### AST_REBINSEQ$<$X$>$

Rebin a region of a sequence of data grids

#### Description:

This set of routines is identical to AST_REBIN$<$X$>$ except that the rebinned input data is added into the supplied output arrays, rather than simply over-writing the contents of the output arrays. Thus, by calling this routine repeatedly, a sequence of input arrays can be rebinned and accumulated into a single output array, effectively forming a mosaic of the input data arrays.

In addition, the weights associated with each output pixel are returned. The weight of an output pixel indicates the number of input pixels which have been accumulated in that output pixel. If the entire value of an input pixel is assigned to a single output pixel, then the weight of that output pixel is incremented by one. If some fraction of the value of an input pixel is assigned to an output pixel, then the weight of that output pixel is incremented by the fraction used.

The start of a new sequence is indicated by specifying the AST__REBININIT flag via the FLAGS argument. This causes the supplied arrays to be filled with zeros before the rebinned input data is added into them. Subsequenct invocations within the same sequence should omit the AST__REBININIT flag.

The last call in a sequence is indicated by specifying the AST__REBINEND flag. Depending on which flags are supplied, this may cause the output data and variance arrays to be normalised before being returned. This normalisation consists of dividing the data array by the weights array, and can eliminate artifacts which may be introduced into the rebinned data as a consequence of aliasing between the input and output grids. This results in each output pixel value being the weighted mean of the input pixel values that fall in the neighbourhood of the output pixel (rather like AST_RESAMPLE$<$X$>$). Optionally, these normalised values can then be multiplied by a scaling factor to ensure that the total data sum in any small area is unchanged. This scaling factor is equivalent to the number of input pixel values that fall into each output pixel. In addition to normalisation of the output data values, any output variances are also appropriately normalised, and any output data values with weight less than WLIM are set to BADVAL.

Output variances can be generated in two ways; by rebinning the supplied input variances with appropriate weights, or by finding the spread of input data values contributing to each output pixel (see the AST__GENVAR and AST__USEVAR flags).

#### Invocation

CALL AST_REBINSEQ$<$X$>$( THIS, WLIM, NDIM_IN, LBND_IN, UBND_IN, IN, IN_VAR, SPREAD, PARAMS, FLAGS, TOL, MAXPIX, BADVAL, NDIM_OUT, LBND_OUT, UBND_OUT, LBND, UBND, OUT, OUT_VAR, WEIGHTS, NUSED, STATUS )

#### Arguments

##### THIS = INTEGER (Given)
Pointer to a Mapping, whose forward transformation will be used to transform the coordinates of pixels in the input grid into the coordinate system of the output grid.

The number of input coordinates used by this Mapping (as given by its Nin attribute) should match the number of input grid dimensions given by the value of NDIM_IN below. Similarly, the number of output coordinates (Nout attribute) should match the number of output grid dimensions given by NDIM_OUT.

##### WLIM = DOUBLE PRECISION (Given)
This value is only used if the AST__REBINEND flag is specified via the FLAGS argument. It gives the required number of input pixel values which must contribute to an output pixel (i.e. the output pixel weight) in order for the output pixel value to be considered valid. If the sum of the input pixel weights contributing to an output pixel is less than the supplied WLIM value, then the output pixel value is returned set to the supplied bad value. If the supplied value is less than 1.0E-10 then 1.0E-10 is used instead.
##### NDIM_IN = INTEGER (Given)
The number of dimensions in the input grid. This should be at least one.
##### LBND_IN( NDIM_IN ) = INTEGER (Given)
An array containing the coordinates of the centre of the first pixel in the input grid along each dimension.
##### UBND_IN( NDIM_IN ) = INTEGER (Given)
An array containing the coordinates of the centre of the last pixel in the input grid along each dimension.

Note that LBND_IN and UBND_IN together define the shape and size of the input grid, its extent along a particular (J’ th) dimension being UBND_IN(J)-LBND_IN(J)$+$1. They also define the input grid’ s coordinate system, each pixel having unit extent along each dimension with integral coordinate values at its centre.

##### IN( $\ast$ ) = $<$Xtype$>$ (Given)
An array, with one element for each pixel in the input grid, containing the input data to be rebined. The numerical type of this array should match the 1- or 2-character type code appended to the function name (e.g. if you are using AST_REBINSEQR, the type of each array element should be REAL).

The storage order of data within this array should be such that the index of the first grid dimension varies most rapidly and that of the final dimension least rapidly (i.e. normal Fortran array storage order).

##### IN_VAR( $\ast$ ) = $<$Xtype$>$ (Given)
An optional second array with the same size and type as the IN array. If given, this should contain a set of non-negative values which represent estimates of the statistical variance associated with each element of the IN array. If neither the AST__USEVAR nor the AST__VARWGT flag is set, no input variance estimates are required and this array will not be used. A dummy (e.g. one-element) array may then be supplied.
##### SPREAD = INTEGER (Given)
This argument specifies the scheme to be used for dividing each input data value up amongst the corresponding output pixels. It may be used to select from a set of pre-defined schemes by supplying one of the values described in the " Pixel Spreading Schemes" section in the description of the AST_REBIN$<$X$>$ routines. If a value of zero is supplied, then the default linear spreading scheme is used (equivalent to supplying the value AST__LINEAR).
##### PARAMS( $\ast$ ) = DOUBLE PRECISION (Given)
An optional array which should contain any additional parameter values required by the pixel spreading scheme. If such parameters are required, this will be noted in the " Pixel Spreading Schemes" section in the description of the AST_REBIN$<$X$>$ routines.

If no additional parameters are required, this array is not used. A dummy (e.g. one-element) array may then be supplied.

##### FLAGS = INTEGER (Given)
The sum of a set of flag values which may be used to provide additional control over the rebinning operation. See the " Control Flags" section below for a description of the options available. If no flag values are to be set, a value of zero should be given.
##### TOL = DOUBLE PRECISION (Given)
The maximum tolerable geometrical distortion which may be introduced as a result of approximating non-linear Mappings by a set of piece-wise linear transformations. This should be expressed as a displacement in pixels in the output grid’ s coordinate system.

If piece-wise linear approximation is not required, a value of zero may be given. This will ensure that the Mapping is used without any approximation, but may increase execution time.

If the value is too high, discontinuities between the linear approximations used in adjacent panel will be higher, and may cause the edges of the panel to be visible when viewing the output image at high contrast. If this is a problem, reduce the tolerance value used.

##### MAXPIX = INTEGER (Given)
A value which specifies an initial scale size (in pixels) for the adaptive algorithm which approximates non-linear Mappings with piece-wise linear transformations. Normally, this should be a large value (larger than any dimension of the region of the input grid being used). In this case, a first attempt to approximate the Mapping by a linear transformation will be made over the entire input region.

If a smaller value is used, the input region will first be divided into sub-regions whose size does not exceed MAXPIX pixels in any dimension. Only at this point will attempts at approximation commence.

This value may occasionally be useful in preventing false convergence of the adaptive algorithm in cases where the Mapping appears approximately linear on large scales, but has irregularities (e.g. holes) on smaller scales. A value of, say, 50 to 100 pixels can also be employed as a safeguard in general-purpose software, since the effect on performance is minimal.

If too small a value is given, it will have the effect of inhibiting linear approximation altogether (equivalent to setting TOL to zero). Although this may degrade performance, accurate results will still be obtained.

##### BADVAL = $<$Xtype$>$ (Given)
This argument should have the same type as the elements of the IN array. It specifies the value used to flag missing data (bad pixels) in the input and output arrays.

If the AST__USEBAD flag is set via the FLAGS argument, then this value is used to test for bad pixels in the IN (and IN_VAR) array(s).

In all cases, this value is also used to flag any output elements in the OUT (and OUT_VAR) array(s) for which rebined values could not be obtained (see the " Propagation of Missing Data" section below for details of the circumstances under which this may occur).

##### NDIM_OUT = INTEGER (Given)
The number of dimensions in the output grid. This should be at least one. It need not necessarily be equal to the number of dimensions in the input grid.
##### LBND_OUT( NDIM_OUT ) = INTEGER (Given)
An array containing the coordinates of the centre of the first pixel in the output grid along each dimension.
##### UBND_OUT( NDIM_OUT ) = INTEGER (Given)
An array containing the coordinates of the centre of the last pixel in the output grid along each dimension.

Note that LBND_OUT and UBND_OUT together define the shape, size and coordinate system of the output grid in the same way as LBND_IN and UBND_IN define the shape, size and coordinate system of the input grid.

##### LBND( NDIM_IN ) = INTEGER (Given)
An array containing the coordinates of the first pixel in the region of the input grid which is to be included in the rebined output array.
##### UBND( NDIM_IN ) = INTEGER (Given)
An array containing the coordinates of the last pixel in the region of the input grid which is to be included in the rebined output array.

Note that LBND and UBND together define the shape and position of a (hyper-)rectangular region of the input grid which is to be included in the rebined output array. This region should lie wholly within the extent of the input grid (as defined by the LBND_IN and UBND_IN arrays). Regions of the input grid lying outside this region will not be used.

##### OUT( $\ast$ ) = $<$Xtype$>$ (Given and Returned)
An array, with one element for each pixel in the output grid. The rebined data values will be added into the original contents of this array. The numerical type of this array should match that of the IN array, and the data storage order should be such that the index of the first grid dimension varies most rapidly and that of the final dimension least rapidly (i.e. normal Fortran array storage order).
##### OUT_VAR( $\ast$ ) = $<$Xtype$>$ (Given and Returned)
A array with the same type and size as the OUT array. This array will only be used if the AST__USEVAR or AST__GENVAR flag is set via the FLAGS argument, via the " flags" parameter, in which case variance estimates for the rebined data values will be added into the array. If neither the AST__USEVAR flag nor the AST__GENVAR flag is set, no output variance estimates will be calculated and this array will not be used. A dummy (e.g. one-element) array may then be supplied.
##### WEIGHTS( $\ast$ ) = DOUBLE PRECISION (Given and Returned)
An array with one or two elements for each pixel in the output grid, depending on whether or not the AST__GENVAR flag has been supplied via the FLAGS parameter. If AST__GENVAR has not been specified then the array should have one element for each output pixel, and it will be used to accumulate the weight associated with each output pixel. If AST__GENVAR has been specified then the array should have two elements for each output pixel. The first half of the array is again used to accumulate the weight associated with each output pixel, and the second half is used to accumulate the square of the weights. In each half, the data storage order should be such that the index of the first grid dimension varies most rapidly and that of the final dimension least rapidly (i.e. normal Fortran array storage order).
##### NUSED = INTEGER$\ast$8 (Given and Returned)
The number of input data values that have been added into the output array so far. The supplied value is incremented on exit by the number of input values used. The value is initially set to zero if the AST__REBININIT flag is set in FLAGS.
##### STATUS = INTEGER (Given and Returned)
The global status.

#### Data Type Codes

To select the appropriate rebinning function, you should replace $<$X$>$ in the generic function name AST_REBINSEQ$<$X$>$ with a 1- or 2-character data type code, so as to match the numerical type $<$Xtype$>$ of the data you are processing, as follows:
• D: DOUBLE PRECISION

• R: REAL

• I: INTEGER

• B: BYTE (treated as signed)

• UB: BYTE (treated as unsigned)

For example, AST_REBIND would be used to process DOUBLE PRECISION data, while AST_REBINI would be used to process integer data (stored in an INTEGER array), etc.

Note that, unlike AST_RESAMPLE$<$X$>$, the AST_REBINSEQ$<$X$>$ set of functions does not yet support unsigned integer data types or integers of different sizes.

#### Control Flags

The following flags are defined in the AST_PAR include file and may be used to provide additional control over the rebinning process. Having selected a set of flags, you should supply the sum of their values via the FLAGS argument:
• AST__REBININIT: Used to mark the first call in a sequence. It indicates that the supplied OUT, OUT_VAR and WEIGHTS arrays should be filled with zeros (thus over-writing any supplied values) before adding the rebinned input data into them. This flag should be used when rebinning the first input array in a sequence.

• AST__REBINEND: Used to mark the last call in a sequence. It causes each value in the OUT and OUT_VAR arrays to be divided by a normalisation factor before being returned. The normalisation factor for each output data value is just the corresponding value from the weights array. The normalisation factor for each output variance value is the square of the data value normalisation factor (see also AST__CONSERVEFLUX). It also causes output data values to be set bad if the corresponding weight is less than the value supplied for argument WLIM. It also causes any temporary values stored in the output variance array (see flag AST__GENVAR below) to be converted into usable variance values. Note, this flag is ignored if the AST__NONORM flag is set.

• AST__USEBAD: Indicates that there may be bad pixels in the input array(s) which must be recognised by comparing with the value given for BADVAL and propagated to the output array(s). If this flag is not set, all input values are treated literally and the BADVAL value is only used for flagging output array values.

• AST__USEVAR: Indicates that output variance estimates should be created by rebinning the supplied input variance estimates. An error will be reported if both this flag and the AST__GENVAR flag are supplied.

• AST__GENVAR: Indicates that output variance estimates should be created based on the spread of input data values contributing to each output pixel. An error will be reported if both this flag and the AST__USEVAR flag are supplied. If the AST__GENVAR flag is specified, the supplied output variance array is first used as a work array to accumulate the temporary values needed to generate the output variances. When the sequence ends (as indicated by the AST__REBINEND flag), the contents of the output variance array are converted into the required variance estimates. If the generation of such output variances is required, this flag should be used on every invocation of this routine within a sequence, and any supplied input variances will have no effect on the output variances (although input variances will still be used to weight the input data if the AST__VARWGT flag is also supplied). The statistical meaning of these output varianes is determined by the presence or absence of the AST__DISVAR flag (see below).

• AST__DISVAR: This flag is ignored unless the AST__GENVAR flag has also been specified. It determines the statistical meaning of the generated output variances. If AST__DISVAR is not specified, generated variances represent variances on the output mean values. If AST__DISVAR is specified, the generated variances represent the variance of the distribution from which the input values were taken. Each output variance created with AST__DISVAR will be larger than that created without AST__DISVAR by a factor equal to the number of input samples that contribute to the output sample.

• AST__VARWGT: Indicates that the input data should be weighted by the reciprocal of the input variances. Otherwise, all input data are given equal weight. If this flag is specified, the calculation of the output variances (if any) is modified to take account of the varying weights assigned to the input data values. See also AST__PARWGT.

• AST__PARWGT: Indicates that a constant weight should be used when pasting each pixel of the supplied input array into the returned arrays. This extra weight value should be inserted at the start of the ’ PARAMS array (which should consequently be one element longer than specified in the " Pixel Spreading Schemes" section in the description of the AST_REBIN$<$X$>$ routines). If the AST__VARWGT flag is also specified, the total weight for each pixel is the product of the reciprocal of the pixel variance and the value supplied in the last element of the ’ PARAMS array.

• AST__NONORM: If the simple unnormalised sum of all input data falling in each output pixel is required, then this flag should be set on each call in the sequence and the AST__REBINEND should not be used on the last call. In this case WEIGHTS and NUSED are ignored. This flag cannot be used with the AST__CONSERVEFLUX, AST__GENVAR, AST__PARWGT or AST__VARWGT flag.

• AST__CONSERVEFLUX: Indicates that the normalized output pixel values generated by the AST__REBINEND flag should be scaled in such a way as to preserve the total data value in a feature on the sky. Without this flag, each normalised output pixel value represents a weighted mean of the input data values around the corresponding input position. (i.e. AST_REBINSEQ$<$F$>$ behaves similarly to AST_RESAMPLE$<$X$>$). This (i.e. AST_REBINSEQ$<$F$>$ behaves similarly to AST_RESAMPLE$<$X$>$). This is appropriate if the input data represents the spatial density of some quantity (e.g. surface brightness in Janskys per square arc-second) because the output pixel values will have the same normalisation and units as the input pixel values. However, if the input data values represent flux (or some other physical quantity) per pixel, then the AST__CONSERVEFLUX flag could be of use. It causes each output pixel value to be scaled by the ratio of the output pixel size to the input pixel size.

This flag can only be used if the Mapping is successfully approximated by one or more linear transformations. Thus an error will be reported if it used when the TOL argument is set to zero (which stops the use of linear approximations), or if the Mapping is too non-linear to be approximated by a piece-wise linear transformation. The ratio of output to input pixel size is evaluated once for each panel of the piece-wise linear approximation to the Mapping, and is assumed to be constant for all output pixels in the panel. The scaling factors for adjacent panels will in general differ slightly, and so the joints between panels may be visible when viewing the output image at high contrast. If this is a problem, reduce the value of the TOL argument until the difference between adjacent panels is sufficiently small to be insignificant.

This flag should normally be supplied on each invocation of AST_REBINSEQ$<$X$>$ within a given sequence.

Note, this flag cannot be used in conjunction with the AST__NOSCALE flag (an error will be reported if both flags are specified).

#### Propagation of Missing Data

Instances of missing data (bad pixels) in the output grid are identified by occurrences of the BADVAL value in the OUT array. These are only produced if the AST__REBINEND flag is specified and a pixel has zero weight.

An input pixel is considered bad (and is consequently ignored) if its data value is equal to BADVAL and the AST__USEBAD flag is set via the FLAGS argument.

In addition, associated output variance estimates (if calculated) may be declared bad and flagged with the BADVAL value in the OUT_VAR array for similar reasons.

#### Handling of Huge Pixel Arrays

If the input or output grid is so large that an integer pixel index, (or a count of pixels) could exceed the largest value that can be represented by a 4-byte integer, then the alternative " 8-byte" interface for this function should be used. This alternative interface uses 8 byte integer arguments (instead of 4-byte) to hold pixel indices and pixel counts. Specifically, the arguments LBND_IN, UBND_IN, LBND_OUT, UBND_OUT, LBND, UBND are changed from type INTEGER to type INTEGER$\ast$8. The function return type is similarly changed to type INTEGER$\ast$8. The function name is changed by inserting the digit " 8" before the trailing data type code. Thus, AST_REBINSEQ$<$X$>$ becomes AST_REBINSEQ8$<$X$>$.