### SQORST

Squashes or stretches an NDF

#### Description:

An output NDF  is produced by squashing or stretching an input NDF along one or more of its dimensions. The shape of the output NDF can be specified in one of two ways, according to the value of the MODE parameter; either a distortion factor is given for each dimension, or its lower and upper pixel bounds are given explicitly.

#### Usage:

sqorst in out $\left\{\right\$
factors lbound=? ubound=? pixscale=?

mode

#### Parameters:

Assigning a value to this parameter indicates that a single axis should be squashed or stretched. If a null (!) value is supplied for AXIS, a squash or stretch factor must be supplied for each axis in the manner indicated by the MODE parameter. If a non-null value is supplied for AXIS, it should be the integer index of the axis to be squashed or stretched (the first axis has index 1). In this case, only a single squash or stretch factor should be supplied, and all other axes will be left unchanged. If MODE is set to PixelScale", then the supplied value should be the index of a WCS axis. Otherwise it should be the index of a pixel axis. [!]
Determines the centre about which the WCS co-ordinates are stretching or squashing. The following values are permitted.
• "Centre" –- The WCS co-ordinates at the centre of the output NDF are the same as those at the centre of the input NDF.

• "Origin" –- The WCS co-ordinates at the pixel origin of the output NDF are the same as those at the pixel origin of the input NDF.

["Centre"]

If set TRUE, then the output pixel values will be scaled in such a way as to preserve the total data value in a feature on the sky. The scaling factor is the ratio of the output pixel size to the input pixel size. This ratio is evaluated once for each panel of a piece-wise linear approximation to the Mapping, and is assumed to be constant for all output pixels in the panel. [FALSE]
##### FACTORS( ) = _DOUBLE (Read)
This parameter is used only if MODE="Factors". It defines the factor by which each dimension will be distorted to produce the output NDF. A factor greater than one is a stretch and less than one is a squash. If no value has been supplied for Parameter AXIS, the number of values supplied for FACTORS must be the same as the number of pixel axes in the NDF. If a non-null value has been supplied for Parameter AXIS, then only a single value should be supplied for FACTORS and that value will be used to distort the axis indicated by Parameter AXIS.
The NDF to be squashed or stretched.
##### LBOUND( ) = _INTEGER (Read)
This parameter is only used if MODE="Bounds". It specifies the lower pixel-index values of the output NDF. If no value has been supplied for Parameter AXIS, the number of values supplied for LBOUND must be the same as the number of pixel axes in the NDF. If a non-null value has been supplied for Parameter AXIS, then only a single value should be supplied for LBOUND and the supplied value will be used as the new lower bounds on the axis indicated by Parameter AXIS. If null (!) is given, the lower pixel bounds of the input NDF will be used.
The interpolation method used to perform the one-dimensional resampling operations which constitute the squash or stretch. The following values are permitted.
• "Auto" –- Equivalent to "BlockAve" with an appropriate PARAMS for squashes by a factor of 2 or more, otherwise equivalent to "Linear".

• "Nearest" –- Nearest-neighbour sampling.

• "Linear" –- Linear interpolation.

• "Sinc" –- Sum of surrounding pixels weighted using a one-dimensional $\mathrm{\text{sinc}}\left(\pi x\right)$ kernel.

• "SincSinc" –- Sum of surrounding pixels weighted using a one-dimensional $\mathrm{\text{sinc}}\left(\pi x\right)\mathrm{\text{sinc}}\left(k\pi x\right)$ kernel.

• "SincCos" –- Sum of surrounding pixels weighted using a one-dimensional
$\mathrm{\text{sinc}}\left(\pi x\right)cos\left(k\pi x\right)$ kernel.

• "SincGauss" –- Sum of surrounding pixels weighted using a one-dimensional $\mathrm{\text{sinc}}\left(\pi x\right){e}^{-k{x}^{2}}$ kernel.

• "BlockAve" –- Block averaging over surrounding pixels.

In the above, $\mathrm{\text{sinc}}\left(z\right)=sin\left(z\right)/z$. Some of these schemes will require additional parameters to be supplied via the PARAMS parameter. A more-detailed discussion of these schemes is given in the "Sub-Pixel Interpolation Schemes" section below. ["Auto"]

This determines how the shape of the output NDF is to be specified. The allowed values and their meanings are as follows.
• "Factors" –- the FACTORS parameter will be used to determine the factor by which each dimension should be multiplied.

• "Bounds" –- the LBOUND and UBOUND parameters will be used to get the lower and upper pixel bounds of the output NDF.

• "PixelScale" –- the PIXSCALE parameter will be used to obtain the new pixel scale to use for each WCS axis.

["Factors"]
##### OUT = NDF (Write)
The squashed or stretched NDF.
##### PARAMS( ) = _DOUBLE (Read)
Parameters required to control the resampling scheme. One or more values may be required to specify the exact resampling behaviour, according to the value of the METHOD parameter. See the section on “Sub-pixel Interpolation Schemes”.
The PIXSCALE parameter is only used if Parameter MODE is set to "PixelScale". It should be supplied as a comma-separated list of the required new pixel scales. In this context, a pixel scale for a WCS axis is the increment in WCS axis value caused by a movement of one pixel along the WCS axis, and are measured at the first pixel in the array. Pixel scales for celestial axes should be given in arcseconds. An asterisk, "$\ast$", can be used instead of a numerical value to indicate that an axis should retain its current scale. The suggested default values are the current pixel scales. If no value has been supplied for Parameter AXIS, the number of values supplied for PIXSCALE must be the same as the number of WCS axes in the NDF. If a non-null value has been supplied for Parameter AXIS, then only a single value should be supplied for PIXSCALE and that value will be used as the new pixel scale on the WCS axis indicated by Parameter AXIS.
Title for the output NDF. A null (!) value causes the input title to be used. [!]
##### UBOUND( ) = _INTEGER (Read)
This parameter is only used if MODE="Bounds". The upper pixel index values of the output NDF. If no value has been supplied for Parameter AXIS, the number of values supplied for UBOUND must be the same as the number of pixel axes in the NDF. If a non-null value has been supplied for Parameter AXIS, then only a single value should be supplied for UBOUND and the supplied value will be used as the new upper bounds on the axis indicated by Parameter AXIS. If null (!) is given, the upper pixel bounds of the input NDF will be used.

#### Examples:

sqorst block blocktall [1,2,1]
The three-dimensional NDF called block is stretched by a factor of two along its second axis to produce an NDF called blocktall with twice as many pixels. The same data block is represented, but each pixel in the output NDF corresponds to half a pixel in the input NDF. The default resampling scheme, linear interpolation in the stretch direction, is used.
sqorst block blocktall [1,2,1] method=sincsinc params=[2,2]
The same operation as the previous example is performed, except that a Lanczos kernel is used for the interpolation.
sqorst cygnus1 squish1 mode=bounds lbound=[1,1] ubound=[50,50]
This turns the two-dimensional NDF cygnus1 into a new NDF squish1 which has 50 pixels along each side. The same region of sky is represented, but the input image is squashed along both axes to fit the specified dimensions.
sqorst fred mode=pixelscale pixscale=5 axis=3
This resamples a cube NDF called fred on to a velocity scale of 5 km/s per pixel along its third axis.

#### Notes:

If the input NDF contains a VARIANCE  component, a VARIANCE component will be written to the output NDF. It will be calculated on the assumption that errors on the input data values are statistically independent and that their variance estimates may simply be summed (with appropriate weighting factors) when several input pixels contribute to an output data value. If this assumption is not valid, then the output error estimates may be biased. In addition, note that the statistical errors on neighbouring output data values (as well as the estimates of those errors) may often be correlated, even if the above assumption about the input data is correct, because of the sub-pixel interpolation schemes employed.

#### Sub-Pixel Interpolation Schemes

When squashing or stretching an NDF, a separate one-dimensional resampling operation is performed for each of the dimensions in which a resize is being done. By default (when METHOD="Auto") this is done using linear interpolation, unless it is a squash of a factor of two or more, in which case a block-averaging scheme which averages over 1/FACTOR pixels. For many purposes this default scheme will be adequate, but for greater control over the resampling process the METHOD and PARAMS parameters can be used. Detailed discussion of the use of these parameters can be found in the “Sub-pixel Interpolation Schemes”  section of the AST_RESAMPLE documentation. By default, all interpolation schemes preserve flux density rather than total flux, but this may be changed using the CONSERVE parameter.