMP1*REAL(A(1,J))
287                  L = 1 - J
288                  IX = JX
289                  IY = JY
290                  DO 110 I = J + 1,MIN(N,J+K)
291                      IX = IX + INCX
292                      IY = IY + INCY
293                      Y(IY) = Y(IY) + TEMP1*A(L+I,J)
294                      TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(IX)
295  110             CONTINUE
296                  Y(JY) = Y(JY) + ALPHA*TEMP2
297                  JX = JX + INCX
298                  JY = JY + INCY
299  120         CONTINUE
300          END IF
301      END IF
302*
303      RETURN
304*
305*     End of CHBMV .
306*
307      END
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