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