 LAPACK  3.10.0 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)```

Definition at line 90 of file sptt01.f.

91 *
92 * -- LAPACK test 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 N
98  REAL RESID
99 * ..
100 * .. Array Arguments ..
101  REAL D( * ), DF( * ), E( * ), EF( * ), WORK( * )
102 * ..
103 *
104 * =====================================================================
105 *
106 * .. Parameters ..
107  REAL ONE, ZERO
108  parameter( one = 1.0e+0, zero = 0.0e+0 )
109 * ..
110 * .. Local Scalars ..
111  INTEGER I
112  REAL ANORM, DE, EPS
113 * ..
114 * .. External Functions ..
115  REAL SLAMCH
116  EXTERNAL slamch
117 * ..
118 * .. Intrinsic Functions ..
119  INTRINSIC abs, max, real
120 * ..
121 * .. Executable Statements ..
122 *
123 * Quick return if possible
124 *
125  IF( n.LE.0 ) THEN
126  resid = zero
127  RETURN
128  END IF
129 *
130  eps = slamch( 'Epsilon' )
131 *
132 * Construct the difference L*D*L' - A.
133 *
134  work( 1 ) = df( 1 ) - d( 1 )
135  DO 10 i = 1, n - 1
136  de = df( i )*ef( i )
137  work( n+i ) = de - e( i )
138  work( 1+i ) = de*ef( i ) + df( i+1 ) - d( i+1 )
139  10 CONTINUE
140 *
141 * Compute the 1-norms of the tridiagonal matrices A and WORK.
142 *
143  IF( n.EQ.1 ) THEN
144  anorm = d( 1 )
145  resid = abs( work( 1 ) )
146  ELSE
147  anorm = max( d( 1 )+abs( e( 1 ) ), d( n )+abs( e( n-1 ) ) )
148  resid = max( abs( work( 1 ) )+abs( work( n+1 ) ),
149  \$ abs( work( n ) )+abs( work( 2*n-1 ) ) )
150  DO 20 i = 2, n - 1
151  anorm = max( anorm, d( i )+abs( e( i ) )+abs( e( i-1 ) ) )
152  resid = max( resid, abs( work( i ) )+abs( work( n+i-1 ) )+
153  \$ abs( work( n+i ) ) )
154  20 CONTINUE
155  END IF
156 *
157 * Compute norm(L*D*L' - A) / (n * norm(A) * EPS)
158 *
159  IF( anorm.LE.zero ) THEN
160  IF( resid.NE.zero )
161  \$ resid = one / eps
162  ELSE
163  resid = ( ( resid / real( n ) ) / anorm ) / eps
164  END IF
165 *
166  RETURN
167 *
168 * End of SPTT01
169 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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