LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cgtsv.f
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1 *> \brief <b> CGTSV computes the solution to system of linear equations A * X = B for GT matrices </b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CGTSV + dependencies
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11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgtsv.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgtsv.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDB, N, NRHS
25 * ..
26 * .. Array Arguments ..
27 * COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> CGTSV solves the equation
37 *>
38 *> A*X = B,
39 *>
40 *> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
41 *> partial pivoting.
42 *>
43 *> Note that the equation A**T *X = B may be solved by interchanging the
44 *> order of the arguments DU and DL.
45 *> \endverbatim
46 *
47 * Arguments:
48 * ==========
49 *
50 *> \param[in] N
51 *> \verbatim
52 *> N is INTEGER
53 *> The order of the matrix A. N >= 0.
54 *> \endverbatim
55 *>
56 *> \param[in] NRHS
57 *> \verbatim
58 *> NRHS is INTEGER
59 *> The number of right hand sides, i.e., the number of columns
60 *> of the matrix B. NRHS >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in,out] DL
64 *> \verbatim
65 *> DL is COMPLEX array, dimension (N-1)
66 *> On entry, DL must contain the (n-1) subdiagonal elements of
67 *> A.
68 *> On exit, DL is overwritten by the (n-2) elements of the
69 *> second superdiagonal of the upper triangular matrix U from
70 *> the LU factorization of A, in DL(1), ..., DL(n-2).
71 *> \endverbatim
72 *>
73 *> \param[in,out] D
74 *> \verbatim
75 *> D is COMPLEX array, dimension (N)
76 *> On entry, D must contain the diagonal elements of A.
77 *> On exit, D is overwritten by the n diagonal elements of U.
78 *> \endverbatim
79 *>
80 *> \param[in,out] DU
81 *> \verbatim
82 *> DU is COMPLEX array, dimension (N-1)
83 *> On entry, DU must contain the (n-1) superdiagonal elements
84 *> of A.
85 *> On exit, DU is overwritten by the (n-1) elements of the first
86 *> superdiagonal of U.
87 *> \endverbatim
88 *>
89 *> \param[in,out] B
90 *> \verbatim
91 *> B is COMPLEX array, dimension (LDB,NRHS)
92 *> On entry, the N-by-NRHS right hand side matrix B.
93 *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
94 *> \endverbatim
95 *>
96 *> \param[in] LDB
97 *> \verbatim
98 *> LDB is INTEGER
99 *> The leading dimension of the array B. LDB >= max(1,N).
100 *> \endverbatim
101 *>
102 *> \param[out] INFO
103 *> \verbatim
104 *> INFO is INTEGER
105 *> = 0: successful exit
106 *> < 0: if INFO = -i, the i-th argument had an illegal value
107 *> > 0: if INFO = i, U(i,i) is exactly zero, and the solution
108 *> has not been computed. The factorization has not been
109 *> completed unless i = N.
110 *> \endverbatim
111 *
112 * Authors:
113 * ========
114 *
115 *> \author Univ. of Tennessee
116 *> \author Univ. of California Berkeley
117 *> \author Univ. of Colorado Denver
118 *> \author NAG Ltd.
119 *
120 *> \ingroup complexGTsolve
121 *
122 * =====================================================================
123  SUBROUTINE cgtsv( N, NRHS, DL, D, DU, B, LDB, INFO )
124 *
125 * -- LAPACK driver routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  INTEGER INFO, LDB, N, NRHS
131 * ..
132 * .. Array Arguments ..
133  COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  COMPLEX ZERO
140  parameter( zero = ( 0.0e+0, 0.0e+0 ) )
141 * ..
142 * .. Local Scalars ..
143  INTEGER J, K
144  COMPLEX MULT, TEMP, ZDUM
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC abs, aimag, max, real
148 * ..
149 * .. External Subroutines ..
150  EXTERNAL xerbla
151 * ..
152 * .. Statement Functions ..
153  REAL CABS1
154 * ..
155 * .. Statement Function definitions ..
156  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
157 * ..
158 * .. Executable Statements ..
159 *
160  info = 0
161  IF( n.LT.0 ) THEN
162  info = -1
163  ELSE IF( nrhs.LT.0 ) THEN
164  info = -2
165  ELSE IF( ldb.LT.max( 1, n ) ) THEN
166  info = -7
167  END IF
168  IF( info.NE.0 ) THEN
169  CALL xerbla( 'CGTSV ', -info )
170  RETURN
171  END IF
172 *
173  IF( n.EQ.0 )
174  $ RETURN
175 *
176  DO 30 k = 1, n - 1
177  IF( dl( k ).EQ.zero ) THEN
178 *
179 * Subdiagonal is zero, no elimination is required.
180 *
181  IF( d( k ).EQ.zero ) THEN
182 *
183 * Diagonal is zero: set INFO = K and return; a unique
184 * solution can not be found.
185 *
186  info = k
187  RETURN
188  END IF
189  ELSE IF( cabs1( d( k ) ).GE.cabs1( dl( k ) ) ) THEN
190 *
191 * No row interchange required
192 *
193  mult = dl( k ) / d( k )
194  d( k+1 ) = d( k+1 ) - mult*du( k )
195  DO 10 j = 1, nrhs
196  b( k+1, j ) = b( k+1, j ) - mult*b( k, j )
197  10 CONTINUE
198  IF( k.LT.( n-1 ) )
199  $ dl( k ) = zero
200  ELSE
201 *
202 * Interchange rows K and K+1
203 *
204  mult = d( k ) / dl( k )
205  d( k ) = dl( k )
206  temp = d( k+1 )
207  d( k+1 ) = du( k ) - mult*temp
208  IF( k.LT.( n-1 ) ) THEN
209  dl( k ) = du( k+1 )
210  du( k+1 ) = -mult*dl( k )
211  END IF
212  du( k ) = temp
213  DO 20 j = 1, nrhs
214  temp = b( k, j )
215  b( k, j ) = b( k+1, j )
216  b( k+1, j ) = temp - mult*b( k+1, j )
217  20 CONTINUE
218  END IF
219  30 CONTINUE
220  IF( d( n ).EQ.zero ) THEN
221  info = n
222  RETURN
223  END IF
224 *
225 * Back solve with the matrix U from the factorization.
226 *
227  DO 50 j = 1, nrhs
228  b( n, j ) = b( n, j ) / d( n )
229  IF( n.GT.1 )
230  $ b( n-1, j ) = ( b( n-1, j )-du( n-1 )*b( n, j ) ) / d( n-1 )
231  DO 40 k = n - 2, 1, -1
232  b( k, j ) = ( b( k, j )-du( k )*b( k+1, j )-dl( k )*
233  $ b( k+2, j ) ) / d( k )
234  40 CONTINUE
235  50 CONTINUE
236 *
237  RETURN
238 *
239 * End of CGTSV
240 *
241  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgtsv(N, NRHS, DL, D, DU, B, LDB, INFO)
CGTSV computes the solution to system of linear equations A * X = B for GT matrices
Definition: cgtsv.f:124