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annotate +util/calc_borrowing.m @ 99:ecf77a50d4fe feature/arclen-param

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The arclength parameter function was slow because it called fzero. Now it is constructed once and for all with splines. Much better performance.
author Martin Almquist <martin.almquist@it.uu.se>
date Sun, 06 Dec 2015 15:41:42 +0100
parents 48b6fb693025
children 03151dd46534
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1
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2 m = 30;
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3 h = 1;
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4
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6 %% 4th order non-compatible
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7 [H, HI, D1, D2, D3, D4, e_1, e_m, M, M4,Q, Q3, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher4(m,h);
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8 S1 = S_1*S_1' + S_m*S_m';
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9 S2 = S2_1*S2_1' + S2_m*S2_m';
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10 S3 = S3_1*S3_1' + S3_m*S3_m';
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11
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12 alpha_II = util.matrixborrow(M4, h*S2 );
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13 alpha_III = util.matrixborrow(M4, h^3*S3);
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14 fprintf('4th order non-compatible\n')
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15 fprintf('alpha_II: %.10f\n',alpha_II)
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16 fprintf('alpha_III: %.10f\n',alpha_III)
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17 fprintf('\n')
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18
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19
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20 %% 6th order non-compatible
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21 [H, HI, D1, D2, D3, D4, e_1, e_m, M, M4,Q, Q3, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher6(m,h);
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22 S1 = S_1*S_1' + S_m*S_m';
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23 S2 = S2_1*S2_1' + S2_m*S2_m';
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24 S3 = S3_1*S3_1' + S3_m*S3_m';
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25
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26 alpha_II = util.matrixborrow(M4, h*S2 );
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27 alpha_III = util.matrixborrow(M4, h^3*S3);
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28 fprintf('6th order non-compatible\n')
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29 fprintf('alpha_II: %.10f\n',alpha_II)
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30 fprintf('alpha_III: %.10f\n',alpha_III)
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31 fprintf('\n')
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32
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33
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34 %% 2nd order compatible
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35 [H, HI, D1, D4, e_1, e_m, M4, Q, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher2_compatible(m,h);
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36 S1 = S_1*S_1' + S_m*S_m';
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37 S2 = S2_1*S2_1' + S2_m*S2_m';
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38 S3 = S3_1*S3_1' + S3_m*S3_m';
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39
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40 alpha_II = util.matrixborrow(M4, h*S2 );
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41 alpha_III = util.matrixborrow(M4, h^3*S3);
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42 fprintf('2nd order compatible\n')
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43 fprintf('alpha_II: %.10f\n',alpha_II)
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44 fprintf('alpha_III: %.10f\n',alpha_III)
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45 fprintf('\n')
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46
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47
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48 %% 4th order compatible
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49 [H, HI, D1, D4, e_1, e_m, M4, Q, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher4_compatible(m,h);
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50 S1 = S_1*S_1' + S_m*S_m';
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51 S2 = S2_1*S2_1' + S2_m*S2_m';
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52 S3 = S3_1*S3_1' + S3_m*S3_m';
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53
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54 alpha_II = util.matrixborrow(M4, h*S2 );
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55 alpha_III = util.matrixborrow(M4, h^3*S3);
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56 fprintf('4th order compatible\n')
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57 fprintf('alpha_II: %.10f\n',alpha_II)
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58 fprintf('alpha_III: %.10f\n',alpha_III)
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59 fprintf('\n')
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60
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61 %% 6th order compatible
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62 [H, HI, D1, D4, e_1, e_m, M4, Q, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher6_compatible(m,h);
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63 S1 = S_1*S_1' + S_m*S_m';
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64 S2 = S2_1*S2_1' + S2_m*S2_m';
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65 S3 = S3_1*S3_1' + S3_m*S3_m';
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66
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67 alpha_II = util.matrixborrow(M4, h*S2 );
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68 alpha_III = util.matrixborrow(M4, h^3*S3);
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69 fprintf('6th order compatible\n')
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70 fprintf('alpha_II: %.10f\n',alpha_II)
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71 fprintf('alpha_III: %.10f\n',alpha_III)