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annotate +sbp/ordinary2.m @ 87:0a29a60e0b21

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In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
author Martin Almquist <martin.almquist@it.uu.se>
date Sun, 29 Nov 2015 22:23:09 +0100
parents 32b39dc44474
children
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29
32b39dc44474 Removed repository inside +sbp to make it part of the root repo.
Jonatan Werpers <jonatan@werpers.com>
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1 function [H, HI, D1, D2, e_1, e_m, M,Q S_1, S_m] = ordinary2(m,h)
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2 e_1=zeros(m,1);e_1(1)=1;
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3 e_m=zeros(m,1);e_m(m)=1;
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5 H=(eye(m,m));H(1,1)=0.5;H(m,m)=0.5;
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6 H=h*H;
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7 HI=inv(H);
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8
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9 D1=((.5*diag(ones(m-1,1),1)-.5*diag(ones(m-1,1),-1)));
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10 D1(1,1)=-1;D1(1,2)=1;D1(m,m-1)=-1;D1(m,m)=1;
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11 D1(m,m-1)=-1;D1(m,m)=1;
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12 D1=D1/h;
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14 Q=H*D1 + 1/2*e_1*e_1' - 1/2*e_m*e_m';
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15
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16 D2=((diag(ones(m-1,1),1)+diag(ones(m-1,1),-1)-2*diag(ones(m,1),0)));
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17 D2(1,1)=1;D2(1,2)=-2;D2(1,3)=1;
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18 D2(m,m-2)=1;D2(m,m-1)=-2;D2(m,m)=1;
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19 D2=D2/h^2;
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20
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21 S_U=[-3/2, 2, -1/2]/h;
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22 S_1=zeros(1,m);
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23 S_1(1:3)=S_U;
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24 S_m=zeros(1,m);
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25 S_m(m-2:m)=fliplr(-S_U);
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28 M=-H*D2-e_1*S_1+e_m*S_m;
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29 S_1 = S_1';
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30 S_m = S_m';
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