M Map-drawing information

An M card starts with M then a CCSL-word, which determines what else is on the card. There is no predetermined sequence for M cards. It would be usual, but not essential, to type all M cards starting with the same CCSL-word consecutively.

DATA FOLLOWING ALLOWED CCSL WORDS:

AXES
Data

9 elements of an orientation matrix U to rotate the Fourier map during calculation or plotting.

Assumptions made

If no M AXES card is present, the unit matrix is used. If the numbers read include decimal points, it will be assumed that the general plane Fourier routine is wanted.

Note

There is a main program GPCARD to generate M AXES for sections passing through three designated atoms.

Details

The 3 sets of 3 numbers may also be viewed as the zone axis symbols of the $x$, $y$ and $z$ axes of the computed map.

Example

M AXES 0,0,1 1,0,0 0,1,0

AXME
Data

9 elements of an orientation matrix U to rotate a maximum entropy map during its reconstruction.

Details

The 3 sets of 3 numbers on AXES or AXME cards may also be viewed as the zone axis symbols of the $x$, $y$ and $z$ axes of the computed map.

CM/A
Data

Number of centimetres per Angstrom if graphical output on a plotter (not a screen) is required.

Assumptions made

If no M CM/A card is read, the scale=2.5

CONT
Data

Real numbers on one or more cards which give the contour levels to be plotted. The CCSL-word STEP allows a range of equally spaced contour levels to be specified; it is followed by 3 numbers, which are the first value, the last value and the step.

Details

The values will be sorted into ascending order. Each contour value is sought and plotted in turn.

Example

M CONT 10,25,40, STEP 50,210,20 235
M CONT 0.5 0.8 1.4

DELT
Data

$\Delta$, the resolution length for Fourier calculation.

Assumptions made

No M DELT card implies no resolution function.

Details

The density is averaged over a cube of side $2\Delta$.

DTYP
Data

(Mandatory if Fourier or Maxent ) an integer (MODED) specifying the type of data input.

MODED=0

the user will provide his own data input routine QFOUIN(K,F,PH) to read $h,k,l$ into array K (dimension 3), the modulus of the Fourier coefficient to F and its phase in radians to PH. QFOUIN may use the free format input routines.

MODED=1

$h,k,l$, F(calc), F(obs), (esd(Fobs))

MODED=2

$h,k,l$, $\mid$(F(calc)$\mid$, phase, F(obs), (esd(Fobs))

MODED=3

$h,k,l$, A(calc), B(calc), F(obs), (esd(Fobs))

MODED=4

$h,k,l$, any F, (esd(F))

For modes 1-4 the reflection data are read in fixed format 3I5, several F10.
Note

The esd is mandatory for maximum entropy calculations

FTYP
Data

(Mandatory if Fourier or Maxent ) an integer MODEF specifying the type of Fourier to be calculated.

MODEF=1

coefficients are F(calc), complex if non-centrosymmetric.

MODEF=2

coefficients are F(obs) and are given with their signs; this can only be used with a centrosymmetric structure and MODED=1 or 4.

MODEF=3

coefficients are $\mid$(F(obs)$\mid$ with the phase (or sign) of the F(calc); this cannot be used with MODED=4.

MODEF=4

coefficients are F(obs)$-$F(calc), both as read, and so can only be used with a centrosymmetric structure and MODED=1.

MODEF=5

coefficients are ($\mid$F(obs)$\mid$-$\mid$F(calc)$\mid$)$\times$phase (or sign) of F(calc); this cannot be used with MODED=4.

MODEF=6

coefficients are F(obs)² (Patterson function).
If used with MODED=4 this will use whatever numbers are typed as coefficients, so these could be F(calc) if the user wishes.

MODEF=7

calculate the standard deviation of the density (using the routine ERRMAP).
All MODED values are allowed, but the coefficient used in the calculation will be esd(F(obs)

GET
Data

Some number of $z$ values of maps which have already been calculated.
M GET cards have the same syntax as M PLOT and M PRIN cards (below). In this case the $z$ values refer to maps which have already been computed in a previous run, and saved on a file using an M SAVE card.

Note

The name of the saved file must be provided in answer to a request from a Fourier program (e.g. FOURPL).

Saving a map means that if the same map is wanted again it need not be recomputed; the most obvious application for this is the contour plotting of the map using a different scale, or new contours, etc.

There are a limited number of things which may be changed if a map is retrieved with GET after having been SAVE d. It would not make sense to change the symmetry, or the MESH , the AXES , the FTYP etc. The only cards it makes sense to change are at present M CM/A and M CONT

When routine PREFIN meets an M GET card, it calls routine MAJUST which replaces almost all the current Crystal Data by the previously dumped Crystal Data which matches the saved maps. It accepts new M PLOT , M PRIN , M GET and M SAVE cards and ignores any old ones; and it replaces any old M CM/A or M CONT cards by new ones if given. It would also accept a new N card.

Example

M GET 0.4 STEP 0.9 0.93 0.01 used with:
M CM/A 2.54
M PLOT STEP 0 0.4 0.1 STEP 0.9 0.93 0.01
would first undump the Crystal Data from the named file, and add to it the above 3 cards (losing its own M CM/A card). It would compute the maps for z=0, 0.1,0.2 and 0.3 (because they are not dumped), then use dumped maps for 0.4, 0.9, 0.91,0.92,0.93; it would contour plot all of them, at a scale of 2.54 cm/Å, using the contour values it found in the undumped Crystal Data.

GRID
Data

(Mandatory for maximum entropy calculations ): 6 (2D) or 9 (3D) numbers defining the grid on the $x$, $y$, and $z$ axes defined by AXME, over which a maximum entropy reconstruction is to be made.

Note

Note that for MAXENT the calculated points are at the centres of the cells whereas the fourier calculation is made for the corners.

LABL
Data

Definition of symbols with which to label atomic positions in the map.

Details

Each card gives an atom name, the symbol size, a colour, a symbol shape and type

Example

M LABL Co 1.5 red circle filled

MAXE
Data

Options for driving a maximum entropy calculation (if this card is not present the options are obtained interactively): 2 integers MSTOP the stopping criterion and MODEL the type of default model

MSTOP = 0

Historic maximum entropy.

MSTOP = 1

Classic maximum entropy.

MSTOP = 2

Classic automatic, noise scaling.

MSTOP = 3

Ad hoc; alpha fixed.

MODEL = 0

Default model is constant with positive entropy

MODEL = 1

User supplied model (positive).

MODEL = 2

Default model is constant with posi/nega entropy.

MODEL = 3

User supplied model (pos/neg)..

Note

If MSTOP=3 the third number on the card is the fixed value for alpha ( smaller values fit better)
if MODEL=0 or 2 a third (or fourth) is the constant default value
if MODEL = 1 or 3 the the default model should be in a file (Numbers in format 8E10.3

MESH
Data

(Mandatory if Fourier ): 6 numbers defining the points at which the map will be calculated. They are the initial value, the final value and the step in fractional coordinates, first for $x$ then for $y$. In this context $x$, $y$, and $z$ are the axes defined by the M AXES card.

Note

SETFOU checks that the step is strictly positive, and that the final value is greater than the initial value.

There are also checks on the allowed storage space in FOUR1Z; if

$n_x =$ no. of $x$ points
$n_y =$ no. of $y$ points
$n_h = 2(h_{max} + 1)$ and
$n_k = k_{max} + 1$

then none of:

$n_xn_y$, $n_hn_k$, or $n_xn_k$ must exceed a maximum which has been set in the program, and is by default 10201 ( $=101\times 101$)
It is possible to alter this number using the variable array dimensions facility of CCSL

Example

M MESH 0 1 0.2, 0.5 1 0.2

NDIM
Data

Number of dimensions for Fourier, 2, 3 or 4

NDIM=2

produces a projection, using 2-D data.

NDIM=3

produces sections of a 3-D Fourier map.

NDIM=4

produces ``bounded" sections i.e. the density between two given $z$ values projected on the $xy$ plane. (This is useful when data of limited resolution in one direction only are available.)

Assumptions made

If no M NDIM card is present, NDIM=3 is assumed.

PLOT
Data

Some number of map $z$ values at which contoured plotted maps are required. If NDIM=2, no numbers are given; for NDIM=3 a set of map $z$ values is given, extending to more than one M PLOT card if necessary. For NDIM=4 alternate positive and negative $z$ values are given to indicate the limits of the bounded sections.

Assumptions made

If no M PLOT card is given, no plotting is wanted.

Details

The $z$ values are given as a list, and the use of STEP (see M CONT ) is allowed. They are sorted into ascending order.

Example

M PLOT 0.5 0.8 STEP 0.9 0.95 0.01

PRIN
Data

These cards are exactly similar to M PLOT , but cause the values of the Fourier map to be printed, rather than to be plotted. Printing is via routine PRNTMP, which writes 21 integers each of width 5 to a printer line, but could easily be changed to suit individual requirements.

Note

The map $z$ values involved need not be the same as, say, on an M PLOT card. The use of STEP (see M CONT ) is allowed.
Since the numbers printed are integer, they may all turn out to be zero if the number on the M SCAL card is not big enough.

Example

M PRIN 0 0.1 0.3564

READ
Data

Numbers with the same syntax as those on M PLOT , M PRIN and M GET cards giving map $z$ values. The relevant maps are assumed to have been previously dumped on to a file, whose name will be requested interactively (if a Fourier program like FOURPL is being used.)

Unlike M GET maps, no more information is expected on the dumped file; the user must match his current Crystal Data to the dumped maps. These maps are then used as though they had just been computed.

The routine READMP reads back such a map into array DENS in COMMON /MAPDA/. The reading is unformatted, a line at a time. Essentially, the map must be read back in the same chunks as that in which it was written, so if the existing reading is not adequate, READMP should be adjusted.

Example

M READ 0.1234

SAVE
Data

Numbers with the same syntax as those on M PLOT , M PRIN and M READ cards, giving map $z$ values. The relevant maps will be dumped on to a file whose name will be requested interactively (if a Fourier program like FOURPL is being used), together with enough information to retrieve them (using an M GET card) and then use them as though they had just been computed.

M SAVE may be used in the same run as M PLOT , M PRIN etc., and its $z$ values may occur on those cards also, or they may be peculiar to the M SAVE card(s).

M SAVE and M GET may also both occur in the same run, as they write to and read from different units.

Example

M SAVE STEP 0.025 0.325 0.025

SCAL
Data

A real number which is the Scale factor by which the Fourier coefficients will be multiplied.

Assumptions made

If no M SCAL card is given, the scale factor is unity

SMAX
Data

(Mandatory for Fourier maps ): Maximum value of for data to be included. Input data for which exceeds this value are not used in the Fourier calculation.

TELESCOPING OF SIMPLE CARDS:

CM/A, DELT, DTYP, FTYP, NDIM, SCAL and SMAX may be put together on the same M card.

ROUTINES WHICH READ THE CARDS:

INPUTM reads and interprets all the M cards given. SETFOU then deals with default values, and sets the system up to perform Fourier calculations.

EXAMPLE:

M DTYP 1 FTYP 1 DELT 0.25 CM/A 1.5 SCAL 1000
M SMAX 0.75
M AXES 0 0 1, 1 1 0, -1 1 0
M MESH -.5 .5 .02 0 1 .01
M PLOT 0
M CONT STEP -9 17 2