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 of 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 of 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 of 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: *> \date November 2015
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 ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
189: *
190: * -- Reference BLAS level2 routine (version 3.6.0) --
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 2015
194: *
195: * .. Scalar Arguments ..
196: COMPLEX*16 ALPHA,BETA
197: INTEGER INCX,INCY,KL,KU,LDA,M,N
198: CHARACTER TRANS
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 TEMP
214: INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
215: LOGICAL NOCONJ
216: * ..
217: * .. External Functions ..
218: LOGICAL LSAME
219: EXTERNAL LSAME
220: * ..
221: * .. External Subroutines ..
222: EXTERNAL XERBLA
223: * ..
224: * .. Intrinsic Functions ..
225: INTRINSIC DCONJG,MAX,MIN
226: * ..
227: *
228: * Test the input parameters.
229: *
230: INFO = 0
231: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
232: + .NOT.LSAME(TRANS,'C')) THEN
233: INFO = 1
234: ELSE IF (M.LT.0) THEN
235: INFO = 2
236: ELSE IF (N.LT.0) THEN
237: INFO = 3
238: ELSE IF (KL.LT.0) THEN
239: INFO = 4
240: ELSE IF (KU.LT.0) THEN
241: INFO = 5
242: ELSE IF (LDA.LT. (KL+KU+1)) THEN
243: INFO = 8
244: ELSE IF (INCX.EQ.0) THEN
245: INFO = 10
246: ELSE IF (INCY.EQ.0) THEN
247: INFO = 13
248: END IF
249: IF (INFO.NE.0) THEN
250: CALL XERBLA('ZGBMV ',INFO)
251: RETURN
252: END IF
253: *
254: * Quick return if possible.
255: *
256: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
257: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
258: *
259: NOCONJ = LSAME(TRANS,'T')
260: *
261: * Set LENX and LENY, the lengths of the vectors x and y, and set
262: * up the start points in X and Y.
263: *
264: IF (LSAME(TRANS,'N')) THEN
265: LENX = N
266: LENY = M
267: ELSE
268: LENX = M
269: LENY = N
270: END IF
271: IF (INCX.GT.0) THEN
272: KX = 1
273: ELSE
274: KX = 1 - (LENX-1)*INCX
275: END IF
276: IF (INCY.GT.0) THEN
277: KY = 1
278: ELSE
279: KY = 1 - (LENY-1)*INCY
280: END IF
281: *
282: * Start the operations. In this version the elements of A are
283: * accessed sequentially with one pass through the band part of A.
284: *
285: * First form y := beta*y.
286: *
287: IF (BETA.NE.ONE) THEN
288: IF (INCY.EQ.1) THEN
289: IF (BETA.EQ.ZERO) THEN
290: DO 10 I = 1,LENY
291: Y(I) = ZERO
292: 10 CONTINUE
293: ELSE
294: DO 20 I = 1,LENY
295: Y(I) = BETA*Y(I)
296: 20 CONTINUE
297: END IF
298: ELSE
299: IY = KY
300: IF (BETA.EQ.ZERO) THEN
301: DO 30 I = 1,LENY
302: Y(IY) = ZERO
303: IY = IY + INCY
304: 30 CONTINUE
305: ELSE
306: DO 40 I = 1,LENY
307: Y(IY) = BETA*Y(IY)
308: IY = IY + INCY
309: 40 CONTINUE
310: END IF
311: END IF
312: END IF
313: IF (ALPHA.EQ.ZERO) RETURN
314: KUP1 = KU + 1
315: IF (LSAME(TRANS,'N')) THEN
316: *
317: * Form y := alpha*A*x + y.
318: *
319: JX = KX
320: IF (INCY.EQ.1) THEN
321: DO 60 J = 1,N
322: TEMP = ALPHA*X(JX)
323: K = KUP1 - J
324: DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
325: Y(I) = Y(I) + TEMP*A(K+I,J)
326: 50 CONTINUE
327: JX = JX + INCX
328: 60 CONTINUE
329: ELSE
330: DO 80 J = 1,N
331: TEMP = ALPHA*X(JX)
332: IY = KY
333: K = KUP1 - J
334: DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
335: Y(IY) = Y(IY) + TEMP*A(K+I,J)
336: IY = IY + INCY
337: 70 CONTINUE
338: JX = JX + INCX
339: IF (J.GT.KU) KY = KY + INCY
340: 80 CONTINUE
341: END IF
342: ELSE
343: *
344: * Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
345: *
346: JY = KY
347: IF (INCX.EQ.1) THEN
348: DO 110 J = 1,N
349: TEMP = ZERO
350: K = KUP1 - J
351: IF (NOCONJ) THEN
352: DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
353: TEMP = TEMP + A(K+I,J)*X(I)
354: 90 CONTINUE
355: ELSE
356: DO 100 I = MAX(1,J-KU),MIN(M,J+KL)
357: TEMP = TEMP + DCONJG(A(K+I,J))*X(I)
358: 100 CONTINUE
359: END IF
360: Y(JY) = Y(JY) + ALPHA*TEMP
361: JY = JY + INCY
362: 110 CONTINUE
363: ELSE
364: DO 140 J = 1,N
365: TEMP = ZERO
366: IX = KX
367: K = KUP1 - J
368: IF (NOCONJ) THEN
369: DO 120 I = MAX(1,J-KU),MIN(M,J+KL)
370: TEMP = TEMP + A(K+I,J)*X(IX)
371: IX = IX + INCX
372: 120 CONTINUE
373: ELSE
374: DO 130 I = MAX(1,J-KU),MIN(M,J+KL)
375: TEMP = TEMP + DCONJG(A(K+I,J))*X(IX)
376: IX = IX + INCX
377: 130 CONTINUE
378: END IF
379: Y(JY) = Y(JY) + ALPHA*TEMP
380: JY = JY + INCY
381: IF (J.GT.KU) KX = KX + INCX
382: 140 CONTINUE
383: END IF
384: END IF
385: *
386: RETURN
387: *
388: * End of ZGBMV .
389: *
390: END
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