testcrcondunit.pas

maths lib with source

unit testcrcondunit;
interface
uses Math, Ap, Sysutils, clu, ctrlinsolve, crcond;

function TestCRCond(Silent : Boolean):Boolean;
function testcrcondunit_test_silent():Boolean;
function testcrcondunit_test():Boolean;

implementation

procedure MakeACopy(const A : TComplex2DArray;
     M : Integer;
     N : Integer;
     var B : TComplex2DArray);forward;
procedure GenerateRandomMatrix(var A0 : TComplex2DArray; N : Integer);forward;
function InvMatTR(var A : TComplex2DArray;
     N : Integer;
     IsUpper : Boolean;
     IsUnitTriangular : Boolean):Boolean;forward;
function InvMatLU(var A : TComplex2DArray;
     const Pivots : TInteger1DArray;
     N : Integer):Boolean;forward;
function InvMat(var A : TComplex2DArray; N : Integer):Boolean;forward;
procedure RefRCond(const A : TComplex2DArray;
     N : Integer;
     var RC1 : Double;
     var RCInf : Double);forward;


function TestCRCond(Silent : Boolean):Boolean;
var
    A : TComplex2DArray;
    LUA : TComplex2DArray;
    P : TInteger1DArray;
    N : Integer;
    MaxN : Integer;
    I : Integer;
    J : Integer;
    Pass : Integer;
    PassCount : Integer;
    WasErrors : Boolean;
    Err50 : Boolean;
    Err90 : Boolean;
    ErrLess : Boolean;
    ERC1 : Double;
    ERCInf : Double;
    Q50 : TReal1DArray;
    Q90 : TReal1DArray;
    V : Double;
    Threshold50 : Double;
    Threshold90 : Double;
begin
    WasErrors := False;
    Err50 := False;
    Err90 := False;
    ErrLess := False;
    MaxN := 10;
    PassCount := 100;
    Threshold50 := 0.5;
    Threshold90 := 0.1;
    SetLength(Q50, 3+1);
    SetLength(Q90, 3+1);
    
    //
    // process
    //
    N:=1;
    while N<=MaxN do
    begin
        SetLength(A, N-1+1, N-1+1);
        I:=0;
        while I<=3 do
        begin
            Q50[I] := 0;
            Q90[I] := 0;
            Inc(I);
        end;
        Pass:=1;
        while Pass<=PassCount do
        begin
            GenerateRandomMatrix(A, N);
            MakeACopy(A, N, N, LUA);
            CMatrixLU(LUA, N, N, P);
            RefRCond(A, N, ERC1, ERCInf);
            
            //
            // 1-norm, normal
            //
            V := 1/CMatrixRCond1(A, N);
            if V>=Threshold50*ERC1 then
            begin
                Q50[0] := Q50[0]+1/PassCount;
            end;
            if V>=Threshold90*ERC1 then
            begin
                Q90[0] := Q90[0]+1/PassCount;
            end;
            ErrLess := ErrLess or (V>ERC1*1.001);
            
            //
            // 1-norm, LU
            //
            V := 1/CMatrixLURCond1(LUA, N);
            if V>=Threshold50*ERC1 then
            begin
                Q50[1] := Q50[1]+1/PassCount;
            end;
            if V>=Threshold90*ERC1 then
            begin
                Q90[1] := Q90[1]+1/PassCount;
            end;
            ErrLess := ErrLess or (V>ERC1*1.001);
            
            //
            // Inf-norm, normal
            //
            V := 1/CMatrixRCondInf(A, N);
            if V>=Threshold50*ERCInf then
            begin
                Q50[2] := Q50[2]+1/PassCount;
            end;
            if V>=Threshold90*ERCInf then
            begin
                Q90[2] := Q90[2]+1/PassCount;
            end;
            ErrLess := ErrLess or (V>ERCInf*1.001);
            
            //
            // Inf-norm, LU
            //
            V := 1/CMatrixLURCondInf(LUA, N);
            if V>=Threshold50*ERCInf then
            begin
                Q50[3] := Q50[3]+1/PassCount;
            end;
            if V>=Threshold90*ERCInf then
            begin
                Q90[3] := Q90[3]+1/PassCount;
            end;
            ErrLess := ErrLess or (V>ERCInf*1.001);
            Inc(Pass);
        end;
        I:=0;
        while I<=3 do
        begin
            Err50 := Err50 or (Q50[I]<0.50);
            Err90 := Err90 or (Q90[I]<0.90);
            Inc(I);
        end;
        Inc(N);
    end;
    
    //
    // report
    //
    WasErrors := Err50 or Err90 or ErrLess;
    if  not Silent then
    begin
        Write(Format('TESTING RCOND (COMPLEX)'#13#10'',[]));
        Write(Format('50%% within [0.5*cond,cond]:              ',[]));
        if Err50 or ErrLess then
        begin
            Write(Format('FAILED'#13#10'',[]));
        end
        else
        begin
            Write(Format('OK'#13#10'',[]));
        end;
        Write(Format('90%% within [0.1*cond,cond]               ',[]));
        if Err90 or ErrLess then
        begin
            Write(Format('FAILED'#13#10'',[]));
        end
        else
        begin
            Write(Format('OK'#13#10'',[]));
        end;
        if WasErrors then
        begin
            Write(Format('TEST FAILED'#13#10'',[]));
        end
        else
        begin
            Write(Format('TEST PASSED'#13#10'',[]));
        end;
        Write(Format(''#13#10''#13#10'',[]));
    end;
    Result :=  not WasErrors;
end;


(*************************************************************************
Copy
*************************************************************************)
procedure MakeACopy(const A : TComplex2DArray;
     M : Integer;
     N : Integer;
     var B : TComplex2DArray);
var
    I : Integer;
    J : Integer;
begin
    SetLength(B, M-1+1, N-1+1);
    I:=0;
    while I<=M-1 do
    begin
        J:=0;
        while J<=N-1 do
        begin
            B[I,J] := A[I,J];
            Inc(J);
        end;
        Inc(I);
    end;
end;


(*************************************************************************
Generate matrix with given condition number C (2-norm)
*************************************************************************)
procedure GenerateRandomMatrix(var A0 : TComplex2DArray; N : Integer);
var
    I : Integer;
    J : Integer;
begin
    I:=0;
    while I<=N-1 do
    begin
        J:=0;
        while J<=N-1 do
        begin
            A0[I,J].X := 2*RandomReal-1;
            A0[I,J].Y := 2*RandomReal-1;
            Inc(J);
        end;
        Inc(I);
    end;
end;


(*************************************************************************
triangular inverse
*************************************************************************)
function InvMatTR(var A : TComplex2DArray;
     N : Integer;
     IsUpper : Boolean;
     IsUnitTriangular : Boolean):Boolean;
var
    NOUNIT : Boolean;
    I : Integer;
    J : Integer;
    V : Complex;
    AJJ : Complex;
    T : TComplex1DArray;
    i_ : Integer;
begin
    Result := True;
    SetLength(T, N-1+1);
    
    //
    // Test the input parameters.
    //
    NOUNIT :=  not IsUnitTriangular;
    if IsUpper then
    begin
        
        //
        // Compute inverse of upper triangular matrix.
        //
        J:=0;
        while J<=N-1 do
        begin
            if NOUNIT then
            begin
                if C_EqualR(A[J,J],0) then
                begin
                    Result := False;
                    Exit;
                end;
                A[J,J] := C_RDiv(1,A[J,J]);
                AJJ := C_Opposite(A[J,J]);
            end
            else
            begin
                AJJ := C_Complex(-1);
            end;
            
            //
            // Compute elements 1:j-1 of j-th column.
            //
            if J>0 then
            begin
                for i_ := 0 to J-1 do
                begin
                    T[i_] := A[i_,J];
                end;
                I:=0;
                while I<=J-1 do
                begin
                    if I<J-1 then
                    begin
                        V := C_Complex(0.0);
                        for i_ := I+1 to J-1 do
                        begin
                            V := C_Add(V,C_Mul(A[I,i_],T[i_]));
                        end;
                    end
                    else
                    begin
                        V := C_Complex(0);
                    end;