LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cgttrf.f
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1 *> \brief \b CGTTRF
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 CGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, N
25 * ..
26 * .. Array Arguments ..
27 * INTEGER IPIV( * )
28 * COMPLEX D( * ), DL( * ), DU( * ), DU2( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CGTTRF computes an LU factorization of a complex tridiagonal matrix A
38 *> using elimination with partial pivoting and row interchanges.
39 *>
40 *> The factorization has the form
41 *> A = L * U
42 *> where L is a product of permutation and unit lower bidiagonal
43 *> matrices and U is upper triangular with nonzeros in only the main
44 *> diagonal and first two superdiagonals.
45 *> \endverbatim
46 *
47 * Arguments:
48 * ==========
49 *
50 *> \param[in] N
51 *> \verbatim
52 *> N is INTEGER
53 *> The order of the matrix A.
54 *> \endverbatim
55 *>
56 *> \param[in,out] DL
57 *> \verbatim
58 *> DL is COMPLEX array, dimension (N-1)
59 *> On entry, DL must contain the (n-1) sub-diagonal elements of
60 *> A.
61 *>
62 *> On exit, DL is overwritten by the (n-1) multipliers that
63 *> define the matrix L from the LU factorization of A.
64 *> \endverbatim
65 *>
66 *> \param[in,out] D
67 *> \verbatim
68 *> D is COMPLEX array, dimension (N)
69 *> On entry, D must contain the diagonal elements of A.
70 *>
71 *> On exit, D is overwritten by the n diagonal elements of the
72 *> upper triangular matrix U from the LU factorization of A.
73 *> \endverbatim
74 *>
75 *> \param[in,out] DU
76 *> \verbatim
77 *> DU is COMPLEX array, dimension (N-1)
78 *> On entry, DU must contain the (n-1) super-diagonal elements
79 *> of A.
80 *>
81 *> On exit, DU is overwritten by the (n-1) elements of the first
82 *> super-diagonal of U.
83 *> \endverbatim
84 *>
85 *> \param[out] DU2
86 *> \verbatim
87 *> DU2 is COMPLEX array, dimension (N-2)
88 *> On exit, DU2 is overwritten by the (n-2) elements of the
89 *> second super-diagonal of U.
90 *> \endverbatim
91 *>
92 *> \param[out] IPIV
93 *> \verbatim
94 *> IPIV is INTEGER array, dimension (N)
95 *> The pivot indices; for 1 <= i <= n, row i of the matrix was
96 *> interchanged with row IPIV(i). IPIV(i) will always be either
97 *> i or i+1; IPIV(i) = i indicates a row interchange was not
98 *> required.
99 *> \endverbatim
100 *>
101 *> \param[out] INFO
102 *> \verbatim
103 *> INFO is INTEGER
104 *> = 0: successful exit
105 *> < 0: if INFO = -k, the k-th argument had an illegal value
106 *> > 0: if INFO = k, U(k,k) is exactly zero. The factorization
107 *> has been completed, but the factor U is exactly
108 *> singular, and division by zero will occur if it is used
109 *> to solve a system of equations.
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 complexGTcomputational
121 *
122 * =====================================================================
123  SUBROUTINE cgttrf( N, DL, D, DU, DU2, IPIV, INFO )
124 *
125 * -- LAPACK computational 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, N
131 * ..
132 * .. Array Arguments ..
133  INTEGER IPIV( * )
134  COMPLEX D( * ), DL( * ), DU( * ), DU2( * )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Parameters ..
140  REAL ZERO
141  parameter( zero = 0.0e+0 )
142 * ..
143 * .. Local Scalars ..
144  INTEGER I
145  COMPLEX FACT, TEMP, ZDUM
146 * ..
147 * .. External Subroutines ..
148  EXTERNAL xerbla
149 * ..
150 * .. Intrinsic Functions ..
151  INTRINSIC abs, aimag, real
152 * ..
153 * .. Statement Functions ..
154  REAL CABS1
155 * ..
156 * .. Statement Function definitions ..
157  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
158 * ..
159 * .. Executable Statements ..
160 *
161  info = 0
162  IF( n.LT.0 ) THEN
163  info = -1
164  CALL xerbla( 'CGTTRF', -info )
165  RETURN
166  END IF
167 *
168 * Quick return if possible
169 *
170  IF( n.EQ.0 )
171  $ RETURN
172 *
173 * Initialize IPIV(i) = i and DU2(i) = 0
174 *
175  DO 10 i = 1, n
176  ipiv( i ) = i
177  10 CONTINUE
178  DO 20 i = 1, n - 2
179  du2( i ) = zero
180  20 CONTINUE
181 *
182  DO 30 i = 1, n - 2
183  IF( cabs1( d( i ) ).GE.cabs1( dl( i ) ) ) THEN
184 *
185 * No row interchange required, eliminate DL(I)
186 *
187  IF( cabs1( d( i ) ).NE.zero ) THEN
188  fact = dl( i ) / d( i )
189  dl( i ) = fact
190  d( i+1 ) = d( i+1 ) - fact*du( i )
191  END IF
192  ELSE
193 *
194 * Interchange rows I and I+1, eliminate DL(I)
195 *
196  fact = d( i ) / dl( i )
197  d( i ) = dl( i )
198  dl( i ) = fact
199  temp = du( i )
200  du( i ) = d( i+1 )
201  d( i+1 ) = temp - fact*d( i+1 )
202  du2( i ) = du( i+1 )
203  du( i+1 ) = -fact*du( i+1 )
204  ipiv( i ) = i + 1
205  END IF
206  30 CONTINUE
207  IF( n.GT.1 ) THEN
208  i = n - 1
209  IF( cabs1( d( i ) ).GE.cabs1( dl( i ) ) ) THEN
210  IF( cabs1( d( i ) ).NE.zero ) THEN
211  fact = dl( i ) / d( i )
212  dl( i ) = fact
213  d( i+1 ) = d( i+1 ) - fact*du( i )
214  END IF
215  ELSE
216  fact = d( i ) / dl( i )
217  d( i ) = dl( i )
218  dl( i ) = fact
219  temp = du( i )
220  du( i ) = d( i+1 )
221  d( i+1 ) = temp - fact*d( i+1 )
222  ipiv( i ) = i + 1
223  END IF
224  END IF
225 *
226 * Check for a zero on the diagonal of U.
227 *
228  DO 40 i = 1, n
229  IF( cabs1( d( i ) ).EQ.zero ) THEN
230  info = i
231  GO TO 50
232  END IF
233  40 CONTINUE
234  50 CONTINUE
235 *
236  RETURN
237 *
238 * End of CGTTRF
239 *
240  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgttrf(N, DL, D, DU, DU2, IPIV, INFO)
CGTTRF
Definition: cgttrf.f:124