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Linear Or Straight Line Interpolation Modules

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CALCULATOR MODULE : Maths Polynomial   ±

Calculate polynomial coefficients, roots or zeros, maximum and minimum, points of inflection, and interpolate polynomial value, slope and curvature.

Polynomials can be calculated for linear (first order), quadratic (second order), cubic (third order), quartic (fourth order), quintic (fifth order), sextic (sixth order), septic (seventh order), octic (eighth order) or nth degree. For polynomials with all real roots, all roots can sometimes be solved simultaneously using the Durand Kerner method. In other cases solve for individual roots. The maximum or minimum points (slope equals zero) and the inflection points (curvature equals zero) can also be calculated. Use a plot page to plot the polynomial and identify the approximate root values if any.

Lagrange's method is used to interpolate between data points. This method is useful for interpolating between data points, but can give poor results when extrapolating outside the data range. Evenly spaced data points can result in cyclic behaviour.

Polynomial coefficients can be calculated from the real roots, and the nth coefficient. There are an infinite number of polynomials with the same roots. The nth coefficient is required in order to calculate unique coefficients. This method only applies if all of the roots are real. Polynomial coefficients can also be calculated from XZ data points.

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CALCULATOR MODULE : Maths Linear Regression   ±

Calculate the best fit line for scatter data points using the least squares linear regression method. The curve does not have to pass through each data point.

For straight line or linear curves (Z = A x + B) the regression is performed directly on the X and Z data values. For power curves (Z = A x^B) the regression is performed on the ln(X) and ln(Z) values. For logarithmic curves (Z = ln(X)) the regression is performed on the ln(X) and Z values. For exponential curves (Z = A e^B) the regression is performed on the X and ln(Z) values. For the user defined transform (Z = A f(X) + B) the regression is performed on f(X) and Z where f(X) is the user defined transform.

The X and Z offsets can be used to change the origin for log values (ln(X - Xo) and ln(Z - Zo)) and user defined transform (f(X - Xo)). The offsets are not used for the X and Z values.

The Z unit value is applied for the log of negative Z values. The Z unit value is not applied for X and Z values, or for user defined transforms (user defined transforms should account for the sign of the data points).

The regression data and regression parameters are displayed in the output view at the bottom of the page. The correlation coefficient r is a measure of how well the curve fits the data points (close to one is better). Extrapolated values should be used carefully.

Enter vector data as X,Z pairs separated by a comma or tab, with each pair on a new line. Or copy and paste the data points from a spreadsheet. Enter array data X and Z values as separate comma or tab separated lists. Store file data to a text file as comma or tab separated pairs (X,Z), with each pair on a new line (or copy and past cells from a spreadsheet). Refer to the example text file in resources.

Use the data plot option on the plot bar to display the data points and the best fit line.

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CALCULATOR MODULE : Weibull Gumbel And Frechet Extreme Event Probability   ±

Calculate extreme event amplitude and return period from return period data using the Weibull, Gumbel and Frechet probability distributions.

A best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for X versus Z instead of Z versus X (the X and Z values are swapped). The three parameter distribution amplitude offset is a minimum amplitude. The regression data points and regression parameters are displayed in the output view at the bottom of the page. Use the Data Plot option on the plot bar to display the data points and the best fit line.

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CALCULATOR MODULE : Ocean Wave Probability And Return Period   ±

Calculate ocean wave height and period from return period data using the Weibull, Gumbel or Frechet probability distributions.

The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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CALCULATOR MODULE : Ocean Current Probability And Return Period   ±

Calculate ocean current velocity from return period data using the Weibull, Gumbel or Frechet probability distributions.

The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). Use the Data Plot option on the plot bar to display the data points and the calculated best fit. The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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CALCULATOR MODULE : Ocean Wave And Current Probability And Return Period   ±

Calculate ocean wave height, wave period and current velocity from return period data using the Weibull, Gumbel or Frechet probability distributions.

The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). Use the Data Plot option on the plot bar to display the data points and the calculated best fit. The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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