matrix of vectors - super slow

• To: mathgroup at smc.vnet.net
• Subject: [mg88038] matrix of vectors - super slow
• From: baaarnes at gmail.com
• Date: Tue, 22 Apr 2008 06:30:10 -0400 (EDT)

```I have an matrix of vectors where each element has to go through
various transformations, that is each element has to be multiplied by
a few different matrices.  Is there a more efficient way of doing that
from what I am currently doing?

n = 128*1;
m = 128*1;
R = 1;
BeamIn = Table[( {
{Sqrt[2]/2},
{Sqrt[2]/2}
} ), {i, n}, {j, m}];
PBeam = Table[0, {i, n}, {j, m}];
SBeam = Table[0, {i, n}, {j, m}];
PInt = Table[0, {i, n}, {j, m}];
SInt = Table[0, {i, n}, {j, m}];

HalfWave[\[Theta]_] = ( {
{Cos[-\[Theta]], Sin[-\[Theta]]},
{-Sin[-\[Theta]], Cos[-\[Theta]]}
} ).( {
{1, 0},
{0, Exp[-I \[Pi]]}
} ).( {
{Cos[\[Theta]], Sin[\[Theta]]},
{-Sin[\[Theta]], Cos[\[Theta]]}
} );
QuarterWave[\[Theta]_] = ( {
{Cos[-\[Theta]], Sin[-\[Theta]]},
{-Sin[-\[Theta]], Cos[-\[Theta]]}
} ).( {
{1, 0},
{0, Exp[-I \[Pi]/2]}
} ).( {
{Cos[\[Theta]], Sin[\[Theta]]},
{-Sin[\[Theta]], Cos[\[Theta]]}
} );
PPol = ( {
{1, 0},
{0, 0}
} );
SPol = ( {
{0, 0},
{0, 1}
} );
LaserRod[TT_, \[Theta]_, Q_] = ( {
{Cos[-\[Theta]], Sin[-\[Theta]]},
{-Sin[-\[Theta]], Cos[-\[Theta]]}
} ).( {
{Exp[-I *2.8 *TT^2*Q], 0},
{0, Exp[I *0.4 *TT^2* Q]}
} ).( {
{Cos[\[Theta]], Sin[\[Theta]]},
{-Sin[\[Theta]], Cos[\[Theta]]}
} );

For[i = 1, i <= n, i++,
For[j = 1, j <= m, j++,
x = R ((2 i - n) - 1);
y = R ((2 j - m) - 1);
r = Sqrt[x^2 + y^2];
\[Theta] = ArcTan[y/x];
PBeam[[i, j]] =
PPol.LaserRod[r, \[Theta], 1*10^-3].QuarterWave[\[Pi]/
2].LaserRod[r, \[Theta], 1*10^-3].PPol.BeamIn[[i, j]];
SBeam[[i, j]] =
SPol.LaserRod[r, \[Theta], 1*10^-3].QuarterWave[\[Pi]/
2].LaserRod[r, \[Theta], 1*10^-3].PPol.BeamIn[[i, j]];
PInt[[i, j]] = Norm[PBeam[[i, j]][[1, 1]]]^2;
SInt[[i, j]] = Norm[SBeam[[i, j]][[2, 1]]]^2;
];
];
ListDensityPlot[PInt]
ListDensityPlot[SInt]

Cheers

```

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