scalation.analytics.par

ResponseSurface

Related Doc: package par

class ResponseSurface extends Predictor with Error

The ResponseSurface class uses multiple regression to fit a quadratic/cubic surface to the data. For example in 2D, the quadratic regression equation is

y = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_0*x_1, x_12] + e

See also

scalation.metamodel.QuadraticFit

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Error, Predictor, AnyRef, Any
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Instance Constructors

  1. new ResponseSurface(x_: MatrixD, y: VectorD, cubic: Boolean = false, technique: RegTechnique = Fac_QR)

    x_

    the input vectors/points

    y

    the response vector

    cubic

    the order of the surface (defaults to quadratic, else cubic)

    technique

    the technique used to solve for b in x.t*x*b = x.t*y

Value Members

  1. final def !=(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  4. def allForms(): MatrixD

    Create all forms/terms for each point placing them in a new matrix.

  5. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  6. def backElim(): (Int, VectorD, Double, Double)

    Perform backward elimination to remove the least predictive variable from the model, returning the variable to eliminate, the new parameter vector, the new R-squared value and the new F statistic.

  7. def cForms(p: VectorD): VectorD

    Given a vector/point 'p', compute the values for all of its cubic, quadratic, linear and constant forms/terms, returning them as a vector.

    Given a vector/point 'p', compute the values for all of its cubic, quadratic, linear and constant forms/terms, returning them as a vector. for 1D: p = (x_0) => VectorD (1, x_0, x_02, x_03) for 2D: p = (x_0, x_1) => VectorD (1, x_0, x_02, x_03, x_0*x_1, x_02*x_1, x_0*x_12, x_1, x_12, x_13)

    p

    the source vector/point for creating forms/terms

  8. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
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    @throws( ... )
  9. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  10. def equals(arg0: Any): Boolean

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    AnyRef → Any
  11. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
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    @throws( classOf[java.lang.Throwable] )
  12. def fit: (VectorD, Double, Double, Double)

    Return the fit (parameter vector b, quality of fit including rSquared).

  13. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes
    Error
  14. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  15. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  16. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  17. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  18. final def notify(): Unit

    Definition Classes
    AnyRef
  19. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  20. def predict(z: Matrix): VectorD

    Predict the value of y = f(z) by evaluating the formula y = b dot zi for each row zi of matrix z.

    Predict the value of y = f(z) by evaluating the formula y = b dot zi for each row zi of matrix z.

    z

    the new matrix to predict

    Definition Classes
    ResponseSurfacePredictor
  21. def predict(z: VectorD): Double

    Given a point z, use the quadratic rsm regression equation to predict a value for the function at z.

    Given a point z, use the quadratic rsm regression equation to predict a value for the function at z. for 1D: b_0 + b_1*z_0 + b_2*z_02 for 2D: b_0 + b_1*z_0 + b_2*z_02 + b_3*z_1 + b_4*z_1*z_0 + b_5*z_1^2

    z

    the point/vector whose functional value is to be predicted

    Definition Classes
    ResponseSurfacePredictor
  22. def predict(z: VectorI): Double

    Given a new discrete data vector z, predict the y-value of f(z).

    Given a new discrete data vector z, predict the y-value of f(z).

    z

    the vector to use for prediction

    Definition Classes
    Predictor
  23. def qForms(p: VectorD): VectorD

    Given a vector/point 'p', compute the values for all of its quadratic, linear and constant forms/terms, returning them as a vector.

    Given a vector/point 'p', compute the values for all of its quadratic, linear and constant forms/terms, returning them as a vector. for 1D: p = (x_0) => VectorD (1, x_0, x_02) for 2D: p = (x_0, x_1) => VectorD (1, x_0, x_02, x_0*x_1, x_1, x_1^2)

    p

    the source vector/point for creating forms/terms

  24. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  25. def toString(): String

    Definition Classes
    AnyRef → Any
  26. def train(yy: VectorD): Unit

    Retrain the predictor by fitting the parameter vector (b-vector) in the quadratic rsm regression equation, e.g., for 2D yy = b dot x + e = [b_0, ...

    Retrain the predictor by fitting the parameter vector (b-vector) in the quadratic rsm regression equation, e.g., for 2D yy = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_1*x_0, x_12] + e using the least squares method.

    yy

    the new response vector

  27. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the quadratic rsm regression equation, e.g., for 2D y = b dot x + e = [b_0, ...

    Train the predictor by fitting the parameter vector (b-vector) in the quadratic rsm regression equation, e.g., for 2D y = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_02, x_1, x_1*x_0, x_12] + e using the least squares method.

    Definition Classes
    ResponseSurfacePredictor
  28. def vif: VectorD

    Compute the Variance Inflation Factor (VIF) for each variable to test for multi-colinearity by regressing xj against the rest of the variables.

    Compute the Variance Inflation Factor (VIF) for each variable to test for multi-colinearity by regressing xj against the rest of the variables. A VIF over 10 indicates that over 90% of the varaince of xj can be predicted from the other variables, so xj is a candidate for removal from the model.

  29. final def wait(): Unit

    Definition Classes
    AnyRef
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    @throws( ... )
  30. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
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    @throws( ... )
  31. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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