1: SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
2: * .. Scalar Arguments ..
3: DOUBLE COMPLEX ALPHA,BETA
4: INTEGER INCX,INCY,K,LDA,N
5: CHARACTER UPLO
6: * ..
7: * .. Array Arguments ..
8: DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
9: * ..
10: *
11: * Purpose
12: * =======
13: *
14: * ZHBMV 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*16 .
48: * On entry, ALPHA specifies the scalar alpha.
49: * Unchanged on exit.
50: *
51: * A - COMPLEX*16 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*16 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*16 .
110: * On entry, BETA specifies the scalar beta.
111: * Unchanged on exit.
112: *
113: * Y - COMPLEX*16 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: * Further Details
124: * ===============
125: *
126: * Level 2 Blas routine.
127: *
128: * -- Written on 22-October-1986.
129: * Jack Dongarra, Argonne National Lab.
130: * Jeremy Du Croz, Nag Central Office.
131: * Sven Hammarling, Nag Central Office.
132: * Richard Hanson, Sandia National Labs.
133: *
134: * =====================================================================
135: *
136: * .. Parameters ..
137: DOUBLE COMPLEX ONE
138: PARAMETER (ONE= (1.0D+0,0.0D+0))
139: DOUBLE COMPLEX ZERO
140: PARAMETER (ZERO= (0.0D+0,0.0D+0))
141: * ..
142: * .. Local Scalars ..
143: DOUBLE COMPLEX TEMP1,TEMP2
144: INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
145: * ..
146: * .. External Functions ..
147: LOGICAL LSAME
148: EXTERNAL LSAME
149: * ..
150: * .. External Subroutines ..
151: EXTERNAL XERBLA
152: * ..
153: * .. Intrinsic Functions ..
154: INTRINSIC DBLE,DCONJG,MAX,MIN
155: * ..
156: *
157: * Test the input parameters.
158: *
159: INFO = 0
160: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
161: INFO = 1
162: ELSE IF (N.LT.0) THEN
163: INFO = 2
164: ELSE IF (K.LT.0) THEN
165: INFO = 3
166: ELSE IF (LDA.LT. (K+1)) THEN
167: INFO = 6
168: ELSE IF (INCX.EQ.0) THEN
169: INFO = 8
170: ELSE IF (INCY.EQ.0) THEN
171: INFO = 11
172: END IF
173: IF (INFO.NE.0) THEN
174: CALL XERBLA('ZHBMV ',INFO)
175: RETURN
176: END IF
177: *
178: * Quick return if possible.
179: *
180: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
181: *
182: * Set up the start points in X and Y.
183: *
184: IF (INCX.GT.0) THEN
185: KX = 1
186: ELSE
187: KX = 1 - (N-1)*INCX
188: END IF
189: IF (INCY.GT.0) THEN
190: KY = 1
191: ELSE
192: KY = 1 - (N-1)*INCY
193: END IF
194: *
195: * Start the operations. In this version the elements of the array A
196: * are accessed sequentially with one pass through A.
197: *
198: * First form y := beta*y.
199: *
200: IF (BETA.NE.ONE) THEN
201: IF (INCY.EQ.1) THEN
202: IF (BETA.EQ.ZERO) THEN
203: DO 10 I = 1,N
204: Y(I) = ZERO
205: 10 CONTINUE
206: ELSE
207: DO 20 I = 1,N
208: Y(I) = BETA*Y(I)
209: 20 CONTINUE
210: END IF
211: ELSE
212: IY = KY
213: IF (BETA.EQ.ZERO) THEN
214: DO 30 I = 1,N
215: Y(IY) = ZERO
216: IY = IY + INCY
217: 30 CONTINUE
218: ELSE
219: DO 40 I = 1,N
220: Y(IY) = BETA*Y(IY)
221: IY = IY + INCY
222: 40 CONTINUE
223: END IF
224: END IF
225: END IF
226: IF (ALPHA.EQ.ZERO) RETURN
227: IF (LSAME(UPLO,'U')) THEN
228: *
229: * Form y when upper triangle of A is stored.
230: *
231: KPLUS1 = K + 1
232: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
233: DO 60 J = 1,N
234: TEMP1 = ALPHA*X(J)
235: TEMP2 = ZERO
236: L = KPLUS1 - J
237: DO 50 I = MAX(1,J-K),J - 1
238: Y(I) = Y(I) + TEMP1*A(L+I,J)
239: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I)
240: 50 CONTINUE
241: Y(J) = Y(J) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2
242: 60 CONTINUE
243: ELSE
244: JX = KX
245: JY = KY
246: DO 80 J = 1,N
247: TEMP1 = ALPHA*X(JX)
248: TEMP2 = ZERO
249: IX = KX
250: IY = KY
251: L = KPLUS1 - J
252: DO 70 I = MAX(1,J-K),J - 1
253: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
254: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX)
255: IX = IX + INCX
256: IY = IY + INCY
257: 70 CONTINUE
258: Y(JY) = Y(JY) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2
259: JX = JX + INCX
260: JY = JY + INCY
261: IF (J.GT.K) THEN
262: KX = KX + INCX
263: KY = KY + INCY
264: END IF
265: 80 CONTINUE
266: END IF
267: ELSE
268: *
269: * Form y when lower triangle of A is stored.
270: *
271: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
272: DO 100 J = 1,N
273: TEMP1 = ALPHA*X(J)
274: TEMP2 = ZERO
275: Y(J) = Y(J) + TEMP1*DBLE(A(1,J))
276: L = 1 - J
277: DO 90 I = J + 1,MIN(N,J+K)
278: Y(I) = Y(I) + TEMP1*A(L+I,J)
279: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I)
280: 90 CONTINUE
281: Y(J) = Y(J) + ALPHA*TEMP2
282: 100 CONTINUE
283: ELSE
284: JX = KX
285: JY = KY
286: DO 120 J = 1,N
287: TEMP1 = ALPHA*X(JX)
288: TEMP2 = ZERO
289: Y(JY) = Y(JY) + TEMP1*DBLE(A(1,J))
290: L = 1 - J
291: IX = JX
292: IY = JY
293: DO 110 I = J + 1,MIN(N,J+K)
294: IX = IX + INCX
295: IY = IY + INCY
296: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
297: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX)
298: 110 CONTINUE
299: Y(JY) = Y(JY) + ALPHA*TEMP2
300: JX = JX + INCX
301: JY = JY + INCY
302: 120 CONTINUE
303: END IF
304: END IF
305: *
306: RETURN
307: *
308: * End of ZHBMV .
309: *
310: END
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