LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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zgtts2.f
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1*> \brief \b ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZGTTS2 + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgtts2.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgtts2.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgtts2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
22*
23* .. Scalar Arguments ..
24* INTEGER ITRANS, LDB, N, NRHS
25* ..
26* .. Array Arguments ..
27* INTEGER IPIV( * )
28* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> ZGTTS2 solves one of the systems of equations
38*> A * X = B, A**T * X = B, or A**H * X = B,
39*> with a tridiagonal matrix A using the LU factorization computed
40*> by ZGTTRF.
41*> \endverbatim
42*
43* Arguments:
44* ==========
45*
46*> \param[in] ITRANS
47*> \verbatim
48*> ITRANS is INTEGER
49*> Specifies the form of the system of equations.
50*> = 0: A * X = B (No transpose)
51*> = 1: A**T * X = B (Transpose)
52*> = 2: A**H * X = B (Conjugate transpose)
53*> \endverbatim
54*>
55*> \param[in] N
56*> \verbatim
57*> N is INTEGER
58*> The order of the matrix A.
59*> \endverbatim
60*>
61*> \param[in] NRHS
62*> \verbatim
63*> NRHS is INTEGER
64*> The number of right hand sides, i.e., the number of columns
65*> of the matrix B. NRHS >= 0.
66*> \endverbatim
67*>
68*> \param[in] DL
69*> \verbatim
70*> DL is COMPLEX*16 array, dimension (N-1)
71*> The (n-1) multipliers that define the matrix L from the
72*> LU factorization of A.
73*> \endverbatim
74*>
75*> \param[in] D
76*> \verbatim
77*> D is COMPLEX*16 array, dimension (N)
78*> The n diagonal elements of the upper triangular matrix U from
79*> the LU factorization of A.
80*> \endverbatim
81*>
82*> \param[in] DU
83*> \verbatim
84*> DU is COMPLEX*16 array, dimension (N-1)
85*> The (n-1) elements of the first super-diagonal of U.
86*> \endverbatim
87*>
88*> \param[in] DU2
89*> \verbatim
90*> DU2 is COMPLEX*16 array, dimension (N-2)
91*> The (n-2) elements of the second super-diagonal of U.
92*> \endverbatim
93*>
94*> \param[in] IPIV
95*> \verbatim
96*> IPIV is INTEGER array, dimension (N)
97*> The pivot indices; for 1 <= i <= n, row i of the matrix was
98*> interchanged with row IPIV(i). IPIV(i) will always be either
99*> i or i+1; IPIV(i) = i indicates a row interchange was not
100*> required.
101*> \endverbatim
102*>
103*> \param[in,out] B
104*> \verbatim
105*> B is COMPLEX*16 array, dimension (LDB,NRHS)
106*> On entry, the matrix of right hand side vectors B.
107*> On exit, B is overwritten by the solution vectors X.
108*> \endverbatim
109*>
110*> \param[in] LDB
111*> \verbatim
112*> LDB is INTEGER
113*> The leading dimension of the array B. LDB >= max(1,N).
114*> \endverbatim
115*
116* Authors:
117* ========
118*
119*> \author Univ. of Tennessee
120*> \author Univ. of California Berkeley
121*> \author Univ. of Colorado Denver
122*> \author NAG Ltd.
123*
124*> \ingroup gtts2
125*
126* =====================================================================
127 SUBROUTINE zgtts2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
128*
129* -- LAPACK computational routine --
130* -- LAPACK is a software package provided by Univ. of Tennessee, --
131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*
133* .. Scalar Arguments ..
134 INTEGER ITRANS, LDB, N, NRHS
135* ..
136* .. Array Arguments ..
137 INTEGER IPIV( * )
138 COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
139* ..
140*
141* =====================================================================
142*
143* .. Local Scalars ..
144 INTEGER I, J
145 COMPLEX*16 TEMP
146* ..
147* .. Intrinsic Functions ..
148 INTRINSIC dconjg
149* ..
150* .. Executable Statements ..
151*
152* Quick return if possible
153*
154 IF( n.EQ.0 .OR. nrhs.EQ.0 )
155 $ RETURN
156*
157 IF( itrans.EQ.0 ) THEN
158*
159* Solve A*X = B using the LU factorization of A,
160* overwriting each right hand side vector with its solution.
161*
162 IF( nrhs.LE.1 ) THEN
163 j = 1
164 10 CONTINUE
165*
166* Solve L*x = b.
167*
168 DO 20 i = 1, n - 1
169 IF( ipiv( i ).EQ.i ) THEN
170 b( i+1, j ) = b( i+1, j ) - dl( i )*b( i, j )
171 ELSE
172 temp = b( i, j )
173 b( i, j ) = b( i+1, j )
174 b( i+1, j ) = temp - dl( i )*b( i, j )
175 END IF
176 20 CONTINUE
177*
178* Solve U*x = b.
179*
180 b( n, j ) = b( n, j ) / d( n )
181 IF( n.GT.1 )
182 $ b( n-1, j ) = ( b( n-1, j )-du( n-1 )*b( n, j ) ) /
183 $ d( n-1 )
184 DO 30 i = n - 2, 1, -1
185 b( i, j ) = ( b( i, j )-du( i )*b( i+1, j )-du2( i )*
186 $ b( i+2, j ) ) / d( i )
187 30 CONTINUE
188 IF( j.LT.nrhs ) THEN
189 j = j + 1
190 GO TO 10
191 END IF
192 ELSE
193 DO 60 j = 1, nrhs
194*
195* Solve L*x = b.
196*
197 DO 40 i = 1, n - 1
198 IF( ipiv( i ).EQ.i ) THEN
199 b( i+1, j ) = b( i+1, j ) - dl( i )*b( i, j )
200 ELSE
201 temp = b( i, j )
202 b( i, j ) = b( i+1, j )
203 b( i+1, j ) = temp - dl( i )*b( i, j )
204 END IF
205 40 CONTINUE
206*
207* Solve U*x = b.
208*
209 b( n, j ) = b( n, j ) / d( n )
210 IF( n.GT.1 )
211 $ b( n-1, j ) = ( b( n-1, j )-du( n-1 )*b( n, j ) ) /
212 $ d( n-1 )
213 DO 50 i = n - 2, 1, -1
214 b( i, j ) = ( b( i, j )-du( i )*b( i+1, j )-du2( i )*
215 $ b( i+2, j ) ) / d( i )
216 50 CONTINUE
217 60 CONTINUE
218 END IF
219 ELSE IF( itrans.EQ.1 ) THEN
220*
221* Solve A**T * X = B.
222*
223 IF( nrhs.LE.1 ) THEN
224 j = 1
225 70 CONTINUE
226*
227* Solve U**T * x = b.
228*
229 b( 1, j ) = b( 1, j ) / d( 1 )
230 IF( n.GT.1 )
231 $ b( 2, j ) = ( b( 2, j )-du( 1 )*b( 1, j ) ) / d( 2 )
232 DO 80 i = 3, n
233 b( i, j ) = ( b( i, j )-du( i-1 )*b( i-1, j )-du2( i-2 )*
234 $ b( i-2, j ) ) / d( i )
235 80 CONTINUE
236*
237* Solve L**T * x = b.
238*
239 DO 90 i = n - 1, 1, -1
240 IF( ipiv( i ).EQ.i ) THEN
241 b( i, j ) = b( i, j ) - dl( i )*b( i+1, j )
242 ELSE
243 temp = b( i+1, j )
244 b( i+1, j ) = b( i, j ) - dl( i )*temp
245 b( i, j ) = temp
246 END IF
247 90 CONTINUE
248 IF( j.LT.nrhs ) THEN
249 j = j + 1
250 GO TO 70
251 END IF
252 ELSE
253 DO 120 j = 1, nrhs
254*
255* Solve U**T * x = b.
256*
257 b( 1, j ) = b( 1, j ) / d( 1 )
258 IF( n.GT.1 )
259 $ b( 2, j ) = ( b( 2, j )-du( 1 )*b( 1, j ) ) / d( 2 )
260 DO 100 i = 3, n
261 b( i, j ) = ( b( i, j )-du( i-1 )*b( i-1, j )-
262 $ du2( i-2 )*b( i-2, j ) ) / d( i )
263 100 CONTINUE
264*
265* Solve L**T * x = b.
266*
267 DO 110 i = n - 1, 1, -1
268 IF( ipiv( i ).EQ.i ) THEN
269 b( i, j ) = b( i, j ) - dl( i )*b( i+1, j )
270 ELSE
271 temp = b( i+1, j )
272 b( i+1, j ) = b( i, j ) - dl( i )*temp
273 b( i, j ) = temp
274 END IF
275 110 CONTINUE
276 120 CONTINUE
277 END IF
278 ELSE
279*
280* Solve A**H * X = B.
281*
282 IF( nrhs.LE.1 ) THEN
283 j = 1
284 130 CONTINUE
285*
286* Solve U**H * x = b.
287*
288 b( 1, j ) = b( 1, j ) / dconjg( d( 1 ) )
289 IF( n.GT.1 )
290 $ b( 2, j ) = ( b( 2, j )-dconjg( du( 1 ) )*b( 1, j ) ) /
291 $ dconjg( d( 2 ) )
292 DO 140 i = 3, n
293 b( i, j ) = ( b( i, j )-dconjg( du( i-1 ) )*b( i-1, j )-
294 $ dconjg( du2( i-2 ) )*b( i-2, j ) ) /
295 $ dconjg( d( i ) )
296 140 CONTINUE
297*
298* Solve L**H * x = b.
299*
300 DO 150 i = n - 1, 1, -1
301 IF( ipiv( i ).EQ.i ) THEN
302 b( i, j ) = b( i, j ) - dconjg( dl( i ) )*b( i+1, j )
303 ELSE
304 temp = b( i+1, j )
305 b( i+1, j ) = b( i, j ) - dconjg( dl( i ) )*temp
306 b( i, j ) = temp
307 END IF
308 150 CONTINUE
309 IF( j.LT.nrhs ) THEN
310 j = j + 1
311 GO TO 130
312 END IF
313 ELSE
314 DO 180 j = 1, nrhs
315*
316* Solve U**H * x = b.
317*
318 b( 1, j ) = b( 1, j ) / dconjg( d( 1 ) )
319 IF( n.GT.1 )
320 $ b( 2, j ) = ( b( 2, j )-dconjg( du( 1 ) )*b( 1, j ) )
321 $ / dconjg( d( 2 ) )
322 DO 160 i = 3, n
323 b( i, j ) = ( b( i, j )-dconjg( du( i-1 ) )*
324 $ b( i-1, j )-dconjg( du2( i-2 ) )*
325 $ b( i-2, j ) ) / dconjg( d( i ) )
326 160 CONTINUE
327*
328* Solve L**H * x = b.
329*
330 DO 170 i = n - 1, 1, -1
331 IF( ipiv( i ).EQ.i ) THEN
332 b( i, j ) = b( i, j ) - dconjg( dl( i ) )*
333 $ b( i+1, j )
334 ELSE
335 temp = b( i+1, j )
336 b( i+1, j ) = b( i, j ) - dconjg( dl( i ) )*temp
337 b( i, j ) = temp
338 END IF
339 170 CONTINUE
340 180 CONTINUE
341 END IF
342 END IF
343*
344* End of ZGTTS2
345*
346 END
zgtts2
subroutine zgtts2(itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization compu...
Definition zgtts2.f:128