DELPHI FAQ: Как инвертировать матрицу?

Как инвертировать матрицу?

type
  RCOMat = array of array of Extended;

var
  DimMat: integer;

procedure InvertMatrix(var aa: RCOMat);
var
  numb, nula1, ipiv, indxr, indxc: array of Integer;
  i, j, l, kod, jmax, k, ll, icol, irow: Integer;
  amax, d, c, pomos, big, dum, pivinv: Double;
  ind: Boolean;
begin
  for j := 0 to Pred(DimMat) do ipiv[j] := 0;

  irow := 1;
  icol := 1;
  for i := 0 to Pred(DimMat) do
  begin
    big := 0;

    for j := 0 to Pred(DimMat) do
    begin
      if (ipiv[j] <> 1) then
      begin
        for k := 0 to Pred(DimMat) do
        begin
          if (ipiv[k] = 0) then
            if (Abs(aa[j, k]) >= big) then
            begin
              big  := Abs(aa[j, k]);
              irow := j;
              icol := k;
            end
            else;
        end;
      end;
    end;

    ipiv[icol] := ipiv[icol] + 1;
    if (irow <> icol) then
    begin
      for l := 0 to Pred(DimMat) do
      begin
        dum         := aa[irow, l];
        aa[irow, l] := aa[icol, l];
        aa[icol, l] := dum;
      end;
      for l := 0 to Pred(DimMat) do
      begin
        dum := aa[irow + DimMat + 1, l];
        aa[irow + DimMat + 1, l] := aa[icol + DimMat + 1, l];
        aa[icol + DimMat + 1, l] := dum;
      end;
    end;
    indxr[i] := irow;
    indxc[i] := icol;
    if (aa[icol, icol] = 0) then;
    pivinv         := 1.0 / aa[icol, icol];
    aa[icol, icol] := 1.0;
    for l := 0 to Pred(DimMat) do aa[icol, l] := aa[icol, l] * pivinv;
    for l := 0 to Pred(DimMat) do aa[icol + DimMat + 1, l] :=
        aa[icol + DimMat + 1, l] * pivinv;
    for ll := 0 to Pred(DimMat) do
    begin
      if (ll <> icol) then
      begin
        dum          := aa[ll, icol];
        aa[ll, icol] := 0.0;
        for l := 0 to Pred(DimMat) do aa[ll, l] := aa[ll, l] - aa[icol, l] * dum;
        for l := 0 to Pred(DimMat) do aa[ll + DimMat + 1, l] :=
            aa[ll + DimMat + 1, l] - aa[icol + DimMat + 1, l] * dum;
      end;
    end;
  end;

  for l := Pred(DimMat) downto 0 do
  begin
    if (indxr[l] <> indxc[l]) then
    begin
      for k := 0 to Pred(DimMat) do
      begin
        dum := aa[k, indxr[l]];
        aa[k, indxr[l]] := aa[k, indxc[l]];
        aa[k, indxc[l]] := dum;
      end;
    end;
  end;
end;

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