LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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sgtts2.f
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1*> \brief \b SGTTS2 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*
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SGTTS2( 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* REAL B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> SGTTS2 solves one of the systems of equations
38*> A*X = B or A**T*X = B,
39*> with a tridiagonal matrix A using the LU factorization computed
40*> by SGTTRF.
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**T* X = B (Conjugate transpose = 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 sgtts2( 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 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*
271 END
subroutine sgtts2(itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization compu...
Definition sgtts2.f:128