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: *> \date September 2012
121: *
122: *> \ingroup doubleGTcomputational
123: *
124: * =====================================================================
125: SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
126: *
127: * -- LAPACK computational routine (version 3.4.2) --
128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130: * September 2012
131: *
132: * .. Scalar Arguments ..
133: INTEGER INFO, N
134: * ..
135: * .. Array Arguments ..
136: INTEGER IPIV( * )
137: DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
138: * ..
139: *
140: * =====================================================================
141: *
142: * .. Parameters ..
143: DOUBLE PRECISION ZERO
144: PARAMETER ( ZERO = 0.0D+0 )
145: * ..
146: * .. Local Scalars ..
147: INTEGER I
148: DOUBLE PRECISION FACT, TEMP
149: * ..
150: * .. Intrinsic Functions ..
151: INTRINSIC ABS
152: * ..
153: * .. External Subroutines ..
154: EXTERNAL XERBLA
155: * ..
156: * .. Executable Statements ..
157: *
158: INFO = 0
159: IF( N.LT.0 ) THEN
160: INFO = -1
161: CALL XERBLA( 'DGTTRF', -INFO )
162: RETURN
163: END IF
164: *
165: * Quick return if possible
166: *
167: IF( N.EQ.0 )
168: $ RETURN
169: *
170: * Initialize IPIV(i) = i and DU2(I) = 0
171: *
172: DO 10 I = 1, N
173: IPIV( I ) = I
174: 10 CONTINUE
175: DO 20 I = 1, N - 2
176: DU2( I ) = ZERO
177: 20 CONTINUE
178: *
179: DO 30 I = 1, N - 2
180: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
181: *
182: * No row interchange required, eliminate DL(I)
183: *
184: IF( D( I ).NE.ZERO ) THEN
185: FACT = DL( I ) / D( I )
186: DL( I ) = FACT
187: D( I+1 ) = D( I+1 ) - FACT*DU( I )
188: END IF
189: ELSE
190: *
191: * Interchange rows I and I+1, eliminate DL(I)
192: *
193: FACT = D( I ) / DL( I )
194: D( I ) = DL( I )
195: DL( I ) = FACT
196: TEMP = DU( I )
197: DU( I ) = D( I+1 )
198: D( I+1 ) = TEMP - FACT*D( I+1 )
199: DU2( I ) = DU( I+1 )
200: DU( I+1 ) = -FACT*DU( I+1 )
201: IPIV( I ) = I + 1
202: END IF
203: 30 CONTINUE
204: IF( N.GT.1 ) THEN
205: I = N - 1
206: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
207: IF( D( I ).NE.ZERO ) THEN
208: FACT = DL( I ) / D( I )
209: DL( I ) = FACT
210: D( I+1 ) = D( I+1 ) - FACT*DU( I )
211: END IF
212: ELSE
213: FACT = D( I ) / DL( I )
214: D( I ) = DL( I )
215: DL( I ) = FACT
216: TEMP = DU( I )
217: DU( I ) = D( I+1 )
218: D( I+1 ) = TEMP - FACT*D( I+1 )
219: IPIV( I ) = I + 1
220: END IF
221: END IF
222: *
223: * Check for a zero on the diagonal of U.
224: *
225: DO 40 I = 1, N
226: IF( D( I ).EQ.ZERO ) THEN
227: INFO = I
228: GO TO 50
229: END IF
230: 40 CONTINUE
231: 50 CONTINUE
232: *
233: RETURN
234: *
235: * End of DGTTRF
236: *
237: END
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