Use QR decomposition instead of gauss elimination for polynomial reg.

Gauss elimination is not a stable algorithm so use QR decomposition
(with other methods). Also use horner's method to evaluate a polynomial
which is the prefered and more stable method of polynomial evaluation.
Still this is not quite enough as you still have to multiply very large
number with very small and you lose percision on high-degree polynomials
or big X values. Some methods evaluate the polynomial in barycentric form
but how to get the polynomial into the barycentric form is now the
question.

Change-Id: If0d93bc1f08253f015e814e187b5a2cb7f78ec49

4 files changed, 109 insertions, 214 deletions

diff --git a/chart2/source/inc/PolynomialRegressionCurveCalculator.hxx b/chart2/source/inc/PolynomialRegressionCurveCalculator.hxx
index e3b43a26095f..6c1d990f9d58 100644
--- a/chart2/source/inc/PolynomialRegressionCurveCalculator.hxx
+++ b/chart2/source/inc/PolynomialRegressionCurveCalculator.hxx
@@ -25,6 +25,7 @@
 namespace chart
 {
 
+
 class PolynomialRegressionCurveCalculator : public RegressionCurveCalculator
 {
 public:
@@ -57,7 +58,7 @@ private:
         throw (com::sun::star::lang::IllegalArgumentException,
                com::sun::star::uno::RuntimeException);
 
-    std::vector<double> mResult;
+    std::vector<double> mCoefficients;
 };
 
 } //  namespace chart
diff --git a/chart2/source/tools/PolynomialRegressionCurveCalculator.cxx b/chart2/source/tools/PolynomialRegressionCurveCalculator.cxx
index 19d224d83cfb..1c84731141e4 100644
--- a/chart2/source/tools/PolynomialRegressionCurveCalculator.cxx
+++ b/chart2/source/tools/PolynomialRegressionCurveCalculator.cxx
@@ -24,11 +24,9 @@
 #include <cmath>
 #include <rtl/math.hxx>
 #include <rtl/ustrbuf.hxx>
-#include "gauss.hxx"
 
 using namespace com::sun::star;
 
-
 namespace chart
 {
 
@@ -49,80 +47,138 @@ void SAL_CALL PolynomialRegressionCurveCalculator::recalculateRegression(
     RegressionCalculationHelper::tDoubleVectorPair aValues(
         RegressionCalculationHelper::cleanup( aXValues, aYValues, RegressionCalculationHelper::isValid()));
 
-    sal_Int32 aNoElements = mForceIntercept ? mDegree : mDegree + 1;
-    sal_Int32 aNumberOfPowers = 2 * aNoElements - 1;
+    const sal_Int32 aNoValues = aValues.first.size();
 
-    std::vector<double> aPowers;
-    aPowers.resize(aNumberOfPowers, 0.0);
+    const sal_Int32 aNoPowers = mForceIntercept ? mDegree : mDegree + 1;
 
-    sal_Int32 aNoColumns = aNoElements;
-    sal_Int32 aNoRows    = aNoElements + 1;
+    mCoefficients.clear();
+    mCoefficients.resize(aNoPowers, 0.0);
 
-    std::vector<double> aMatrix;
-    aMatrix.resize(aNoColumns * aNoRows, 0.0);
+    double yAverage = 0.0;
 
-    const size_t aNoValues = aValues.first.size();
+    std::vector<double> aQRTransposed;
+    aQRTransposed.resize(aNoValues * aNoPowers, 0.0);
 
-    double yAverage = 0.0;
+    std::vector<double> yVector;
+    yVector.resize(aNoValues, 0.0);
 
-    for( size_t i = 0; i < aNoValues; ++i )
+    for(sal_Int32 i = 0; i < aNoValues; i++)
     {
-        double x = aValues.first[i];
-        double y = aValues.second[i];
+        double yValue = aValues.second[i];
+        if (mForceIntercept)
+            yValue -= mInterceptValue;
+        yVector[i] = yValue;
+        yAverage += yValue;
+    }
+    yAverage /= aNoValues;
 
-        for (sal_Int32 j = 0; j < aNumberOfPowers; j++)
+    for(sal_Int32 j = 0; j < aNoPowers; j++)
+    {
+        sal_Int32 aPower = mForceIntercept ? j+1 : j;
+        sal_Int32 aColumnIndex = j * aNoValues;
+        for(sal_Int32 i = 0; i < aNoValues; i++)
         {
-            if (mForceIntercept)
-                aPowers[j] += std::pow(x, (int) j + 2);
-            else
-                aPowers[j] += std::pow(x, (int) j);
+            double xValue = aValues.first[i];
+            aQRTransposed[i + aColumnIndex] = std::pow(xValue, aPower);
         }
+    }
+
+    // QR decomposition - based on org.apache.commons.math.linear.QRDecomposition from apache commons math (ASF)
+    sal_Int32 aMinorSize = std::min(aNoValues, aNoPowers);
+
+    std::vector<double> aDiagonal;
+    aDiagonal.resize(aMinorSize, 0.0);
 
-        for (sal_Int32 j = 0; j < aNoElements; j++)
+    // Calculate Householder reflectors
+    for (sal_Int32 aMinor = 0; aMinor < aMinorSize; aMinor++)
+    {
+        double aNormSqr = 0.0;
+        for (sal_Int32 x = aMinor; x < aNoValues; x++)
         {
-            if (mForceIntercept)
-                aMatrix[j * aNoRows + aNoElements] += std::pow(x, (int) j + 1) * ( y - mInterceptValue );
-            else
-                aMatrix[j * aNoRows + aNoElements] += std::pow(x, (int) j) * y;
+            double c = aQRTransposed[x + aMinor * aNoValues];
+            aNormSqr += c * c;
         }
 
-        yAverage += y;
-    }
+        double a;
+
+        if (aQRTransposed[aMinor + aMinor * aNoValues] > 0.0)
+            a = -std::sqrt(aNormSqr);
+        else
+            a = std::sqrt(aNormSqr);
+
+        aDiagonal[aMinor] = a;
 
-    yAverage = yAverage / aNoValues;
+        if (a != 0.0)
+        {
+            aQRTransposed[aMinor + aMinor * aNoValues] -= a;
 
-    for (sal_Int32 y = 0; y < aNoElements; y++)
+            for (sal_Int32 aColumn = aMinor + 1; aColumn < aNoPowers; aColumn++)
+            {
+                double alpha = 0.0;
+                for (sal_Int32 aRow = aMinor; aRow < aNoValues; aRow++)
+                {
+                    alpha -= aQRTransposed[aRow + aColumn * aNoValues] * aQRTransposed[aRow + aMinor * aNoValues];
+                }
+                alpha /= a * aQRTransposed[aMinor + aMinor * aNoValues];
+
+                for (sal_Int32 aRow = aMinor; aRow < aNoValues; aRow++)
+                {
+                    aQRTransposed[aRow + aColumn * aNoValues] -= alpha * aQRTransposed[aRow + aMinor * aNoValues];
+                }
+            }
+        }
+    }
+
+    // Solve the linear equation
+    for (sal_Int32 aMinor = 0; aMinor < aMinorSize; aMinor++)
     {
-        for (sal_Int32 x = 0; x < aNoElements; x++)
+        double aDotProduct = 0;
+
+        for (sal_Int32 aRow = aMinor; aRow < aNoValues; aRow++)
+        {
+            aDotProduct += yVector[aRow] * aQRTransposed[aRow + aMinor * aNoValues];
+        }
+        aDotProduct /= aDiagonal[aMinor] * aQRTransposed[aMinor + aMinor * aNoValues];
+
+        for (sal_Int32 aRow = aMinor; aRow < aNoValues; aRow++)
         {
-            aMatrix[y * aNoRows + x] = aPowers[y + x];
+            yVector[aRow] += aDotProduct * aQRTransposed[aRow + aMinor * aNoValues];
         }
+
     }
 
-    mResult.clear();
-    mResult.resize(aNoElements, 0.0);
+    for (sal_Int32 aRow = aDiagonal.size() - 1; aRow >= 0; aRow--)
+    {
+        yVector[aRow] /= aDiagonal[aRow];
+        double yRow = yVector[aRow];
+        mCoefficients[aRow] = yRow;
 
-    solve(aMatrix, aNoColumns, aNoRows, mResult, 1.0e-20);
+        for (sal_Int32 i = 0; i < aRow; i++)
+        {
+            yVector[i] -= yRow * aQRTransposed[i + aRow * aNoValues];
+        }
+    }
 
-    // Set intercept value if force intercept is enabled
-    if (mForceIntercept) {
-        mResult.insert( mResult.begin(), mInterceptValue );
+    if(mForceIntercept)
+    {
+        mCoefficients.insert(mCoefficients.begin(), mInterceptValue);
     }
 
     // Calculate correlation coeffitient
     double aSumError = 0.0;
     double aSumTotal = 0.0;
 
-    for( size_t i = 0; i < aNoValues; ++i )
+    for( sal_Int32 i = 0; i < aNoValues; i++ )
     {
-        double x = aValues.first[i];
+        double xValue = aValues.first[i];
         double yActual = aValues.second[i];
-        double yPredicted = getCurveValue( x );
+        double yPredicted = getCurveValue( xValue );
         aSumTotal += (yActual - yAverage) * (yActual - yAverage);
         aSumError += (yActual - yPredicted) * (yActual - yPredicted);
     }
 
     double aRSquared = 1.0 - (aSumError / aSumTotal);
+
     if (aRSquared > 0.0)
         m_fCorrelationCoeffitient = std::sqrt(aRSquared);
     else
@@ -136,15 +192,18 @@ double SAL_CALL PolynomialRegressionCurveCalculator::getCurveValue( double x )
     double fResult;
     rtl::math::setNan(&fResult);
 
-    if (mResult.empty())
+    if (mCoefficients.empty())
     {
         return fResult;
     }
 
+    sal_Int32 aNoCoefficients = (sal_Int32) mCoefficients.size();
+
+    // Horner's method
     fResult = 0.0;
-    for (size_t i = 0; i<mResult.size(); i++)
+    for (sal_Int32 i = aNoCoefficients - 1; i >= 0; i--)
     {
-        fResult += mResult[i] * std::pow(x, (int) i);
+        fResult = mCoefficients[i] + (x * fResult);
     }
     return fResult;
 }
@@ -167,10 +226,10 @@ OUString PolynomialRegressionCurveCalculator::ImplGetRepresentation(
 {
     OUStringBuffer aBuf( "f(x) = ");
 
-    sal_Int32 aLastIndex = mResult.size() - 1;
+    sal_Int32 aLastIndex = mCoefficients.size() - 1;
     for (sal_Int32 i = aLastIndex; i >= 0; i--)
     {
-        double aValue = mResult[i];
+        double aValue = mCoefficients[i];
         if (aValue == 0.0)
         {
             continue;
diff --git a/chart2/source/tools/gauss.hxx b/chart2/source/tools/gauss.hxx
deleted file mode 100644
index 6cd63ce30691..000000000000
--- a/chart2/source/tools/gauss.hxx
+++ /dev/null
@@ -1,166 +0,0 @@
-/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
-/*
- * This file is part of the LibreOffice project.
- *
- * This Source Code Form is subject to the terms of the Mozilla Public
- * License, v. 2.0. If a copy of the MPL was not distributed with this
- * file, You can obtain one at http://mozilla.org/MPL/2.0/.
- *
- * This file incorporates work covered by the following license notice:
- *
- *   Licensed to the Apache Software Foundation (ASF) under one or more
- *   contributor license agreements. See the NOTICE file distributed
- *   with this work for additional information regarding copyright
- *   ownership. The ASF licenses this file to you under the Apache
- *   License, Version 2.0 (the "License"); you may not use this file
- *   except in compliance with the License. You may obtain a copy of
- *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
- */
-
-/** This method eliminates elements below main diagonal in the given
-    matrix by gaussian elimination.
-
-    @param matrix
-    The matrix to operate on. Last column is the result vector (right
-    hand side of the linear equation). After successful termination,
-    the matrix is upper triangular. The matrix is expected to be in
-    row major order.
-
-    @param rows
-    Number of rows in matrix
-
-    @param cols
-    Number of columns in matrix
-
-    @param minPivot
-    If the pivot element gets lesser than minPivot, this method fails,
-    otherwise, elimination succeeds and true is returned.
-
-    @return true, if elimination succeeded.
- */
-template <class Matrix, typename BaseType>
-bool eliminate(     Matrix&         matrix,
-                    int             rows,
-                    int             cols,
-                    const BaseType& minPivot    )
-{
-    BaseType    temp;
-    int         max, i, j, k;   /* *must* be signed, when looping like: j>=0 ! */
-
-    /* eliminate below main diagonal */
-    for(i=0; i<cols-1; ++i)
-    {
-        /* find best pivot */
-        max = i;
-        for(j=i+1; j<rows; ++j)
-            if( fabs(matrix[ j*cols + i ]) > fabs(matrix[ max*cols + i ]) )
-                max = j;
-
-        /* check pivot value */
-        if( fabs(matrix[ max*cols + i ]) < minPivot )
-            return false;   /* pivot too small! */
-
-        /* interchange rows 'max' and 'i' */
-        for(k=0; k<cols; ++k)
-        {
-            temp = matrix[ i*cols + k ];
-            matrix[ i*cols + k ] = matrix[ max*cols + k ];
-            matrix[ max*cols + k ] = temp;
-        }
-
-        /* eliminate column */
-        for(j=i+1; j<rows; ++j)
-            for(k=cols-1; k>=i; --k)
-                matrix[ j*cols + k ] -= matrix[ i*cols + k ] *
-                    matrix[ j*cols + i ] / matrix[ i*cols + i ];
-    }
-
-    /* everything went well */
-    return true;
-}
-
-
-/** Retrieve solution vector of linear system by substituting backwards.
-
-    This operation _relies_ on the previous successful
-    application of eliminate()!
-
-    @param matrix
-    Matrix in upper diagonal form, as e.g. generated by eliminate()
-
-    @param rows
-    Number of rows in matrix
-
-    @param cols
-    Number of columns in matrix
-
-    @param result
-    Result vector. Given matrix must have space for one column (rows entries).
-
-    @return true, if back substitution was possible (i.e. no division
-    by zero occurred).
- */
-template <class Matrix, class Vector, typename BaseType>
-bool substitute(    const Matrix&   matrix,
-                    int             rows,
-                    int             cols,
-                    Vector&         result  )
-{
-    BaseType    temp;
-    int         j,k;    /* *must* be signed, when looping like: j>=0 ! */
-
-    /* substitute backwards */
-    for(j=rows-1; j>=0; --j)
-    {
-        temp = 0.0;
-        for(k=j+1; k<cols-1; ++k)
-            temp += matrix[ j*cols + k ] * result[k];
-
-        if( matrix[ j*cols + j ] == 0.0 )
-            return false;   /* imminent division by zero! */
-
-        result[j] = (matrix[ j*cols + cols-1 ] - temp) / matrix[ j*cols + j ];
-    }
-
-    /* everything went well */
-    return true;
-}
-
-
-/** This method determines solution of given linear system, if any
-
-    This is a wrapper for eliminate and substitute, given matrix must
-    contain right side of equation as the last column.
-
-    @param matrix
-    The matrix to operate on. Last column is the result vector (right
-    hand side of the linear equation). After successful termination,
-    the matrix is upper triangular. The matrix is expected to be in
-    row major order.
-
-    @param rows
-    Number of rows in matrix
-
-    @param cols
-    Number of columns in matrix
-
-    @param minPivot
-    If the pivot element gets lesser than minPivot, this method fails,
-    otherwise, elimination succeeds and true is returned.
-
-    @return true, if elimination succeeded.
- */
-template <class Matrix, class Vector, typename BaseType>
-bool solve( Matrix&     matrix,
-            int         rows,
-            int         cols,
-            Vector&     result,
-            BaseType    minPivot    )
-{
-    if( eliminate<Matrix,BaseType>(matrix, rows, cols, minPivot) )
-        return substitute<Matrix,Vector,BaseType>(matrix, rows, cols, result);
-
-    return false;
-}
-
-/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/chart2/source/view/charttypes/VSeriesPlotter.cxx b/chart2/source/view/charttypes/VSeriesPlotter.cxx
index 6a9a62a33704..40bf94cab050 100644
--- a/chart2/source/view/charttypes/VSeriesPlotter.cxx
+++ b/chart2/source/view/charttypes/VSeriesPlotter.cxx
@@ -1025,12 +1025,13 @@ void VSeriesPlotter::createRegressionCurvesShapes( VDataSeries& rVDataSeries,
 
             fPointScale = (fMaxX - fMinX) / (fChartMaxX - fChartMinX);
         }
-
         xCalculator->setRegressionProperties(aDegree, aForceIntercept, aInterceptValue, aPeriod);
         xCalculator->recalculateRegression( rVDataSeries.getAllX(), rVDataSeries.getAllY() );
-
         sal_Int32 nPointCount = 100 * fPointScale;
 
+        if ( nPointCount < 2 )
+            nPointCount = 2;
+
         drawing::PolyPolygonShape3D aRegressionPoly;
         aRegressionPoly.SequenceX.realloc(1);
         aRegressionPoly.SequenceY.realloc(1);