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Suggestions for improving speed
*To*: mathgroup at smc.vnet.net
*Subject*: [mg113304] Suggestions for improving speed
*From*: Joe Hays <hays.joe at gmail.com>
*Date*: Sat, 23 Oct 2010 07:04:10 -0400 (EDT)
Hello all,
Today I've been studying B-Splines. I know that Mathematica has a built-in
function to build the basis of a B-Spline but I wanted to better understand
it so I coded up my own following the "Cox-de Boor recursion formula" found
at: http://en.wikipedia.org/wiki/B-spline#Cubic_B-Spline
I tested it against Mathematica's version to make sure things were working
OK. After I got the right answer I timed the two implementations.
Mathematica's took ~ 0.12 seconds. My version took ~15.53 seconds. I
expected my implementation to be slower but not 125X slower!
I realize that I still approach things from the procedural point of view.
So, I thought I'd ask the Mathematica gurus if they see obvious coding
choices that cause the drastic slow down...
My tests were:
Given,
m=15;
n=3;
knots=Range[0,m-1]
j=3;
time=3.5;
Mathematica's version:
<snip>
tmpT=AbsoluteTime[];
Plot[Table[BSplineBasis[{n,knots},j,time],{j,0,m-n-2}],{time,0,m-1},
PlotRange->All]
AbsoluteTime[] - tmpT
</snip>
this took ~0.12 seconds
my version,
<snip>
tmpT=AbsoluteTime[];
Plot[Table[NthBasisRecursive[{n,knots},j,time],{j,0,m-n-2}],{time,0,m-1},
PlotRange->All]
AbsoluteTime[] - tmpT
</snip>
this took ~15.53 seconds
Now, for my code defining "NthBasisRecursive"
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NthBasisRecursive[{n_, knots_}, j_, time_] :=
Module[{jj, nn, myBasis, jIdx},
myBasis = ConstantArray[0, {n + 1, n + 1}];
For[nn = 1, nn <= n + 1, nn++,
For[jj = 1, jj <= n + 1, jj++,
jIdx = j + jj; (* Need to offset the knot indexing by the jth basis I'm
solving for *)
If[nn == 1,
If[knots[[jIdx]] <= time < knots[[jIdx + 1]],
myBasis[[jj, nn]] = 1;
];
,
If[(jj - 1) <= n - (nn - 1),
myBasis[[jj, nn]] = (time - knots[[jIdx]])/(knots[[jIdx + nn - 1]] -
knots[[jIdx]])*myBasis[[jj, (nn - 1)]]
+ (knots[[jIdx + nn]] - time)/(knots[[jIdx + nn]] - knots[[jIdx +
1]])*myBasis[[(jj + 1), (nn - 1)]];
,
];(* end of inner IF *)
];(* end of outer IF *)
];(* end of JJ loop *)
];(* end of nn loop *)
myBasis[[1, n + 1]]
]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Any insight to help me learn how to make things faster would be greatly
appreciated!
Joe
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