LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zgtts2()

 subroutine zgtts2 ( integer ITRANS, integer N, integer NRHS, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB )

ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:
``` ZGTTS2 solves one of the systems of equations
A * X = B,  A**T * X = B,  or  A**H * X = B,
with a tridiagonal matrix A using the LU factorization computed
by ZGTTRF.```
Parameters
 [in] ITRANS ``` ITRANS is INTEGER Specifies the form of the system of equations. = 0: A * X = B (No transpose) = 1: A**T * X = B (Transpose) = 2: A**H * X = B (Conjugate transpose)``` [in] N ``` N is INTEGER The order of the matrix A.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.``` [in] DL ``` DL is COMPLEX*16 array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.``` [in] D ``` D is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.``` [in] DU ``` DU is COMPLEX*16 array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.``` [in] DU2 ``` DU2 is COMPLEX*16 array, dimension (N-2) The (n-2) elements of the second super-diagonal of U.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B. On exit, B is overwritten by the solution vectors X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).```

Definition at line 127 of file zgtts2.f.

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*
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