AST_QUADAPPROX

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AST_QUADAPPROX

Obtain a quadratic approximation to a 2D Mapping

Description:

This function returns the co-efficients of a quadratic fit to the supplied Mapping over the input area specified by LBND and UBND. The Mapping must have 2 inputs, but may have any number of outputs. The i’ th Mapping output is modelled as a quadratic function of the 2 inputs (x,y):

output_i = a_i_0 $+$ a_i_1 $*$ x $+$ a_i_2 $*$ y $+$ a_i_3 $*$ x $*$ y $+$ a_i_4 $*$ x $*$ x $+$ a_i_5 $*$ y $*$ y

The FIT array is returned holding the values of the co-efficients a_0_0, a_0_1, etc.

Invocation

RESULT = AST_QUADAPPROX( THIS, LBND, UBND, NX, NY, FIT, RMS, STATUS )

Arguments

THIS = INTEGER (Given)

Pointer to the Mapping.

LBND( $*$ ) = DOUBLE PRECISION (Given)

An array containing the lower bounds of a box defined within the input coordinate system of the Mapping. The number of elements in this array should equal the value of the Mapping’ s Nin attribute. This box should specify the region over which the fit is to be performed.

UBND( $*$ ) = DOUBLE PRECISION (Given)

An array containing the upper bounds of the box specifying the region over which the fit is to be performed.

NX = INTEGER (Given)

The number of points to place along the first Mapping input. The first point is at LBND( 1 ) and the last is at UBND( 1 ). If a value less than three is supplied a value of three will be used.

NY = INTEGER (Given)

The number of points to place along the second Mapping input. The first point is at LBND( 2 ) and the last is at UBND( 2 ). If a value less than three is supplied a value of three will be used.

FIT( $*$ ) = DOUBLE PRECISION (Returned)

An array in which to return the co-efficients of the quadratic approximation to the specified transformation. This array should have at least " 6

*

Nout" , elements. The first 6 elements hold the fit to the first Mapping output. The next 6 elements hold the fit to the second Mapping output, etc. So if the Mapping has 2 inputs and 2 outputs the quadratic approximation to the forward transformation is:

X_out = fit(1) $+$ fit(2) $*$ X_in $+$ fit(3) $*$ Y_in $+$ fit(4) $*$ X_in $*$ Y_in $+$ fit(5) $*$ X_in $*$ X_in $+$ fit(6) $*$ Y_in $*$ Y_in Y_out = fit(7) $+$ fit(8) $*$ X_in $+$ fit(9) $*$ Y_in $+$ fit(10) $*$ X_in $*$ Y_in $+$ fit(11) $*$ X_in $*$ X_in $+$ fit(12) $*$ Y_in $*$ Y_in

RMS = DOUBLE PRECISION (Returned)

The RMS residual between the fit and the Mapping, summed over all Mapping outputs.

STATUS = INTEGER (Given and Returned)

The global status.

Returned Value

AST_QUADAPPROX = LOGICAL

If a quadratic approximation was created, .TRUE is returned. Otherwise .FALSE. is returned and the fit co-efficients are set to AST__BAD.

Notes:

This function fits the Mapping’ s forward transformation. To fit the inverse transformation, the Mapping should be inverted using AST_INVERT before invoking this function.
A value of .FALSE. will be returned if this function is invoked with the global error status set, or if it should fail for any reason.

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AST
A Library for Handling
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