 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dpttrf()

 subroutine dpttrf ( integer N, double precision, dimension( * ) D, double precision, dimension( * ) E, integer INFO )

DPTTRF

Purpose:
``` DPTTRF computes the L*D*L**T factorization of a real symmetric
positive definite tridiagonal matrix A.  The factorization may also
be regarded as having the form A = U**T*D*U.```
Parameters
 [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] D ``` D is DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.``` [in,out] E ``` E is DOUBLE PRECISION array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value > 0: if INFO = k, the leading minor of order k is not positive definite; if k < N, the factorization could not be completed, while if k = N, the factorization was completed, but D(N) <= 0.```

Definition at line 90 of file dpttrf.f.

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 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
Here is the call graph for this function:
Here is the caller graph for this function: