PDA_CHE2D - Evaluates a 2-dimensional Chebyshev polynomial

Description:

This routine evaluates a two-dimensional Chebyshev polynomial for one or more arguments. It uses Clenshaw's recurrence relationship twice.

Invocation:

CALL PDA_CHE2D( NPTS, XMIN, XMAX, X, YMIN, YMAX, Y, XDEG, YDEG, NCOEF, CC, NW, WORK, EVAL, IFAIL )

Arguments:

XMIN = DOUBLE PRECISION (Given)

The lower endpoint of the range of the fit along the first dimension. The Chebyshev series representation is in terms of a normalised variable, evaluated as (2x - (XMAX $+$ XMIN) ) / (XMAX - XMIN), where x is the original variable. XMIN must be less than XMAX.

XMAX = DOUBLE PRECISION (Given)

The upper endpoint of the range of the fit along the second dimension. See XMIN.

X( NPTS ) = DOUBLE PRECISION (Given)

The co-ordinates along the first dimension for which the Chebyshev polynomial is to be evaluated.

YMIN = DOUBLE PRECISION (Given)

The lower endpoint of the range of the fit along the first dimension. The Chebyshev series representation is in terms of a normalised variable, evaluated as (2y - (YMAX $+$ YMIN) ) / (YMAX - YMIN), where y is the original variable. YMIN must be less than YMAX.

YMAX = DOUBLE PRECISION (Given)

The upper endpoint of the range of the fit along the second dimension. See YMIN.

Y = DOUBLE PRECISION (Given)

The co-ordinate along the second dimension for which the Chebyshev polynomial is to be evaluated.

XDEG = INTEGER (Given)

The degree of the polynomial along the first dimension.

YDEG = INTEGER (Given)

The degree of the polynomial along the second dimension.

MCOEF = INTEGER (Given)

The number of coefficients. This must be at least the product of (XDEG$+$1) $*$ (YDEG$+$1).

CC( MCOEF ) = DOUBLE PRECISION (Given)

The Chebyshev coefficients. These should be the order such that CCij is in CC( i$*$(YDEG$+$1)$+$j$+$1 ) for i=0,XDEG; j=0,YDEG. In other words the opposite order to Fortran standard.

NW = INTEGER (Given)

The number of elements in the work array. It must be at least XDEG $+$ 1.

WORK( NW ) = DOUBLE PRECISION (Returned)

Workspace.

EVAL( NPTS ) = DOUBLE PRECISION (Returned)

The evaluated polynomial for the supplied arguments. Should an element of argument X lie beyond the range [XMIN,XMAX], IFAIL=7 is returned.

IFAIL = INTEGER (Returned)

The status. A value of 0 indicates that the routine completed successfully. Positive values indicate the following errors:

IFAIL = 1 XMAX less than or equal to XMIN IFAIL = 2 YMAX less than or equal to YMIN IFAIL = 3 NCOEF less than 1. IFAIL = 4 XDEG or YDEG less than 1. IFAIL = 5 Number of coefficients is too great, namely (XDEG$+$1)$*$(YDEG$+$1) is greater than NCOEF. IFAIL = 6 Y lies outside the range YMIN to YMAX. IFAIL = 7 An element of X lies outside the range XMIN to XMAX.

Notes:

• A single precision version of this function is available, named PDA_CHE2R.