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\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/input nepip.input}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{License}
<<license>>=
--Copyright The Numerical Algorithms Group Limited 1996.
@
<<*>>=
<<license>>
-- Note that the conversions of results from DoubleFloat to Float
-- will become unnecessary if outputGeneral is extended to apply to
-- DoubleFloat quantities.
outputGeneral 5
mA1 := matrix [[ 0.5 , 1.5 , 6.6 , 4.8], _
[ 1.5 , 6.5 , 16.2 , 8.6], _
[ 6.6 , 16.2 , 37.6 , 9.8], _
[ 4.8 , 8.6 , 9.8 , -17.1]];
mB1 := matrix[[ 1 , 3 , 4 , 1], _
[ 3 , 13 , 16 , 11], _
[ 4 , 16 , 24 , 18], _
[ 1 , 11 , 18 , 27]];
mA2 := matrix [[ 3.9 , 12.5 , -34.5 , -0.5], _
[ 4.3 , 21.5 , -47.5 , 7.5], _
[ 4.3 , 21.5 , -43.5 , 3.5], _
[ 4.4 , 26.0 , -46.0 , 6.0]];
mB2 := matrix[[ 1 , 2 , -3 , 1], _
[ 1 , 3 , -5 , 4], _
[ 1 , 3 , -4 , 3], _
[ 1 , 3 , -4 , 4]];
nagEigenvalues(mA1,mB1) :: List Float
-- [- 3.0,- 1.0,2.0,4.0]
vv1 := nagEigenvectors(mA1,mB1);
(vv1.eigenvalues) :: List Float
-- [- 3.0,- 1.0,2.0,4.0]
(vv1.eigenvectors) :: List Vector Complex Float
-- [[- 4.35,0.05,1.0,- 0.5], [- 2.05,0.15,0.5,- 0.5], [- 3.95,0.85,0.5,- 0.5],
-- [2.65,0.05,- 1.0,0.5]]
nagEigenvalues(mA2,mB2)
-- all components are O(1) or more so:
% :: List Complex Float
-- [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0]
vv2 := nagEigenvectors(mA2,mB2);
vv2.eigenvalues
-- all components are O(1) or more so:
% :: List Complex Float
-- [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0]
vv2.eigenvectors :: List Vector Complex Float
-- [[0.99606,0.0056917,0.062609,0.062609],
--
-- [0.94491, 0.18898 + 0.26077 E -14 %i, 0.11339 - 0.15119 %i,
-- 0.11339 - 0.15119 %i]
-- ,
--
-- [0.94491, 0.18898 - 0.26077 E -14 %i, 0.11339 + 0.15119 %i,
-- 0.11339 + 0.15119 %i]
-- ,
-- [0.98752,0.010972,- 0.032917,0.15361]]
-- The same call with eps=0.0001:
vv2a := nagEigenvectors(mA2,mB2,0.0001);
vv2a.eigenvalues :: List Complex Float
-- [1.9989,3.0003 + 3.9994 %i,3.0003 - 3.9994 %i,4.0]
vv2a.eigenvectors :: List Vector Complex Float
-- [[0.99605,0.0057355,0.062656,0.062656],
--
-- [0.94491, 0.18899 - 0.000048882 %i, 0.11336 - 0.15119 %i,
-- 0.11336 - 0.15119 %i]
-- ,
--
-- [0.94491, 0.18899 + 0.000048882 %i, 0.11336 + 0.15119 %i,
-- 0.11336 + 0.15119 %i]
-- ,
-- [0.98751,0.011031,- 0.032912,0.15367]]
mB1(1,1) := -1;
-- The next test should fail on F02ADF then call F02BJF:
nagEigenvalues(mA1,mB1)
-- all components are O(1) or more so:
% :: List Complex Float
-- [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i]
-- Similarly, this should fail on F02AEF then call F02BJF:
vv3 := nagEigenvectors(mA1,mB1);
vv3.eigenvalues
-- all components are O(1) or more so:
% :: List Complex Float
-- [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i]
vv3.eigenvectors :: List Vector Complex Float
-- [[- 0.034577,0.63045,- 0.75202,0.1892],
-- [0.17876,- 0.73845,0.047413,0.64845],
--
-- [0.80838, - 0.00095133 + 0.47557 %i, - 0.20354 - 0.21737 %i,
-- 0.15404 + 0.089179 %i]
-- ,
--
-- [0.80838, - 0.00095133 - 0.47557 %i, - 0.20354 + 0.21737 %i,
-- 0.15404 - 0.089179 %i]
-- ]
outputGeneral()
output "End of tests"
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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