 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sgtts2()

 subroutine sgtts2 ( integer ITRANS, integer N, integer NRHS, real, dimension( * ) DL, real, dimension( * ) D, real, dimension( * ) DU, real, dimension( * ) DU2, integer, dimension( * ) IPIV, real, dimension( ldb, * ) B, integer LDB )

SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:
``` SGTTS2 solves one of the systems of equations
A*X = B  or  A**T*X = B,
with a tridiagonal matrix A using the LU factorization computed
by SGTTRF.```
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**T* X = B (Conjugate transpose = 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 REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.``` [in] D ``` D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.``` [in] DU ``` DU is REAL array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.``` [in] DU2 ``` DU2 is REAL 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 REAL 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 sgtts2.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 REAL B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
139* ..
140*
141* =====================================================================
142*
143* .. Local Scalars ..
144 INTEGER I, IP, J
145 REAL TEMP
146* ..
147* .. Executable Statements ..
148*
149* Quick return if possible
150*
151 IF( n.EQ.0 .OR. nrhs.EQ.0 )
152 \$ RETURN
153*
154 IF( itrans.EQ.0 ) THEN
155*
156* Solve A*X = B using the LU factorization of A,
157* overwriting each right hand side vector with its solution.
158*
159 IF( nrhs.LE.1 ) THEN
160 j = 1
161 10 CONTINUE
162*
163* Solve L*x = b.
164*
165 DO 20 i = 1, n - 1
166 ip = ipiv( i )
167 temp = b( i+1-ip+i, j ) - dl( i )*b( ip, j )
168 b( i, j ) = b( ip, j )
169 b( i+1, j ) = temp
170 20 CONTINUE
171*
172* Solve U*x = b.
173*
174 b( n, j ) = b( n, j ) / d( n )
175 IF( n.GT.1 )
176 \$ b( n-1, j ) = ( b( n-1, j )-du( n-1 )*b( n, j ) ) /
177 \$ d( n-1 )
178 DO 30 i = n - 2, 1, -1
179 b( i, j ) = ( b( i, j )-du( i )*b( i+1, j )-du2( i )*
180 \$ b( i+2, j ) ) / d( i )
181 30 CONTINUE
182 IF( j.LT.nrhs ) THEN
183 j = j + 1
184 GO TO 10
185 END IF
186 ELSE
187 DO 60 j = 1, nrhs
188*
189* Solve L*x = b.
190*
191 DO 40 i = 1, n - 1
192 IF( ipiv( i ).EQ.i ) THEN
193 b( i+1, j ) = b( i+1, j ) - dl( i )*b( i, j )
194 ELSE
195 temp = b( i, j )
196 b( i, j ) = b( i+1, j )
197 b( i+1, j ) = temp - dl( i )*b( i, j )
198 END IF
199 40 CONTINUE
200*
201* Solve U*x = b.
202*
203 b( n, j ) = b( n, j ) / d( n )
204 IF( n.GT.1 )
205 \$ b( n-1, j ) = ( b( n-1, j )-du( n-1 )*b( n, j ) ) /
206 \$ d( n-1 )
207 DO 50 i = n - 2, 1, -1
208 b( i, j ) = ( b( i, j )-du( i )*b( i+1, j )-du2( i )*
209 \$ b( i+2, j ) ) / d( i )
210 50 CONTINUE
211 60 CONTINUE
212 END IF
213 ELSE
214*
215* Solve A**T * X = B.
216*
217 IF( nrhs.LE.1 ) THEN
218*
219* Solve U**T*x = b.
220*
221 j = 1
222 70 CONTINUE
223 b( 1, j ) = b( 1, j ) / d( 1 )
224 IF( n.GT.1 )
225 \$ b( 2, j ) = ( b( 2, j )-du( 1 )*b( 1, j ) ) / d( 2 )
226 DO 80 i = 3, n
227 b( i, j ) = ( b( i, j )-du( i-1 )*b( i-1, j )-du2( i-2 )*
228 \$ b( i-2, j ) ) / d( i )
229 80 CONTINUE
230*
231* Solve L**T*x = b.
232*
233 DO 90 i = n - 1, 1, -1
234 ip = ipiv( i )
235 temp = b( i, j ) - dl( i )*b( i+1, j )
236 b( i, j ) = b( ip, j )
237 b( ip, j ) = temp
238 90 CONTINUE
239 IF( j.LT.nrhs ) THEN
240 j = j + 1
241 GO TO 70
242 END IF
243*
244 ELSE
245 DO 120 j = 1, nrhs
246*
247* Solve U**T*x = b.
248*
249 b( 1, j ) = b( 1, j ) / d( 1 )
250 IF( n.GT.1 )
251 \$ b( 2, j ) = ( b( 2, j )-du( 1 )*b( 1, j ) ) / d( 2 )
252 DO 100 i = 3, n
253 b( i, j ) = ( b( i, j )-du( i-1 )*b( i-1, j )-
254 \$ du2( i-2 )*b( i-2, j ) ) / d( i )
255 100 CONTINUE
256 DO 110 i = n - 1, 1, -1
257 IF( ipiv( i ).EQ.i ) THEN
258 b( i, j ) = b( i, j ) - dl( i )*b( i+1, j )
259 ELSE
260 temp = b( i+1, j )
261 b( i+1, j ) = b( i, j ) - dl( i )*temp
262 b( i, j ) = temp
263 END IF
264 110 CONTINUE
265 120 CONTINUE
266 END IF
267 END IF
268*
269* End of SGTTS2
270*
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