LAPACK  3.9.1
LAPACK: Linear Algebra PACKage
ztrsv.f
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1 *> \brief \b ZTRSV
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 ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
12 *
13 * .. Scalar Arguments ..
14 * INTEGER INCX,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 *> ZTRSV 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 matrix.
33 *>
34 *> No test for singularity or near-singularity is included in this
35 *> routine. Such tests must be performed before calling this routine.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] UPLO
42 *> \verbatim
43 *> UPLO is CHARACTER*1
44 *> On entry, UPLO specifies whether the matrix is an upper or
45 *> lower triangular matrix as follows:
46 *>
47 *> UPLO = 'U' or 'u' A is an upper triangular matrix.
48 *>
49 *> UPLO = 'L' or 'l' A is a lower triangular matrix.
50 *> \endverbatim
51 *>
52 *> \param[in] TRANS
53 *> \verbatim
54 *> TRANS is CHARACTER*1
55 *> On entry, TRANS specifies the equations to be solved as
56 *> follows:
57 *>
58 *> TRANS = 'N' or 'n' A*x = b.
59 *>
60 *> TRANS = 'T' or 't' A**T*x = b.
61 *>
62 *> TRANS = 'C' or 'c' A**H*x = b.
63 *> \endverbatim
64 *>
65 *> \param[in] DIAG
66 *> \verbatim
67 *> DIAG is CHARACTER*1
68 *> On entry, DIAG specifies whether or not A is unit
69 *> triangular as follows:
70 *>
71 *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
72 *>
73 *> DIAG = 'N' or 'n' A is not assumed to be unit
74 *> triangular.
75 *> \endverbatim
76 *>
77 *> \param[in] N
78 *> \verbatim
79 *> N is INTEGER
80 *> On entry, N specifies the order of the matrix A.
81 *> N must be at least zero.
82 *> \endverbatim
83 *>
84 *> \param[in] A
85 *> \verbatim
86 *> A is COMPLEX*16 array, dimension ( LDA, N )
87 *> Before entry with UPLO = 'U' or 'u', the leading n by n
88 *> upper triangular part of the array A must contain the upper
89 *> triangular matrix and the strictly lower triangular part of
90 *> A is not referenced.
91 *> Before entry with UPLO = 'L' or 'l', the leading n by n
92 *> lower triangular part of the array A must contain the lower
93 *> triangular matrix and the strictly upper triangular part of
94 *> A is not referenced.
95 *> Note that when DIAG = 'U' or 'u', the diagonal elements of
96 *> A are not referenced either, but are assumed to be unity.
97 *> \endverbatim
98 *>
99 *> \param[in] LDA
100 *> \verbatim
101 *> LDA is INTEGER
102 *> On entry, LDA specifies the first dimension of A as declared
103 *> in the calling (sub) program. LDA must be at least
104 *> max( 1, n ).
105 *> \endverbatim
106 *>
107 *> \param[in,out] X
108 *> \verbatim
109 *> X is COMPLEX*16 array, dimension at least
110 *> ( 1 + ( n - 1 )*abs( INCX ) ).
111 *> Before entry, the incremented array X must contain the n
112 *> element right-hand side vector b. On exit, X is overwritten
113 *> with the solution vector x.
114 *> \endverbatim
115 *>
116 *> \param[in] INCX
117 *> \verbatim
118 *> INCX is INTEGER
119 *> On entry, INCX specifies the increment for the elements of
120 *> X. INCX must not be zero.
121 *> \endverbatim
122 *
123 * Authors:
124 * ========
125 *
126 *> \author Univ. of Tennessee
127 *> \author Univ. of California Berkeley
128 *> \author Univ. of Colorado Denver
129 *> \author NAG Ltd.
130 *
131 *> \ingroup complex16_blas_level2
132 *
133 *> \par Further Details:
134 * =====================
135 *>
136 *> \verbatim
137 *>
138 *> Level 2 Blas routine.
139 *>
140 *> -- Written on 22-October-1986.
141 *> Jack Dongarra, Argonne National Lab.
142 *> Jeremy Du Croz, Nag Central Office.
143 *> Sven Hammarling, Nag Central Office.
144 *> Richard Hanson, Sandia National Labs.
145 *> \endverbatim
146 *>
147 * =====================================================================
148  SUBROUTINE ztrsv(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
149 *
150 * -- Reference BLAS level2 routine --
151 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153 *
154 * .. Scalar Arguments ..
155  INTEGER INCX,LDA,N
156  CHARACTER DIAG,TRANS,UPLO
157 * ..
158 * .. Array Arguments ..
159  COMPLEX*16 A(LDA,*),X(*)
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  COMPLEX*16 ZERO
166  parameter(zero= (0.0d+0,0.0d+0))
167 * ..
168 * .. Local Scalars ..
169  COMPLEX*16 TEMP
170  INTEGER I,INFO,IX,J,JX,KX
171  LOGICAL NOCONJ,NOUNIT
172 * ..
173 * .. External Functions ..
174  LOGICAL LSAME
175  EXTERNAL lsame
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL xerbla
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC dconjg,max
182 * ..
183 *
184 * Test the input parameters.
185 *
186  info = 0
187  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
188  info = 1
189  ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
190  + .NOT.lsame(trans,'C')) THEN
191  info = 2
192  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
193  info = 3
194  ELSE IF (n.LT.0) THEN
195  info = 4
196  ELSE IF (lda.LT.max(1,n)) THEN
197  info = 6
198  ELSE IF (incx.EQ.0) THEN
199  info = 8
200  END IF
201  IF (info.NE.0) THEN
202  CALL xerbla('ZTRSV ',info)
203  RETURN
204  END IF
205 *
206 * Quick return if possible.
207 *
208  IF (n.EQ.0) RETURN
209 *
210  noconj = lsame(trans,'T')
211  nounit = lsame(diag,'N')
212 *
213 * Set up the start point in X if the increment is not unity. This
214 * will be ( N - 1 )*INCX too small for descending loops.
215 *
216  IF (incx.LE.0) THEN
217  kx = 1 - (n-1)*incx
218  ELSE IF (incx.NE.1) THEN
219  kx = 1
220  END IF
221 *
222 * Start the operations. In this version the elements of A are
223 * accessed sequentially with one pass through A.
224 *
225  IF (lsame(trans,'N')) THEN
226 *
227 * Form x := inv( A )*x.
228 *
229  IF (lsame(uplo,'U')) THEN
230  IF (incx.EQ.1) THEN
231  DO 20 j = n,1,-1
232  IF (x(j).NE.zero) THEN
233  IF (nounit) x(j) = x(j)/a(j,j)
234  temp = x(j)
235  DO 10 i = j - 1,1,-1
236  x(i) = x(i) - temp*a(i,j)
237  10 CONTINUE
238  END IF
239  20 CONTINUE
240  ELSE
241  jx = kx + (n-1)*incx
242  DO 40 j = n,1,-1
243  IF (x(jx).NE.zero) THEN
244  IF (nounit) x(jx) = x(jx)/a(j,j)
245  temp = x(jx)
246  ix = jx
247  DO 30 i = j - 1,1,-1
248  ix = ix - incx
249  x(ix) = x(ix) - temp*a(i,j)
250  30 CONTINUE
251  END IF
252  jx = jx - incx
253  40 CONTINUE
254  END IF
255  ELSE
256  IF (incx.EQ.1) THEN
257  DO 60 j = 1,n
258  IF (x(j).NE.zero) THEN
259  IF (nounit) x(j) = x(j)/a(j,j)
260  temp = x(j)
261  DO 50 i = j + 1,n
262  x(i) = x(i) - temp*a(i,j)
263  50 CONTINUE
264  END IF
265  60 CONTINUE
266  ELSE
267  jx = kx
268  DO 80 j = 1,n
269  IF (x(jx).NE.zero) THEN
270  IF (nounit) x(jx) = x(jx)/a(j,j)
271  temp = x(jx)
272  ix = jx
273  DO 70 i = j + 1,n
274  ix = ix + incx
275  x(ix) = x(ix) - temp*a(i,j)
276  70 CONTINUE
277  END IF
278  jx = jx + incx
279  80 CONTINUE
280  END IF
281  END IF
282  ELSE
283 *
284 * Form x := inv( A**T )*x or x := inv( A**H )*x.
285 *
286  IF (lsame(uplo,'U')) THEN
287  IF (incx.EQ.1) THEN
288  DO 110 j = 1,n
289  temp = x(j)
290  IF (noconj) THEN
291  DO 90 i = 1,j - 1
292  temp = temp - a(i,j)*x(i)
293  90 CONTINUE
294  IF (nounit) temp = temp/a(j,j)
295  ELSE
296  DO 100 i = 1,j - 1
297  temp = temp - dconjg(a(i,j))*x(i)
298  100 CONTINUE
299  IF (nounit) temp = temp/dconjg(a(j,j))
300  END IF
301  x(j) = temp
302  110 CONTINUE
303  ELSE
304  jx = kx
305  DO 140 j = 1,n
306  ix = kx
307  temp = x(jx)
308  IF (noconj) THEN
309  DO 120 i = 1,j - 1
310  temp = temp - a(i,j)*x(ix)
311  ix = ix + incx
312  120 CONTINUE
313  IF (nounit) temp = temp/a(j,j)
314  ELSE
315  DO 130 i = 1,j - 1
316  temp = temp - dconjg(a(i,j))*x(ix)
317  ix = ix + incx
318  130 CONTINUE
319  IF (nounit) temp = temp/dconjg(a(j,j))
320  END IF
321  x(jx) = temp
322  jx = jx + incx
323  140 CONTINUE
324  END IF
325  ELSE
326  IF (incx.EQ.1) THEN
327  DO 170 j = n,1,-1
328  temp = x(j)
329  IF (noconj) THEN
330  DO 150 i = n,j + 1,-1
331  temp = temp - a(i,j)*x(i)
332  150 CONTINUE
333  IF (nounit) temp = temp/a(j,j)
334  ELSE
335  DO 160 i = n,j + 1,-1
336  temp = temp - dconjg(a(i,j))*x(i)
337  160 CONTINUE
338  IF (nounit) temp = temp/dconjg(a(j,j))
339  END IF
340  x(j) = temp
341  170 CONTINUE
342  ELSE
343  kx = kx + (n-1)*incx
344  jx = kx
345  DO 200 j = n,1,-1
346  ix = kx
347  temp = x(jx)
348  IF (noconj) THEN
349  DO 180 i = n,j + 1,-1
350  temp = temp - a(i,j)*x(ix)
351  ix = ix - incx
352  180 CONTINUE
353  IF (nounit) temp = temp/a(j,j)
354  ELSE
355  DO 190 i = n,j + 1,-1
356  temp = temp - dconjg(a(i,j))*x(ix)
357  ix = ix - incx
358  190 CONTINUE
359  IF (nounit) temp = temp/dconjg(a(j,j))
360  END IF
361  x(jx) = temp
362  jx = jx - incx
363  200 CONTINUE
364  END IF
365  END IF
366  END IF
367 *
368  RETURN
369 *
370 * End of ZTRSV .
371 *
372  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztrsv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRSV
Definition: ztrsv.f:149