1: *> \brief \b DGTTRF
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DGTTRF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgttrf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgttrf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgttrf.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, N
25: * ..
26: * .. Array Arguments ..
27: * INTEGER IPIV( * )
28: * DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DGTTRF computes an LU factorization of a real 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doubleGTcomputational
121: *
122: * =====================================================================
123: SUBROUTINE DGTTRF( 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: DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
135: * ..
136: *
137: * =====================================================================
138: *
139: * .. Parameters ..
140: DOUBLE PRECISION ZERO
141: PARAMETER ( ZERO = 0.0D+0 )
142: * ..
143: * .. Local Scalars ..
144: INTEGER I
145: DOUBLE PRECISION FACT, TEMP
146: * ..
147: * .. Intrinsic Functions ..
148: INTRINSIC ABS
149: * ..
150: * .. External Subroutines ..
151: EXTERNAL XERBLA
152: * ..
153: * .. Executable Statements ..
154: *
155: INFO = 0
156: IF( N.LT.0 ) THEN
157: INFO = -1
158: CALL XERBLA( 'DGTTRF', -INFO )
159: RETURN
160: END IF
161: *
162: * Quick return if possible
163: *
164: IF( N.EQ.0 )
165: $ RETURN
166: *
167: * Initialize IPIV(i) = i and DU2(I) = 0
168: *
169: DO 10 I = 1, N
170: IPIV( I ) = I
171: 10 CONTINUE
172: DO 20 I = 1, N - 2
173: DU2( I ) = ZERO
174: 20 CONTINUE
175: *
176: DO 30 I = 1, N - 2
177: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
178: *
179: * No row interchange required, eliminate DL(I)
180: *
181: IF( D( I ).NE.ZERO ) THEN
182: FACT = DL( I ) / D( I )
183: DL( I ) = FACT
184: D( I+1 ) = D( I+1 ) - FACT*DU( I )
185: END IF
186: ELSE
187: *
188: * Interchange rows I and I+1, eliminate DL(I)
189: *
190: FACT = D( I ) / DL( I )
191: D( I ) = DL( I )
192: DL( I ) = FACT
193: TEMP = DU( I )
194: DU( I ) = D( I+1 )
195: D( I+1 ) = TEMP - FACT*D( I+1 )
196: DU2( I ) = DU( I+1 )
197: DU( I+1 ) = -FACT*DU( I+1 )
198: IPIV( I ) = I + 1
199: END IF
200: 30 CONTINUE
201: IF( N.GT.1 ) THEN
202: I = N - 1
203: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
204: IF( D( I ).NE.ZERO ) THEN
205: FACT = DL( I ) / D( I )
206: DL( I ) = FACT
207: D( I+1 ) = D( I+1 ) - FACT*DU( I )
208: END IF
209: ELSE
210: FACT = D( I ) / DL( I )
211: D( I ) = DL( I )
212: DL( I ) = FACT
213: TEMP = DU( I )
214: DU( I ) = D( I+1 )
215: D( I+1 ) = TEMP - FACT*D( I+1 )
216: IPIV( I ) = I + 1
217: END IF
218: END IF
219: *
220: * Check for a zero on the diagonal of U.
221: *
222: DO 40 I = 1, N
223: IF( D( I ).EQ.ZERO ) THEN
224: INFO = I
225: GO TO 50
226: END IF
227: 40 CONTINUE
228: 50 CONTINUE
229: *
230: RETURN
231: *
232: * End of DGTTRF
233: *
234: END
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