2.23 ********************
* LSQROT WRITE-UP *
********************
This program refines the orientation and position of a
noncrystallographic symmetry axis by least squares. It is applicable
only to pure rotational noncrystallographic symmetry axes, and the
rotation must be N-FOLD where N is an integer. An input map (which
MUST be orthogonal) is read in along with control information
specifying initial values for the operator, and what area in the map
to consider. The map area considered can be all points within a given
distance from an arbitrary input point, all points within an input
mask, or all points simultaneously satisfying both conditions. The
input map usually encompasses a dimer, trimer etc and was extracted
from a FSFOUR map via programs MAPVIEW or EXTRMAP. The input mask, if
one is used, must correspond precisely to the input map. If the input
map (and mask) does not correspond to an orthogonal system, program
MAPORTH should be used to convert them before they can be used here.
After each cycle of refinement the correlation coefficient is printed
along with the new parameters. One should always start with a low
resolution map (roughly 6 angstrom data, on a 2 angstrom grid) in case
the initial estimates are inaccurate. As the refinement converges
higher resolution data and finer map grids should be used. It is often
sufficient to refine within a sphere of radius 25-35 angstroms
centered on a point on the rotational axis near the center of gravity
of the dimer, trimer etc. This enables refinement of the operator
without the need for an input mask (although one will be needed later
for averaging). Usually correlation coefficients of about 0.4 or
higher (in a 4 angstrom map) indicate the noncrystallographic symmetry
axis is well positioned, and that averaging will be useful.
INPUT DATA (UNIT 5)
CARD I PAMFIL (free format)
PAMFIL = Input file specifying cell and symmetry
parameters, used only to get "running log" file
CARD II INPMAP (free format)
INPMAP = Input map (orthogonal)
CARD III PHI, PSI, OX, OY, OZ, NFOLD (free format)
PHI = Spherical polar angles defining direction of the non-
crystallographic symmetry axis, oriented with respect
PSI = to orthogonal frame with X along a, Y along c* cross
a, and Z along x cross y (i.e. c*). PSI = angle
between NC symmetry axis and +Y axis. PHI = angle
between projection of NC symmetry axis on XZ plane
and +X axis. +PHI= CCW rotation about +Y axis as
measured from +X axis.
OX =
Origin of NC symmetry rotation axis, in angstroms
OY = with respect to the orthogonal axes. The axis passes
through this point.
OZ =
NFOLD = Order of the rotational axis, e.g 2,3,4 etc.
CARD IV NOBS, NCYCLE, ISPHER, IMASK (free format)
NOBS = 2 times number of reflections used to compute map
(used only to compute sigmas)
NCYCLE = Number of refinement cycles
ISPHER = 0 use all points in map
= 1 use only grid points within a specified sphere.
IMASK = 0 for no mask input
= 1 to only use grid points within envelope specified
by input mask. (also subject to ISPHER criteria)
CARD V INPMSK (free format)
******** include this card ONLY if IMASK=1 ********
IMASK = Input mask file
CARD VI XCEN, YCEN, ZCEN RAD (free format)
******** include this card ONLY if ISPHER=1 ********
XCEN =
Sphere center, in Angstroms, with respect to orthogonal
YCEN =
coordinate system.
ZCEN =
RAD = Sphere radius, in Angstroms
CARD VII ( IVAR(I), I=1,5 ) (free format)
Variable selection information
IVAR(1) = 1 to refine PHI, 0 to hold fixed
IVAR(2) = 1 to refine PSI, 0 to hold fixed
IVAR(3) = 1 to refine OX, 0 to hold fixed
IVAR(4) = 1 to refine OY, 0 to hold fixed
IVAR(5) = 1 to refine OZ, 0 to hold fixed
NOTES: Input map must be orthogonal. If the crystal system does not
have orthogonal axes, program MAPORTH must be run to orthogonalize
the map (and mask, if one is to be used).
If a mask is input, it must coincide exactly with the input map.
Normally all parameters are refined, but occasionally one must use
the IVAR selection flags to hold a parameter fixed. An example would
be the case where PSI is close to 0, in which case PHI is then
indeterminate (and irrelevant!). One could then hold PHI fixed to
avoid matrix singularities.
******** FILES ********
INPUT MAP FILE (BINARY)
record 1) A,B,C,AL,BE,GA,NX,NY,NZ,IXMN,IYMN,IZMN,IXMX,IYMX,IZMX
with first 6 values REAL*4, next 9 INTEGER*4, lengths in Angstroms,
angles in degrees.
NX =
Number of grid points defining one "cell length" along
NY = respective axis. Implicitly defines grid spacing as
del x = A/NX, del y = B/NY and del z = C/NZ
NZ =
IXMN, IXMX =
Minimum, maximum grid index defining map region such
IYMN, IYMX = that x (fractional) = IX * (del x) / A etc.
There are no restrictions on magnitudes or signs.
IZMN, IZMX =
The map follows as (IYMX-IYMN+1)*(IZMX-IZMN+1) records, with each
containing one row (IXMX-IXMN+1 REAL*4 values) along X, starting at
IXMN. Y is slowest varying, i.e. the file could have been created with
the following FORTRAN code:
DO 30 IY=IYMN,IYMX
DO 20 IZ=IZMN,IZMX
20 WRITE(LU)(RHO(IX,IY,IZ),IX=IXMN,IXMX)
30 CONTINUE
INPUT MASK FILE (BINARY), if needed
Header record identical to map file.
Mask records similar to normal map records except that the mask values
are written as FORTRAN type "BYTE" (INTEGER*1). Only grid points with
mask values of 0, 10, 20, 30, 40 etc will be used (i.e. inside
envelope masks 1,2,3,4,5 etc, respectively).