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1: *> \brief \b DTBMV
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 DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
12: *
13: * .. Scalar Arguments ..
14: * INTEGER INCX,K,LDA,N
15: * CHARACTER DIAG,TRANS,UPLO
16: * ..
17: * .. Array Arguments ..
18: * DOUBLE PRECISION A(LDA,*),X(*)
19: * ..
20: *
21: *
22: *> \par Purpose:
23: * =============
24: *>
25: *> \verbatim
26: *>
27: *> DTBMV performs one of the matrix-vector operations
28: *>
29: *> x := A*x, or x := A**T*x,
30: *>
31: *> where x is an n element vector and A is an n by n unit, or non-unit,
32: *> upper or lower triangular band matrix, with ( k + 1 ) diagonals.
33: *> \endverbatim
34: *
35: * Arguments:
36: * ==========
37: *
38: *> \param[in] UPLO
39: *> \verbatim
40: *> UPLO is CHARACTER*1
41: *> On entry, UPLO specifies whether the matrix is an upper or
42: *> lower triangular matrix as follows:
43: *>
44: *> UPLO = 'U' or 'u' A is an upper triangular matrix.
45: *>
46: *> UPLO = 'L' or 'l' A is a lower triangular matrix.
47: *> \endverbatim
48: *>
49: *> \param[in] TRANS
50: *> \verbatim
51: *> TRANS is CHARACTER*1
52: *> On entry, TRANS specifies the operation to be performed as
53: *> follows:
54: *>
55: *> TRANS = 'N' or 'n' x := A*x.
56: *>
57: *> TRANS = 'T' or 't' x := A**T*x.
58: *>
59: *> TRANS = 'C' or 'c' x := A**T*x.
60: *> \endverbatim
61: *>
62: *> \param[in] DIAG
63: *> \verbatim
64: *> DIAG is CHARACTER*1
65: *> On entry, DIAG specifies whether or not A is unit
66: *> triangular as follows:
67: *>
68: *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
69: *>
70: *> DIAG = 'N' or 'n' A is not assumed to be unit
71: *> triangular.
72: *> \endverbatim
73: *>
74: *> \param[in] N
75: *> \verbatim
76: *> N is INTEGER
77: *> On entry, N specifies the order of the matrix A.
78: *> N must be at least zero.
79: *> \endverbatim
80: *>
81: *> \param[in] K
82: *> \verbatim
83: *> K is INTEGER
84: *> On entry with UPLO = 'U' or 'u', K specifies the number of
85: *> super-diagonals of the matrix A.
86: *> On entry with UPLO = 'L' or 'l', K specifies the number of
87: *> sub-diagonals of the matrix A.
88: *> K must satisfy 0 .le. K.
89: *> \endverbatim
90: *>
91: *> \param[in] A
92: *> \verbatim
93: *> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
94: *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
95: *> by n part of the array A must contain the upper triangular
96: *> band part of the matrix of coefficients, supplied column by
97: *> column, with the leading diagonal of the matrix in row
98: *> ( k + 1 ) of the array, the first super-diagonal starting at
99: *> position 2 in row k, and so on. The top left k by k triangle
100: *> of the array A is not referenced.
101: *> The following program segment will transfer an upper
102: *> triangular band matrix from conventional full matrix storage
103: *> to band storage:
104: *>
105: *> DO 20, J = 1, N
106: *> M = K + 1 - J
107: *> DO 10, I = MAX( 1, J - K ), J
108: *> A( M + I, J ) = matrix( I, J )
109: *> 10 CONTINUE
110: *> 20 CONTINUE
111: *>
112: *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
113: *> by n part of the array A must contain the lower triangular
114: *> band part of the matrix of coefficients, supplied column by
115: *> column, with the leading diagonal of the matrix in row 1 of
116: *> the array, the first sub-diagonal starting at position 1 in
117: *> row 2, and so on. The bottom right k by k triangle of the
118: *> array A is not referenced.
119: *> The following program segment will transfer a lower
120: *> triangular band matrix from conventional full matrix storage
121: *> to band storage:
122: *>
123: *> DO 20, J = 1, N
124: *> M = 1 - J
125: *> DO 10, I = J, MIN( N, J + K )
126: *> A( M + I, J ) = matrix( I, J )
127: *> 10 CONTINUE
128: *> 20 CONTINUE
129: *>
130: *> Note that when DIAG = 'U' or 'u' the elements of the array A
131: *> corresponding to the diagonal elements of the matrix are not
132: *> referenced, but are assumed to be unity.
133: *> \endverbatim
134: *>
135: *> \param[in] LDA
136: *> \verbatim
137: *> LDA is INTEGER
138: *> On entry, LDA specifies the first dimension of A as declared
139: *> in the calling (sub) program. LDA must be at least
140: *> ( k + 1 ).
141: *> \endverbatim
142: *>
143: *> \param[in,out] X
144: *> \verbatim
145: *> X is DOUBLE PRECISION array of dimension at least
146: *> ( 1 + ( n - 1 )*abs( INCX ) ).
147: *> Before entry, the incremented array X must contain the n
148: *> element vector x. On exit, X is overwritten with the
149: *> tranformed vector x.
150: *> \endverbatim
151: *>
152: *> \param[in] INCX
153: *> \verbatim
154: *> INCX is INTEGER
155: *> On entry, INCX specifies the increment for the elements of
156: *> X. INCX must not be zero.
157: *> \endverbatim
158: *
159: * Authors:
160: * ========
161: *
162: *> \author Univ. of Tennessee
163: *> \author Univ. of California Berkeley
164: *> \author Univ. of Colorado Denver
165: *> \author NAG Ltd.
166: *
167: *> \date November 2011
168: *
169: *> \ingroup double_blas_level2
170: *
171: *> \par Further Details:
172: * =====================
173: *>
174: *> \verbatim
175: *>
176: *> Level 2 Blas routine.
177: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
178: *>
179: *> -- Written on 22-October-1986.
180: *> Jack Dongarra, Argonne National Lab.
181: *> Jeremy Du Croz, Nag Central Office.
182: *> Sven Hammarling, Nag Central Office.
183: *> Richard Hanson, Sandia National Labs.
184: *> \endverbatim
185: *>
186: * =====================================================================
187: SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
188: *
189: * -- Reference BLAS level2 routine (version 3.4.0) --
190: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
191: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
192: * November 2011
193: *
194: * .. Scalar Arguments ..
195: INTEGER INCX,K,LDA,N
196: CHARACTER DIAG,TRANS,UPLO
197: * ..
198: * .. Array Arguments ..
199: DOUBLE PRECISION A(LDA,*),X(*)
200: * ..
201: *
202: * =====================================================================
203: *
204: * .. Parameters ..
205: DOUBLE PRECISION ZERO
206: PARAMETER (ZERO=0.0D+0)
207: * ..
208: * .. Local Scalars ..
209: DOUBLE PRECISION TEMP
210: INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
211: LOGICAL NOUNIT
212: * ..
213: * .. External Functions ..
214: LOGICAL LSAME
215: EXTERNAL LSAME
216: * ..
217: * .. External Subroutines ..
218: EXTERNAL XERBLA
219: * ..
220: * .. Intrinsic Functions ..
221: INTRINSIC MAX,MIN
222: * ..
223: *
224: * Test the input parameters.
225: *
226: INFO = 0
227: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
228: INFO = 1
229: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
230: + .NOT.LSAME(TRANS,'C')) THEN
231: INFO = 2
232: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
233: INFO = 3
234: ELSE IF (N.LT.0) THEN
235: INFO = 4
236: ELSE IF (K.LT.0) THEN
237: INFO = 5
238: ELSE IF (LDA.LT. (K+1)) THEN
239: INFO = 7
240: ELSE IF (INCX.EQ.0) THEN
241: INFO = 9
242: END IF
243: IF (INFO.NE.0) THEN
244: CALL XERBLA('DTBMV ',INFO)
245: RETURN
246: END IF
247: *
248: * Quick return if possible.
249: *
250: IF (N.EQ.0) RETURN
251: *
252: NOUNIT = LSAME(DIAG,'N')
253: *
254: * Set up the start point in X if the increment is not unity. This
255: * will be ( N - 1 )*INCX too small for descending loops.
256: *
257: IF (INCX.LE.0) THEN
258: KX = 1 - (N-1)*INCX
259: ELSE IF (INCX.NE.1) THEN
260: KX = 1
261: END IF
262: *
263: * Start the operations. In this version the elements of A are
264: * accessed sequentially with one pass through A.
265: *
266: IF (LSAME(TRANS,'N')) THEN
267: *
268: * Form x := A*x.
269: *
270: IF (LSAME(UPLO,'U')) THEN
271: KPLUS1 = K + 1
272: IF (INCX.EQ.1) THEN
273: DO 20 J = 1,N
274: IF (X(J).NE.ZERO) THEN
275: TEMP = X(J)
276: L = KPLUS1 - J
277: DO 10 I = MAX(1,J-K),J - 1
278: X(I) = X(I) + TEMP*A(L+I,J)
279: 10 CONTINUE
280: IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
281: END IF
282: 20 CONTINUE
283: ELSE
284: JX = KX
285: DO 40 J = 1,N
286: IF (X(JX).NE.ZERO) THEN
287: TEMP = X(JX)
288: IX = KX
289: L = KPLUS1 - J
290: DO 30 I = MAX(1,J-K),J - 1
291: X(IX) = X(IX) + TEMP*A(L+I,J)
292: IX = IX + INCX
293: 30 CONTINUE
294: IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
295: END IF
296: JX = JX + INCX
297: IF (J.GT.K) KX = KX + INCX
298: 40 CONTINUE
299: END IF
300: ELSE
301: IF (INCX.EQ.1) THEN
302: DO 60 J = N,1,-1
303: IF (X(J).NE.ZERO) THEN
304: TEMP = X(J)
305: L = 1 - J
306: DO 50 I = MIN(N,J+K),J + 1,-1
307: X(I) = X(I) + TEMP*A(L+I,J)
308: 50 CONTINUE
309: IF (NOUNIT) X(J) = X(J)*A(1,J)
310: END IF
311: 60 CONTINUE
312: ELSE
313: KX = KX + (N-1)*INCX
314: JX = KX
315: DO 80 J = N,1,-1
316: IF (X(JX).NE.ZERO) THEN
317: TEMP = X(JX)
318: IX = KX
319: L = 1 - J
320: DO 70 I = MIN(N,J+K),J + 1,-1
321: X(IX) = X(IX) + TEMP*A(L+I,J)
322: IX = IX - INCX
323: 70 CONTINUE
324: IF (NOUNIT) X(JX) = X(JX)*A(1,J)
325: END IF
326: JX = JX - INCX
327: IF ((N-J).GE.K) KX = KX - INCX
328: 80 CONTINUE
329: END IF
330: END IF
331: ELSE
332: *
333: * Form x := A**T*x.
334: *
335: IF (LSAME(UPLO,'U')) THEN
336: KPLUS1 = K + 1
337: IF (INCX.EQ.1) THEN
338: DO 100 J = N,1,-1
339: TEMP = X(J)
340: L = KPLUS1 - J
341: IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
342: DO 90 I = J - 1,MAX(1,J-K),-1
343: TEMP = TEMP + A(L+I,J)*X(I)
344: 90 CONTINUE
345: X(J) = TEMP
346: 100 CONTINUE
347: ELSE
348: KX = KX + (N-1)*INCX
349: JX = KX
350: DO 120 J = N,1,-1
351: TEMP = X(JX)
352: KX = KX - INCX
353: IX = KX
354: L = KPLUS1 - J
355: IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
356: DO 110 I = J - 1,MAX(1,J-K),-1
357: TEMP = TEMP + A(L+I,J)*X(IX)
358: IX = IX - INCX
359: 110 CONTINUE
360: X(JX) = TEMP
361: JX = JX - INCX
362: 120 CONTINUE
363: END IF
364: ELSE
365: IF (INCX.EQ.1) THEN
366: DO 140 J = 1,N
367: TEMP = X(J)
368: L = 1 - J
369: IF (NOUNIT) TEMP = TEMP*A(1,J)
370: DO 130 I = J + 1,MIN(N,J+K)
371: TEMP = TEMP + A(L+I,J)*X(I)
372: 130 CONTINUE
373: X(J) = TEMP
374: 140 CONTINUE
375: ELSE
376: JX = KX
377: DO 160 J = 1,N
378: TEMP = X(JX)
379: KX = KX + INCX
380: IX = KX
381: L = 1 - J
382: IF (NOUNIT) TEMP = TEMP*A(1,J)
383: DO 150 I = J + 1,MIN(N,J+K)
384: TEMP = TEMP + A(L+I,J)*X(IX)
385: IX = IX + INCX
386: 150 CONTINUE
387: X(JX) = TEMP
388: JX = JX + INCX
389: 160 CONTINUE
390: END IF
391: END IF
392: END IF
393: *
394: RETURN
395: *
396: * End of DTBMV .
397: *
398: END
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