LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
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/
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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 *> \date December 2016
88 *
89 *> \ingroup doublePTcomputational
90 *
91 * =====================================================================
92  SUBROUTINE dpttrf( N, D, E, INFO )
93 *
94 * -- LAPACK computational routine (version 3.7.0) --
95 * -- LAPACK is a software package provided by Univ. of Tennessee, --
96 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
97 * December 2016
98 *
99 * .. Scalar Arguments ..
100  INTEGER INFO, N
101 * ..
102 * .. Array Arguments ..
103  DOUBLE PRECISION D( * ), E( * )
104 * ..
105 *
106 * =====================================================================
107 *
108 * .. Parameters ..
109  DOUBLE PRECISION ZERO
110  parameter( zero = 0.0d+0 )
111 * ..
112 * .. Local Scalars ..
113  INTEGER I, I4
114  DOUBLE PRECISION EI
115 * ..
116 * .. External Subroutines ..
117  EXTERNAL xerbla
118 * ..
119 * .. Intrinsic Functions ..
120  INTRINSIC mod
121 * ..
122 * .. Executable Statements ..
123 *
124 * Test the input parameters.
125 *
126  info = 0
127  IF( n.LT.0 ) THEN
128  info = -1
129  CALL xerbla( 'DPTTRF', -info )
130  RETURN
131  END IF
132 *
133 * Quick return if possible
134 *
135  IF( n.EQ.0 )
136  \$ RETURN
137 *
138 * Compute the L*D*L**T (or U**T*D*U) factorization of A.
139 *
140  i4 = mod( n-1, 4 )
141  DO 10 i = 1, i4
142  IF( d( i ).LE.zero ) THEN
143  info = i
144  GO TO 30
145  END IF
146  ei = e( i )
147  e( i ) = ei / d( i )
148  d( i+1 ) = d( i+1 ) - e( i )*ei
149  10 CONTINUE
150 *
151  DO 20 i = i4 + 1, n - 4, 4
152 *
153 * Drop out of the loop if d(i) <= 0: the matrix is not positive
154 * definite.
155 *
156  IF( d( i ).LE.zero ) THEN
157  info = i
158  GO TO 30
159  END IF
160 *
161 * Solve for e(i) and d(i+1).
162 *
163  ei = e( i )
164  e( i ) = ei / d( i )
165  d( i+1 ) = d( i+1 ) - e( i )*ei
166 *
167  IF( d( i+1 ).LE.zero ) THEN
168  info = i + 1
169  GO TO 30
170  END IF
171 *
172 * Solve for e(i+1) and d(i+2).
173 *
174  ei = e( i+1 )
175  e( i+1 ) = ei / d( i+1 )
176  d( i+2 ) = d( i+2 ) - e( i+1 )*ei
177 *
178  IF( d( i+2 ).LE.zero ) THEN
179  info = i + 2
180  GO TO 30
181  END IF
182 *
183 * Solve for e(i+2) and d(i+3).
184 *
185  ei = e( i+2 )
186  e( i+2 ) = ei / d( i+2 )
187  d( i+3 ) = d( i+3 ) - e( i+2 )*ei
188 *
189  IF( d( i+3 ).LE.zero ) THEN
190  info = i + 3
191  GO TO 30
192  END IF
193 *
194 * Solve for e(i+3) and d(i+4).
195 *
196  ei = e( i+3 )
197  e( i+3 ) = ei / d( i+3 )
198  d( i+4 ) = d( i+4 ) - e( i+3 )*ei
199  20 CONTINUE
200 *
201 * Check d(n) for positive definiteness.
202 *
203  IF( d( n ).LE.zero )
204  \$ info = n
205 *
206  30 CONTINUE
207  RETURN
208 *
209 * End of DPTTRF
210 *
211  END
subroutine dpttrf(N, D, E, INFO)
DPTTRF
Definition: dpttrf.f:93
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62