[Key-worded input]

This is a modified version of the **EXTEND** program that attempts to
compute the standard uncertainty of the electron density. To do this
the input map must be a true difference map (i.e. of the type Fo-Fc, not
nFo-(n-1)Fc) and must consist of **exactly one** asymmetric unit (an
integral number of a.u.'s such as **exactly** half or an **exact** complete unit
cell is also valid input). Note that the program does **NOT**
check that the input map covers an exact integral number of a.u.'s: it
is the user's responsibility to ensure this. However this will
normally be the case if the **FFT** program has been used to prepare
the input map.

The rationale for this is statistical rigour: the asymmetric unit of the map represents the true population of electron density values in the statistical sense and therefore the values of the mean and RMS deviation for the asymmetric unit can be considered to be those of the true population mean and population standard deviation respectively. Any other subset or superset of the map that is not an integral number of asymmetric units is a sample in the statistical sense, with corresponding sample mean and sample standard deviation.

It may even be a biased sample either because the density covers only a specific region of the structure and is therefore non-representative of the map as a whole, or because when a map is extended, density values related by the map symmetry are very likely to be generated more than once. Sample statistics, whether biased or not, are always only approximations to population statistics.

Note that the standard deviation of the density, unlike the RMS
deviation of the density from its mean value, is a property of the
density that does **NOT** change simply because a different map
extent is chosen. Most other programs that output electron density
maps that do not cover an exact integral number of a.u.'s always
automatically recompute both the mean and RMSD - if this is done it is
then not valid to treat the RMSD in subsequent calculations as though it
were the SU of the density.

Default = 10 Angstroms. This card is only needed if XYZLIM is not given; otherwise limits are determined from the XYZIN coordinate file.

Set map values outside borders of input map to <fill>.

Keep the input RMSD of the density. This option should be used only
for 2mFo-DFc and other types of non-difference Fouriers, *i.e.*
with coefficients of the form nFo-(n-1)Fc. In some cases the
program can detect that a non-difference Fourier has been input and will
not recompute the standard uncertainty; however it would not be wise to
rely on this!

The RMSD of a 2mFo-DFc or equivalent map is completely devoid of any statistical meaning anyway: it will greatly depend on the solvent content, so comparing Fourier maps contoured at 1 sigma is nonsense (pointed out by Dale Tronrud!).

For mFo-DFc and other types of true difference Fouriers this option must
be **omitted** so that the program is allowed to recompute the standard
uncertainty. In this case the input map must consist of **exactly one**
asymmetric unit (an integral number of a.u.'s such as **exactly** half or
a complete unit cell is also valid input). This will normally be the
case if the **FFT** program has been used to prepare the input map.

This option should also be used in the case that the input map does not cover an exact integral number of a.u.'s, but the SU of the density has been previously correctly computed, so that the correct SU is kept and copied to the output map.

- MAPIN
- input map (from FFT)
- MAPOUT
- extended output map
- XYZIN
- input coordinates, optional unless limits not given.

Ian Tickle, Astex Technology, Cambridge (mods for SU calculation)

extends MAPIN 2fofc.map MAPOUT 2fofc-ext.map << END-extends BORD 4 KEEP ! Only for nFo-(n-1)Fc type maps. END-extends extends MAPIN fofc.map MAPOUT fofc-ext.map << END-extends BORD 4 END-extends