"fitte 2d-Gauße an ..." neu

7 files changed, 936 insertions, 104 deletions

diff --git a/epost.lpr b/epost.lpr
index a6d0430..93ff2e3 100644
--- a/epost.lpr
+++ b/epost.lpr
@@ -361,6 +361,17 @@ begin
         aufraeumen;
         halt(1);
       end;
+      if istDasBefehl('fitte 2d-Gauße an',s,bekannteBefehle,true) then begin
+        i:=findeWerte(s,nil,@wertes,@konturen,false);
+        if i<0 then begin
+          aufraeumen;
+          halt(1);
+        end;
+        if wertes[i].fitte2dGausze(syntaxTest,inf) then
+          continue;
+        aufraeumen;
+        halt(1);
+      end;
       if istDasBefehl('Zeitfrequenzanalyse',s,bekannteBefehle,true) then begin
         j:=findeWerte(erstesArgument(s),nil,@wertes,@konturen,false);
         if j<0 then begin
diff --git a/epost.lps b/epost.lps
index 6d72110..9a18fd4 100644
--- a/epost.lps
+++ b/epost.lps
@@ -3,12 +3,11 @@
   <ProjectSession>
     <Version Value="10"/>
     <BuildModes Active="Default"/>
-    <Units Count="25">
+    <Units Count="26">
       <Unit0>
         <Filename Value="epost.lpr"/>
         <IsPartOfProject Value="True"/>
-        <TopLine Value="565"/>
-        <CursorPos Y="583"/>
+        <CursorPos X="54" Y="13"/>
         <UsageCount Value="202"/>
         <Loaded Value="True"/>
       </Unit0>
@@ -23,143 +22,134 @@
         <Filename Value="epostunit.pas"/>
         <IsPartOfProject Value="True"/>
         <EditorIndex Value="1"/>
-        <TopLine Value="2025"/>
-        <CursorPos X="78" Y="1953"/>
+        <TopLine Value="6927"/>
+        <CursorPos X="25" Y="6956"/>
         <UsageCount Value="201"/>
         <Loaded Value="True"/>
       </Unit2>
       <Unit3>
         <Filename Value="werteunit.pas"/>
         <IsPartOfProject Value="True"/>
-        <EditorIndex Value="9"/>
-        <TopLine Value="1249"/>
-        <CursorPos X="53" Y="1281"/>
+        <EditorIndex Value="2"/>
+        <TopLine Value="961"/>
+        <CursorPos X="18" Y="977"/>
         <UsageCount Value="200"/>
         <Loaded Value="True"/>
       </Unit3>
       <Unit4>
         <Filename Value="typenunit.pas"/>
         <IsPartOfProject Value="True"/>
-        <IsVisibleTab Value="True"/>
-        <EditorIndex Value="12"/>
-        <TopLine Value="998"/>
-        <CursorPos X="25" Y="1011"/>
+        <EditorIndex Value="4"/>
+        <TopLine Value="3"/>
+        <CursorPos X="3" Y="21"/>
         <UsageCount Value="200"/>
         <Loaded Value="True"/>
       </Unit4>
       <Unit5>
         <Filename Value="../units/fftunit.pas"/>
         <IsPartOfProject Value="True"/>
-        <EditorIndex Value="3"/>
+        <EditorIndex Value="-1"/>
         <TopLine Value="13"/>
         <CursorPos X="100" Y="13"/>
         <UsageCount Value="201"/>
-        <Loaded Value="True"/>
       </Unit5>
       <Unit6>
         <Filename Value="../units/fftunit.inc"/>
         <IsPartOfProject Value="True"/>
-        <EditorIndex Value="4"/>
+        <EditorIndex Value="-1"/>
         <TopLine Value="152"/>
         <CursorPos Y="179"/>
         <UsageCount Value="202"/>
-        <Loaded Value="True"/>
       </Unit6>
       <Unit7>
         <Filename Value="gauszFit.inc"/>
         <IsPartOfProject Value="True"/>
-        <EditorIndex Value="11"/>
-        <CursorPos X="35" Y="10"/>
+        <IsVisibleTab Value="True"/>
+        <EditorIndex Value="3"/>
         <UsageCount Value="201"/>
         <Loaded Value="True"/>
       </Unit7>
       <Unit8>
         <Filename Value="werteunit.inc"/>
         <IsPartOfProject Value="True"/>
-        <EditorIndex Value="10"/>
+        <EditorIndex Value="-1"/>
         <TopLine Value="480"/>
         <CursorPos Y="515"/>
-        <UsageCount Value="196"/>
-        <Loaded Value="True"/>
+        <UsageCount Value="200"/>
       </Unit8>
       <Unit9>
         <Filename Value="fileunit.pas"/>
         <EditorIndex Value="-1"/>
         <CursorPos Y="204"/>
-        <UsageCount Value="196"/>
+        <UsageCount Value="194"/>
       </Unit9>
       <Unit10>
         <Filename Value="../units/mystringlistunit.pas"/>
-        <EditorIndex Value="8"/>
-        <TopLine Value="713"/>
+        <EditorIndex Value="-1"/>
+        <TopLine Value="712"/>
         <CursorPos X="22" Y="735"/>
-        <UsageCount Value="95"/>
-        <Loaded Value="True"/>
+        <UsageCount Value="94"/>
       </Unit10>
       <Unit11>
         <Filename Value="../units/lowlevelunit.pas"/>
-        <EditorIndex Value="7"/>
-        <TopLine Value="728"/>
-        <CursorPos X="22" Y="755"/>
-        <UsageCount Value="100"/>
-        <Loaded Value="True"/>
+        <EditorIndex Value="-1"/>
+        <TopLine Value="16"/>
+        <UsageCount Value="98"/>
       </Unit11>
       <Unit12>
         <Filename Value="../units/matheunit.pas"/>
-        <EditorIndex Value="5"/>
+        <EditorIndex Value="-1"/>
         <TopLine Value="1045"/>
         <CursorPos X="28" Y="1045"/>
-        <UsageCount Value="101"/>
-        <Loaded Value="True"/>
+        <UsageCount Value="99"/>
       </Unit12>
       <Unit13>
         <Filename Value="../units/systemunit.pas"/>
-        <EditorIndex Value="2"/>
+        <EditorIndex Value="-1"/>
         <TopLine Value="190"/>
         <CursorPos X="22" Y="195"/>
-        <UsageCount Value="100"/>
-        <Loaded Value="True"/>
+        <UsageCount Value="98"/>
       </Unit13>
       <Unit14>
         <Filename Value="/usr/lib/fpc/src/rtl/inc/objpash.inc"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="176"/>
         <CursorPos X="23" Y="194"/>
-        <UsageCount Value="6"/>
+        <UsageCount Value="4"/>
       </Unit14>
       <Unit15>
         <Filename Value="/usr/lib/fpc/src/rtl/unix/bunxovlh.inc"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="61"/>
         <CursorPos X="10" Y="99"/>
-        <UsageCount Value="1"/>
+        <UsageCount Value="9"/>
       </Unit15>
       <Unit16>
         <Filename Value="/usr/lib/fpc/src/rtl/unix/baseunix.pp"/>
         <UnitName Value="BaseUnix"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="61"/>
-        <UsageCount Value="1"/>
+        <UsageCount Value="9"/>
       </Unit16>
       <Unit17>
         <Filename Value="/usr/lib/fpc/src/rtl/unix/bunxovl.inc"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="414"/>
         <CursorPos X="20" Y="434"/>
-        <UsageCount Value="1"/>
+        <UsageCount Value="9"/>
       </Unit17>
       <Unit18>
         <Filename Value="/usr/lib/fpc/src/rtl/linux/bunxsysc.inc"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="16"/>
-        <UsageCount Value="1"/>
+        <UsageCount Value="9"/>
       </Unit18>
       <Unit19>
         <Filename Value="/usr/lib/fpc/src/rtl/unix/bunxh.inc"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="74"/>
         <CursorPos X="15" Y="102"/>
-        <UsageCount Value="1"/>
+        <UsageCount Value="9"/>
       </Unit19>
       <Unit20>
         <Filename Value="/usr/lib/fpc/src/packages/fcl-image/src/fpimage.pp"/>
@@ -167,158 +157,157 @@
         <EditorIndex Value="-1"/>
         <TopLine Value="10"/>
         <CursorPos X="3" Y="30"/>
-        <UsageCount Value="1"/>
+        <UsageCount Value="9"/>
       </Unit20>
       <Unit21>
         <Filename Value="/usr/lib/fpc/src/rtl/objpas/math.pp"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="351"/>
         <CursorPos X="10" Y="368"/>
-        <UsageCount Value="2"/>
+        <UsageCount Value="0"/>
       </Unit21>
       <Unit22>
         <Filename Value="GTIWebServerTestAggActionHandlerUnit.pas"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="53"/>
         <CursorPos X="49" Y="82"/>
-        <UsageCount Value="2"/>
+        <UsageCount Value="0"/>
       </Unit22>
       <Unit23>
         <Filename Value="../units/protokollunit.pas"/>
-        <EditorIndex Value="6"/>
-        <TopLine Value="87"/>
+        <EditorIndex Value="-1"/>
+        <TopLine Value="18"/>
         <CursorPos X="3" Y="18"/>
-        <UsageCount Value="44"/>
-        <Loaded Value="True"/>
+        <UsageCount Value="43"/>
       </Unit23>
       <Unit24>
         <Filename Value="../fpGUI/src/corelib/render/software/agg_2D.pas"/>
         <EditorIndex Value="-1"/>
         <TopLine Value="2116"/>
         <CursorPos X="2" Y="2134"/>
-        <UsageCount Value="10"/>
+        <UsageCount Value="8"/>
       </Unit24>
+      <Unit25>
+        <Filename Value="../units/randomunit.pas"/>
+        <EditorIndex Value="-1"/>
+        <CursorPos X="19" Y="11"/>
+        <UsageCount Value="8"/>
+      </Unit25>
     </Units>
-    <JumpHistory Count="30" HistoryIndex="29">
+    <JumpHistory Count="29" HistoryIndex="28">
       <Position1>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="773" Column="72" TopLine="772"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1753" Column="35" TopLine="1735"/>
       </Position1>
       <Position2>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="891" Column="33" TopLine="862"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1709" Column="13" TopLine="1684"/>
       </Position2>
       <Position3>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="903" Column="33" TopLine="874"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1706" Column="27" TopLine="1686"/>
       </Position3>
       <Position4>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="909" Column="46" TopLine="880"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1707" Column="57" TopLine="1689"/>
       </Position4>
       <Position5>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="1047" Column="48" TopLine="1018"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1680" Column="35" TopLine="1663"/>
       </Position5>
       <Position6>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="1048" Column="44" TopLine="1019"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="81" Column="77" TopLine="65"/>
       </Position6>
       <Position7>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="1049" Column="50" TopLine="1020"/>
+        <Filename Value="werteunit.pas"/>
       </Position7>
       <Position8>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="1050" Column="50" TopLine="1021"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="81" Column="77" TopLine="53"/>
       </Position8>
       <Position9>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="1051" Column="52" TopLine="1022"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1623" Column="82" TopLine="1595"/>
       </Position9>
       <Position10>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="2282" Column="27" TopLine="2282"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1633" Column="26" TopLine="1605"/>
       </Position10>
       <Position11>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="2729" Column="22" TopLine="2718"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1634" Column="98" TopLine="1606"/>
       </Position11>
       <Position12>
-        <Filename Value="typenunit.pas"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1678" Column="37" TopLine="1652"/>
       </Position12>
       <Position13>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="891" Column="33" TopLine="862"/>
+        <Filename Value="werteunit.pas"/>
       </Position13>
       <Position14>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="903" Column="33" TopLine="874"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="81" Column="77" TopLine="53"/>
       </Position14>
       <Position15>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="2281" Column="24" TopLine="2251"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1623" Column="82" TopLine="1595"/>
       </Position15>
       <Position16>
-        <Filename Value="epostunit.pas"/>
-        <Caret Line="1157" Column="40" TopLine="1154"/>
+        <Filename Value="gauszFit.inc"/>
+        <Caret Line="18" Column="10"/>
       </Position16>
       <Position17>
-        <Filename Value="epostunit.pas"/>
-        <Caret Line="97" Column="43" TopLine="79"/>
+        <Filename Value="gauszFit.inc"/>
+        <Caret Line="17" Column="65"/>
       </Position17>
       <Position18>
-        <Filename Value="epostunit.pas"/>
-        <Caret Line="1157" Column="46" TopLine="1128"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1687" Column="30" TopLine="1629"/>
       </Position18>
       <Position19>
-        <Filename Value="epostunit.pas"/>
-        <Caret Line="2447" Column="27" TopLine="2436"/>
+        <Filename Value="typenunit.pas"/>
+        <Caret Line="21" Column="3" TopLine="3"/>
       </Position19>
       <Position20>
-        <Filename Value="epostunit.pas"/>
-        <Caret Line="98" Column="43" TopLine="80"/>
+        <Filename Value="werteunit.pas"/>
+        <Caret Line="1842" Column="12" TopLine="1815"/>
       </Position20>
       <Position21>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="1430" Column="46" TopLine="1785"/>
+        <Caret Line="3870" Column="44" TopLine="3870"/>
       </Position21>
       <Position22>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="2454" Column="17" TopLine="2431"/>
+        <Caret Line="7930" Column="16" TopLine="7901"/>
       </Position22>
       <Position23>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="2444" Column="49" TopLine="2427"/>
+        <Caret Line="2590" Column="40" TopLine="2573"/>
       </Position23>
       <Position24>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="97" Column="43" TopLine="79"/>
       </Position24>
       <Position25>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="1241" Column="18" TopLine="1222"/>
+        <Caret Line="2590" Column="40" TopLine="2562"/>
       </Position25>
       <Position26>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="2431" TopLine="2417"/>
+        <Caret Line="2591" Column="35" TopLine="2563"/>
       </Position26>
       <Position27>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="2456" TopLine="2436"/>
+        <Caret Line="2598" Column="55" TopLine="2570"/>
       </Position27>
       <Position28>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="2455" Column="66" TopLine="2436"/>
+        <Caret Line="6954" Column="9" TopLine="6925"/>
       </Position28>
       <Position29>
         <Filename Value="epostunit.pas"/>
-        <Caret Line="2441" Column="89" TopLine="2421"/>
+        <Caret Line="6955" Column="31" TopLine="6926"/>
       </Position29>
-      <Position30>
-        <Filename Value="typenunit.pas"/>
-        <Caret Line="748" Column="127" TopLine="727"/>
-      </Position30>
     </JumpHistory>
   </ProjectSession>
   <Debugging>
diff --git a/epostunit.pas b/epostunit.pas
index ee920ec..91d8a55 100644
--- a/epostunit.pas
+++ b/epostunit.pas
@@ -165,6 +165,7 @@ type
     function fft(threads: longint; senkrecht,invers: boolean; const vor,nach: tFFTDatenordnung; fen: tFenster; hg: tExtendedArray; out pvFehler: extended; warn: tWarnStufe): boolean; overload;
     procedure initFuerGauszFit(sT: boolean; daten: tWerte; senkrecht: boolean; adLaenge: longint; adStart,adStop: extended);
     function fitteGausze(sT: boolean; f: tMyStringList; threads: longint): boolean;
+    function fitte2dGausze(sT: boolean; f: tMyStringList): boolean;
     function berechneZeitfrequenzanalyse(sT: boolean; f: tMyStringList; threads: longint; quelle: tWerte; warn: tWarnStufe): boolean;
     function berechneVerzerrung(sT: boolean; f: tMyStringList; threads: longint; quelle: tWerte; warn: tWarnStufe): boolean;
     function berechneLambdaZuOmegaVerzerrung(sT: boolean; f: tMyStringList; threads: longint; quelle: tWerte): boolean;
@@ -3817,6 +3818,116 @@ begin
   result:=true;
 end;
 
+function tWerte.fitte2dGausze(sT: boolean; f: tMyStringList): boolean;
+var
+  bekannteBefehle:         tMyStringList;
+  Zeit,offset,relVerb:     extended;
+  anzahl,i:                longint;
+  schritte,maximalSamples: int64;
+  s,datei:                 string;
+  pDatei:                  textFile;
+  parameter:               tGausz2dParameterArray;
+  residuenBerechnen:       boolean;
+begin
+  result:=false;
+  if not sT then
+    gibAus('2d-Gauße fitten ...',3);
+  bekannteBefehle:=tMyStringList.create;
+  Zeit:=now;
+  anzahl:=1;
+  datei:='';
+  relVerb:=0.001;
+  residuenBerechnen:=false;
+  maximalSamples:=256;
+  repeat
+    if not f.metaReadln(s,true) then begin
+      gibAus('Unerwartetes Dateiende!',3);
+      exit;
+    end;
+    bekannteBefehle.clear;
+    if istDasBefehl('Ende',s,bekannteBefehle,false) then break;
+    if istDasBefehl('Anzahl:',s,bekannteBefehle,true) then begin
+      anzahl:=round(exprToFloat(sT,s));
+      continue;
+    end;
+    if istDasBefehl('maximale Sampleanzahl:',s,bekannteBefehle,true) then begin
+      maximalSamples:=round(sqrt(exprToFloat(sT,s)));
+      continue;
+    end;
+    if istDasBefehl('Residuen berechnen',s,bekannteBefehle,false) then begin
+      residuenBerechnen:=true;
+      continue;
+    end;
+    if istDasBefehl('Datei:',s,bekannteBefehle,true) then begin
+      if datei<>'' then begin
+        gibAus('Habe bereits eine Zieldatei beim Fitten eines 2d-Gaußes!',3);
+        bekannteBefehle.free;
+        exit;
+      end;
+      datei:=s;
+      continue;
+    end;
+    if istDasBefehl('relative Verbesserung:',s,bekannteBefehle,true) then begin
+      relVerb:=exprToFloat(sT,s);
+      continue;
+    end;
+    bekannteBefehle.sort;
+    gibAus('Verstehe Option '''+s+''' nicht beim Fitten eines 2d-Gaußes!'#10'Ich kenne:'#10+bekannteBefehle.text,3);
+    bekannteBefehle.free;
+    exit;
+  until false;
+  bekannteBefehle.free;
+
+  if datei='' then begin
+    gibAus('Keine Datei zum 2dGauße-Fitten angegeben!',3);
+    exit;
+  end;
+
+  if sT then begin
+    result:=true;
+    exit;
+  end;
+
+  case genauigkeit of
+    gSingle:
+      schritte:=sWerte.gauszFit2d(anzahl,maximalSamples,relVerb,offset,parameter);
+    gDouble:
+      schritte:=dWerte.gauszFit2d(anzahl,maximalSamples,relVerb,offset,parameter);
+    gExtended:
+      schritte:=eWerte.gauszFit2d(anzahl,maximalSamples,relVerb,offset,parameter);
+  end{of case};
+
+  gibAus('... das waren '+intToStr(schritte)+' Schritte, Parameter speichern ...',3);
+  assignFile(pDatei,datei);
+  rewrite(pDatei);
+  writeln(pDatei,myFloatToStr(offset));
+  for i:=0 to length(parameter)-1 do
+    with parameter[i] do
+      writeln(
+        pDatei,
+        myFloatToStr(xx)+' '+
+        myFloatToStr(yy)+' '+
+        myFloatToStr(x0)+' '+
+        myFloatToStr(y0)+' '+
+        myFloatToStr(a)+' '+
+        myFloatToStr(e)
+      );
+  closeFile(pDatei);
+  if residuenBerechnen then begin
+    gibAus('... Residuen berechnen ...',3);
+    case genauigkeit of
+      gSingle:
+        sWerte.gausz2dSubtrahieren(offset,parameter);
+      gDouble:
+        dWerte.gausz2dSubtrahieren(offset,parameter);
+      gExtended:
+        eWerte.gausz2dSubtrahieren(offset,parameter);
+    end{of case};
+  end;
+  gibAus('... fertig '+timetostr(now-Zeit),3);
+  result:=true;
+end;
+
 function tWerte.berechneZeitfrequenzanalyse(sT: boolean; f: tMyStringList; threads: longint; quelle: tWerte; warn: tWarnStufe): boolean;
 var
   i,tMin,tMax,qlen:    longint;
diff --git a/gausz2d.nb b/gausz2d.nb
new file mode 100644
index 0000000..90d3e5d
--- /dev/null
+++ b/gausz2d.nb
@@ -0,0 +1,441 @@
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+WindowFrame->Normal*)
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diff --git a/gauszFit.inc b/gauszFit.inc
index 61be566..006ab36 100644
--- a/gauszFit.inc
+++ b/gauszFit.inc
@@ -15,3 +15,54 @@ for ii:=wiMin to wiMax do begin
   parameter[nParams,true,3]:=parameter[nParams,true,3] - t3;
 end;
 {$ENDIF}
+
+{$IFDEF gausz2dFitBerechneWerte}
+dOffset:=0;
+for i:=0 to iteration-1 do begin
+  with dParameter[i] do begin
+    e:=0;
+    xx:=0;
+    yy:=0;
+    x0:=0;
+    y0:=0;
+    a:=0;
+  end;
+  with parameter[i] do begin
+    cas[i]:=cos(a);
+    sas[i]:=sin(a);
+    xxs[i]:=-sqr(xx*cas[i])-sqr(yy*sas[i]);
+    yys[i]:=-sqr(yy*cas[i])-sqr(xx*sas[i]);
+    xys[i]:=(sqr(xx)-sqr(yy))*2*cas[i]*sas[i];
+    writeln(i,': xxs = ',xxs[i],'   yys = ',yys[i],'   xys = ',xys[i]);
+  end;
+end;
+abstand:=0;
+for x:=0 to sXSteps-1 do
+  for y:=0 to sTSiz-1 do begin
+    val:= samples[x + y*sXSteps];
+    tmp:= offset - val;
+    for i:=0 to iteration-1 do begin
+      dxs[i]:= x - parameter[i].x0;
+      dys[i]:= y - parameter[i].y0;
+      tmp:= tmp +
+        exp(
+          parameter[i].e +
+          xxs[i] * sqr(dxs[i]) +
+          yys[i] * sqr(dys[i]) +
+          xys[i] * dxs[i] * dys[i]
+        );
+    end;
+    dOffset:= dOffset - tmp;
+    abstand:= abstand + sqr(tmp);
+    tmp:= tmp * (tmp - offset + val); // * vFit
+    for i:=0 to iteration-1 do
+      with dParameter[i] do begin
+        e:= e + tmp;
+        xx:= xx - 2 * tmp * parameter[i].xx * sqr(dxs[i]*cas[i] - dys[i]*sas[i]);
+        yy:= yy - 2 * tmp * parameter[i].yy * sqr(dys[i]*cas[i] + dxs[i]*sas[i]);
+        x0:= x0 - tmp * (2 * dxs[i] * xxs[i] + xys[i] * dys[i]);
+        y0:= y0 - tmp * (2 * dys[i] * yys[i] + xys[i] * dxs[i]);
+        a:= a - tmp * 2 * (sqr(parameter[i].xx) - sqr(parameter[i].yy)) * (dys[i]*cas[i] + dxs[i]*sas[i]) * (dxs[i]*cas[i] - dys[i]*sas[i]);
+      end;
+  end;
+{$ENDIF}
diff --git a/typenunit.pas b/typenunit.pas
index 14660d4..bc5843d 100644
--- a/typenunit.pas
+++ b/typenunit.pas
@@ -14,6 +14,11 @@ const speicherHappen = 32768; // Anzahl an mit einem Mal zu reservierender Array
 
 type
   tExtraInfos = class;
+  tGausz2dParameter = record
+    xx,yy,x0,y0,a,e: extended;
+    // exp ( -(xx^2 * cos(a)^2 + yy^2 * sin(a)^2) * (X-x0)^2 - (yy^2 * cos(a)^2 + xx^2 * sin(a)^2) * (Y-y0)^2 + 2(xx^2 - yy^2) * cos(a)sin(a) * (X-x0) * (Y-y0) + e)
+  end;
+  tGausz2dParameterArray = array of tGausz2dParameter;
   tKomplexMachModus = (kmmReNull,kmmImNull,kmmPhZuf);
   tLowLevelHintergrundAbzugsArt = (haaKeine,haaRandDurchschnitt,haaRandMinimum,haaRandPerzentil,haaMinimum,haaVertikaleMittel,haaVertikaleMedianMittel);
   tHintergrundAbzugsArt = record
diff --git a/werteunit.pas b/werteunit.pas
index 07a33cb..05b5925 100644
--- a/werteunit.pas
+++ b/werteunit.pas
@@ -78,6 +78,8 @@ type
     procedure integriere(qu: pTLLWerteDouble; xMi,xMa,tMi,tMa,xOf,tOf: longint; richtung: tIntegrationsRichtung); overload;
     procedure integriere(qu: pTLLWerteExtended; xMi,xMa,tMi,tMa,xOf,tOf: longint; richtung: tIntegrationsRichtung); overload;
     procedure gauszFit(amplituden,breiten,positionen,ueberlappe,hintergruende: pTLLWerteExtended; von,bis: longint; senkrecht: boolean; fensterBreite,maxBreite,maxVerschiebung: extended; positionsMitten: tExtendedArray);
+    function gauszFit2d(anzahl,maximalSamples: longint; relativeVerbesserung: extended; out offset: extended; out parameter: tGausz2dParameterArray): int64;
+    procedure gausz2dSubtrahieren(offset: extended; parameter: tGausz2dParameterArray);
     function ermittleRandDurchschnitt: extended;
     function ermittleRandMinimum: extended;
     function ermittleRandPerzentil(p: extended): extended;
@@ -1618,6 +1620,228 @@ begin
     end;
 end;
 
+function tLLWerte.gauszFit2d(anzahl,maximalSamples: longint; relativeVerbesserung: extended; out offset: extended; out parameter: tGausz2dParameterArray): int64;
+var
+  i,x,y,sXSteps,sTSiz,iteration: int64;
+  abstand,altAbstand,dOffset,
+    schritt,gradLen,tmp,val:     extended;
+  samples,cas,sas,xxs,yys,xys,
+    dxs,dys,samples2:            tExtendedArray;
+  dParameter:                    tGausz2dParameterArray;
+  bitteNochMal:                  boolean;
+begin
+  if relativeVerbesserung<=0 then
+    fehler('die relative Verbesserung wird niemals besser als ' + floatToStr(relativeVerbesserung));
+  relativeVerbesserung:=sqr(relativeVerbesserung);
+
+  i:=1;
+  while (params.xSteps div i > maximalSamples) or
+    (params.tSiz div i > maximalSamples) or
+    (params.xSteps mod i > 0) or
+    (params.tSiz mod i > 0) do begin
+    inc(i);
+    if i>params.xSteps then
+      fehler('So ein Mist, '+intToStr(params.xSteps)+' und '+intToStr(params.tSiz)+' scheinen einen zu kleinen größten gemeinsame Teiler zu haben.');
+  end;
+  sXSteps:=params.xSteps div i;
+  sTSiz:=params.tSiz div i;
+  setLength(samples,sXSteps*sTSiz);
+  setLength(samples2,length(samples));
+  for x:=0 to sXSteps-1 do
+    for y:=0 to sTSiz-1 do
+      samples[x+y*sXSteps]:=0;
+  for x:=0 to params.xSteps-1 do
+    for y:=0 to params.tSiz-1 do
+      samples[round(x/(params.xSteps-1)*(sXSteps-1)) + round(y/(params.tSiz-1)*(sTSiz-1))*sTSiz]:=
+        samples[round(x/(params.xSteps-1)*(sXSteps-1)) + round(y/(params.tSiz-1)*(sTSiz-1))*sTSiz] +
+        werte[x + y*params.xSteps];
+  for x:=0 to sXSteps-1 do
+    for y:=0 to sTSiz-1 do
+      samples[x+y*sXSteps]:=
+        samples[x+y*sXSteps] / params.xSteps * sXSteps / params.tSiz * sTSiz;
+
+  offset:=params.minW + 0.1 * random * (params.maxW - params.minW);
+  dOffset:=0;
+  setLength(parameter,anzahl);
+  setLength(dParameter,anzahl);
+  setLength(cas,anzahl);
+  setLength(sas,anzahl);
+  setLength(xxs,anzahl);
+  setLength(yys,anzahl);
+  setLength(xys,anzahl);
+  setLength(dxs,anzahl);
+  setLength(dys,anzahl);
+  iteration:=0;
+
+  result:=0;
+  schritt:=1;
+  abstand:=1e9*sXSteps*sTSiz;
+  gradLen:=0;
+  bitteNochMal:=false;
+  repeat
+    if (gradLen<relativeVerbesserung) and not bitteNochMal then begin
+      inc(iteration);
+      if iteration>anzahl then
+        break;
+      for i:=0 to iteration-2 do
+        with parameter[i] do begin
+          xxs[i]:=-sqr(xx*cos(a))-sqr(yy*sin(a));
+          yys[i]:=-sqr(yy*cos(a))-sqr(xx*sin(a));
+          xys[i]:=(sqr(xx)-sqr(yy))*2*cos(a)*sin(a);
+        end;
+      for y:=0 to sTSiz-1 do
+        for x:=0 to sXSteps-1 do begin
+          samples2[x+y*sXSteps]:=samples[x+y*sXSteps] - offset;
+          for i:=0 to iteration-2 do
+            samples2[x+y*sXSteps]:=samples2[x+y*sXSteps] - exp(
+              parameter[i].e +
+              xxs[i] * sqr(x - parameter[i].x0) +
+              yys[i] * sqr(y - parameter[i].y0) +
+              xys[i] * (x - parameter[i].x0) * (y - parameter[i].y0)
+            );
+        end;
+      with parameter[iteration-1] do begin
+        e:=0;
+        xx:=(10 + 0.5 * random) / sXSteps;
+        yy:=(10 + 0.5 * random) / sTSiz;
+        x0:=0;
+        y0:=0;
+        a:=0.01 * random - 0.005;
+        tmp:=offset-1;
+        for y:=0 to sTSiz-1 do
+          for x:=0 to sXSteps-1 do
+            if samples2[x+y*sXSteps]>tmp then begin
+              tmp:= samples2[x+y*sXSteps];
+              x0:=x;
+              y0:=y;
+            end;
+        if tmp>0 then
+          e:=ln(tmp)
+        else
+          e:=0;
+        x:=round(x0);
+        y:=round(y0);
+        for i:=1 to min(x,sXSteps-1-x) do
+          if samples2[x+i+y*sXSteps] + samples2[x-i+y*sXSteps] < 2 * exp(-1) * samples2[x+y*sXSteps] then begin
+            xx:=1/i;
+            break;
+          end;
+        for i:=1 to min(y,sTSiz-1-y) do
+          if samples2[x+(y+i)*sXSteps] + samples2[x+(y-i)*sXSteps] - 2 * offset < 2 * exp(-1) * samples2[x+y*sXSteps] then begin
+            yy:=1/i;
+            break;
+          end;
+        writeln('+['+intToStr(iteration-1)+']: e = ',e,'   1/xx = ',1/xx,'   1/yy = ',1/yy,'   x0 = ',x0,'   y0 = ',y0,'   a = ',a);
+      end;
+    end;
+    bitteNochMal:=false;
+    inc(result);
+    altAbstand:=abstand;
+    {$DEFINE gausz2dFitBerechneWerte}
+    {$I gauszFit.inc}
+    {$UNDEF gausz2dFitBerechneWerte}
+
+    if abstand > altAbstand then
+      schritt:=schritt/2
+    else if abstand > 0.7*altAbstand then
+      schritt:=schritt*1.1;
+
+    for i:=0 to iteration-1 do
+      with dParameter[i] do begin
+        if abs(schritt*e)>=1 then begin                     // e darf sich maximal um 1 verändern
+          schritt:=abs(1/e);
+          bitteNochMal:=true;
+        end;
+        if abs(schritt*x0*2)>=sXSteps then begin            // x0 darf sich maximal um sXSteps/2 verändern
+          schritt:=abs(sXSteps/2/x0);
+          bitteNochMal:=true;
+        end;
+        if abs(schritt*y0*2)>=sTSiz then begin               // y0 darf sich maximal um sTSiz/2 verändern
+          schritt:=abs(sTSiz/2/y0);
+          bitteNochMal:=true;
+        end;
+        if abs(schritt*a*2)>=pi then begin                   // a darf sich maximal um pi/2 verändern
+          schritt:=abs(pi/2/a);
+          bitteNochMal:=true;
+        end;
+        if parameter[i].xx - 2 * xx * schritt < 0 then begin // xx darf sich höchstens halbieren
+          schritt:=parameter[i].xx / 2 / xx;
+          bitteNochMal:=true;
+        end;
+        if parameter[i].yy - 2 * yy * schritt < 0 then begin // yy darf sich höchstens halbieren
+          schritt:=parameter[i].yy / 2 / yy;
+          bitteNochMal:=true;
+        end;
+      end;
+
+    writeln(iteration,': ',abstand,' ',schritt);
+
+    offset:=offset - dOffset * schritt;
+    gradLen:=sqr(dOffset * schritt);
+    for i:=0 to iteration-1 do
+      with parameter[i] do begin
+        writeln('d['+intToStr(i)+']: e = ',dParameter[i].e,'   xx = ',dParameter[i].xx,'   yy = ',dParameter[i].yy,'   x0 = ',dParameter[i].x0,'   y0 = ',dParameter[i].y0,'   a = ',dParameter[i].a);
+        e:=e - dParameter[i].e * schritt;
+        gradLen:=gradLen + sqr(dParameter[i].e * schritt);
+        xx:=xx - dParameter[i].xx * schritt;
+        if xx<0 then
+          xx:=-xx;
+        gradLen:=gradLen + sqr(dParameter[i].xx * schritt);
+        yy:=yy - dParameter[i].yy * schritt;
+        if yy<0 then
+          yy:=-yy;
+        gradLen:=gradLen + sqr(dParameter[i].yy * schritt);
+        x0:=x0 - dParameter[i].x0 * schritt;
+        gradLen:=gradLen + sqr(dParameter[i].x0 * schritt);
+        y0:=y0 - dParameter[i].y0 * schritt;
+        gradLen:=gradLen + sqr(dParameter[i].y0 * schritt);
+        a:=(a - dParameter[i].a * schritt) / 2 / pi;
+        a:=(a - round(a)) * 2 * pi;
+        gradLen:=gradLen + sqr(dParameter[i].a * schritt);
+      end;
+  until false;
+  for i:=0 to length(parameter)-1 do
+    with parameter[i] do begin
+      xx:=xx * sXSteps / params.xSteps;
+      yy:=yy * sTSiz / params.tSiz;
+      x0:=x0 / sXSteps * params.xSteps;
+      y0:=y0 / sTSiz * params.tSiz;
+    end;
+  setLength(samples,0);
+end;
+
+procedure tLLWerte.gausz2dSubtrahieren(offset: extended; parameter: tGausz2dParameterArray);
+var
+  x,y,i:       longint;
+  xxs,yys,xys: tExtendedArray;
+begin
+  setLength(xxs,length(parameter));
+  setLength(yys,length(parameter));
+  setLength(xys,length(parameter));
+  for i:=0 to length(parameter)-1 do
+    with parameter[i] do begin
+      xxs[i]:=-sqr(xx*cos(a))-sqr(yy*sin(a));
+      yys[i]:=-sqr(yy*cos(a))-sqr(xx*sin(a));
+      xys[i]:=(sqr(xx)-sqr(yy))*2*cos(a)*sin(a);
+    end;
+  for y:=0 to params.tSiz-1 do
+    for x:=0 to params.xSteps-1 do begin
+      werte[x+y*params.xSteps]:= werte[x+y*params.xSteps] - offset;
+      for i:=0 to length(parameter)-1 do
+        werte[x+y*params.xSteps]:=
+          werte[x+y*params.xSteps]
+          - exp(
+            parameter[i].e +
+            xxs[i] * sqr(x - parameter[i].x0) +
+            yys[i] * sqr(y - parameter[i].y0) +
+            xys[i] * (x - parameter[i].x0) * (y - parameter[i].y0)
+          );
+    end;
+  setLength(xxs,0);
+  setLength(yys,0);
+  setLength(xys,0);
+end;
+
 function tLLWerte.ermittleRandDurchschnitt: extended;
 var
   i: int64;