• Savitzky-Golay filter smoothing
  
  • Smoothed data
  • Smoothed derivatives,   
    
• Moving average window smoothing
  
  • Smoothed data

• Interpolation within the smoothed data

• Table of methods
• Listing of the ThreeDimensionalSmooth.java source code (Last update: 16 March 2012)
• Other classes, in this library, used by this class
• Main Page of Michael Thomas Flanagan's Java Scientific Library

CONSTRUCTORS

SMOOTHING METHODS

The Savitzky-Golay Filter
public double[][] getSGcoefficients()
Usage:                      sgCoefficients = tds.getSGcoefficients();
This method returns the Savitzky-Golay filter coefficients, c, used in the smoothing

l_w, m_w and n_w are the lengths of the filter in the x, y and z directions respectively, l_l, m_l and n_l are the number of points preceeding the data point on which the filter is operating, v_z,x,y, in the x, y and z directions respectively and l_u, m_u and n_u are the number of points following the data point, z_z,y,x,in the x, y and z directions respectively. If the filter is used as a smoothing filter s_z,y,x is the smoothed value of the data point v_z,y,x and the c values used are those stored in the zeroth row of the returned matrix sgCoefficients. Each row of sgCoefficients is the array of coefficients c[l_w][m_w][n_w] arranged linearly. Each row of sgCoefficients corresponds to the indices of the fitting polynomial coefficients, e.g. for a polynomial of degree 4,

Each row, when applied to the data, gives the smoothed derivatives, where p, q and r are given by the three subscripts of the polynomial coefficients, e.g. the zeroth row, indices 0,0,0, gives the smoothed zeroth derivative, i.e. the smoothed data values; the second row, indices 0,0,1, gives the derivatives . The trio of indices associated with each row may be obtained by calling the method

MOVING AVERAGE WINDOW SMOOTHING
public double[][][] movingAverage(int windowWidthx, int windowWidthy, int windowWidthz)
public double[][][] movingAverage(int windowWidth)
public BigDecimal[][][] movingAverageAsBigDecimal(int windowWidthx, int windowWidthy, int windowWidthz)
public BigDecimal[][][] movingAverageAsBigDecimal(int windowWidth)
public double[][][] getMovingAverageValues()
public BigDecimal[][][] getMovingAverageValuesAsBigDecimal()
Usage:                      smoothedData = tds.movingAverage(windowWidthx, windowWidthy, windowWidthz);
This method returns the smoothed v values, for the data entered via the constructor arguments, using a moving average cube of l_w [argument windowWidthx] points in the x dimension, of m_w [argument windowWidthy] points in the y dimension and of n_w [argument windowWidthz] points in the z dimension:

s_z,y,x is the smoothed value of the data point z_z,y,x. The entered value for the number of points in the windows are adjusted to the next higher odd number if an even number has been entered. The values of l_l, l_u, m_l, m_u, n_l, and n_u are truncated appropriately if, when close to the data extremes, they fall below or above the first or last data point respectively. The smoothed data is returned as type double.

Usage:                      smoothedData = tds.movingAverage(windowWidth);
As immediately above for movingAverage(windowWidthx, windowWidthy, windowWidthz) with a smoothing cube of equal sides, i.e. windowWidthx = windowWidth, windowWidthy = windowWidth and windowWidthz = windowWidth.

Usage:                      smoothedData = tds.movingAverageAsBigDecimal(windowWidthx, windowWidthy, windowWidthz);
As above for movingAverage(windowWidthx, windowWidthy, windowWidthz) with the exception that the smoothed data is returned as type BigDecimal. If the data was entered as type BigDecimal or BigInteger the smoothing will have been performed in arbitrary arithmetic.

Usage:                      smoothedData = tds.movingAverageAsBigDecimal(windowWidthx);
As above for movingAverage(windowWidthx, windowWidthy, windowWidthz) with a smoothing cube of equal sides, i.e. windowWidthx = windowWidth, windowWidthy = windowWidth and windowWidthz = windowWidth, and with the exception that the smoothed data is returned as type BigDecimal. If the data was entered as type BigDecimal or BigInteger the smoothing will have been performed in arbitrary arithmetic.

Usage:                      smoothedData = tds.getMovingAverageValues();
This method returns the smoothed v values if the above moving average window method has already been called.

Usage:                      smoothedData = tds.getMovingAverageValuesAsBigDecimal();
This method returns the smoothed v values if the above moving average window method has already been called. The smoothed values are returned as type BigDecimal.

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EXTENT OF SMOOTHING

public double extentSavitzkyGolay()
public double extentMovingAverage()
These methods return the value of the function
    
where v_i,j,k is the original v value of the ith, jth, kth data point, s_i,j,k is its smoothed value, v_min is the minimum value of the v_i,j,k, v_max is the maximum value of the z_i,j,k and p is the number of x coordinates, q is the number of y coordinates and r is the number of z coordinates.

Usage:                      extent = tds.extentSavitzkyGolay();
In this method s_i,j,k is the Savitzky-Golay smoothed value.

Usage:                      extent = tds.extentMovingAverage();
In this method s_i,j,k is its moving average smoothed value.

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