LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ sptt01()

subroutine sptt01 ( integer  N,
real, dimension( * )  D,
real, dimension( * )  E,
real, dimension( * )  DF,
real, dimension( * )  EF,
real, dimension( * )  WORK,
real  RESID 
)

SPTT01

Purpose:
 SPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
 factorization and computes the residual
    norm(L*D*L' - A) / ( n * norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]N
          N is INTEGTER
          The order of the matrix A.
[in]D
          D is REAL array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.
[in]E
          E is REAL array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in]DF
          DF is REAL array, dimension (N)
          The n diagonal elements of the factor L from the L*D*L'
          factorization of A.
[in]EF
          EF is REAL array, dimension (N-1)
          The (n-1) subdiagonal elements of the factor L from the
          L*D*L' factorization of A.
[out]WORK
          WORK is REAL array, dimension (2*N)
[out]RESID
          RESID is REAL
          norm(L*D*L' - A) / (n * norm(A) * EPS)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 93 of file sptt01.f.

93 *
94 * -- LAPACK test 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 n
101  REAL resid
102 * ..
103 * .. Array Arguments ..
104  REAL d( * ), df( * ), e( * ), ef( * ), work( * )
105 * ..
106 *
107 * =====================================================================
108 *
109 * .. Parameters ..
110  REAL one, zero
111  parameter( one = 1.0e+0, zero = 0.0e+0 )
112 * ..
113 * .. Local Scalars ..
114  INTEGER i
115  REAL anorm, de, eps
116 * ..
117 * .. External Functions ..
118  REAL slamch
119  EXTERNAL slamch
120 * ..
121 * .. Intrinsic Functions ..
122  INTRINSIC abs, max, real
123 * ..
124 * .. Executable Statements ..
125 *
126 * Quick return if possible
127 *
128  IF( n.LE.0 ) THEN
129  resid = zero
130  RETURN
131  END IF
132 *
133  eps = slamch( 'Epsilon' )
134 *
135 * Construct the difference L*D*L' - A.
136 *
137  work( 1 ) = df( 1 ) - d( 1 )
138  DO 10 i = 1, n - 1
139  de = df( i )*ef( i )
140  work( n+i ) = de - e( i )
141  work( 1+i ) = de*ef( i ) + df( i+1 ) - d( i+1 )
142  10 CONTINUE
143 *
144 * Compute the 1-norms of the tridiagonal matrices A and WORK.
145 *
146  IF( n.EQ.1 ) THEN
147  anorm = d( 1 )
148  resid = abs( work( 1 ) )
149  ELSE
150  anorm = max( d( 1 )+abs( e( 1 ) ), d( n )+abs( e( n-1 ) ) )
151  resid = max( abs( work( 1 ) )+abs( work( n+1 ) ),
152  $ abs( work( n ) )+abs( work( 2*n-1 ) ) )
153  DO 20 i = 2, n - 1
154  anorm = max( anorm, d( i )+abs( e( i ) )+abs( e( i-1 ) ) )
155  resid = max( resid, abs( work( i ) )+abs( work( n+i-1 ) )+
156  $ abs( work( n+i ) ) )
157  20 CONTINUE
158  END IF
159 *
160 * Compute norm(L*D*L' - A) / (n * norm(A) * EPS)
161 *
162  IF( anorm.LE.zero ) THEN
163  IF( resid.NE.zero )
164  $ resid = one / eps
165  ELSE
166  resid = ( ( resid / REAL( N ) ) / anorm ) / eps
167  END IF
168 *
169  RETURN
170 *
171 * End of SPTT01
172 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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