1: SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
2: * .. Scalar Arguments ..
3: DOUBLE PRECISION ALPHA,BETA
4: INTEGER INCX,INCY,K,LDA,N
5: CHARACTER UPLO
6: * ..
7: * .. Array Arguments ..
8: DOUBLE PRECISION A(LDA,*),X(*),Y(*)
9: * ..
10: *
11: * Purpose
12: * =======
13: *
14: * DSBMV performs the matrix-vector operation
15: *
16: * y := alpha*A*x + beta*y,
17: *
18: * where alpha and beta are scalars, x and y are n element vectors and
19: * A is an n by n symmetric band matrix, with k super-diagonals.
20: *
21: * Arguments
22: * ==========
23: *
24: * UPLO - CHARACTER*1.
25: * On entry, UPLO specifies whether the upper or lower
26: * triangular part of the band matrix A is being supplied as
27: * follows:
28: *
29: * UPLO = 'U' or 'u' The upper triangular part of A is
30: * being supplied.
31: *
32: * UPLO = 'L' or 'l' The lower triangular part of A is
33: * being supplied.
34: *
35: * Unchanged on exit.
36: *
37: * N - INTEGER.
38: * On entry, N specifies the order of the matrix A.
39: * N must be at least zero.
40: * Unchanged on exit.
41: *
42: * K - INTEGER.
43: * On entry, K specifies the number of super-diagonals of the
44: * matrix A. K must satisfy 0 .le. K.
45: * Unchanged on exit.
46: *
47: * ALPHA - DOUBLE PRECISION.
48: * On entry, ALPHA specifies the scalar alpha.
49: * Unchanged on exit.
50: *
51: * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
52: * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
53: * by n part of the array A must contain the upper triangular
54: * band part of the symmetric matrix, supplied column by
55: * column, with the leading diagonal of the matrix in row
56: * ( k + 1 ) of the array, the first super-diagonal starting at
57: * position 2 in row k, and so on. The top left k by k triangle
58: * of the array A is not referenced.
59: * The following program segment will transfer the upper
60: * triangular part of a symmetric band matrix from conventional
61: * full matrix storage to band storage:
62: *
63: * DO 20, J = 1, N
64: * M = K + 1 - J
65: * DO 10, I = MAX( 1, J - K ), J
66: * A( M + I, J ) = matrix( I, J )
67: * 10 CONTINUE
68: * 20 CONTINUE
69: *
70: * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
71: * by n part of the array A must contain the lower triangular
72: * band part of the symmetric matrix, supplied column by
73: * column, with the leading diagonal of the matrix in row 1 of
74: * the array, the first sub-diagonal starting at position 1 in
75: * row 2, and so on. The bottom right k by k triangle of the
76: * array A is not referenced.
77: * The following program segment will transfer the lower
78: * triangular part of a symmetric band matrix from conventional
79: * full matrix storage to band storage:
80: *
81: * DO 20, J = 1, N
82: * M = 1 - J
83: * DO 10, I = J, MIN( N, J + K )
84: * A( M + I, J ) = matrix( I, J )
85: * 10 CONTINUE
86: * 20 CONTINUE
87: *
88: * Unchanged on exit.
89: *
90: * LDA - INTEGER.
91: * On entry, LDA specifies the first dimension of A as declared
92: * in the calling (sub) program. LDA must be at least
93: * ( k + 1 ).
94: * Unchanged on exit.
95: *
96: * X - DOUBLE PRECISION array of DIMENSION at least
97: * ( 1 + ( n - 1 )*abs( INCX ) ).
98: * Before entry, the incremented array X must contain the
99: * vector x.
100: * Unchanged on exit.
101: *
102: * INCX - INTEGER.
103: * On entry, INCX specifies the increment for the elements of
104: * X. INCX must not be zero.
105: * Unchanged on exit.
106: *
107: * BETA - DOUBLE PRECISION.
108: * On entry, BETA specifies the scalar beta.
109: * Unchanged on exit.
110: *
111: * Y - DOUBLE PRECISION array of DIMENSION at least
112: * ( 1 + ( n - 1 )*abs( INCY ) ).
113: * Before entry, the incremented array Y must contain the
114: * vector y. On exit, Y is overwritten by the updated vector y.
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: * The vector and matrix arguments are not referenced when N = 0, or M = 0
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 PRECISION ONE,ZERO
137: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
138: * ..
139: * .. Local Scalars ..
140: DOUBLE PRECISION TEMP1,TEMP2
141: INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
142: * ..
143: * .. External Functions ..
144: LOGICAL LSAME
145: EXTERNAL LSAME
146: * ..
147: * .. External Subroutines ..
148: EXTERNAL XERBLA
149: * ..
150: * .. Intrinsic Functions ..
151: INTRINSIC MAX,MIN
152: * ..
153: *
154: * Test the input parameters.
155: *
156: INFO = 0
157: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
158: INFO = 1
159: ELSE IF (N.LT.0) THEN
160: INFO = 2
161: ELSE IF (K.LT.0) THEN
162: INFO = 3
163: ELSE IF (LDA.LT. (K+1)) THEN
164: INFO = 6
165: ELSE IF (INCX.EQ.0) THEN
166: INFO = 8
167: ELSE IF (INCY.EQ.0) THEN
168: INFO = 11
169: END IF
170: IF (INFO.NE.0) THEN
171: CALL XERBLA('DSBMV ',INFO)
172: RETURN
173: END IF
174: *
175: * Quick return if possible.
176: *
177: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
178: *
179: * Set up the start points in X and Y.
180: *
181: IF (INCX.GT.0) THEN
182: KX = 1
183: ELSE
184: KX = 1 - (N-1)*INCX
185: END IF
186: IF (INCY.GT.0) THEN
187: KY = 1
188: ELSE
189: KY = 1 - (N-1)*INCY
190: END IF
191: *
192: * Start the operations. In this version the elements of the array A
193: * are accessed sequentially with one pass through A.
194: *
195: * First form y := beta*y.
196: *
197: IF (BETA.NE.ONE) THEN
198: IF (INCY.EQ.1) THEN
199: IF (BETA.EQ.ZERO) THEN
200: DO 10 I = 1,N
201: Y(I) = ZERO
202: 10 CONTINUE
203: ELSE
204: DO 20 I = 1,N
205: Y(I) = BETA*Y(I)
206: 20 CONTINUE
207: END IF
208: ELSE
209: IY = KY
210: IF (BETA.EQ.ZERO) THEN
211: DO 30 I = 1,N
212: Y(IY) = ZERO
213: IY = IY + INCY
214: 30 CONTINUE
215: ELSE
216: DO 40 I = 1,N
217: Y(IY) = BETA*Y(IY)
218: IY = IY + INCY
219: 40 CONTINUE
220: END IF
221: END IF
222: END IF
223: IF (ALPHA.EQ.ZERO) RETURN
224: IF (LSAME(UPLO,'U')) THEN
225: *
226: * Form y when upper triangle of A is stored.
227: *
228: KPLUS1 = K + 1
229: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
230: DO 60 J = 1,N
231: TEMP1 = ALPHA*X(J)
232: TEMP2 = ZERO
233: L = KPLUS1 - J
234: DO 50 I = MAX(1,J-K),J - 1
235: Y(I) = Y(I) + TEMP1*A(L+I,J)
236: TEMP2 = TEMP2 + A(L+I,J)*X(I)
237: 50 CONTINUE
238: Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2
239: 60 CONTINUE
240: ELSE
241: JX = KX
242: JY = KY
243: DO 80 J = 1,N
244: TEMP1 = ALPHA*X(JX)
245: TEMP2 = ZERO
246: IX = KX
247: IY = KY
248: L = KPLUS1 - J
249: DO 70 I = MAX(1,J-K),J - 1
250: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
251: TEMP2 = TEMP2 + A(L+I,J)*X(IX)
252: IX = IX + INCX
253: IY = IY + INCY
254: 70 CONTINUE
255: Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2
256: JX = JX + INCX
257: JY = JY + INCY
258: IF (J.GT.K) THEN
259: KX = KX + INCX
260: KY = KY + INCY
261: END IF
262: 80 CONTINUE
263: END IF
264: ELSE
265: *
266: * Form y when lower triangle of A is stored.
267: *
268: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
269: DO 100 J = 1,N
270: TEMP1 = ALPHA*X(J)
271: TEMP2 = ZERO
272: Y(J) = Y(J) + TEMP1*A(1,J)
273: L = 1 - J
274: DO 90 I = J + 1,MIN(N,J+K)
275: Y(I) = Y(I) + TEMP1*A(L+I,J)
276: TEMP2 = TEMP2 + A(L+I,J)*X(I)
277: 90 CONTINUE
278: Y(J) = Y(J) + ALPHA*TEMP2
279: 100 CONTINUE
280: ELSE
281: JX = KX
282: JY = KY
283: DO 120 J = 1,N
284: TEMP1 = ALPHA*X(JX)
285: TEMP2 = ZERO
286: Y(JY) = Y(JY) + TEMP1*A(1,J)
287: L = 1 - J
288: IX = JX
289: IY = JY
290: DO 110 I = J + 1,MIN(N,J+K)
291: IX = IX + INCX
292: IY = IY + INCY
293: Y(IY) = Y(IY) + TEMP1*A(L+I,J)
294: TEMP2 = TEMP2 + A(L+I,J)*X(IX)
295: 110 CONTINUE
296: Y(JY) = Y(JY) + ALPHA*TEMP2
297: JX = JX + INCX
298: JY = JY + INCY
299: 120 CONTINUE
300: END IF
301: END IF
302: *
303: RETURN
304: *
305: * End of DSBMV .
306: *
307: END
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