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1: *> \brief \b ZHBMV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12: *
13: * .. Scalar Arguments ..
14: * COMPLEX*16 ALPHA,BETA
15: * INTEGER INCX,INCY,K,LDA,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 A(LDA,*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZHBMV performs the matrix-vector operation
29: *>
30: *> y := alpha*A*x + beta*y,
31: *>
32: *> where alpha and beta are scalars, x and y are n element vectors and
33: *> A is an n by n hermitian band matrix, with k super-diagonals.
34: *> \endverbatim
35: *
36: * Arguments:
37: * ==========
38: *
39: *> \param[in] UPLO
40: *> \verbatim
41: *> UPLO is CHARACTER*1
42: *> On entry, UPLO specifies whether the upper or lower
43: *> triangular part of the band matrix A is being supplied as
44: *> follows:
45: *>
46: *> UPLO = 'U' or 'u' The upper triangular part of A is
47: *> being supplied.
48: *>
49: *> UPLO = 'L' or 'l' The lower triangular part of A is
50: *> being supplied.
51: *> \endverbatim
52: *>
53: *> \param[in] N
54: *> \verbatim
55: *> N is INTEGER
56: *> On entry, N specifies the order of the matrix A.
57: *> N must be at least zero.
58: *> \endverbatim
59: *>
60: *> \param[in] K
61: *> \verbatim
62: *> K is INTEGER
63: *> On entry, K specifies the number of super-diagonals of the
64: *> matrix A. K must satisfy 0 .le. K.
65: *> \endverbatim
66: *>
67: *> \param[in] ALPHA
68: *> \verbatim
69: *> ALPHA is COMPLEX*16
70: *> On entry, ALPHA specifies the scalar alpha.
71: *> \endverbatim
72: *>
73: *> \param[in] A
74: *> \verbatim
75: *> A is COMPLEX*16 array of DIMENSION ( LDA, n ).
76: *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
77: *> by n part of the array A must contain the upper triangular
78: *> band part of the hermitian matrix, supplied column by
79: *> column, with the leading diagonal of the matrix in row
80: *> ( k + 1 ) of the array, the first super-diagonal starting at
81: *> position 2 in row k, and so on. The top left k by k triangle
82: *> of the array A is not referenced.
83: *> The following program segment will transfer the upper
84: *> triangular part of a hermitian band matrix from conventional
85: *> full matrix storage to band storage:
86: *>
87: *> DO 20, J = 1, N
88: *> M = K + 1 - J
89: *> DO 10, I = MAX( 1, J - K ), J
90: *> A( M + I, J ) = matrix( I, J )
91: *> 10 CONTINUE
92: *> 20 CONTINUE
93: *>
94: *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
95: *> by n part of the array A must contain the lower triangular
96: *> band part of the hermitian matrix, supplied column by
97: *> column, with the leading diagonal of the matrix in row 1 of
98: *> the array, the first sub-diagonal starting at position 1 in
99: *> row 2, and so on. The bottom right k by k triangle of the
100: *> array A is not referenced.
101: *> The following program segment will transfer the lower
102: *> triangular part of a hermitian band matrix from conventional
103: *> full matrix storage to band storage:
104: *>
105: *> DO 20, J = 1, N
106: *> M = 1 - J
107: *> DO 10, I = J, MIN( N, J + K )
108: *> A( M + I, J ) = matrix( I, J )
109: *> 10 CONTINUE
110: *> 20 CONTINUE
111: *>
112: *> Note that the imaginary parts of the diagonal elements need
113: *> not be set and are assumed to be zero.
114: *> \endverbatim
115: *>
116: *> \param[in] LDA
117: *> \verbatim
118: *> LDA is INTEGER
119: *> On entry, LDA specifies the first dimension of A as declared
120: *> in the calling (sub) program. LDA must be at least
121: *> ( k + 1 ).
122: *> \endverbatim
123: *>
124: *> \param[in] X
125: *> \verbatim
126: *> X is COMPLEX*16 array of DIMENSION at least
127: *> ( 1 + ( n - 1 )*abs( INCX ) ).
128: *> Before entry, the incremented array X must contain the
129: *> vector x.
130: *> \endverbatim
131: *>
132: *> \param[in] INCX
133: *> \verbatim
134: *> INCX is INTEGER
135: *> On entry, INCX specifies the increment for the elements of
136: *> X. INCX must not be zero.
137: *> \endverbatim
138: *>
139: *> \param[in] BETA
140: *> \verbatim
141: *> BETA is COMPLEX*16
142: *> On entry, BETA specifies the scalar beta.
143: *> \endverbatim
144: *>
145: *> \param[in,out] Y
146: *> \verbatim
147: *> Y is COMPLEX*16 array of DIMENSION at least
148: *> ( 1 + ( n - 1 )*abs( INCY ) ).
149: *> Before entry, the incremented array Y must contain the
150: *> vector y. On exit, Y is overwritten by the updated vector y.
151: *> \endverbatim
152: *>
153: *> \param[in] INCY
154: *> \verbatim
155: *> INCY is INTEGER
156: *> On entry, INCY specifies the increment for the elements of
157: *> Y. INCY must not be zero.
158: *> \endverbatim
159: *
160: * Authors:
161: * ========
162: *
163: *> \author Univ. of Tennessee
164: *> \author Univ. of California Berkeley
165: *> \author Univ. of Colorado Denver
166: *> \author NAG Ltd.
167: *
168: *> \date November 2011
169: *
170: *> \ingroup complex16_blas_level2
171: *
172: *> \par Further Details:
173: * =====================
174: *>
175: *> \verbatim
176: *>
177: *> Level 2 Blas routine.
178: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
179: *>
180: *> -- Written on 22-October-1986.
181: *> Jack Dongarra, Argonne National Lab.
182: *> Jeremy Du Croz, Nag Central Office.
183: *> Sven Hammarling, Nag Central Office.
184: *> Richard Hanson, Sandia National Labs.
185: *> \endverbatim
186: *>
187: * =====================================================================
188: SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
189: *
190: * -- Reference BLAS level2 routine (version 3.4.0) --
191: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
192: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193: * November 2011
194: *
195: * .. Scalar Arguments ..
196: COMPLEX*16 ALPHA,BETA
197: INTEGER INCX,INCY,K,LDA,N
198: CHARACTER UPLO
199: * ..
200: * .. Array Arguments ..
201: COMPLEX*16 A(LDA,*),X(*),Y(*)
202: * ..
203: *
204: * =====================================================================
205: *
206: * .. Parameters ..
207: COMPLEX*16 ONE
208: PARAMETER (ONE= (1.0D+0,0.0D+0))
209: COMPLEX*16 ZERO
210: PARAMETER (ZERO= (0.0D+0,0.0D+0))
211: * ..
212: * .. Local Scalars ..
213: COMPLEX*16 TEMP1,TEMP2
214: INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
215: * ..
216: * .. External Functions ..
217: LOGICAL LSAME
218: EXTERNAL LSAME
219: * ..
220: * .. External Subroutines ..
221: EXTERNAL XERBLA
222: * ..
223: * .. Intrinsic Functions ..
224: INTRINSIC DBLE,DCONJG,MAX,MIN
225: * ..
226: *
227: * Test the input parameters.
228: *
229: INFO = 0
230: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
231: INFO = 1
232: ELSE IF (N.LT.0) THEN
233: INFO = 2
234: ELSE IF (K.LT.0) THEN
235: INFO = 3
236: ELSE IF (LDA.LT. (K+1)) THEN
237: INFO = 6
238: ELSE IF (INCX.EQ.0) THEN
239: INFO = 8
240: ELSE IF (INCY.EQ.0) THEN
241: INFO = 11
242: END IF
243: IF (INFO.NE.0) THEN
244: CALL XERBLA('ZHBMV ',INFO)
245: RETURN
246: END IF
247: *
248: * Quick return if possible.
249: *
250: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
251: *
252: * Set up the start points in X and Y.
253: *
254: IF (INCX.GT.0) THEN
255: KX = 1
256: ELSE
257: KX = 1 - (N-1)*INCX
258: END IF
259: IF (INCY.GT.0) THEN
260: KY = 1
261: ELSE
262: KY = 1 - (N-1)*INCY
263: END IF
264: *
265: * Start the operations. In this version the elements of the array A
266: * are accessed sequentially with one pass through A.
267: *
268: * First form y := beta*y.
269: *
270: IF (BETA.NE.ONE) THEN
271: IF (INCY.EQ.1) THEN
272: IF (BETA.EQ.ZERO) THEN
273: DO 10 I = 1,N
274: Y(I) = ZERO
275: 10 CONTINUE
276: ELSE
277: DO 20 I = 1,N
278: Y(I) = BETA*Y(I)
279: 20 CONTINUE
280: END IF
281: ELSE
282: IY = KY
283: IF (BETA.EQ.ZERO) THEN
284: DO 30 I = 1,N
285: Y(IY) = ZERO
286: IY = IY + INCY
287: 30 CONTINUE
288: ELSE
289: DO 40 I = 1,N
290: Y(IY) = BETA*Y(IY)
291: IY = IY + INCY
292: 40 CONTINUE
293: END IF
294: END IF
295: END IF
296: IF (ALPHA.EQ.ZERO) RETURN
297: IF (LSAME(UPLO,'U')) THEN
298: *
299: * Form y when upper triangle of A is stored.
300: *
301: KPLUS1 = K + 1
302: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
303: DO 60 J = 1,N
304: TEMP1 = ALPHA*X(J)
305: TEMP2 = ZERO
306: L = KPLUS1 - J
307: DO 50 I = MAX(1,J-K),J - 1
308: Y(I) = Y(I) + TEMP1*A(L+I,J)
309: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I)
310: 50 CONTINUE
311: Y(J) = Y(J) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2
312: 60 CONTINUE
313: ELSE
314: JX = KX
315: JY = KY
316: DO 80 J = 1,N
317: TEMP1 = ALPHA*X(JX)
318: TEMP2 = ZERO
319: IX = KX
320: IY = KY
321: L = KPLUS1 - J
322: DO 70 I = MAX(1,J-K),J - 1
323: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
324: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX)
325: IX = IX + INCX
326: IY = IY + INCY
327: 70 CONTINUE
328: Y(JY) = Y(JY) + TEMP1*DBLE(A(KPLUS1,J)) + ALPHA*TEMP2
329: JX = JX + INCX
330: JY = JY + INCY
331: IF (J.GT.K) THEN
332: KX = KX + INCX
333: KY = KY + INCY
334: END IF
335: 80 CONTINUE
336: END IF
337: ELSE
338: *
339: * Form y when lower triangle of A is stored.
340: *
341: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
342: DO 100 J = 1,N
343: TEMP1 = ALPHA*X(J)
344: TEMP2 = ZERO
345: Y(J) = Y(J) + TEMP1*DBLE(A(1,J))
346: L = 1 - J
347: DO 90 I = J + 1,MIN(N,J+K)
348: Y(I) = Y(I) + TEMP1*A(L+I,J)
349: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(I)
350: 90 CONTINUE
351: Y(J) = Y(J) + ALPHA*TEMP2
352: 100 CONTINUE
353: ELSE
354: JX = KX
355: JY = KY
356: DO 120 J = 1,N
357: TEMP1 = ALPHA*X(JX)
358: TEMP2 = ZERO
359: Y(JY) = Y(JY) + TEMP1*DBLE(A(1,J))
360: L = 1 - J
361: IX = JX
362: IY = JY
363: DO 110 I = J + 1,MIN(N,J+K)
364: IX = IX + INCX
365: IY = IY + INCY
366: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
367: TEMP2 = TEMP2 + DCONJG(A(L+I,J))*X(IX)
368: 110 CONTINUE
369: Y(JY) = Y(JY) + ALPHA*TEMP2
370: JX = JX + INCX
371: JY = JY + INCY
372: 120 CONTINUE
373: END IF
374: END IF
375: *
376: RETURN
377: *
378: * End of ZHBMV .
379: *
380: END
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