Robert M. Corless
Department of Applied Mathematics
University of Western Ontario
London, Canada

Copyright 2001 by Robert M. Corless
All rights reserved

Programming in Maple 

Программирование в Maple

Procedures 

Процедуры

Example: Modified Gram-Schmidt 

Пример: Преобразования Грэм-Шмидта

> restart;
> read "D:/books/ess/programs/mgs.mpl";
> with(LinearAlgebra):
> m, n := 30,27;

m, n := 30, 27
> A := RandomMatrix(m,n);

A := _rtable[4521592]
> Digits := trunc(evalhf(Digits));

Digits := 14
> #st := time(): Q,R := MGS1(A); time()-st; # BAD THING TO DO
> st := time(): Q,R := MGS1( evalf(A) ); time()-st;

Q, R := _rtable[4430752], _rtable[4410600]

1.929
> Norm( Q.R - A, infinity )/Norm(A,infinity);

.27550946273835e-13
> Norm( HermitianTranspose(Q).Q - IdentityMatrix(n), infinity );

.159951392408874682e-11
> st := time(): Q,R := MGS2( evalf(A) ): time()-st;

3.780
> Norm( Q.R - A, infinity)/Norm(A,infinity);

.95130874855135e-14
> Norm( HermitianTranspose(Q).Q - IdentityMatrix(n), infinity );

.837810723575138638e-12
> st := time(): Q,R := MGS3( evalf(A) ): time()-st;

1.828
> Norm( Q.R - A, infinity)/Norm(A,infinity);

.95130874855135e-14
> Norm( HermitianTranspose(Q).Q - IdentityMatrix(n), infinity );

.837810723575138638e-12
> st := time(): Q,R := MGS4( evalf(A) ): time()-st;

1.749
> Norm( Q.R - A, infinity)/Norm(A,infinity);

.95130874855135e-14
> Norm( HermitianTranspose(Q).Q - IdentityMatrix(n), infinity );

.837810723575138638e-12
> read "D:/books/ess/programs/mgs.mpl";
> st := time(): Q,R := MGS5( evalf(A) ): time()-st;

2.303
> Norm( Q.R - A, infinity)/Norm(A,infinity);

.21137775625707e-13
> Norm( HermitianTranspose(Q).Q - IdentityMatrix(n), infinity );

.824002324706363254e-12

С официального разрешения                    © 2002 Waterloo Maple, Inc

 
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