chap4_1.bas

介绍一些matlab在数学方面的应用

Attribute VB_Name = "chap4_1"
Public Sub PutOnClipboard(str As Variant)
    Dim MyDataObj As New DataObject
    MyDataObj.SetText Format(str)
    MyDataObj.PutInClipboard
End Sub
Sub d1()
PutOnClipboard ("A=zeros(3,8)")
End Sub
Sub d2()
PutOnClipboard ("B=eye(size(A))")
End Sub
Sub d3()
PutOnClipboard ("C=[1 2 3]; V=diag(C)")
End Sub
Sub d4()
PutOnClipboard ("V1=diag(V)'")
End Sub
Sub d5()
PutOnClipboard ("C=[1 2 3]; V=diag(C,2)")
End Sub
Sub d6()
PutOnClipboard ("V=diag([1 2 3 4])+diag([2 3 4],1)+diag([5 4 3],-1)")
End Sub
Sub d7()
CR = Chr(13) + Chr(10)
PutOnClipboard ("C=[1 2 3]; R=[3 4 5 6 7 8 9];" + CR + " H=hankel(C,R)")
End Sub
Sub d8()
PutOnClipboard ("C=[1 2 3]; H1=hankel(C)")
End Sub
Sub d9()
PutOnClipboard ("C=[1, 2, 3, 4, 5]; V=vander(C)")
End Sub
Sub d10()
PutOnClipboard ("P=[2 0 4 5 6]; A=compan(P)")
End Sub
Sub d11()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms a1 a2 a3 a4 a5 a6 a7 a8 a9 a10" + CR + "A=compan([a1 a2 a3 a4 a5 a6 a7 a8 a9 a10])")
End Sub
Sub d12()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1];" + CR + "det(A)")
End Sub
Sub d13()
CR = Chr(13) + Chr(10)
PutOnClipboard ("tic, A=sym(hilb(20)); det(A), toc")
End Sub
Sub d14()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]; rank(A)")
End Sub
Sub d15()
PutOnClipboard ("H=hilb(20); rank(H)")
End Sub
Sub d16()
PutOnClipboard ("H=sym(hilb(20)); rank(H)")
End Sub
Sub d17()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1];" + CR + "[norm(A), norm(A,2), norm(A,1), norm(A,Inf), norm(A,'fro')] ")
End Sub
Sub d18()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1];" + CR + "poly(A)")
End Sub
Sub d19()
PutOnClipboard ("A=sym(A); poly(A)")
End Sub
Sub d20()
PutOnClipboard ("poly1(A)")
End Sub
Sub d21()
CR = Chr(13) + Chr(10)
PutOnClipboard ("syms a1 a2 a3 a4 a5; " + CR + "A=vander([a1 a2 a3 a4 a5]);" + CR + "collect(poly(A),x)")
End Sub
Sub d22()
PutOnClipboard ("A=vander([1 2 3 4 5 6 7])")
End Sub
Sub d23()
PutOnClipboard ("aa=poly(A); B=polyvalm(aa, A); norm(B)")
End Sub
Sub d24()
PutOnClipboard ("aa1=poly1(A); B1=polyvalm(aa1, A); norm(B1)")
End Sub
Sub d25()
PutOnClipboard ("P=[1 2 3 4 5 6];f=poly2sym(P,'v')")
End Sub
Sub d26()
PutOnClipboard ("P=sym2poly(f)")
End Sub
Sub d27()
PutOnClipboard ("format long; H=hilb(4); H1=inv(H)")
End Sub
Sub d28()
PutOnClipboard ("H*H1")
End Sub
Sub d29()
PutOnClipboard ("norm(H*inv(H)-eye(size(H)))")
End Sub
Sub d30()
PutOnClipboard ("H2=invhilb(4); norm(H*H2-eye(size(H)))")
End Sub
Sub d31()
PutOnClipboard ("H=hilb(10); H1=inv(H); norm(H*H1-eye(size(H)))")
End Sub
Sub d32()
PutOnClipboard ("H2=invhilb(10); norm(H*H2-eye(size(H)))")
End Sub
Sub d33()
PutOnClipboard ("H=hilb(13); H1=inv(H); norm(H*H1-eye(size(H)))")
End Sub
Sub d34()
PutOnClipboard ("H2=invhilb(13); norm(H*H2-eye(size(H)))")
End Sub
Sub d35()
PutOnClipboard ("H=sym(hilb(7)); inv(H)")
End Sub
Sub d36()
PutOnClipboard ("H=sym(hilb(30)); norm(double(H*inv(H)-eye(size(H))))")
End Sub
Sub d37()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1];" + CR + "format long; B = inv(A)")
End Sub
Sub d38()
PutOnClipboard ("norm(A*B-eye(size(A)))")
End Sub
Sub d39()
PutOnClipboard ("A=sym(A); inv(A)")
End Sub
Sub d40()
PutOnClipboard ("syms a1 a2 a3 a4; H=hankel([a1 a2 a3 a4]); inv(H)")
End Sub
Sub d41()
PutOnClipboard ("A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1];" + CR + "B=pinv(A)")
End Sub
Sub d42()
PutOnClipboard ("A*B")
End Sub
Sub d43()
PutOnClipboard ("norm(A*B*A-A)")
End Sub
Sub d44()
PutOnClipboard ("norm(B*A*B-B)")
End Sub
Sub d45()
PutOnClipboard ("[norm(A*B-(A*B)'), norm(B*A-(B*A)')]")
End Sub
Sub d46()
PutOnClipboard ("pinv(B)")
End Sub
Sub d47()
PutOnClipboard ("A=[6,1,4,2,1; 3,0,1,4,2; -3,-2,-5,8,4]; rank(A)")
End Sub
Sub d48()
PutOnClipboard ("iA = pinv(A)")
End Sub
Sub d49()
PutOnClipboard ("norm(iA*A*iA-iA)")
End Sub
Sub d50()
PutOnClipboard ("norm(A*iA*A-A)")
End Sub
Sub d51()
PutOnClipboard ("norm(iA*A-A'*iA')")
End Sub
Sub d52()
PutOnClipboard ("norm(A*iA-iA'*A')")
End Sub
Sub d53()
PutOnClipboard ("A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]; eig(A)")
End Sub
Sub d54()
PutOnClipboard ("eig(sym(A))")
End Sub
Sub d55()
PutOnClipboard ("vpa(ans,70)")
End Sub
Sub d56()
PutOnClipboard ("[v, d] = eig(A)")
End Sub
Sub d57()
PutOnClipboard ("[v,d]=eig(sym(A))")
End Sub
Sub d58()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[5,7,6,5; 7,10,8,7; 6,8,10,9; 5,7,9,10];" + CR + "B=[2,6,-1,-2; 5,-1,2,3; -3,-4,1,10; 5,-2,-3,8];" + CR + "[V, D] = eig(A, B)")
End Sub
Sub d59()
PutOnClipboard ("norm(A*V-B*V*D)")
End Sub
Sub d60()
PutOnClipboard ("B=magic(4); eig(A,B)")
End Sub
Sub d61()
PutOnClipboard ("A=[5,9,8,3; 0,3,2,4; 2,3,5,9; 3,4,5,8];Q=orth(A)")
End Sub
Sub d62()
PutOnClipboard ("norm(Q'*Q-eye(4))")
End Sub
Sub d63()
PutOnClipboard ("norm(Q*Q'-eye(4))")
End Sub
Sub d64()
PutOnClipboard ("A=[16,2,3,13; 5,11,10,8; 9,7,6,12; 4,14,15,1];Q=orth(A)")
End Sub
Sub d65()
PutOnClipboard ("norm(Q'*Q-eye(3))")
End Sub
Sub d66()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1];" + CR + "[L1,U1]=lu(A)")
End Sub
Sub d67()
PutOnClipboard ("[L, U, P] = lu(A)")
End Sub
Sub d68()
PutOnClipboard ("inv(P)*L*U")
End Sub
Sub d69()
PutOnClipboard ("A=[9,3,4,2; 3,6,0,7; 4,0,6,0; 2,7,0,9];D=chol(A)")
End Sub
Sub d70()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[7,5,5,8; 5,6,9,7; 5,9,9,0; 8,7,0,1];" + CR + "[D,p]=chol(A)")
End Sub
Sub d71()
PutOnClipboard ("norm(A*A'-A'*A)<eps")
End Sub
Sub d72()
CR = Chr(13) + Chr(10)
PutOnClipboard (" A=[-71,-65,-81,-46; 75,89,117,50; 0,4,8,4; -67,-121,-173,-58];" + CR + "D=eig(A)")
End Sub
Sub d73()
PutOnClipboard ("[v,d]=eig(sym(A))")
End Sub
Sub d74()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[-71,-65,-81,-46; 75,89,117,50; 0,4,8,4; -67,-121,-173,-58];" + CR + "[V,J]=jordan(sym(A))")
End Sub
Sub d75()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[-10,-14,-17,-9; 10,16,18,10; 0,-1,0,0; -9,-15,-17,-10];" + CR + "[V,J]=jordan(sym(A))")
End Sub
Sub d76()
PutOnClipboard ("A=[1 1; 5*eps,0; 0,5*eps]; rank(A)")
End Sub
Sub d77()
CR = Chr(13) + Chr(10)
PutOnClipboard ("[16,2,3,13; 5,11,10,8; 9,7,6,12; 4,14,15,1];" + CR + "[L, A1, M]=svd(A)")
End Sub
Sub d78()
PutOnClipboard ("cond(A)")
End Sub
Sub d79()
PutOnClipboard ("A=[1,3,5,7; 2,4,6,8]; [L,A1,M]=svd(A)")
End Sub
Sub d80()
PutOnClipboard ("A2=L*A1*M'")
End Sub
Sub d81()
PutOnClipboard ("norm(A-A2)")
End Sub
Sub d82()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2];" + CR + " B=[5 1; 4 2; 3 3; 2 4];" + CR + "x=inv(A)*B")
End Sub
Sub d83()
PutOnClipboard ("norm(A*x-B)")
End Sub
Sub d84()
PutOnClipboard ("x1=inv(sym(A))*B")
End Sub
Sub d85()
PutOnClipboard ("norm(double(A*x1-B))")
End Sub
Sub d86()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[1 2 3 4; 2 2 1 1; 2 4 6 8; 4 4 2 2]; " + CR + "B=[1;3;2;6];" + CR + "C=[A B]; [rank(A), rank(C)]")
End Sub
Sub d87()
PutOnClipboard ("Z=null(A,'r')")
End Sub
Sub d88()
PutOnClipboard ("x0=pinv(A)*B")
End Sub
Sub d89()
CR = Chr(13) + Chr(10)
PutOnClipboard ("a1=randn(1); a2=rand(1);" + CR + "x=a1*Z(:,1)+a2*Z(:,2)+x0; norm(A*x-B)")
End Sub
Sub d90()
PutOnClipboard ("Z=null(sym(A))")
End Sub
Sub d91()
PutOnClipboard ("x0=sym(pinv(A)*B)")
End Sub
Sub d92()
CR = Chr(13) + Chr(10)
PutOnClipboard ("a1=randn(1); a2=rand(1);" + CR + "x=a1*Z(:,1)+a2*Z(:,2)+x0; " + CR + "norm(double(A*x-B))")
End Sub
Sub d93()
PutOnClipboard ("syms a1 a2;x=a1*Z(:,1)+a2*Z(:,2)+x0")
End Sub
Sub d94()
PutOnClipboard ("B=[1:4]'; C=[A B]; [rank(A), rank(C)]")
End Sub
Sub d95()
PutOnClipboard ("x=pinv(A)*B")
End Sub
Sub d96()
PutOnClipboard ("norm(A*x-B)")
End Sub
Sub d97()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A=[1 2 3;4 5 6; 7 8 0];" + CR + " C=-[10, 5, 4; 5, 6, 7; 4, 7, 9];" + CR + "X=lyap(A,C)")
End Sub
Sub d98()
PutOnClipboard ("norm(A*X+X*A'+C)")
End Sub
Sub d99()
CR = Chr(13) + Chr(10)
PutOnClipboard ("A0=sym(kron(A,eye(3))+kron(eye(3),A));" + CR + "c=reshape(C',9,1); " + CR + "x0=-inv(A0)*c; x=reshape(x0,3,3)'")
End Sub
Sub d100()
PutOnClipboard ("norm(double(A*x+x*A'+C))")
End Sub