196 lines
5.9 KiB
Text
196 lines
5.9 KiB
Text
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//#define WANT_STREAM
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#include "include.h"
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#include "newmatap.h"
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#include "tmt.h"
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#ifdef use_namespace
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using namespace NEWMAT;
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#endif
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ReturnMatrix Inverter(const CroutMatrix& X)
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{
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Matrix Y = X.i();
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Y.Release();
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return Y.ForReturn();
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}
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void trymatd()
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{
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Tracer et("Thirteenth test of Matrix package");
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Tracer::PrintTrace();
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Matrix X(5,20);
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int i,j;
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for (j=1;j<=20;j++) X(1,j) = j+1;
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for (i=2;i<=5;i++) for (j=1;j<=20; j++) X(i,j) = (long)X(i-1,j) * j % 1001;
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SymmetricMatrix S; S << X * X.t();
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Matrix SM = X * X.t() - S;
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Print(SM);
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LowerTriangularMatrix L = Cholesky(S);
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Matrix Diff = L*L.t()-S; Clean(Diff, 0.000000001);
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Print(Diff);
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{
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Tracer et1("Stage 1");
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LowerTriangularMatrix L1(5);
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Matrix Xt = X.t(); Matrix Xt2 = Xt;
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QRZT(X,L1);
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Diff = L - L1; Clean(Diff,0.000000001); Print(Diff);
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UpperTriangularMatrix Ut(5);
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QRZ(Xt,Ut);
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Diff = L - Ut.t(); Clean(Diff,0.000000001); Print(Diff);
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Matrix Y(3,20);
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for (j=1;j<=20;j++) Y(1,j) = 22-j;
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for (i=2;i<=3;i++) for (j=1;j<=20; j++)
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Y(i,j) = (long)Y(i-1,j) * j % 101;
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Matrix Yt = Y.t(); Matrix M,Mt; Matrix Y2=Y;
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QRZT(X,Y,M); QRZ(Xt,Yt,Mt);
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Diff = Xt - X.t(); Clean(Diff,0.000000001); Print(Diff);
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Diff = Yt - Y.t(); Clean(Diff,0.000000001); Print(Diff);
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Diff = Mt - M.t(); Clean(Diff,0.000000001); Print(Diff);
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Diff = Y2 * Xt2 * S.i() - M * L.i();
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Clean(Diff,0.000000001); Print(Diff);
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}
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ColumnVector C1(5);
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{
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Tracer et1("Stage 2");
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X.ReSize(5,5);
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for (j=1;j<=5;j++) X(1,j) = j+1;
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for (i=2;i<=5;i++) for (j=1;j<=5; j++)
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X(i,j) = (long)X(i-1,j) * j % 1001;
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for (i=1;i<=5;i++) C1(i) = i*i;
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CroutMatrix A = X;
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ColumnVector C2 = A.i() * C1; C1 = X.i() * C1;
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X = C1 - C2; Clean(X,0.000000001); Print(X);
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}
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{
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Tracer et1("Stage 3");
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X.ReSize(7,7);
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for (j=1;j<=7;j++) X(1,j) = j+1;
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for (i=2;i<=7;i++) for (j=1;j<=7; j++)
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X(i,j) = (long)X(i-1,j) * j % 1001;
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C1.ReSize(7);
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for (i=1;i<=7;i++) C1(i) = i*i;
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RowVector R1 = C1.t();
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Diff = R1 * X.i() - ( X.t().i() * R1.t() ).t(); Clean(Diff,0.000000001);
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Print(Diff);
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}
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{
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Tracer et1("Stage 4");
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X.ReSize(5,5);
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for (j=1;j<=5;j++) X(1,j) = j+1;
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for (i=2;i<=5;i++) for (j=1;j<=5; j++)
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X(i,j) = (long)X(i-1,j) * j % 1001;
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C1.ReSize(5);
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for (i=1;i<=5;i++) C1(i) = i*i;
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CroutMatrix A1 = X*X;
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ColumnVector C2 = A1.i() * C1; C1 = X.i() * C1; C1 = X.i() * C1;
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X = C1 - C2; Clean(X,0.000000001); Print(X);
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}
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{
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Tracer et1("Stage 5");
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int n = 40;
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SymmetricBandMatrix B(n,2); B = 0.0;
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for (i=1; i<=n; i++)
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{
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B(i,i) = 6;
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if (i<=n-1) B(i,i+1) = -4;
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if (i<=n-2) B(i,i+2) = 1;
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}
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B(1,1) = 5; B(n,n) = 5;
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SymmetricMatrix A = B;
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ColumnVector X(n);
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X(1) = 429;
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for (i=2;i<=n;i++) X(i) = (long)X(i-1) * 31 % 1001;
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X = X / 100000L;
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// the matrix B is rather ill-conditioned so the difficulty is getting
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// good agreement (we have chosen X very small) may not be surprising;
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// maximum element size in B.i() is around 1400
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ColumnVector Y1 = A.i() * X;
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LowerTriangularMatrix C1 = Cholesky(A);
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ColumnVector Y2 = C1.t().i() * (C1.i() * X) - Y1;
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Clean(Y2, 0.000000001); Print(Y2);
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UpperTriangularMatrix CU = C1.t().i();
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LowerTriangularMatrix CL = C1.i();
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Y2 = CU * (CL * X) - Y1;
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Clean(Y2, 0.000000001); Print(Y2);
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Y2 = B.i() * X - Y1; Clean(Y2, 0.000000001); Print(Y2);
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LowerBandMatrix C2 = Cholesky(B);
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Matrix M = C2 - C1; Clean(M, 0.000000001); Print(M);
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ColumnVector Y3 = C2.t().i() * (C2.i() * X) - Y1;
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Clean(Y3, 0.000000001); Print(Y3);
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CU = C1.t().i();
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CL = C1.i();
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Y3 = CU * (CL * X) - Y1;
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Clean(Y3, 0.000000001); Print(Y3);
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Y3 = B.i() * X - Y1; Clean(Y3, 0.000000001); Print(Y3);
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SymmetricMatrix AI = A.i();
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Y2 = AI*X - Y1; Clean(Y2, 0.000000001); Print(Y2);
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SymmetricMatrix BI = B.i();
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BandMatrix C = B; Matrix CI = C.i();
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M = A.i() - CI; Clean(M, 0.000000001); Print(M);
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M = B.i() - CI; Clean(M, 0.000000001); Print(M);
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M = AI-BI; Clean(M, 0.000000001); Print(M);
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M = AI-CI; Clean(M, 0.000000001); Print(M);
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M = A; AI << M; M = AI-A; Clean(M, 0.000000001); Print(M);
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C = B; BI << C; M = BI-B; Clean(M, 0.000000001); Print(M);
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}
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{
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Tracer et1("Stage 5");
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SymmetricMatrix A(4), B(4);
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A << 5
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<< 1 << 4
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<< 2 << 1 << 6
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<< 1 << 0 << 1 << 7;
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B << 8
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<< 1 << 5
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<< 1 << 0 << 9
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<< 2 << 1 << 0 << 6;
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LowerTriangularMatrix AB = Cholesky(A) * Cholesky(B);
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Matrix M = Cholesky(A) * B * Cholesky(A).t() - AB*AB.t();
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Clean(M, 0.000000001); Print(M);
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M = A * Cholesky(B); M = M * M.t() - A * B * A;
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Clean(M, 0.000000001); Print(M);
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}
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{
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Tracer et1("Stage 6");
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int N=49;
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int i;
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SymmetricBandMatrix S(N,1);
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Matrix B(N,N+1); B=0;
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for (i=1;i<=N;i++) { S(i,i)=1; B(i,i)=1; B(i,i+1)=-1; }
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for (i=1;i<N; i++) S(i,i+1)=-.5;
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DiagonalMatrix D(N+1); D = 1;
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B = B.t()*S.i()*B - (D-1.0/(N+1))*2.0;
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Clean(B, 0.000000001); Print(B);
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}
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{
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Tracer et1("Stage 7");
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// See if you can pass a CroutMatrix to a function
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Matrix A(4,4);
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A.Row(1) << 3 << 2 << -1 << 4;
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A.Row(2) << -8 << 7 << 2 << 0;
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A.Row(3) << 2 << -2 << 3 << 1;
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A.Row(4) << -1 << 5 << 2 << 2;
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CroutMatrix B = A;
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Matrix C = A * Inverter(B) - IdentityMatrix(4);
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Clean(C, 0.000000001); Print(C);
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}
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// cout << "\nEnd of Thirteenth test\n";
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}
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