1: *> \brief \b ZGBMV
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 ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12: *
13: * .. Scalar Arguments ..
14: * COMPLEX*16 ALPHA,BETA
15: * INTEGER INCX,INCY,KL,KU,LDA,M,N
16: * CHARACTER TRANS
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 A(LDA,*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZGBMV performs one of the matrix-vector operations
29: *>
30: *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
31: *>
32: *> y := alpha*A**H*x + beta*y,
33: *>
34: *> where alpha and beta are scalars, x and y are vectors and A is an
35: *> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
36: *> \endverbatim
37: *
38: * Arguments:
39: * ==========
40: *
41: *> \param[in] TRANS
42: *> \verbatim
43: *> TRANS is CHARACTER*1
44: *> On entry, TRANS specifies the operation to be performed as
45: *> follows:
46: *>
47: *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
48: *>
49: *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
50: *>
51: *> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.
52: *> \endverbatim
53: *>
54: *> \param[in] M
55: *> \verbatim
56: *> M is INTEGER
57: *> On entry, M specifies the number of rows of the matrix A.
58: *> M must be at least zero.
59: *> \endverbatim
60: *>
61: *> \param[in] N
62: *> \verbatim
63: *> N is INTEGER
64: *> On entry, N specifies the number of columns of the matrix A.
65: *> N must be at least zero.
66: *> \endverbatim
67: *>
68: *> \param[in] KL
69: *> \verbatim
70: *> KL is INTEGER
71: *> On entry, KL specifies the number of sub-diagonals of the
72: *> matrix A. KL must satisfy 0 .le. KL.
73: *> \endverbatim
74: *>
75: *> \param[in] KU
76: *> \verbatim
77: *> KU is INTEGER
78: *> On entry, KU specifies the number of super-diagonals of the
79: *> matrix A. KU must satisfy 0 .le. KU.
80: *> \endverbatim
81: *>
82: *> \param[in] ALPHA
83: *> \verbatim
84: *> ALPHA is COMPLEX*16
85: *> On entry, ALPHA specifies the scalar alpha.
86: *> \endverbatim
87: *>
88: *> \param[in] A
89: *> \verbatim
90: *> A is COMPLEX*16 array, dimension ( LDA, N )
91: *> Before entry, the leading ( kl + ku + 1 ) by n part of the
92: *> array A must contain the matrix of coefficients, supplied
93: *> column by column, with the leading diagonal of the matrix in
94: *> row ( ku + 1 ) of the array, the first super-diagonal
95: *> starting at position 2 in row ku, the first sub-diagonal
96: *> starting at position 1 in row ( ku + 2 ), and so on.
97: *> Elements in the array A that do not correspond to elements
98: *> in the band matrix (such as the top left ku by ku triangle)
99: *> are not referenced.
100: *> The following program segment will transfer a band matrix
101: *> from conventional full matrix storage to band storage:
102: *>
103: *> DO 20, J = 1, N
104: *> K = KU + 1 - J
105: *> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
106: *> A( K + I, J ) = matrix( I, J )
107: *> 10 CONTINUE
108: *> 20 CONTINUE
109: *> \endverbatim
110: *>
111: *> \param[in] LDA
112: *> \verbatim
113: *> LDA is INTEGER
114: *> On entry, LDA specifies the first dimension of A as declared
115: *> in the calling (sub) program. LDA must be at least
116: *> ( kl + ku + 1 ).
117: *> \endverbatim
118: *>
119: *> \param[in] X
120: *> \verbatim
121: *> X is COMPLEX*16 array, dimension at least
122: *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
123: *> and at least
124: *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
125: *> Before entry, the incremented array X must contain the
126: *> vector x.
127: *> \endverbatim
128: *>
129: *> \param[in] INCX
130: *> \verbatim
131: *> INCX is INTEGER
132: *> On entry, INCX specifies the increment for the elements of
133: *> X. INCX must not be zero.
134: *> \endverbatim
135: *>
136: *> \param[in] BETA
137: *> \verbatim
138: *> BETA is COMPLEX*16
139: *> On entry, BETA specifies the scalar beta. When BETA is
140: *> supplied as zero then Y need not be set on input.
141: *> \endverbatim
142: *>
143: *> \param[in,out] Y
144: *> \verbatim
145: *> Y is COMPLEX*16 array, dimension at least
146: *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
147: *> and at least
148: *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
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: *> \ingroup complex16_blas_level2
169: *
170: *> \par Further Details:
171: * =====================
172: *>
173: *> \verbatim
174: *>
175: *> Level 2 Blas routine.
176: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
177: *>
178: *> -- Written on 22-October-1986.
179: *> Jack Dongarra, Argonne National Lab.
180: *> Jeremy Du Croz, Nag Central Office.
181: *> Sven Hammarling, Nag Central Office.
182: *> Richard Hanson, Sandia National Labs.
183: *> \endverbatim
184: *>
185: * =====================================================================
186: SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
187: *
188: * -- Reference BLAS level2 routine --
189: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
190: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191: *
192: * .. Scalar Arguments ..
193: COMPLEX*16 ALPHA,BETA
194: INTEGER INCX,INCY,KL,KU,LDA,M,N
195: CHARACTER TRANS
196: * ..
197: * .. Array Arguments ..
198: COMPLEX*16 A(LDA,*),X(*),Y(*)
199: * ..
200: *
201: * =====================================================================
202: *
203: * .. Parameters ..
204: COMPLEX*16 ONE
205: PARAMETER (ONE= (1.0D+0,0.0D+0))
206: COMPLEX*16 ZERO
207: PARAMETER (ZERO= (0.0D+0,0.0D+0))
208: * ..
209: * .. Local Scalars ..
210: COMPLEX*16 TEMP
211: INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
212: LOGICAL NOCONJ
213: * ..
214: * .. External Functions ..
215: LOGICAL LSAME
216: EXTERNAL LSAME
217: * ..
218: * .. External Subroutines ..
219: EXTERNAL XERBLA
220: * ..
221: * .. Intrinsic Functions ..
222: INTRINSIC DCONJG,MAX,MIN
223: * ..
224: *
225: * Test the input parameters.
226: *
227: INFO = 0
228: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
229: + .NOT.LSAME(TRANS,'C')) THEN
230: INFO = 1
231: ELSE IF (M.LT.0) THEN
232: INFO = 2
233: ELSE IF (N.LT.0) THEN
234: INFO = 3
235: ELSE IF (KL.LT.0) THEN
236: INFO = 4
237: ELSE IF (KU.LT.0) THEN
238: INFO = 5
239: ELSE IF (LDA.LT. (KL+KU+1)) THEN
240: INFO = 8
241: ELSE IF (INCX.EQ.0) THEN
242: INFO = 10
243: ELSE IF (INCY.EQ.0) THEN
244: INFO = 13
245: END IF
246: IF (INFO.NE.0) THEN
247: CALL XERBLA('ZGBMV ',INFO)
248: RETURN
249: END IF
250: *
251: * Quick return if possible.
252: *
253: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
254: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
255: *
256: NOCONJ = LSAME(TRANS,'T')
257: *
258: * Set LENX and LENY, the lengths of the vectors x and y, and set
259: * up the start points in X and Y.
260: *
261: IF (LSAME(TRANS,'N')) THEN
262: LENX = N
263: LENY = M
264: ELSE
265: LENX = M
266: LENY = N
267: END IF
268: IF (INCX.GT.0) THEN
269: KX = 1
270: ELSE
271: KX = 1 - (LENX-1)*INCX
272: END IF
273: IF (INCY.GT.0) THEN
274: KY = 1
275: ELSE
276: KY = 1 - (LENY-1)*INCY
277: END IF
278: *
279: * Start the operations. In this version the elements of A are
280: * accessed sequentially with one pass through the band part of A.
281: *
282: * First form y := beta*y.
283: *
284: IF (BETA.NE.ONE) THEN
285: IF (INCY.EQ.1) THEN
286: IF (BETA.EQ.ZERO) THEN
287: DO 10 I = 1,LENY
288: Y(I) = ZERO
289: 10 CONTINUE
290: ELSE
291: DO 20 I = 1,LENY
292: Y(I) = BETA*Y(I)
293: 20 CONTINUE
294: END IF
295: ELSE
296: IY = KY
297: IF (BETA.EQ.ZERO) THEN
298: DO 30 I = 1,LENY
299: Y(IY) = ZERO
300: IY = IY + INCY
301: 30 CONTINUE
302: ELSE
303: DO 40 I = 1,LENY
304: Y(IY) = BETA*Y(IY)
305: IY = IY + INCY
306: 40 CONTINUE
307: END IF
308: END IF
309: END IF
310: IF (ALPHA.EQ.ZERO) RETURN
311: KUP1 = KU + 1
312: IF (LSAME(TRANS,'N')) THEN
313: *
314: * Form y := alpha*A*x + y.
315: *
316: JX = KX
317: IF (INCY.EQ.1) THEN
318: DO 60 J = 1,N
319: TEMP = ALPHA*X(JX)
320: K = KUP1 - J
321: DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
322: Y(I) = Y(I) + TEMP*A(K+I,J)
323: 50 CONTINUE
324: JX = JX + INCX
325: 60 CONTINUE
326: ELSE
327: DO 80 J = 1,N
328: TEMP = ALPHA*X(JX)
329: IY = KY
330: K = KUP1 - J
331: DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
332: Y(IY) = Y(IY) + TEMP*A(K+I,J)
333: IY = IY + INCY
334: 70 CONTINUE
335: JX = JX + INCX
336: IF (J.GT.KU) KY = KY + INCY
337: 80 CONTINUE
338: END IF
339: ELSE
340: *
341: * Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
342: *
343: JY = KY
344: IF (INCX.EQ.1) THEN
345: DO 110 J = 1,N
346: TEMP = ZERO
347: K = KUP1 - J
348: IF (NOCONJ) THEN
349: DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
350: TEMP = TEMP + A(K+I,J)*X(I)
351: 90 CONTINUE
352: ELSE
353: DO 100 I = MAX(1,J-KU),MIN(M,J+KL)
354: TEMP = TEMP + DCONJG(A(K+I,J))*X(I)
355: 100 CONTINUE
356: END IF
357: Y(JY) = Y(JY) + ALPHA*TEMP
358: JY = JY + INCY
359: 110 CONTINUE
360: ELSE
361: DO 140 J = 1,N
362: TEMP = ZERO
363: IX = KX
364: K = KUP1 - J
365: IF (NOCONJ) THEN
366: DO 120 I = MAX(1,J-KU),MIN(M,J+KL)
367: TEMP = TEMP + A(K+I,J)*X(IX)
368: IX = IX + INCX
369: 120 CONTINUE
370: ELSE
371: DO 130 I = MAX(1,J-KU),MIN(M,J+KL)
372: TEMP = TEMP + DCONJG(A(K+I,J))*X(IX)
373: IX = IX + INCX
374: 130 CONTINUE
375: END IF
376: Y(JY) = Y(JY) + ALPHA*TEMP
377: JY = JY + INCY
378: IF (J.GT.KU) KX = KX + INCX
379: 140 CONTINUE
380: END IF
381: END IF
382: *
383: RETURN
384: *
385: * End of ZGBMV
386: *
387: END
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