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, 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, 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: *> transformed 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: *> \ingroup double_blas_level2
168: *
169: *> \par Further Details:
170: * =====================
171: *>
172: *> \verbatim
173: *>
174: *> Level 2 Blas routine.
175: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
176: *>
177: *> -- Written on 22-October-1986.
178: *> Jack Dongarra, Argonne National Lab.
179: *> Jeremy Du Croz, Nag Central Office.
180: *> Sven Hammarling, Nag Central Office.
181: *> Richard Hanson, Sandia National Labs.
182: *> \endverbatim
183: *>
184: * =====================================================================
185: SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
186: *
187: * -- Reference BLAS level2 routine --
188: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
189: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190: *
191: * .. Scalar Arguments ..
192: INTEGER INCX,K,LDA,N
193: CHARACTER DIAG,TRANS,UPLO
194: * ..
195: * .. Array Arguments ..
196: DOUBLE PRECISION A(LDA,*),X(*)
197: * ..
198: *
199: * =====================================================================
200: *
201: * .. Parameters ..
202: DOUBLE PRECISION ZERO
203: PARAMETER (ZERO=0.0D+0)
204: * ..
205: * .. Local Scalars ..
206: DOUBLE PRECISION TEMP
207: INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
208: LOGICAL NOUNIT
209: * ..
210: * .. External Functions ..
211: LOGICAL LSAME
212: EXTERNAL LSAME
213: * ..
214: * .. External Subroutines ..
215: EXTERNAL XERBLA
216: * ..
217: * .. Intrinsic Functions ..
218: INTRINSIC MAX,MIN
219: * ..
220: *
221: * Test the input parameters.
222: *
223: INFO = 0
224: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
225: INFO = 1
226: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
227: + .NOT.LSAME(TRANS,'C')) THEN
228: INFO = 2
229: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
230: INFO = 3
231: ELSE IF (N.LT.0) THEN
232: INFO = 4
233: ELSE IF (K.LT.0) THEN
234: INFO = 5
235: ELSE IF (LDA.LT. (K+1)) THEN
236: INFO = 7
237: ELSE IF (INCX.EQ.0) THEN
238: INFO = 9
239: END IF
240: IF (INFO.NE.0) THEN
241: CALL XERBLA('DTBMV ',INFO)
242: RETURN
243: END IF
244: *
245: * Quick return if possible.
246: *
247: IF (N.EQ.0) RETURN
248: *
249: NOUNIT = LSAME(DIAG,'N')
250: *
251: * Set up the start point in X if the increment is not unity. This
252: * will be ( N - 1 )*INCX too small for descending loops.
253: *
254: IF (INCX.LE.0) THEN
255: KX = 1 - (N-1)*INCX
256: ELSE IF (INCX.NE.1) THEN
257: KX = 1
258: END IF
259: *
260: * Start the operations. In this version the elements of A are
261: * accessed sequentially with one pass through A.
262: *
263: IF (LSAME(TRANS,'N')) THEN
264: *
265: * Form x := A*x.
266: *
267: IF (LSAME(UPLO,'U')) THEN
268: KPLUS1 = K + 1
269: IF (INCX.EQ.1) THEN
270: DO 20 J = 1,N
271: IF (X(J).NE.ZERO) THEN
272: TEMP = X(J)
273: L = KPLUS1 - J
274: DO 10 I = MAX(1,J-K),J - 1
275: X(I) = X(I) + TEMP*A(L+I,J)
276: 10 CONTINUE
277: IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
278: END IF
279: 20 CONTINUE
280: ELSE
281: JX = KX
282: DO 40 J = 1,N
283: IF (X(JX).NE.ZERO) THEN
284: TEMP = X(JX)
285: IX = KX
286: L = KPLUS1 - J
287: DO 30 I = MAX(1,J-K),J - 1
288: X(IX) = X(IX) + TEMP*A(L+I,J)
289: IX = IX + INCX
290: 30 CONTINUE
291: IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
292: END IF
293: JX = JX + INCX
294: IF (J.GT.K) KX = KX + INCX
295: 40 CONTINUE
296: END IF
297: ELSE
298: IF (INCX.EQ.1) THEN
299: DO 60 J = N,1,-1
300: IF (X(J).NE.ZERO) THEN
301: TEMP = X(J)
302: L = 1 - J
303: DO 50 I = MIN(N,J+K),J + 1,-1
304: X(I) = X(I) + TEMP*A(L+I,J)
305: 50 CONTINUE
306: IF (NOUNIT) X(J) = X(J)*A(1,J)
307: END IF
308: 60 CONTINUE
309: ELSE
310: KX = KX + (N-1)*INCX
311: JX = KX
312: DO 80 J = N,1,-1
313: IF (X(JX).NE.ZERO) THEN
314: TEMP = X(JX)
315: IX = KX
316: L = 1 - J
317: DO 70 I = MIN(N,J+K),J + 1,-1
318: X(IX) = X(IX) + TEMP*A(L+I,J)
319: IX = IX - INCX
320: 70 CONTINUE
321: IF (NOUNIT) X(JX) = X(JX)*A(1,J)
322: END IF
323: JX = JX - INCX
324: IF ((N-J).GE.K) KX = KX - INCX
325: 80 CONTINUE
326: END IF
327: END IF
328: ELSE
329: *
330: * Form x := A**T*x.
331: *
332: IF (LSAME(UPLO,'U')) THEN
333: KPLUS1 = K + 1
334: IF (INCX.EQ.1) THEN
335: DO 100 J = N,1,-1
336: TEMP = X(J)
337: L = KPLUS1 - J
338: IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
339: DO 90 I = J - 1,MAX(1,J-K),-1
340: TEMP = TEMP + A(L+I,J)*X(I)
341: 90 CONTINUE
342: X(J) = TEMP
343: 100 CONTINUE
344: ELSE
345: KX = KX + (N-1)*INCX
346: JX = KX
347: DO 120 J = N,1,-1
348: TEMP = X(JX)
349: KX = KX - INCX
350: IX = KX
351: L = KPLUS1 - J
352: IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
353: DO 110 I = J - 1,MAX(1,J-K),-1
354: TEMP = TEMP + A(L+I,J)*X(IX)
355: IX = IX - INCX
356: 110 CONTINUE
357: X(JX) = TEMP
358: JX = JX - INCX
359: 120 CONTINUE
360: END IF
361: ELSE
362: IF (INCX.EQ.1) THEN
363: DO 140 J = 1,N
364: TEMP = X(J)
365: L = 1 - J
366: IF (NOUNIT) TEMP = TEMP*A(1,J)
367: DO 130 I = J + 1,MIN(N,J+K)
368: TEMP = TEMP + A(L+I,J)*X(I)
369: 130 CONTINUE
370: X(J) = TEMP
371: 140 CONTINUE
372: ELSE
373: JX = KX
374: DO 160 J = 1,N
375: TEMP = X(JX)
376: KX = KX + INCX
377: IX = KX
378: L = 1 - J
379: IF (NOUNIT) TEMP = TEMP*A(1,J)
380: DO 150 I = J + 1,MIN(N,J+K)
381: TEMP = TEMP + A(L+I,J)*X(IX)
382: IX = IX + INCX
383: 150 CONTINUE
384: X(JX) = TEMP
385: JX = JX + INCX
386: 160 CONTINUE
387: END IF
388: END IF
389: END IF
390: *
391: RETURN
392: *
393: * End of DTBMV
394: *
395: END
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