LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zgttrs.f
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1*> \brief \b ZGTTRS
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgttrs.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgttrs.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgttrs.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
22* INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER TRANS
26* INTEGER INFO, LDB, N, NRHS
27* ..
28* .. Array Arguments ..
29* INTEGER IPIV( * )
30* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> ZGTTRS solves one of the systems of equations
40*> A * X = B, A**T * X = B, or A**H * X = B,
41*> with a tridiagonal matrix A using the LU factorization computed
42*> by ZGTTRF.
43*> \endverbatim
44*
45* Arguments:
46* ==========
47*
48*> \param[in] TRANS
49*> \verbatim
50*> TRANS is CHARACTER*1
51*> Specifies the form of the system of equations.
52*> = 'N': A * X = B (No transpose)
53*> = 'T': A**T * X = B (Transpose)
54*> = 'C': A**H * X = B (Conjugate transpose)
55*> \endverbatim
56*>
57*> \param[in] N
58*> \verbatim
59*> N is INTEGER
60*> The order of the matrix A.
61*> \endverbatim
62*>
63*> \param[in] NRHS
64*> \verbatim
65*> NRHS is INTEGER
66*> The number of right hand sides, i.e., the number of columns
67*> of the matrix B. NRHS >= 0.
68*> \endverbatim
69*>
70*> \param[in] DL
71*> \verbatim
72*> DL is COMPLEX*16 array, dimension (N-1)
73*> The (n-1) multipliers that define the matrix L from the
74*> LU factorization of A.
75*> \endverbatim
76*>
77*> \param[in] D
78*> \verbatim
79*> D is COMPLEX*16 array, dimension (N)
80*> The n diagonal elements of the upper triangular matrix U from
81*> the LU factorization of A.
82*> \endverbatim
83*>
84*> \param[in] DU
85*> \verbatim
86*> DU is COMPLEX*16 array, dimension (N-1)
87*> The (n-1) elements of the first super-diagonal of U.
88*> \endverbatim
89*>
90*> \param[in] DU2
91*> \verbatim
92*> DU2 is COMPLEX*16 array, dimension (N-2)
93*> The (n-2) elements of the second super-diagonal of U.
94*> \endverbatim
95*>
96*> \param[in] IPIV
97*> \verbatim
98*> IPIV is INTEGER array, dimension (N)
99*> The pivot indices; for 1 <= i <= n, row i of the matrix was
100*> interchanged with row IPIV(i). IPIV(i) will always be either
101*> i or i+1; IPIV(i) = i indicates a row interchange was not
102*> required.
103*> \endverbatim
104*>
105*> \param[in,out] B
106*> \verbatim
107*> B is COMPLEX*16 array, dimension (LDB,NRHS)
108*> On entry, the matrix of right hand side vectors B.
109*> On exit, B is overwritten by the solution vectors X.
110*> \endverbatim
111*>
112*> \param[in] LDB
113*> \verbatim
114*> LDB is INTEGER
115*> The leading dimension of the array B. LDB >= max(1,N).
116*> \endverbatim
117*>
118*> \param[out] INFO
119*> \verbatim
120*> INFO is INTEGER
121*> = 0: successful exit
122*> < 0: if INFO = -k, the k-th argument had an illegal value
123*> \endverbatim
124*
125* Authors:
126* ========
127*
128*> \author Univ. of Tennessee
129*> \author Univ. of California Berkeley
130*> \author Univ. of Colorado Denver
131*> \author NAG Ltd.
132*
133*> \ingroup gttrs
134*
135* =====================================================================
136 SUBROUTINE zgttrs( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
137 \$ INFO )
138*
139* -- LAPACK computational routine --
140* -- LAPACK is a software package provided by Univ. of Tennessee, --
141* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142*
143* .. Scalar Arguments ..
144 CHARACTER TRANS
145 INTEGER INFO, LDB, N, NRHS
146* ..
147* .. Array Arguments ..
148 INTEGER IPIV( * )
149 COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
150* ..
151*
152* =====================================================================
153*
154* .. Local Scalars ..
155 LOGICAL NOTRAN
156 INTEGER ITRANS, J, JB, NB
157* ..
158* .. External Functions ..
159 INTEGER ILAENV
160 EXTERNAL ilaenv
161* ..
162* .. External Subroutines ..
163 EXTERNAL xerbla, zgtts2
164* ..
165* .. Intrinsic Functions ..
166 INTRINSIC max, min
167* ..
168* .. Executable Statements ..
169*
170 info = 0
171 notran = ( trans.EQ.'N' .OR. trans.EQ.'n' )
172 IF( .NOT.notran .AND. .NOT.( trans.EQ.'T' .OR. trans.EQ.
173 \$ 't' ) .AND. .NOT.( trans.EQ.'C' .OR. trans.EQ.'c' ) ) THEN
174 info = -1
175 ELSE IF( n.LT.0 ) THEN
176 info = -2
177 ELSE IF( nrhs.LT.0 ) THEN
178 info = -3
179 ELSE IF( ldb.LT.max( n, 1 ) ) THEN
180 info = -10
181 END IF
182 IF( info.NE.0 ) THEN
183 CALL xerbla( 'ZGTTRS', -info )
184 RETURN
185 END IF
186*
187* Quick return if possible
188*
189 IF( n.EQ.0 .OR. nrhs.EQ.0 )
190 \$ RETURN
191*
192* Decode TRANS
193*
194 IF( notran ) THEN
195 itrans = 0
196 ELSE IF( trans.EQ.'T' .OR. trans.EQ.'t' ) THEN
197 itrans = 1
198 ELSE
199 itrans = 2
200 END IF
201*
202* Determine the number of right-hand sides to solve at a time.
203*
204 IF( nrhs.EQ.1 ) THEN
205 nb = 1
206 ELSE
207 nb = max( 1, ilaenv( 1, 'ZGTTRS', trans, n, nrhs, -1, -1 ) )
208 END IF
209*
210 IF( nb.GE.nrhs ) THEN
211 CALL zgtts2( itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb )
212 ELSE
213 DO 10 j = 1, nrhs, nb
214 jb = min( nrhs-j+1, nb )
215 CALL zgtts2( itrans, n, jb, dl, d, du, du2, ipiv, b( 1, j ),
216 \$ ldb )
217 10 CONTINUE
218 END IF
219*
220* End of ZGTTRS
221*
222 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zgttrs(trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
ZGTTRS
Definition zgttrs.f:138
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