source: pacpussensors/trunk/Vislab/lib3dv/eigen/blas/ztbmv.f@ 138

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1 SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
2* .. Scalar Arguments ..
3 INTEGER INCX,K,LDA,N
4 CHARACTER DIAG,TRANS,UPLO
5* ..
6* .. Array Arguments ..
7 DOUBLE COMPLEX A(LDA,*),X(*)
8* ..
9*
10* Purpose
11* =======
12*
13* ZTBMV performs one of the matrix-vector operations
14*
15* x := A*x, or x := A'*x, or x := conjg( A' )*x,
16*
17* where x is an n element vector and A is an n by n unit, or non-unit,
18* upper or lower triangular band matrix, with ( k + 1 ) diagonals.
19*
20* Arguments
21* ==========
22*
23* UPLO - CHARACTER*1.
24* On entry, UPLO specifies whether the matrix is an upper or
25* lower triangular matrix as follows:
26*
27* UPLO = 'U' or 'u' A is an upper triangular matrix.
28*
29* UPLO = 'L' or 'l' A is a lower triangular matrix.
30*
31* Unchanged on exit.
32*
33* TRANS - CHARACTER*1.
34* On entry, TRANS specifies the operation to be performed as
35* follows:
36*
37* TRANS = 'N' or 'n' x := A*x.
38*
39* TRANS = 'T' or 't' x := A'*x.
40*
41* TRANS = 'C' or 'c' x := conjg( A' )*x.
42*
43* Unchanged on exit.
44*
45* DIAG - CHARACTER*1.
46* On entry, DIAG specifies whether or not A is unit
47* triangular as follows:
48*
49* DIAG = 'U' or 'u' A is assumed to be unit triangular.
50*
51* DIAG = 'N' or 'n' A is not assumed to be unit
52* triangular.
53*
54* Unchanged on exit.
55*
56* N - INTEGER.
57* On entry, N specifies the order of the matrix A.
58* N must be at least zero.
59* Unchanged on exit.
60*
61* K - INTEGER.
62* On entry with UPLO = 'U' or 'u', K specifies the number of
63* super-diagonals of the matrix A.
64* On entry with UPLO = 'L' or 'l', K specifies the number of
65* sub-diagonals of the matrix A.
66* K must satisfy 0 .le. K.
67* Unchanged on exit.
68*
69* A - COMPLEX*16 array of DIMENSION ( LDA, n ).
70* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
71* by n part of the array A must contain the upper triangular
72* band part of the matrix of coefficients, supplied column by
73* column, with the leading diagonal of the matrix in row
74* ( k + 1 ) of the array, the first super-diagonal starting at
75* position 2 in row k, and so on. The top left k by k triangle
76* of the array A is not referenced.
77* The following program segment will transfer an upper
78* triangular band matrix from conventional full matrix storage
79* to band storage:
80*
81* DO 20, J = 1, N
82* M = K + 1 - J
83* DO 10, I = MAX( 1, J - K ), J
84* A( M + I, J ) = matrix( I, J )
85* 10 CONTINUE
86* 20 CONTINUE
87*
88* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
89* by n part of the array A must contain the lower triangular
90* band part of the matrix of coefficients, supplied column by
91* column, with the leading diagonal of the matrix in row 1 of
92* the array, the first sub-diagonal starting at position 1 in
93* row 2, and so on. The bottom right k by k triangle of the
94* array A is not referenced.
95* The following program segment will transfer a lower
96* triangular band matrix from conventional full matrix storage
97* to band storage:
98*
99* DO 20, J = 1, N
100* M = 1 - J
101* DO 10, I = J, MIN( N, J + K )
102* A( M + I, J ) = matrix( I, J )
103* 10 CONTINUE
104* 20 CONTINUE
105*
106* Note that when DIAG = 'U' or 'u' the elements of the array A
107* corresponding to the diagonal elements of the matrix are not
108* referenced, but are assumed to be unity.
109* Unchanged on exit.
110*
111* LDA - 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* ( k + 1 ).
115* Unchanged on exit.
116*
117* X - COMPLEX*16 array of dimension at least
118* ( 1 + ( n - 1 )*abs( INCX ) ).
119* Before entry, the incremented array X must contain the n
120* element vector x. On exit, X is overwritten with the
121* tranformed vector x.
122*
123* INCX - INTEGER.
124* On entry, INCX specifies the increment for the elements of
125* X. INCX must not be zero.
126* Unchanged on exit.
127*
128* Further Details
129* ===============
130*
131* Level 2 Blas routine.
132*
133* -- Written on 22-October-1986.
134* Jack Dongarra, Argonne National Lab.
135* Jeremy Du Croz, Nag Central Office.
136* Sven Hammarling, Nag Central Office.
137* Richard Hanson, Sandia National Labs.
138*
139* =====================================================================
140*
141* .. Parameters ..
142 DOUBLE COMPLEX ZERO
143 PARAMETER (ZERO= (0.0D+0,0.0D+0))
144* ..
145* .. Local Scalars ..
146 DOUBLE COMPLEX TEMP
147 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
148 LOGICAL NOCONJ,NOUNIT
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 EXTERNAL LSAME
153* ..
154* .. External Subroutines ..
155 EXTERNAL XERBLA
156* ..
157* .. Intrinsic Functions ..
158 INTRINSIC DCONJG,MAX,MIN
159* ..
160*
161* Test the input parameters.
162*
163 INFO = 0
164 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
165 INFO = 1
166 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
167 + .NOT.LSAME(TRANS,'C')) THEN
168 INFO = 2
169 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
170 INFO = 3
171 ELSE IF (N.LT.0) THEN
172 INFO = 4
173 ELSE IF (K.LT.0) THEN
174 INFO = 5
175 ELSE IF (LDA.LT. (K+1)) THEN
176 INFO = 7
177 ELSE IF (INCX.EQ.0) THEN
178 INFO = 9
179 END IF
180 IF (INFO.NE.0) THEN
181 CALL XERBLA('ZTBMV ',INFO)
182 RETURN
183 END IF
184*
185* Quick return if possible.
186*
187 IF (N.EQ.0) RETURN
188*
189 NOCONJ = LSAME(TRANS,'T')
190 NOUNIT = LSAME(DIAG,'N')
191*
192* Set up the start point in X if the increment is not unity. This
193* will be ( N - 1 )*INCX too small for descending loops.
194*
195 IF (INCX.LE.0) THEN
196 KX = 1 - (N-1)*INCX
197 ELSE IF (INCX.NE.1) THEN
198 KX = 1
199 END IF
200*
201* Start the operations. In this version the elements of A are
202* accessed sequentially with one pass through A.
203*
204 IF (LSAME(TRANS,'N')) THEN
205*
206* Form x := A*x.
207*
208 IF (LSAME(UPLO,'U')) THEN
209 KPLUS1 = K + 1
210 IF (INCX.EQ.1) THEN
211 DO 20 J = 1,N
212 IF (X(J).NE.ZERO) THEN
213 TEMP = X(J)
214 L = KPLUS1 - J
215 DO 10 I = MAX(1,J-K),J - 1
216 X(I) = X(I) + TEMP*A(L+I,J)
217 10 CONTINUE
218 IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
219 END IF
220 20 CONTINUE
221 ELSE
222 JX = KX
223 DO 40 J = 1,N
224 IF (X(JX).NE.ZERO) THEN
225 TEMP = X(JX)
226 IX = KX
227 L = KPLUS1 - J
228 DO 30 I = MAX(1,J-K),J - 1
229 X(IX) = X(IX) + TEMP*A(L+I,J)
230 IX = IX + INCX
231 30 CONTINUE
232 IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
233 END IF
234 JX = JX + INCX
235 IF (J.GT.K) KX = KX + INCX
236 40 CONTINUE
237 END IF
238 ELSE
239 IF (INCX.EQ.1) THEN
240 DO 60 J = N,1,-1
241 IF (X(J).NE.ZERO) THEN
242 TEMP = X(J)
243 L = 1 - J
244 DO 50 I = MIN(N,J+K),J + 1,-1
245 X(I) = X(I) + TEMP*A(L+I,J)
246 50 CONTINUE
247 IF (NOUNIT) X(J) = X(J)*A(1,J)
248 END IF
249 60 CONTINUE
250 ELSE
251 KX = KX + (N-1)*INCX
252 JX = KX
253 DO 80 J = N,1,-1
254 IF (X(JX).NE.ZERO) THEN
255 TEMP = X(JX)
256 IX = KX
257 L = 1 - J
258 DO 70 I = MIN(N,J+K),J + 1,-1
259 X(IX) = X(IX) + TEMP*A(L+I,J)
260 IX = IX - INCX
261 70 CONTINUE
262 IF (NOUNIT) X(JX) = X(JX)*A(1,J)
263 END IF
264 JX = JX - INCX
265 IF ((N-J).GE.K) KX = KX - INCX
266 80 CONTINUE
267 END IF
268 END IF
269 ELSE
270*
271* Form x := A'*x or x := conjg( A' )*x.
272*
273 IF (LSAME(UPLO,'U')) THEN
274 KPLUS1 = K + 1
275 IF (INCX.EQ.1) THEN
276 DO 110 J = N,1,-1
277 TEMP = X(J)
278 L = KPLUS1 - J
279 IF (NOCONJ) THEN
280 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
281 DO 90 I = J - 1,MAX(1,J-K),-1
282 TEMP = TEMP + A(L+I,J)*X(I)
283 90 CONTINUE
284 ELSE
285 IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J))
286 DO 100 I = J - 1,MAX(1,J-K),-1
287 TEMP = TEMP + DCONJG(A(L+I,J))*X(I)
288 100 CONTINUE
289 END IF
290 X(J) = TEMP
291 110 CONTINUE
292 ELSE
293 KX = KX + (N-1)*INCX
294 JX = KX
295 DO 140 J = N,1,-1
296 TEMP = X(JX)
297 KX = KX - INCX
298 IX = KX
299 L = KPLUS1 - J
300 IF (NOCONJ) THEN
301 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
302 DO 120 I = J - 1,MAX(1,J-K),-1
303 TEMP = TEMP + A(L+I,J)*X(IX)
304 IX = IX - INCX
305 120 CONTINUE
306 ELSE
307 IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J))
308 DO 130 I = J - 1,MAX(1,J-K),-1
309 TEMP = TEMP + DCONJG(A(L+I,J))*X(IX)
310 IX = IX - INCX
311 130 CONTINUE
312 END IF
313 X(JX) = TEMP
314 JX = JX - INCX
315 140 CONTINUE
316 END IF
317 ELSE
318 IF (INCX.EQ.1) THEN
319 DO 170 J = 1,N
320 TEMP = X(J)
321 L = 1 - J
322 IF (NOCONJ) THEN
323 IF (NOUNIT) TEMP = TEMP*A(1,J)
324 DO 150 I = J + 1,MIN(N,J+K)
325 TEMP = TEMP + A(L+I,J)*X(I)
326 150 CONTINUE
327 ELSE
328 IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J))
329 DO 160 I = J + 1,MIN(N,J+K)
330 TEMP = TEMP + DCONJG(A(L+I,J))*X(I)
331 160 CONTINUE
332 END IF
333 X(J) = TEMP
334 170 CONTINUE
335 ELSE
336 JX = KX
337 DO 200 J = 1,N
338 TEMP = X(JX)
339 KX = KX + INCX
340 IX = KX
341 L = 1 - J
342 IF (NOCONJ) THEN
343 IF (NOUNIT) TEMP = TEMP*A(1,J)
344 DO 180 I = J + 1,MIN(N,J+K)
345 TEMP = TEMP + A(L+I,J)*X(IX)
346 IX = IX + INCX
347 180 CONTINUE
348 ELSE
349 IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J))
350 DO 190 I = J + 1,MIN(N,J+K)
351 TEMP = TEMP + DCONJG(A(L+I,J))*X(IX)
352 IX = IX + INCX
353 190 CONTINUE
354 END IF
355 X(JX) = TEMP
356 JX = JX + INCX
357 200 CONTINUE
358 END IF
359 END IF
360 END IF
361*
362 RETURN
363*
364* End of ZTBMV .
365*
366 END
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