{CORREL.TLS Prozeduren und Funktionen:
function pearson_corr_koeff(x,y:DatVectorType_TLS):real;
function spearman(x,y:DatVectorType_TLS):real;
procedure corr_mat(x,y:DatMatrixType_TLS;VAR corr_mat:RealMatrixType_TLS);
function fisher_z_tr(r:real;inv:boolean):real;
procedure corr_w_test(r:real;n:integer;roh0:real;VAR tg:real;VAR f:integer);
function mult_corr(rxy:RealVectorType_TLS;ryy:RealMatrixType_TLS;
  n:integer;VAR tg:real;VAR f1,f2:integer):real;
}

function pearson_corr_koeff(x,y:DatVectorType_TLS):real;
const err_pos='<pearson_corr_koeff>';
var x_var,y_var,dummy:real;
begin
  average(x,ari,dummy,x_var,dummy,dummy,dummy);
  average(y,ari,dummy,y_var,dummy,dummy,dummy);
  dummy:=x_var*y_var;
  if dummy>NULL then pearson_corr_koeff:=covariance(x,y)/sqrt(dummy)
    else error(3,err_pos)
end;

function spearman(x,y:DatVectorType_TLS):real;
var i,j,k:integer;
begin
  rank_class(x,x);rank_class(y,y);
  spearman:=pearson_corr_koeff(x,y)
end;

procedure corr_mat(x,y:DatMatrixType_TLS;VAR corr_mat:RealMatrixType_TLS);
var i,j;
begin
  corr_mat.p:=x.p;corr_mat.q:=y.p;
  for i:=1 to x.p do
    for j:=1 to y.p do
      corr_mat.elt[i,j]:=pearson_corr_koeff(x.line[i],y.line[j])
end;

function fisher_z_tr(r:real;inv:boolean):real;
const err_pos='<fisher_z_tr>';
begin
  if inv then fisher_z_tr:=(exp(2*r)-1)/(exp(2*r)+1)
  else if 1-abs(r)>NULL then fisher_z_tr:=ln((1+r)/(1-r))/2
  else error(2,err_pos)
end;

procedure corr_w_test(r:real;n:integer;roh0:real;VAR tg:real;VAR f:integer);
const err_pos='<corr_w_test>';
begin
  if(1-abs(r)>NULL)and(n>3) then
    if abs(roh0)<=NULL then begin
      tg:=r*sqrt(n-2)/sqrt(1-r*r);
      f:=n-2;
    end
    else tg:=abs((fisher_z_tr(r,false)-fisher_z_tr(roh0,false)-roh0/(2*(n-1)))*sqrt(n-3))
  else error(3,err_pos)
end;

function mult_corr(rxy:RealVectorType_TLS;ryy:RealMatrixType_TLS;
  n:integer;VAR tg:real;VAR f1,f2:integer):real;
const err_pos='<mult_corr>';
var p:integer;
  help:real;
begin
  p:=ryy.p;
  invert_mat(ryy.elt,p);
  help:=vec_mat_vec_prod(rxy,ryy);
  if help>NULL then begin
    mult_corr:=sqrt(help);
    if abs(1-help)>NULL then tg:=(n-p-1)*help/(p*(1-help)) else error(2,err_pos);
    f1:=p;
    f2:=n-p-1;
  end
  else error(3,err_pos)
end;