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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/input/nepip.input.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/input/nepip.input.pamphlet')
-rw-r--r-- | src/input/nepip.input.pamphlet | 154 |
1 files changed, 154 insertions, 0 deletions
diff --git a/src/input/nepip.input.pamphlet b/src/input/nepip.input.pamphlet new file mode 100644 index 00000000..f92484d8 --- /dev/null +++ b/src/input/nepip.input.pamphlet @@ -0,0 +1,154 @@ +\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} |