# Created by Octave 3.4.0, Sun Aug 12 10:09:04 2012 UTC <builder@localhost.localdomain>
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gpr_predict


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 -- Loadable Function: Y = gpr_predict (GPM,X)
 -- Loadable Function: [Y,SIG] = gpr_predict (GPM,X)
 -- Loadable Function: [Y,SIG,DY] = gpr_predict (GPM,X)
     Uses the model GPM to predict values, standard deviations and model
     derivatives in spatial points. X is the matrix of independent
     variables.  (The organization is determined by GPM.theta, as in
     `gpr_train').

     Y is set to the predicted dependent variable values.  If SIG is
     requested, it is set to the estimated prediction deviations.  If
     DY is requested, it is populated with the prediction gradients.

     See also: gpr_train, gpr_setup





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Uses the model GPM to predict values, standard deviations and model
derivatives 



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gpr_train


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 -- Loadable Function: GPM = gpr_train (X, Y, THETA, OPTS)
 -- Loadable Function: [GPM, NLL] = gpr_train (X, Y, THETA, NU, NLIN,
          CORF, OPTS)
     If requested, estimates the hyperparameters for Gaussian Process
     Regression (inverse length scales and relative noise) via reduced
     maximum likelihood, and then sets up the model for inference
     (prediction), storing necessary information in the structure GPM,
     intended for use with `gpr_predict'.

     X is the matrix of independent variables of the observations, Y is
     a vector containing the dependent variables, THETA contains the
     (initial) inverse length scales for the regression model.  If
     THETA is a row vector, rows of X correspond to observations,
     columns to variables. Otherwise, it is the other way around.

     NU specifies the (initial) relative noise level. If not supplied,
     it defaults to 1e-5.  NLIN specifies the number of leading
     variables to include in linear underlying trend. If not supplied,
     it defaults to 0 (constant trend).

     CORF specifies the decreasing function type for correlation
     function: `corr(x,y) = f(norm(theta.*(x-y)))'. Possible values:

    `gau'
          `f(t) = exp(-t^2)' (gaussian)

    `exp'
          `f(t) = exp(-t)' (exponential)

    `imq'
          `f(t) = 1/sqrt(1+t^2)' (inverse multiquadric)

    `mt3'
          `f(t) = (1+sqrt(6*t))*exp(-sqrt(6*t))' (Matern-3/2 covariance)

    `mt5'
          `f(t) = (1+sqrt(10*t)+10*t^2/3)*exp(-sqrt(10*t))' (Matern-5/2
          covariance)

     OPTS is a cell array in the form {"option name",option value,...}.
     Possible options:

    `maxev'
          maximum number of factorizations to be used during training.
          default 500.

    `tol'
          stopping tolerance (minimum trust-region radius). default
          1e-6.  the iteration terminates if the trust region gets
          below tol.

    `ftol'
          stopping tolerance (minimum objective reduction). default
          1e-4.  the iteration terminates if the relative reduction of
          two successive downhill steps gets below ftol and the second
          one is smaller.

    `numin'
          minimum allowable noise. Default is `sqrt(1e1*eps)'.

     Training cell array OPTS is recognized even if other arguments are
     omitted.  If it is not supplied (the last argument is not a cell
     array), training is skipped.

     On return the function creates the GPM structure, which can
     subsequently be used for predictions with `gpr_predict'.  If NLL
     is present, it is set to the resulting negative log likelihood.

     See also: gpr_predict





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If requested, estimates the hyperparameters for Gaussian Process
Regression (inv



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pdist2_mw


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 -- Loadable Function: D = pdist2_mw (X, Y, P)
 -- Loadable Function: D = pdist2_mw (X, P)
     Assembles a pairwise minkowski-distance matrix for two given sets
     of points.  X and Y should be real or complex matrices with a
     point per row, so numbers of columns must match. The matrix
     contains the pairwise distances `D(i,j) = norm(X(i,:)-Y(j,:),P)'.
     P can also be the string 'ssq' requesting squared euclidean
     distance.  (not a metric, but often useful and faster than `P=2')
     If Y is not given, a symmetric distance matrix is calculated
     efficiently.

     See also: norm





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Assembles a pairwise minkowski-distance matrix for two given sets of
points.



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pgp_predict


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 -- Loadable Function: Y = pgp_predict (GPM,X)
 -- Loadable Function: [Y,SIG] = pgp_predict (GPM,X)
 -- Loadable Function: [Y,SIG,DY] = pgp_predict (GPM,X)
     Uses the model GPM to predict values, standard deviations and model
     derivatives in spatial points. X is the matrix of independent
     variables.  (The organization is determined by GPM.theta, as in
     `pgp_train').

     Y is set to the predicted dependent variable values.  If SIG is
     requested, it is set to the estimated prediction deviations.  If
     DY is requested, it is populated with the prediction gradients.

     See also: pgp_train, pgp_setup





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Uses the model GPM to predict values, standard deviations and model
derivatives 



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pgp_train


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 -- Loadable Function: GPM = pgp_train (X, F, Y, THETA, OPTS)
 -- Loadable Function: [GPM, NLL] = pgp_train (X, F, Y, THETA, NU,
          NLIN, CORF, OPTS)
     If requested, estimates the hyperparameters for Gaussian Process
     Regression (inverse length scales and relative noise) via reduced
     maximum likelihood, and then sets up the model for inference
     (prediction), storing necessary information in the structure GPM,
     intended for use with `pgp_predict'.

     X is the matrix of independent variables of the observations, F is
     the matrix of inducing points (cluster centers), Y is a vector
     containing the dependent variables, THETA contains the (initial)
     inverse length scales for the regression model.  If THETA is a row
     vector, rows of X correspond to observations, columns to
     variables. Otherwise, it is the other way around.

     NU specifies the (initial) relative noise level. If not supplied,
     it defaults to 1e-5.  NLIN specifies the number of leading
     variables to include in linear underlying trend. If not supplied,
     it defaults to 0 (constant trend).

     CORF specifies the decreasing function type for correlation
     function: `corr(x,y) = f(norm(theta.*(x-y)))'. Possible values:

    `gau'
          `f(t) = exp(-t^2)' (gaussian)

    `exp'
          `f(t) = exp(-t)' (exponential)

    `imq'
          `f(t) = 1/sqrt(1+t^2)' (inverse multiquadric)

    `mt3'
          `f(t) = (1+sqrt(6*t))*exp(-sqrt(6*t))' (Matern-3/2 covariance)

    `mt5'
          `f(t) = (1+sqrt(10*t)+10*t^2/3)*exp(-sqrt(10*t))' (Matern-5/2
          covariance)

     OPTS is a cell array in the form {"option name",option value,...}.
     Possible options:

    `maxev'
          maximum number of factorizations to be used during training.
          default 500.

    `tol'
          stopping tolerance (minimum trust-region radius). default
          1e-6.  the iteration terminates if the trust region gets
          below tol.

    `ftol'
          stopping tolerance (minimum objective reduction). default
          1e-4.  the iteration terminates if the relative reduction of
          two successive downhill steps gets below ftol and the second
          one is smaller.

    `numin'
          minimum allowable noise. Default is `sqrt(1e1*eps)'.

     Training cell array OPTS is recognized even if other arguments are
     omitted.  If it is not supplied (the last argument is not a cell
     array), training is skipped.

     On return the function creates the GPM structure, which can
     subsequently be used for predictions with `pgp_predict'.  If NLL
     is present, it is set to the resulting negative log likelihood.

     See also: pgp_predict





# name: <cell-element>
# type: sq_string
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If requested, estimates the hyperparameters for Gaussian Process
Regression (inv





