1: SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
2: * .. Scalar Arguments ..
3: DOUBLE COMPLEX ALPHA,BETA
4: INTEGER INCX,INCY,KL,KU,LDA,M,N
5: CHARACTER TRANS
6: * ..
7: * .. Array Arguments ..
8: DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
9: * ..
10: *
11: * Purpose
12: * =======
13: *
14: * ZGBMV performs one of the matrix-vector operations
15: *
16: * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
17: *
18: * y := alpha*conjg( A' )*x + beta*y,
19: *
20: * where alpha and beta are scalars, x and y are vectors and A is an
21: * m by n band matrix, with kl sub-diagonals and ku super-diagonals.
22: *
23: * Arguments
24: * ==========
25: *
26: * TRANS - CHARACTER*1.
27: * On entry, TRANS specifies the operation to be performed as
28: * follows:
29: *
30: * TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
31: *
32: * TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
33: *
34: * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
35: *
36: * Unchanged on exit.
37: *
38: * M - INTEGER.
39: * On entry, M specifies the number of rows of the matrix A.
40: * M must be at least zero.
41: * Unchanged on exit.
42: *
43: * N - INTEGER.
44: * On entry, N specifies the number of columns of the matrix A.
45: * N must be at least zero.
46: * Unchanged on exit.
47: *
48: * KL - INTEGER.
49: * On entry, KL specifies the number of sub-diagonals of the
50: * matrix A. KL must satisfy 0 .le. KL.
51: * Unchanged on exit.
52: *
53: * KU - INTEGER.
54: * On entry, KU specifies the number of super-diagonals of the
55: * matrix A. KU must satisfy 0 .le. KU.
56: * Unchanged on exit.
57: *
58: * ALPHA - COMPLEX*16 .
59: * On entry, ALPHA specifies the scalar alpha.
60: * Unchanged on exit.
61: *
62: * A - COMPLEX*16 array of DIMENSION ( LDA, n ).
63: * Before entry, the leading ( kl + ku + 1 ) by n part of the
64: * array A must contain the matrix of coefficients, supplied
65: * column by column, with the leading diagonal of the matrix in
66: * row ( ku + 1 ) of the array, the first super-diagonal
67: * starting at position 2 in row ku, the first sub-diagonal
68: * starting at position 1 in row ( ku + 2 ), and so on.
69: * Elements in the array A that do not correspond to elements
70: * in the band matrix (such as the top left ku by ku triangle)
71: * are not referenced.
72: * The following program segment will transfer a band matrix
73: * from conventional full matrix storage to band storage:
74: *
75: * DO 20, J = 1, N
76: * K = KU + 1 - J
77: * DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
78: * A( K + I, J ) = matrix( I, J )
79: * 10 CONTINUE
80: * 20 CONTINUE
81: *
82: * Unchanged on exit.
83: *
84: * LDA - INTEGER.
85: * On entry, LDA specifies the first dimension of A as declared
86: * in the calling (sub) program. LDA must be at least
87: * ( kl + ku + 1 ).
88: * Unchanged on exit.
89: *
90: * X - COMPLEX*16 array of DIMENSION at least
91: * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
92: * and at least
93: * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
94: * Before entry, the incremented array X must contain the
95: * vector x.
96: * Unchanged on exit.
97: *
98: * INCX - INTEGER.
99: * On entry, INCX specifies the increment for the elements of
100: * X. INCX must not be zero.
101: * Unchanged on exit.
102: *
103: * BETA - COMPLEX*16 .
104: * On entry, BETA specifies the scalar beta. When BETA is
105: * supplied as zero then Y need not be set on input.
106: * Unchanged on exit.
107: *
108: * Y - COMPLEX*16 array of DIMENSION at least
109: * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
110: * and at least
111: * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
112: * Before entry, the incremented array Y must contain the
113: * vector y. On exit, Y is overwritten by the updated vector y.
114: *
115: *
116: * INCY - INTEGER.
117: * On entry, INCY specifies the increment for the elements of
118: * Y. INCY must not be zero.
119: * Unchanged on exit.
120: *
121: * Further Details
122: * ===============
123: *
124: * Level 2 Blas routine.
125: *
126: * -- Written on 22-October-1986.
127: * Jack Dongarra, Argonne National Lab.
128: * Jeremy Du Croz, Nag Central Office.
129: * Sven Hammarling, Nag Central Office.
130: * Richard Hanson, Sandia National Labs.
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: DOUBLE COMPLEX ONE
136: PARAMETER (ONE= (1.0D+0,0.0D+0))
137: DOUBLE COMPLEX ZERO
138: PARAMETER (ZERO= (0.0D+0,0.0D+0))
139: * ..
140: * .. Local Scalars ..
141: DOUBLE COMPLEX TEMP
142: INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
143: LOGICAL NOCONJ
144: * ..
145: * .. External Functions ..
146: LOGICAL LSAME
147: EXTERNAL LSAME
148: * ..
149: * .. External Subroutines ..
150: EXTERNAL XERBLA
151: * ..
152: * .. Intrinsic Functions ..
153: INTRINSIC DCONJG,MAX,MIN
154: * ..
155: *
156: * Test the input parameters.
157: *
158: INFO = 0
159: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
160: + .NOT.LSAME(TRANS,'C')) THEN
161: INFO = 1
162: ELSE IF (M.LT.0) THEN
163: INFO = 2
164: ELSE IF (N.LT.0) THEN
165: INFO = 3
166: ELSE IF (KL.LT.0) THEN
167: INFO = 4
168: ELSE IF (KU.LT.0) THEN
169: INFO = 5
170: ELSE IF (LDA.LT. (KL+KU+1)) THEN
171: INFO = 8
172: ELSE IF (INCX.EQ.0) THEN
173: INFO = 10
174: ELSE IF (INCY.EQ.0) THEN
175: INFO = 13
176: END IF
177: IF (INFO.NE.0) THEN
178: CALL XERBLA('ZGBMV ',INFO)
179: RETURN
180: END IF
181: *
182: * Quick return if possible.
183: *
184: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
185: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
186: *
187: NOCONJ = LSAME(TRANS,'T')
188: *
189: * Set LENX and LENY, the lengths of the vectors x and y, and set
190: * up the start points in X and Y.
191: *
192: IF (LSAME(TRANS,'N')) THEN
193: LENX = N
194: LENY = M
195: ELSE
196: LENX = M
197: LENY = N
198: END IF
199: IF (INCX.GT.0) THEN
200: KX = 1
201: ELSE
202: KX = 1 - (LENX-1)*INCX
203: END IF
204: IF (INCY.GT.0) THEN
205: KY = 1
206: ELSE
207: KY = 1 - (LENY-1)*INCY
208: END IF
209: *
210: * Start the operations. In this version the elements of A are
211: * accessed sequentially with one pass through the band part of A.
212: *
213: * First form y := beta*y.
214: *
215: IF (BETA.NE.ONE) THEN
216: IF (INCY.EQ.1) THEN
217: IF (BETA.EQ.ZERO) THEN
218: DO 10 I = 1,LENY
219: Y(I) = ZERO
220: 10 CONTINUE
221: ELSE
222: DO 20 I = 1,LENY
223: Y(I) = BETA*Y(I)
224: 20 CONTINUE
225: END IF
226: ELSE
227: IY = KY
228: IF (BETA.EQ.ZERO) THEN
229: DO 30 I = 1,LENY
230: Y(IY) = ZERO
231: IY = IY + INCY
232: 30 CONTINUE
233: ELSE
234: DO 40 I = 1,LENY
235: Y(IY) = BETA*Y(IY)
236: IY = IY + INCY
237: 40 CONTINUE
238: END IF
239: END IF
240: END IF
241: IF (ALPHA.EQ.ZERO) RETURN
242: KUP1 = KU + 1
243: IF (LSAME(TRANS,'N')) THEN
244: *
245: * Form y := alpha*A*x + y.
246: *
247: JX = KX
248: IF (INCY.EQ.1) THEN
249: DO 60 J = 1,N
250: IF (X(JX).NE.ZERO) THEN
251: TEMP = ALPHA*X(JX)
252: K = KUP1 - J
253: DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
254: Y(I) = Y(I) + TEMP*A(K+I,J)
255: 50 CONTINUE
256: END IF
257: JX = JX + INCX
258: 60 CONTINUE
259: ELSE
260: DO 80 J = 1,N
261: IF (X(JX).NE.ZERO) THEN
262: TEMP = ALPHA*X(JX)
263: IY = KY
264: K = KUP1 - J
265: DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
266: Y(IY) = Y(IY) + TEMP*A(K+I,J)
267: IY = IY + INCY
268: 70 CONTINUE
269: END IF
270: JX = JX + INCX
271: IF (J.GT.KU) KY = KY + INCY
272: 80 CONTINUE
273: END IF
274: ELSE
275: *
276: * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y.
277: *
278: JY = KY
279: IF (INCX.EQ.1) THEN
280: DO 110 J = 1,N
281: TEMP = ZERO
282: K = KUP1 - J
283: IF (NOCONJ) THEN
284: DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
285: TEMP = TEMP + A(K+I,J)*X(I)
286: 90 CONTINUE
287: ELSE
288: DO 100 I = MAX(1,J-KU),MIN(M,J+KL)
289: TEMP = TEMP + DCONJG(A(K+I,J))*X(I)
290: 100 CONTINUE
291: END IF
292: Y(JY) = Y(JY) + ALPHA*TEMP
293: JY = JY + INCY
294: 110 CONTINUE
295: ELSE
296: DO 140 J = 1,N
297: TEMP = ZERO
298: IX = KX
299: K = KUP1 - J
300: IF (NOCONJ) THEN
301: DO 120 I = MAX(1,J-KU),MIN(M,J+KL)
302: TEMP = TEMP + A(K+I,J)*X(IX)
303: IX = IX + INCX
304: 120 CONTINUE
305: ELSE
306: DO 130 I = MAX(1,J-KU),MIN(M,J+KL)
307: TEMP = TEMP + DCONJG(A(K+I,J))*X(IX)
308: IX = IX + INCX
309: 130 CONTINUE
310: END IF
311: Y(JY) = Y(JY) + ALPHA*TEMP
312: JY = JY + INCY
313: IF (J.GT.KU) KX = KX + INCX
314: 140 CONTINUE
315: END IF
316: END IF
317: *
318: RETURN
319: *
320: * End of ZGBMV .
321: *
322: END
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