1: *> \brief \b DGBMV
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 DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12: *
13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA,BETA
15: * INTEGER INCX,INCY,KL,KU,LDA,M,N
16: * CHARACTER TRANS
17: * ..
18: * .. Array Arguments ..
19: * DOUBLE PRECISION A(LDA,*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> DGBMV performs one of the matrix-vector operations
29: *>
30: *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y,
31: *>
32: *> where alpha and beta are scalars, x and y are vectors and A is an
33: *> m by n band matrix, with kl sub-diagonals and ku super-diagonals.
34: *> \endverbatim
35: *
36: * Arguments:
37: * ==========
38: *
39: *> \param[in] TRANS
40: *> \verbatim
41: *> TRANS is CHARACTER*1
42: *> On entry, TRANS specifies the operation to be performed as
43: *> follows:
44: *>
45: *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
46: *>
47: *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
48: *>
49: *> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y.
50: *> \endverbatim
51: *>
52: *> \param[in] M
53: *> \verbatim
54: *> M is INTEGER
55: *> On entry, M specifies the number of rows of the matrix A.
56: *> M must be at least zero.
57: *> \endverbatim
58: *>
59: *> \param[in] N
60: *> \verbatim
61: *> N is INTEGER
62: *> On entry, N specifies the number of columns of the matrix A.
63: *> N must be at least zero.
64: *> \endverbatim
65: *>
66: *> \param[in] KL
67: *> \verbatim
68: *> KL is INTEGER
69: *> On entry, KL specifies the number of sub-diagonals of the
70: *> matrix A. KL must satisfy 0 .le. KL.
71: *> \endverbatim
72: *>
73: *> \param[in] KU
74: *> \verbatim
75: *> KU is INTEGER
76: *> On entry, KU specifies the number of super-diagonals of the
77: *> matrix A. KU must satisfy 0 .le. KU.
78: *> \endverbatim
79: *>
80: *> \param[in] ALPHA
81: *> \verbatim
82: *> ALPHA is DOUBLE PRECISION.
83: *> On entry, ALPHA specifies the scalar alpha.
84: *> \endverbatim
85: *>
86: *> \param[in] A
87: *> \verbatim
88: *> A is DOUBLE PRECISION array, dimension ( LDA, N )
89: *> Before entry, the leading ( kl + ku + 1 ) by n part of the
90: *> array A must contain the matrix of coefficients, supplied
91: *> column by column, with the leading diagonal of the matrix in
92: *> row ( ku + 1 ) of the array, the first super-diagonal
93: *> starting at position 2 in row ku, the first sub-diagonal
94: *> starting at position 1 in row ( ku + 2 ), and so on.
95: *> Elements in the array A that do not correspond to elements
96: *> in the band matrix (such as the top left ku by ku triangle)
97: *> are not referenced.
98: *> The following program segment will transfer a band matrix
99: *> from conventional full matrix storage to band storage:
100: *>
101: *> DO 20, J = 1, N
102: *> K = KU + 1 - J
103: *> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
104: *> A( K + I, J ) = matrix( I, J )
105: *> 10 CONTINUE
106: *> 20 CONTINUE
107: *> \endverbatim
108: *>
109: *> \param[in] LDA
110: *> \verbatim
111: *> LDA is INTEGER
112: *> On entry, LDA specifies the first dimension of A as declared
113: *> in the calling (sub) program. LDA must be at least
114: *> ( kl + ku + 1 ).
115: *> \endverbatim
116: *>
117: *> \param[in] X
118: *> \verbatim
119: *> X is DOUBLE PRECISION array, dimension at least
120: *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
121: *> and at least
122: *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
123: *> Before entry, the incremented array X must contain the
124: *> vector x.
125: *> \endverbatim
126: *>
127: *> \param[in] INCX
128: *> \verbatim
129: *> INCX is INTEGER
130: *> On entry, INCX specifies the increment for the elements of
131: *> X. INCX must not be zero.
132: *> \endverbatim
133: *>
134: *> \param[in] BETA
135: *> \verbatim
136: *> BETA is DOUBLE PRECISION.
137: *> On entry, BETA specifies the scalar beta. When BETA is
138: *> supplied as zero then Y need not be set on input.
139: *> \endverbatim
140: *>
141: *> \param[in,out] Y
142: *> \verbatim
143: *> Y is DOUBLE PRECISION array, dimension at least
144: *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
145: *> and at least
146: *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
147: *> Before entry, the incremented array Y must contain the
148: *> vector y. On exit, Y is overwritten by the updated vector y.
149: *> \endverbatim
150: *>
151: *> \param[in] INCY
152: *> \verbatim
153: *> INCY is INTEGER
154: *> On entry, INCY specifies the increment for the elements of
155: *> Y. INCY must not be zero.
156: *> \endverbatim
157: *
158: * Authors:
159: * ========
160: *
161: *> \author Univ. of Tennessee
162: *> \author Univ. of California Berkeley
163: *> \author Univ. of Colorado Denver
164: *> \author NAG Ltd.
165: *
166: *> \ingroup double_blas_level2
167: *
168: *> \par Further Details:
169: * =====================
170: *>
171: *> \verbatim
172: *>
173: *> Level 2 Blas routine.
174: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
175: *>
176: *> -- Written on 22-October-1986.
177: *> Jack Dongarra, Argonne National Lab.
178: *> Jeremy Du Croz, Nag Central Office.
179: *> Sven Hammarling, Nag Central Office.
180: *> Richard Hanson, Sandia National Labs.
181: *> \endverbatim
182: *>
183: * =====================================================================
184: SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
185: *
186: * -- Reference BLAS level2 routine --
187: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
188: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
189: *
190: * .. Scalar Arguments ..
191: DOUBLE PRECISION ALPHA,BETA
192: INTEGER INCX,INCY,KL,KU,LDA,M,N
193: CHARACTER TRANS
194: * ..
195: * .. Array Arguments ..
196: DOUBLE PRECISION A(LDA,*),X(*),Y(*)
197: * ..
198: *
199: * =====================================================================
200: *
201: * .. Parameters ..
202: DOUBLE PRECISION ONE,ZERO
203: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
204: * ..
205: * .. Local Scalars ..
206: DOUBLE PRECISION TEMP
207: INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
208: * ..
209: * .. External Functions ..
210: LOGICAL LSAME
211: EXTERNAL LSAME
212: * ..
213: * .. External Subroutines ..
214: EXTERNAL XERBLA
215: * ..
216: * .. Intrinsic Functions ..
217: INTRINSIC MAX,MIN
218: * ..
219: *
220: * Test the input parameters.
221: *
222: INFO = 0
223: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
224: + .NOT.LSAME(TRANS,'C')) THEN
225: INFO = 1
226: ELSE IF (M.LT.0) THEN
227: INFO = 2
228: ELSE IF (N.LT.0) THEN
229: INFO = 3
230: ELSE IF (KL.LT.0) THEN
231: INFO = 4
232: ELSE IF (KU.LT.0) THEN
233: INFO = 5
234: ELSE IF (LDA.LT. (KL+KU+1)) THEN
235: INFO = 8
236: ELSE IF (INCX.EQ.0) THEN
237: INFO = 10
238: ELSE IF (INCY.EQ.0) THEN
239: INFO = 13
240: END IF
241: IF (INFO.NE.0) THEN
242: CALL XERBLA('DGBMV ',INFO)
243: RETURN
244: END IF
245: *
246: * Quick return if possible.
247: *
248: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
249: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
250: *
251: * Set LENX and LENY, the lengths of the vectors x and y, and set
252: * up the start points in X and Y.
253: *
254: IF (LSAME(TRANS,'N')) THEN
255: LENX = N
256: LENY = M
257: ELSE
258: LENX = M
259: LENY = N
260: END IF
261: IF (INCX.GT.0) THEN
262: KX = 1
263: ELSE
264: KX = 1 - (LENX-1)*INCX
265: END IF
266: IF (INCY.GT.0) THEN
267: KY = 1
268: ELSE
269: KY = 1 - (LENY-1)*INCY
270: END IF
271: *
272: * Start the operations. In this version the elements of A are
273: * accessed sequentially with one pass through the band part of A.
274: *
275: * First form y := beta*y.
276: *
277: IF (BETA.NE.ONE) THEN
278: IF (INCY.EQ.1) THEN
279: IF (BETA.EQ.ZERO) THEN
280: DO 10 I = 1,LENY
281: Y(I) = ZERO
282: 10 CONTINUE
283: ELSE
284: DO 20 I = 1,LENY
285: Y(I) = BETA*Y(I)
286: 20 CONTINUE
287: END IF
288: ELSE
289: IY = KY
290: IF (BETA.EQ.ZERO) THEN
291: DO 30 I = 1,LENY
292: Y(IY) = ZERO
293: IY = IY + INCY
294: 30 CONTINUE
295: ELSE
296: DO 40 I = 1,LENY
297: Y(IY) = BETA*Y(IY)
298: IY = IY + INCY
299: 40 CONTINUE
300: END IF
301: END IF
302: END IF
303: IF (ALPHA.EQ.ZERO) RETURN
304: KUP1 = KU + 1
305: IF (LSAME(TRANS,'N')) THEN
306: *
307: * Form y := alpha*A*x + y.
308: *
309: JX = KX
310: IF (INCY.EQ.1) THEN
311: DO 60 J = 1,N
312: TEMP = ALPHA*X(JX)
313: K = KUP1 - J
314: DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
315: Y(I) = Y(I) + TEMP*A(K+I,J)
316: 50 CONTINUE
317: JX = JX + INCX
318: 60 CONTINUE
319: ELSE
320: DO 80 J = 1,N
321: TEMP = ALPHA*X(JX)
322: IY = KY
323: K = KUP1 - J
324: DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
325: Y(IY) = Y(IY) + TEMP*A(K+I,J)
326: IY = IY + INCY
327: 70 CONTINUE
328: JX = JX + INCX
329: IF (J.GT.KU) KY = KY + INCY
330: 80 CONTINUE
331: END IF
332: ELSE
333: *
334: * Form y := alpha*A**T*x + y.
335: *
336: JY = KY
337: IF (INCX.EQ.1) THEN
338: DO 100 J = 1,N
339: TEMP = ZERO
340: K = KUP1 - J
341: DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
342: TEMP = TEMP + A(K+I,J)*X(I)
343: 90 CONTINUE
344: Y(JY) = Y(JY) + ALPHA*TEMP
345: JY = JY + INCY
346: 100 CONTINUE
347: ELSE
348: DO 120 J = 1,N
349: TEMP = ZERO
350: IX = KX
351: K = KUP1 - J
352: DO 110 I = MAX(1,J-KU),MIN(M,J+KL)
353: TEMP = TEMP + A(K+I,J)*X(IX)
354: IX = IX + INCX
355: 110 CONTINUE
356: Y(JY) = Y(JY) + ALPHA*TEMP
357: JY = JY + INCY
358: IF (J.GT.KU) KX = KX + INCX
359: 120 CONTINUE
360: END IF
361: END IF
362: *
363: RETURN
364: *
365: * End of DGBMV
366: *
367: END
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