LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ztbsv.f
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1 *> \brief \b ZTBSV
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 ZTBSV(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 * COMPLEX*16 A(LDA,*),X(*)
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> ZTBSV solves one of the systems of equations
28 *>
29 *> A*x = b, or A**T*x = b, or A**H*x = b,
30 *>
31 *> where b and x are n element vectors and A is an n by n unit, or
32 *> non-unit, upper or lower triangular band matrix, with ( k + 1 )
33 *> diagonals.
34 *>
35 *> No test for singularity or near-singularity is included in this
36 *> routine. Such tests must be performed before calling this routine.
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] UPLO
43 *> \verbatim
44 *> UPLO is CHARACTER*1
45 *> On entry, UPLO specifies whether the matrix is an upper or
46 *> lower triangular matrix as follows:
47 *>
48 *> UPLO = 'U' or 'u' A is an upper triangular matrix.
49 *>
50 *> UPLO = 'L' or 'l' A is a lower triangular matrix.
51 *> \endverbatim
52 *>
53 *> \param[in] TRANS
54 *> \verbatim
55 *> TRANS is CHARACTER*1
56 *> On entry, TRANS specifies the equations to be solved as
57 *> follows:
58 *>
59 *> TRANS = 'N' or 'n' A*x = b.
60 *>
61 *> TRANS = 'T' or 't' A**T*x = b.
62 *>
63 *> TRANS = 'C' or 'c' A**H*x = b.
64 *> \endverbatim
65 *>
66 *> \param[in] DIAG
67 *> \verbatim
68 *> DIAG is CHARACTER*1
69 *> On entry, DIAG specifies whether or not A is unit
70 *> triangular as follows:
71 *>
72 *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
73 *>
74 *> DIAG = 'N' or 'n' A is not assumed to be unit
75 *> triangular.
76 *> \endverbatim
77 *>
78 *> \param[in] N
79 *> \verbatim
80 *> N is INTEGER
81 *> On entry, N specifies the order of the matrix A.
82 *> N must be at least zero.
83 *> \endverbatim
84 *>
85 *> \param[in] K
86 *> \verbatim
87 *> K is INTEGER
88 *> On entry with UPLO = 'U' or 'u', K specifies the number of
89 *> super-diagonals of the matrix A.
90 *> On entry with UPLO = 'L' or 'l', K specifies the number of
91 *> sub-diagonals of the matrix A.
92 *> K must satisfy 0 .le. K.
93 *> \endverbatim
94 *>
95 *> \param[in] A
96 *> \verbatim
97 *> A is COMPLEX*16 array, dimension ( LDA, N )
98 *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
99 *> by n part of the array A must contain the upper triangular
100 *> band part of the matrix of coefficients, supplied column by
101 *> column, with the leading diagonal of the matrix in row
102 *> ( k + 1 ) of the array, the first super-diagonal starting at
103 *> position 2 in row k, and so on. The top left k by k triangle
104 *> of the array A is not referenced.
105 *> The following program segment will transfer an upper
106 *> triangular band matrix from conventional full matrix storage
107 *> to band storage:
108 *>
109 *> DO 20, J = 1, N
110 *> M = K + 1 - J
111 *> DO 10, I = MAX( 1, J - K ), J
112 *> A( M + I, J ) = matrix( I, J )
113 *> 10 CONTINUE
114 *> 20 CONTINUE
115 *>
116 *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
117 *> by n part of the array A must contain the lower triangular
118 *> band part of the matrix of coefficients, supplied column by
119 *> column, with the leading diagonal of the matrix in row 1 of
120 *> the array, the first sub-diagonal starting at position 1 in
121 *> row 2, and so on. The bottom right k by k triangle of the
122 *> array A is not referenced.
123 *> The following program segment will transfer a lower
124 *> triangular band matrix from conventional full matrix storage
125 *> to band storage:
126 *>
127 *> DO 20, J = 1, N
128 *> M = 1 - J
129 *> DO 10, I = J, MIN( N, J + K )
130 *> A( M + I, J ) = matrix( I, J )
131 *> 10 CONTINUE
132 *> 20 CONTINUE
133 *>
134 *> Note that when DIAG = 'U' or 'u' the elements of the array A
135 *> corresponding to the diagonal elements of the matrix are not
136 *> referenced, but are assumed to be unity.
137 *> \endverbatim
138 *>
139 *> \param[in] LDA
140 *> \verbatim
141 *> LDA is INTEGER
142 *> On entry, LDA specifies the first dimension of A as declared
143 *> in the calling (sub) program. LDA must be at least
144 *> ( k + 1 ).
145 *> \endverbatim
146 *>
147 *> \param[in,out] X
148 *> \verbatim
149 *> X is COMPLEX*16 array, dimension at least
150 *> ( 1 + ( n - 1 )*abs( INCX ) ).
151 *> Before entry, the incremented array X must contain the n
152 *> element right-hand side vector b. On exit, X is overwritten
153 *> with the solution vector x.
154 *> \endverbatim
155 *>
156 *> \param[in] INCX
157 *> \verbatim
158 *> INCX is INTEGER
159 *> On entry, INCX specifies the increment for the elements of
160 *> X. INCX must not be zero.
161 *> \endverbatim
162 *
163 * Authors:
164 * ========
165 *
166 *> \author Univ. of Tennessee
167 *> \author Univ. of California Berkeley
168 *> \author Univ. of Colorado Denver
169 *> \author NAG Ltd.
170 *
171 *> \ingroup complex16_blas_level2
172 *
173 *> \par Further Details:
174 * =====================
175 *>
176 *> \verbatim
177 *>
178 *> Level 2 Blas routine.
179 *>
180 *> -- Written on 22-October-1986.
181 *> Jack Dongarra, Argonne National Lab.
182 *> Jeremy Du Croz, Nag Central Office.
183 *> Sven Hammarling, Nag Central Office.
184 *> Richard Hanson, Sandia National Labs.
185 *> \endverbatim
186 *>
187 * =====================================================================
188  SUBROUTINE ztbsv(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
189 *
190 * -- Reference BLAS level2 routine --
191 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193 *
194 * .. Scalar Arguments ..
195  INTEGER INCX,K,LDA,N
196  CHARACTER DIAG,TRANS,UPLO
197 * ..
198 * .. Array Arguments ..
199  COMPLEX*16 A(LDA,*),X(*)
200 * ..
201 *
202 * =====================================================================
203 *
204 * .. Parameters ..
205  COMPLEX*16 ZERO
206  parameter(zero= (0.0d+0,0.0d+0))
207 * ..
208 * .. Local Scalars ..
209  COMPLEX*16 TEMP
210  INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
211  LOGICAL NOCONJ,NOUNIT
212 * ..
213 * .. External Functions ..
214  LOGICAL LSAME
215  EXTERNAL lsame
216 * ..
217 * .. External Subroutines ..
218  EXTERNAL xerbla
219 * ..
220 * .. Intrinsic Functions ..
221  INTRINSIC dconjg,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('ZTBSV ',info)
245  RETURN
246  END IF
247 *
248 * Quick return if possible.
249 *
250  IF (n.EQ.0) RETURN
251 *
252  noconj = lsame(trans,'T')
253  nounit = lsame(diag,'N')
254 *
255 * Set up the start point in X if the increment is not unity. This
256 * will be ( N - 1 )*INCX too small for descending loops.
257 *
258  IF (incx.LE.0) THEN
259  kx = 1 - (n-1)*incx
260  ELSE IF (incx.NE.1) THEN
261  kx = 1
262  END IF
263 *
264 * Start the operations. In this version the elements of A are
265 * accessed by sequentially with one pass through A.
266 *
267  IF (lsame(trans,'N')) THEN
268 *
269 * Form x := inv( A )*x.
270 *
271  IF (lsame(uplo,'U')) THEN
272  kplus1 = k + 1
273  IF (incx.EQ.1) THEN
274  DO 20 j = n,1,-1
275  IF (x(j).NE.zero) THEN
276  l = kplus1 - j
277  IF (nounit) x(j) = x(j)/a(kplus1,j)
278  temp = x(j)
279  DO 10 i = j - 1,max(1,j-k),-1
280  x(i) = x(i) - temp*a(l+i,j)
281  10 CONTINUE
282  END IF
283  20 CONTINUE
284  ELSE
285  kx = kx + (n-1)*incx
286  jx = kx
287  DO 40 j = n,1,-1
288  kx = kx - incx
289  IF (x(jx).NE.zero) THEN
290  ix = kx
291  l = kplus1 - j
292  IF (nounit) x(jx) = x(jx)/a(kplus1,j)
293  temp = x(jx)
294  DO 30 i = j - 1,max(1,j-k),-1
295  x(ix) = x(ix) - temp*a(l+i,j)
296  ix = ix - incx
297  30 CONTINUE
298  END IF
299  jx = jx - incx
300  40 CONTINUE
301  END IF
302  ELSE
303  IF (incx.EQ.1) THEN
304  DO 60 j = 1,n
305  IF (x(j).NE.zero) THEN
306  l = 1 - j
307  IF (nounit) x(j) = x(j)/a(1,j)
308  temp = x(j)
309  DO 50 i = j + 1,min(n,j+k)
310  x(i) = x(i) - temp*a(l+i,j)
311  50 CONTINUE
312  END IF
313  60 CONTINUE
314  ELSE
315  jx = kx
316  DO 80 j = 1,n
317  kx = kx + incx
318  IF (x(jx).NE.zero) THEN
319  ix = kx
320  l = 1 - j
321  IF (nounit) x(jx) = x(jx)/a(1,j)
322  temp = x(jx)
323  DO 70 i = j + 1,min(n,j+k)
324  x(ix) = x(ix) - temp*a(l+i,j)
325  ix = ix + incx
326  70 CONTINUE
327  END IF
328  jx = jx + incx
329  80 CONTINUE
330  END IF
331  END IF
332  ELSE
333 *
334 * Form x := inv( A**T )*x or x := inv( A**H )*x.
335 *
336  IF (lsame(uplo,'U')) THEN
337  kplus1 = k + 1
338  IF (incx.EQ.1) THEN
339  DO 110 j = 1,n
340  temp = x(j)
341  l = kplus1 - j
342  IF (noconj) THEN
343  DO 90 i = max(1,j-k),j - 1
344  temp = temp - a(l+i,j)*x(i)
345  90 CONTINUE
346  IF (nounit) temp = temp/a(kplus1,j)
347  ELSE
348  DO 100 i = max(1,j-k),j - 1
349  temp = temp - dconjg(a(l+i,j))*x(i)
350  100 CONTINUE
351  IF (nounit) temp = temp/dconjg(a(kplus1,j))
352  END IF
353  x(j) = temp
354  110 CONTINUE
355  ELSE
356  jx = kx
357  DO 140 j = 1,n
358  temp = x(jx)
359  ix = kx
360  l = kplus1 - j
361  IF (noconj) THEN
362  DO 120 i = max(1,j-k),j - 1
363  temp = temp - a(l+i,j)*x(ix)
364  ix = ix + incx
365  120 CONTINUE
366  IF (nounit) temp = temp/a(kplus1,j)
367  ELSE
368  DO 130 i = max(1,j-k),j - 1
369  temp = temp - dconjg(a(l+i,j))*x(ix)
370  ix = ix + incx
371  130 CONTINUE
372  IF (nounit) temp = temp/dconjg(a(kplus1,j))
373  END IF
374  x(jx) = temp
375  jx = jx + incx
376  IF (j.GT.k) kx = kx + incx
377  140 CONTINUE
378  END IF
379  ELSE
380  IF (incx.EQ.1) THEN
381  DO 170 j = n,1,-1
382  temp = x(j)
383  l = 1 - j
384  IF (noconj) THEN
385  DO 150 i = min(n,j+k),j + 1,-1
386  temp = temp - a(l+i,j)*x(i)
387  150 CONTINUE
388  IF (nounit) temp = temp/a(1,j)
389  ELSE
390  DO 160 i = min(n,j+k),j + 1,-1
391  temp = temp - dconjg(a(l+i,j))*x(i)
392  160 CONTINUE
393  IF (nounit) temp = temp/dconjg(a(1,j))
394  END IF
395  x(j) = temp
396  170 CONTINUE
397  ELSE
398  kx = kx + (n-1)*incx
399  jx = kx
400  DO 200 j = n,1,-1
401  temp = x(jx)
402  ix = kx
403  l = 1 - j
404  IF (noconj) THEN
405  DO 180 i = min(n,j+k),j + 1,-1
406  temp = temp - a(l+i,j)*x(ix)
407  ix = ix - incx
408  180 CONTINUE
409  IF (nounit) temp = temp/a(1,j)
410  ELSE
411  DO 190 i = min(n,j+k),j + 1,-1
412  temp = temp - dconjg(a(l+i,j))*x(ix)
413  ix = ix - incx
414  190 CONTINUE
415  IF (nounit) temp = temp/dconjg(a(1,j))
416  END IF
417  x(jx) = temp
418  jx = jx - incx
419  IF ((n-j).GE.k) kx = kx - incx
420  200 CONTINUE
421  END IF
422  END IF
423  END IF
424 *
425  RETURN
426 *
427 * End of ZTBSV
428 *
429  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBSV
Definition: ztbsv.f:189