Packages

c

scalation.analytics.par

ResponseSurface

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

Linear Supertypes
Error, Predictor, AnyRef, Any
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  1. ResponseSurface
  2. Error
  3. Predictor
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Instance Constructors

  1. new ResponseSurface(x_: MatrixD, y: VectorD, cubic: Boolean = false, technique: RegTechnique = 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. val b: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  7. def backElim(): (Int, VectoD, VectoD)

    Perform backward elimination to remove the least predictive variable from the model, returning the variable to eliminate, the new parameter vector, the new quality of fit.

  8. 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

  9. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  10. def coefficient: VectoD

    Return the vector of coefficient/parameter values.

    Return the vector of coefficient/parameter values.

    Definition Classes
    Predictor
  11. def diagnose(yy: VectoD): Unit

    Compute diagostics for the predictor.

    Compute diagostics for the predictor. Override to add more diagostics. Note, for 'rmse', 'sse' is divided by the number of instances 'm' rather than degrees of freedom.

    yy

    the response vector

    Definition Classes
    Predictor
    See also

    en.wikipedia.org/wiki/Mean_squared_error

  12. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  13. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  14. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  15. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  16. def fit: VectoD

    Return the quality of fit including 'rSquared'.

    Return the quality of fit including 'rSquared'.

    Definition Classes
    ResponseSurface → Predictor
  17. def fitLabels: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit. Override when necessary.

    Definition Classes
    Predictor
  18. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  19. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  20. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  21. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  22. val mae: Double
    Attributes
    protected
    Definition Classes
    Predictor
  23. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. final def notify(): Unit
    Definition Classes
    AnyRef
  25. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  26. def predict(z: VectoD): 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
    ResponseSurface → Predictor
  27. def predict(z: VectoI): 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
  28. 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

  29. val rSq: Double
    Attributes
    protected
    Definition Classes
    Predictor
  30. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    Predictor
  31. val rmse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  32. val sse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  33. val ssr: Double
    Attributes
    protected
    Definition Classes
    Predictor
  34. val sst: Double
    Attributes
    protected
    Definition Classes
    Predictor
  35. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  36. def toString(): String
    Definition Classes
    AnyRef → Any
  37. def train(yy: VectoD): 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

    Definition Classes
    ResponseSurface → Predictor
  38. 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
    ResponseSurface → Predictor
  39. def vif: VectorD

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

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

  40. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  41. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  42. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

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