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cholcov


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statistics: T = cholcov ( sigma )
statistics: [ T , p = cholcov ( sigma )
statistics: [&hellip;] = cholcov ( sigma , flag )

Cholesky-like decomposition for covariance matrix.

T = cholcov ( sigma ) computes matrix T such that
sigma = T &rsquo; T . sigma must be square, symmetric, and
positive semi-definite.

If sigma is positive definite, then T is the square, upper
triangular Cholesky factor. If sigma is not positive definite, T
is computed with an eigenvalue decomposition of sigma , but in this case
T is not necessarily triangular or square. Any eigenvectors whose
corresponding eigenvalue is close to zero (within a tolerance) are omitted.
If any remaining eigenvalues are negative, T is empty.

The tolerance is calculated as 10 * eps (max (abs (diag (sigma)))) .

[ T , p = cholcov ( sigma ) returns in p the
number of negative eigenvalues of sigma . If p > 0, then T
is empty, whereas if p = 0, sigma ) is positive semi-definite.

If sigma is not square and symmetric, P is NaN and T is empty.

[ T , p = cholcov ( sigma , 0) returns p = 0 if
sigma is positive definite, in which case T is the Cholesky
factor. If sigma is not positive definite, p is a positive
integer and T is empty.

[&hellip;] = cholcov ( sigma , 1) is equivalent to
[&hellip;] = cholcov ( sigma ) .

See also:
chov


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Cholesky-like decomposition for covariance matrix.



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loadmodel


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statistics: obj = loadmodel ( filename )

Load a Classification or Regression model from a file.

obj = loadmodel ( filename ) loads a Classification or
Regression object, obj , from a file defined in filename .

See also:
savemodel,
ClassificationDiscriminant,
ClassificationGAM,
ClassificationKNN,
ClassificationNeuralNetwork,
ClassificationPartitionedModel,
ClassificationSVM,
RegressionGAM


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Load a Classification or Regression model from a file.



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logit


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statistics: x = logit ( p )

Compute the logit for each value of p

The logit is defined as
$$ {\rm logit}(p) = \log\Big({p \over 1-p}\Big) $$

See also:
probit,
logicdf


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Compute the logit for each value of p



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makima


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statistics: yi = makima ( x , y , xq )
statistics: yi = makima ( y , xq )
statistics: yi = makima (&hellip;, 'extrap' )

Compute the 1-D Modified Akima piecewise cubic Hermite interpolant of
sample data x and y .

The Modified Akima (MAKIMA) algorithm generates a shape-preserving
piecewise cubic interpolant. It differs from standard splines by avoiding
excessive local undulations and overshoots, and it connects collinear points
(flat regions) with straight lines. It is particularly well-suited for
oscillatory data where pchip might aggressively flatten local
extrema.

The sample points x must be a vector of unique values. If x
is not sorted, the function will automatically sort it and rearrange
y accordingly.

The sample values y can be a scalar, vector, or an N-dimensional
array. If y is an N-dimensional array, the interpolation is
performed along its last dimension, which must have the same length as
x . Complex values for y are supported.

If query points xq are provided, the function evaluates the
interpolant and returns the interpolated values yi . By default,
makima uses the boundary polynomials to extrapolate for points
outside the range of x . The optional string argument 'extrap'
is accepted for compatibility with other interpolation functions.

If only x and y are provided, the function returns a
piecewise polynomial structure pp that represents the interpolant.
This structure can be evaluated later at specific query points using
ppval .

Evaluating the interpolant at query points outside the domain of x
automatically extrapolates using the boundary polynomials.

See also:
interp1,
pchip,
spline


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Compute the 1-D Modified Akima piecewise cubic Hermite interpolant of sample data x and y.



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probit


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statistics: x = probit ( p )

Probit transformation

Return the probit (the quantile of the standard normal distribution) for
each element of p .

See also:
logit


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Probit transformation



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statget


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statistics: value = statget ( options , name )
statistics: value = statget ( options , name , default )

Read one option out of a statistics options structure.

value = statget ( options , name ) returns the value
the option name carries in options , or [] when that
option is unset. options is a structure as built by statset ,
although any structure is accepted.

value = statget ( options , name , default )
returns default instead whenever the option is unset, which is the
form a calling function uses to fall back on its own default. Note that
default is returned when the option is empty , not only when it
is absent, since an empty option is precisely how statset spells
"unset" .

name is matched case-insensitively, and may be abbreviated to any
leading portion that singles out one option: statget ( options ,
"MaxI") reads "MaxIter" . An abbreviation matching more than one
option raises, rather than choosing between them; an exact match is taken
as exact even where it is also a prefix of a longer name.

See also:
statset


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Read one option out of a statistics options structure.



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statset


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statistics: options = statset ()
statistics: options = statset ( funcname )
statistics: options = statset ( name , value , &hellip;)
statistics: options = statset ( oldopts , name , value , &hellip;)
statistics: options = statset ( oldopts , newopts )
statistics: statset ()

Create or modify an options structure for iterative statistics algorithms.

options = statset () returns a structure carrying every
recognized option name, each set to an empty value. An empty option means
"use the calling function's own default" , so an all-empty structure
changes nothing wherever it is passed.

options = statset ( funcname ) returns the options that
funcname uses by default, with the remaining fields left empty.
funcname must name a function of this package that documents an
"Options" argument; see the list below. Unlike the name/value
forms, this form takes no further arguments.

options = statset ( name , value , &hellip;) returns an
otherwise empty structure with the named options set. Option names are
matched case-insensitively and must be given in full.

options = statset ( oldopts , name , value ,
&hellip;) copies oldopts and applies the given name/value pairs to the
copy. oldopts is left unchanged.

options = statset ( oldopts , newopts ) merges two
structures: every non-empty field of newopts overrides its
counterpart in oldopts , while an empty field of newopts leaves
the oldopts value in place. Fields that are not recognized option
names are ignored in both structures.

statset () called with no output argument displays the recognized
option names together with their permitted values, marking each default
in braces.

The recognized options are:

Option Description
"Display" Level of reporting: "off" ,
"final" , or "iter" .
"MaxFunEvals" Maximum number of objective function
evaluations, a positive scalar.
"MaxIter" Maximum number of iterations, a positive scalar.
"TolBnd" Positive scalar tolerance on parameter bounds.
"TolFun" Positive scalar tolerance on the objective
function value.
"TolTypeFun" Whether "TolFun" is absolute,
"abs" , or relative, "rel" .
"TolX" Positive scalar tolerance on the parameters.
"TolTypeX" Whether "TolX" is absolute,
"abs" , or relative, "rel" .
"GradObj" Whether the objective function returns a
gradient, "off" or "on" .
"Jacobian" Whether the model function returns a Jacobian,
"off" or "on" .
"DerivStep" Relative step size for finite-difference
derivatives, a positive scalar or vector.
"FunValCheck" Whether to check the objective function for
invalid values, "off" or "on" .
"Robust" Whether to invoke a robust fit, "off" or
"on" . Superseded by "RobustWgtFun" .
"RobustWgtFun" Weight function for robust fitting: one of
"andrews" , "bisquare" , "cauchy" , "fair" ,
"huber" , "logistic" , "talwar" , "welsch" , a
function handle, or empty for a non-robust fit.
"WgtFun" Weight function used with "Robust" .
Superseded by "RobustWgtFun" .
"Tune" Positive tuning constant for the robust weight
function. Set automatically for a named weight function; required for a
function handle.
"UseParallel" Logical flag requesting parallel
computation.
"UseSubstreams" Logical flag requesting reproducible
random substreams.
"Streams" A random stream or a cell array of them.
"OutputFcn" A function handle, or a cell array of them,
called after each iteration.

funcname may name any of the following functions, each of which
documents an "Options" argument: copulafit , coxphfit ,
crossval , evfit , factoran , fitcox ,
fitglm , fitglme , fitlme ,
fitlmematrix , fitnlm , gamfit , gevfit ,
glmfit , gmdistribution , gpfit , kmeans ,
kmedoids , lasso , lassoglm , lognfit ,
mdscale , mlecov , mlecustom , mvncdf ,
mvtcdf , nbinfit , nlinfit , nnmf , normfit ,
pca , plsregress , ppca , rocmetrics , tsne ,
wblfit , GeneralizedLinearMixedModel , and
LinearMixedModel .

Any function accepting an "Options" argument also accepts a plain
structure carrying only the fields it needs, so statset is a
convenience rather than a requirement.

MATLAB&rsquo;s statset additionally accepts the names of functions this
package does not provide. Those names are rejected here rather than
answered, since returning options for an absent function would assert a
capability that does not exist.

See also:
statget,
nlinfit,
fitnlm,
nnmf,
mdscale,
ppca,
tsne,
kmedoids


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Create or modify an options structure for iterative statistics algorithms.





