testhevdbiunit.pas

maths lib with source

unit testhevdbiunit;
interface
uses Math, Ap, Sysutils, cblas, creflections, hblas, htridiagonal, blas, tdbisinv, hbisinv;

function TestHEVDBI(Silent : Boolean):Boolean;
function testhevdbiunit_test_silent():Boolean;
function testhevdbiunit_test():Boolean;

implementation

procedure Unset2D(var A : TComplex2DArray);forward;
procedure Unset1D(var A : TReal1DArray);forward;
function RefEVD(A : TComplex2DArray;
     N : Integer;
     var Lambda : TReal1DArray;
     var Z : TComplex2DArray):Boolean;forward;
function HBITridiagonalQLIEigenValuesAndVectors(var d : TReal1DArray;
     e : TReal1DArray;
     n : Integer;
     var z : TComplex2DArray):Boolean;forward;
function TestProduct(const D : TReal1DArray;
     const E : TReal1DArray;
     N : Integer;
     const Z : TReal2DArray;
     const Lambda : TReal1DArray):Double;forward;
function TestOrt(const Z : TReal2DArray; N : Integer):Double;forward;
procedure TestEVDProblem(const AFull : TComplex2DArray;
     const AL : TComplex2DArray;
     const AU : TComplex2DArray;
     N : Integer;
     var ValErr : Double;
     var VecErr : Double;
     var WNSorted : Boolean;
     var FailC : Integer);forward;


(*************************************************************************
Testing hermitian EVD, BI
*************************************************************************)
function TestHEVDBI(Silent : Boolean):Boolean;
var
    A : TComplex2DArray;
    AL : TComplex2DArray;
    AU : TComplex2DArray;
    Pass : Integer;
    N : Integer;
    I : Integer;
    J : Integer;
    MKind : Integer;
    PassCount : Integer;
    MaxN : Integer;
    ValErr : Double;
    VecErr : Double;
    WNSorted : Boolean;
    FailC : Integer;
    Runs : Integer;
    FailR : Double;
    FailThreshold : Double;
    Threshold : Double;
    WasErrors : Boolean;
    WFailed : Boolean;
    M : Integer;
    Z : TReal2DArray;
begin
    FailThreshold := 0.005;
    Threshold := 1000*MachineEpsilon;
    ValErr := 0;
    VecErr := 0;
    WNSorted := False;
    WFailed := False;
    FailC := 0;
    Runs := 0;
    MaxN := 10;
    PassCount := 3;
    
    //
    // Main cycle
    //
    N:=1;
    while N<=MaxN do
    begin
        Pass:=1;
        while Pass<=PassCount do
        begin
            
            //
            // Prepare
            //
            SetLength(A, N-1+1, N-1+1);
            SetLength(AL, N-1+1, N-1+1);
            SetLength(AU, N-1+1, N-1+1);
            I:=0;
            while I<=N-1 do
            begin
                J:=I+1;
                while J<=N-1 do
                begin
                    
                    //
                    // A
                    //
                    A[I,J].X := 2*RandomReal-1;
                    A[I,J].Y := 2*RandomReal-1;
                    A[J,I] := Conj(A[I,J]);
                    
                    //
                    // A lower
                    //
                    AL[I,J].X := 2*RandomReal-1;
                    AL[I,J].Y := 2*RandomReal-1;
                    AL[J,I] := A[J,I];
                    
                    //
                    // A upper
                    //
                    AU[I,J] := A[I,J];
                    AU[J,I].X := 2*RandomReal-1;
                    AU[J,I].Y := 2*RandomReal-1;
                    Inc(J);
                end;
                A[I,I] := C_Complex(2*RandomReal-1);
                AL[I,I] := A[I,I];
                AU[I,I] := A[I,I];
                Inc(I);
            end;
            TestEVDProblem(A, AL, AU, N, ValErr, VecErr, WNSorted, FailC);
            Runs := Runs+1;
            Inc(Pass);
        end;
        Inc(N);
    end;
    
    //
    // report
    //
    FailR := FailC/Runs;
    WFailed := FailR>FailThreshold;
    WasErrors := (ValErr>Threshold) or (VecErr>Threshold) or WNSorted or WFailed;
    if  not Silent then
    begin
        Write(Format('TESTING HERMITIAN BISECTION AND INVERSE ITERATION EVD'#13#10'',[]));
        Write(Format('EVD values error (different variants):   %5.4e'#13#10'',[
            ValErr]));
        Write(Format('EVD vectors error:                       %5.4e'#13#10'',[
            VecErr]));
        Write(Format('Eigen values order:                      ',[]));
        if  not WNSorted then
        begin
            Write(Format('OK'#13#10'',[]));
        end
        else
        begin
            Write(Format('FAILED'#13#10'',[]));
        end;
        Write(Format('Always successfully converged:           ',[]));
        if  not WFailed then
        begin
            Write(Format('YES'#13#10'',[]));
        end
        else
        begin
            Write(Format('NO'#13#10'',[]));
            Write(Format('Fail ratio:                              %5.3f'#13#10'',[
                FailR]));
        end;
        Write(Format('Threshold:                               %5.4e'#13#10'',[
            Threshold]));
        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;


(*************************************************************************
Unsets 2D array.
*************************************************************************)
procedure Unset2D(var A : TComplex2DArray);
begin
    SetLength(A, 0+1, 0+1);
    A[0,0] := C_Complex(2*RandomReal-1);
end;


(*************************************************************************
Unsets 1D array.
*************************************************************************)
procedure Unset1D(var A : TReal1DArray);
begin
    SetLength(A, 0+1);
    A[0] := 2*RandomReal-1;
end;


(*************************************************************************
Reference EVD
*************************************************************************)
function RefEVD(A : TComplex2DArray;
     N : Integer;
     var Lambda : TReal1DArray;
     var Z : TComplex2DArray):Boolean;
var
    Z2 : TComplex2DArray;
    Z1 : TComplex2DArray;
    Tau : TComplex1DArray;
    D : TReal1DArray;
    E : TReal1DArray;
    D1 : TReal1DArray;
    E1 : TReal1DArray;
    I : Integer;
    J : Integer;
    K : Integer;
    VR : Double;
    V : Complex;
begin
    A := DynamicArrayCopy(A);
    
    //
    // to tridiagonal
    //
    HMatrixTD(A, N, True, Tau, D, E);
    HMatrixTDUnpackQ(A, N, True, Tau, Z2);
    
    //
    // TDEVD
    //
    SetLength(Z1, N+1, N+1);
    I:=1;
    while I<=N do
    begin
        J:=1;
        while J<=N do
        begin
            Z1[I,J] := Z2[I-1,J-1];
            Inc(J);
        end;
        Inc(I);
    end;
    SetLength(D1, N+1);
    I:=1;
    while I<=N do
    begin
        D1[I] := D[I-1];
        Inc(I);
    end;
    SetLength(E1, N+1);
    I:=2;
    while I<=N do
    begin
        E1[I] := E[I-2];
        Inc(I);
    end;
    Result := HBITridiagonalQLIEigenValuesAndVectors(D1, E1, N, Z1);
    if Result then
    begin
        
        //
        // copy
        //
        SetLength(Lambda, N-1+1);
        I:=0;
        while I<=N-1 do
        begin
            Lambda[I] := D1[I+1];
            Inc(I);
        end;
        SetLength(Z, N-1+1, N-1+1);
        I:=0;
        while I<=N-1 do
        begin
            J:=0;
            while J<=N-1 do
            begin
                Z[I,J] := Z1[I+1,J+1];
                Inc(J);
            end;
            Inc(I);
        end;
        
        //
        // Use Selection Sort to minimize swaps of eigenvectors
        //
        I:=0;
        while I<=N-2 do
        begin
            K := I;
            J:=I+1;
            while J<=N-1 do
            begin
                if Lambda[J]<Lambda[K] then
                begin
                    K := J;
                end;
                Inc(J);
            end;
            if K<>I then
            begin
                VR := Lambda[I];
                Lambda[I] := Lambda[K];
                Lambda[K] := VR;
                J:=0;
                while J<=N-1 do
                begin
                    V := Z[J,I];
                    Z[J,I] := Z[J,K];
                    Z[J,K] := V;
                    Inc(J);
                end;
            end;
            Inc(I);
        end;
    end;
end;


function HBITridiagonalQLIEigenValuesAndVectors(var d : TReal1DArray;
     e : TReal1DArray;
     n : Integer;
     var z : TComplex2DArray):Boolean;
var
    m : Integer;
    l : Integer;
    iter : Integer;
    i : Integer;
    k : Integer;
    s : Double;
    r : Double;
    p : Double;
    g : Double;
    f : Double;
    fc : Complex;
    dd : Double;
    c : Double;
    b : Double;
begin
    e := DynamicArrayCopy(e);
    Result := True;
    if n=1 then
    begin
        Exit;
    end;
    i:=2;
    while i<=n do
    begin
        e[i-1] := e[i];
        Inc(i);
    end;
    e[n] := 0.0;
    l:=1;
    while l<=n do
    begin
        iter := 0;
        repeat
            m:=l;
            while m<=n-1 do
            begin
                dd := AbsReal(d[m])+AbsReal(d[m+1]);
                if AbsReal(e[m])+dd=dd then
                begin
                    Break;
                end;
                Inc(m);
            end;
            if m<>l then
            begin
                if iter=30 then
                begin
                    Result := False;
                    Exit;
                end;
                iter := iter+1;
                g := (d[l+1]-d[l])/(2*e[l]);
                if AbsReal(g)<1 then
                begin
                    r := Sqrt(1+Sqr(g));
                end
                else
                begin
                    r := AbsReal(g)*Sqrt(1+Sqr(1/g));
                end;
                if g<0 then
                begin
                    g := d[m]-d[l]+e[l]/(g-r);
                end
                else
                begin
                    g := d[m]-d[l]+e[l]/(g+r);
                end;
                s := 1;
                c := 1;
                p := 0;
                i:=m-1;
                while i>=l do
                begin
                    f := s*e[i];
                    b := c*e[i];
                    if AbsReal(f)<AbsReal(g) then
                    begin
                        r := AbsReal(g)*Sqrt(1+Sqr(f/g));
                    end
                    else
                    begin
                        r := AbsReal(f)*Sqrt(1+Sqr(g/f));
                    end;
                    e[i+1] := r;
                    if r=0 then
                    begin
                        d[i+1] := d[i+1]-p;
                        e[m] := 0;
                        Break;
                    end;
                    s := f/r;
                    c := g/r;
                    g := d[i+1]-p;
                    r := (d[i]-g)*s+2.0*c*b;
                    p := s*r;
                    d[i+1] := g+p;
                    g := c*r-b;
                    k:=1;
                    while k<=n do
                    begin
                        fc := z[k,i+1];
                        z[k,i+1] := C_Add(C_MulR(z[k,i],s),C_MulR(fc,c));
                        z[k,i] := C_Sub(C_MulR(z[k,i],c),C_MulR(fc,s));
                        Inc(k);
                    end;
                    Dec(i);
                end;
                if (r=0) and (i>=1) then
                begin
                    Continue;
                end;
                d[l] := d[l]-p;
                e[l] := g;
                e[m] := 0.0;
            end;
        until m=l;
        Inc(l);
    end;
end;


(*************************************************************************
Tests Z*Lambda*Z' against tridiag(D,E).
Returns relative error.
*************************************************************************)
function TestProduct(const D : TReal1DArray;
     const E : TReal1DArray;
     N : Integer;
     const Z : TReal2DArray;
     const Lambda : TReal1DArray):Double;
var