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1.1 bertrand 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: *
1.7 ! bertrand 16: * y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
1.1 bertrand 17: *
1.7 ! bertrand 18: * y := alpha*A**H*x + beta*y,
1.1 bertrand 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: *
1.7 ! bertrand 32: * TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
1.1 bertrand 33: *
1.7 ! bertrand 34: * TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.
1.1 bertrand 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.
1.7 ! bertrand 125: * The vector and matrix arguments are not referenced when N = 0, or M = 0
1.1 bertrand 126: *
127: * -- Written on 22-October-1986.
128: * Jack Dongarra, Argonne National Lab.
129: * Jeremy Du Croz, Nag Central Office.
130: * Sven Hammarling, Nag Central Office.
131: * Richard Hanson, Sandia National Labs.
132: *
133: * =====================================================================
134: *
135: * .. Parameters ..
136: DOUBLE COMPLEX ONE
137: PARAMETER (ONE= (1.0D+0,0.0D+0))
138: DOUBLE COMPLEX ZERO
139: PARAMETER (ZERO= (0.0D+0,0.0D+0))
140: * ..
141: * .. Local Scalars ..
142: DOUBLE COMPLEX TEMP
143: INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
144: LOGICAL NOCONJ
145: * ..
146: * .. External Functions ..
147: LOGICAL LSAME
148: EXTERNAL LSAME
149: * ..
150: * .. External Subroutines ..
151: EXTERNAL XERBLA
152: * ..
153: * .. Intrinsic Functions ..
154: INTRINSIC DCONJG,MAX,MIN
155: * ..
156: *
157: * Test the input parameters.
158: *
159: INFO = 0
160: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
161: + .NOT.LSAME(TRANS,'C')) THEN
162: INFO = 1
163: ELSE IF (M.LT.0) THEN
164: INFO = 2
165: ELSE IF (N.LT.0) THEN
166: INFO = 3
167: ELSE IF (KL.LT.0) THEN
168: INFO = 4
169: ELSE IF (KU.LT.0) THEN
170: INFO = 5
171: ELSE IF (LDA.LT. (KL+KU+1)) THEN
172: INFO = 8
173: ELSE IF (INCX.EQ.0) THEN
174: INFO = 10
175: ELSE IF (INCY.EQ.0) THEN
176: INFO = 13
177: END IF
178: IF (INFO.NE.0) THEN
179: CALL XERBLA('ZGBMV ',INFO)
180: RETURN
181: END IF
182: *
183: * Quick return if possible.
184: *
185: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
186: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
187: *
188: NOCONJ = LSAME(TRANS,'T')
189: *
190: * Set LENX and LENY, the lengths of the vectors x and y, and set
191: * up the start points in X and Y.
192: *
193: IF (LSAME(TRANS,'N')) THEN
194: LENX = N
195: LENY = M
196: ELSE
197: LENX = M
198: LENY = N
199: END IF
200: IF (INCX.GT.0) THEN
201: KX = 1
202: ELSE
203: KX = 1 - (LENX-1)*INCX
204: END IF
205: IF (INCY.GT.0) THEN
206: KY = 1
207: ELSE
208: KY = 1 - (LENY-1)*INCY
209: END IF
210: *
211: * Start the operations. In this version the elements of A are
212: * accessed sequentially with one pass through the band part of A.
213: *
214: * First form y := beta*y.
215: *
216: IF (BETA.NE.ONE) THEN
217: IF (INCY.EQ.1) THEN
218: IF (BETA.EQ.ZERO) THEN
219: DO 10 I = 1,LENY
220: Y(I) = ZERO
221: 10 CONTINUE
222: ELSE
223: DO 20 I = 1,LENY
224: Y(I) = BETA*Y(I)
225: 20 CONTINUE
226: END IF
227: ELSE
228: IY = KY
229: IF (BETA.EQ.ZERO) THEN
230: DO 30 I = 1,LENY
231: Y(IY) = ZERO
232: IY = IY + INCY
233: 30 CONTINUE
234: ELSE
235: DO 40 I = 1,LENY
236: Y(IY) = BETA*Y(IY)
237: IY = IY + INCY
238: 40 CONTINUE
239: END IF
240: END IF
241: END IF
242: IF (ALPHA.EQ.ZERO) RETURN
243: KUP1 = KU + 1
244: IF (LSAME(TRANS,'N')) THEN
245: *
246: * Form y := alpha*A*x + y.
247: *
248: JX = KX
249: IF (INCY.EQ.1) THEN
250: DO 60 J = 1,N
251: IF (X(JX).NE.ZERO) THEN
252: TEMP = ALPHA*X(JX)
253: K = KUP1 - J
254: DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
255: Y(I) = Y(I) + TEMP*A(K+I,J)
256: 50 CONTINUE
257: END IF
258: JX = JX + INCX
259: 60 CONTINUE
260: ELSE
261: DO 80 J = 1,N
262: IF (X(JX).NE.ZERO) THEN
263: TEMP = ALPHA*X(JX)
264: IY = KY
265: K = KUP1 - J
266: DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
267: Y(IY) = Y(IY) + TEMP*A(K+I,J)
268: IY = IY + INCY
269: 70 CONTINUE
270: END IF
271: JX = JX + INCX
272: IF (J.GT.KU) KY = KY + INCY
273: 80 CONTINUE
274: END IF
275: ELSE
276: *
1.7 ! bertrand 277: * Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
1.1 bertrand 278: *
279: JY = KY
280: IF (INCX.EQ.1) THEN
281: DO 110 J = 1,N
282: TEMP = ZERO
283: K = KUP1 - J
284: IF (NOCONJ) THEN
285: DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
286: TEMP = TEMP + A(K+I,J)*X(I)
287: 90 CONTINUE
288: ELSE
289: DO 100 I = MAX(1,J-KU),MIN(M,J+KL)
290: TEMP = TEMP + DCONJG(A(K+I,J))*X(I)
291: 100 CONTINUE
292: END IF
293: Y(JY) = Y(JY) + ALPHA*TEMP
294: JY = JY + INCY
295: 110 CONTINUE
296: ELSE
297: DO 140 J = 1,N
298: TEMP = ZERO
299: IX = KX
300: K = KUP1 - J
301: IF (NOCONJ) THEN
302: DO 120 I = MAX(1,J-KU),MIN(M,J+KL)
303: TEMP = TEMP + A(K+I,J)*X(IX)
304: IX = IX + INCX
305: 120 CONTINUE
306: ELSE
307: DO 130 I = MAX(1,J-KU),MIN(M,J+KL)
308: TEMP = TEMP + DCONJG(A(K+I,J))*X(IX)
309: IX = IX + INCX
310: 130 CONTINUE
311: END IF
312: Y(JY) = Y(JY) + ALPHA*TEMP
313: JY = JY + INCY
314: IF (J.GT.KU) KX = KX + INCX
315: 140 CONTINUE
316: END IF
317: END IF
318: *
319: RETURN
320: *
321: * End of ZGBMV .
322: *
323: END