LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dpttrf.f
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1*> \brief \b DPTTRF
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DPTTRF + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpttrf.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpttrf.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpttrf.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DPTTRF( N, D, E, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, N
25* ..
26* .. Array Arguments ..
27* DOUBLE PRECISION D( * ), E( * )
28* ..
29*
30*
31*> \par Purpose:
32* =============
33*>
34*> \verbatim
35*>
36*> DPTTRF computes the L*D*L**T factorization of a real symmetric
37*> positive definite tridiagonal matrix A. The factorization may also
38*> be regarded as having the form A = U**T*D*U.
39*> \endverbatim
40*
41* Arguments:
42* ==========
43*
44*> \param[in] N
45*> \verbatim
46*> N is INTEGER
47*> The order of the matrix A. N >= 0.
48*> \endverbatim
49*>
50*> \param[in,out] D
51*> \verbatim
52*> D is DOUBLE PRECISION array, dimension (N)
53*> On entry, the n diagonal elements of the tridiagonal matrix
54*> A. On exit, the n diagonal elements of the diagonal matrix
55*> D from the L*D*L**T factorization of A.
56*> \endverbatim
57*>
58*> \param[in,out] E
59*> \verbatim
60*> E is DOUBLE PRECISION array, dimension (N-1)
61*> On entry, the (n-1) subdiagonal elements of the tridiagonal
62*> matrix A. On exit, the (n-1) subdiagonal elements of the
63*> unit bidiagonal factor L from the L*D*L**T factorization of A.
64*> E can also be regarded as the superdiagonal of the unit
65*> bidiagonal factor U from the U**T*D*U factorization of A.
66*> \endverbatim
67*>
68*> \param[out] INFO
69*> \verbatim
70*> INFO is INTEGER
71*> = 0: successful exit
72*> < 0: if INFO = -k, the k-th argument had an illegal value
73*> > 0: if INFO = k, the leading minor of order k is not
74*> positive definite; if k < N, the factorization could not
75*> be completed, while if k = N, the factorization was
76*> completed, but D(N) <= 0.
77*> \endverbatim
78*
79* Authors:
80* ========
81*
82*> \author Univ. of Tennessee
83*> \author Univ. of California Berkeley
84*> \author Univ. of Colorado Denver
85*> \author NAG Ltd.
86*
87*> \ingroup doublePTcomputational
88*
89* =====================================================================
90 SUBROUTINE dpttrf( N, D, E, INFO )
91*
92* -- LAPACK computational routine --
93* -- LAPACK is a software package provided by Univ. of Tennessee, --
94* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
95*
96* .. Scalar Arguments ..
97 INTEGER INFO, N
98* ..
99* .. Array Arguments ..
100 DOUBLE PRECISION D( * ), E( * )
101* ..
102*
103* =====================================================================
104*
105* .. Parameters ..
106 DOUBLE PRECISION ZERO
107 parameter( zero = 0.0d+0 )
108* ..
109* .. Local Scalars ..
110 INTEGER I, I4
111 DOUBLE PRECISION EI
112* ..
113* .. External Subroutines ..
114 EXTERNAL xerbla
115* ..
116* .. Intrinsic Functions ..
117 INTRINSIC mod
118* ..
119* .. Executable Statements ..
120*
121* Test the input parameters.
122*
123 info = 0
124 IF( n.LT.0 ) THEN
125 info = -1
126 CALL xerbla( 'DPTTRF', -info )
127 RETURN
128 END IF
129*
130* Quick return if possible
131*
132 IF( n.EQ.0 )
133 $ RETURN
134*
135* Compute the L*D*L**T (or U**T*D*U) factorization of A.
136*
137 i4 = mod( n-1, 4 )
138 DO 10 i = 1, i4
139 IF( d( i ).LE.zero ) THEN
140 info = i
141 GO TO 30
142 END IF
143 ei = e( i )
144 e( i ) = ei / d( i )
145 d( i+1 ) = d( i+1 ) - e( i )*ei
146 10 CONTINUE
147*
148 DO 20 i = i4 + 1, n - 4, 4
149*
150* Drop out of the loop if d(i) <= 0: the matrix is not positive
151* definite.
152*
153 IF( d( i ).LE.zero ) THEN
154 info = i
155 GO TO 30
156 END IF
157*
158* Solve for e(i) and d(i+1).
159*
160 ei = e( i )
161 e( i ) = ei / d( i )
162 d( i+1 ) = d( i+1 ) - e( i )*ei
163*
164 IF( d( i+1 ).LE.zero ) THEN
165 info = i + 1
166 GO TO 30
167 END IF
168*
169* Solve for e(i+1) and d(i+2).
170*
171 ei = e( i+1 )
172 e( i+1 ) = ei / d( i+1 )
173 d( i+2 ) = d( i+2 ) - e( i+1 )*ei
174*
175 IF( d( i+2 ).LE.zero ) THEN
176 info = i + 2
177 GO TO 30
178 END IF
179*
180* Solve for e(i+2) and d(i+3).
181*
182 ei = e( i+2 )
183 e( i+2 ) = ei / d( i+2 )
184 d( i+3 ) = d( i+3 ) - e( i+2 )*ei
185*
186 IF( d( i+3 ).LE.zero ) THEN
187 info = i + 3
188 GO TO 30
189 END IF
190*
191* Solve for e(i+3) and d(i+4).
192*
193 ei = e( i+3 )
194 e( i+3 ) = ei / d( i+3 )
195 d( i+4 ) = d( i+4 ) - e( i+3 )*ei
196 20 CONTINUE
197*
198* Check d(n) for positive definiteness.
199*
200 IF( d( n ).LE.zero )
201 $ info = n
202*
203 30 CONTINUE
204 RETURN
205*
206* End of DPTTRF
207*
208 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dpttrf(N, D, E, INFO)
DPTTRF
Definition: dpttrf.f:91