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attitude.m
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attitude.m
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classdef attitude
%static
properties(Constant,GetAccess=private)
%list of data fields
%NOTICE: needs updated when adding a new data type
data_type_list={'quat','ang','angr','anga'};
%default value of parameters
%NOTICE: needs updated when adding a new parameter
%NOTICE: it's not a bad idea to define attitude_dir in project.yaml, to have the proper value for data_dir.
% If there is no attitude_dir in project.yaml, the 'attitude' dir will need to exist in the same
% dir as this script.
parameter_list={...
'satname', 'unknown',@ischar;...
'frame_from','srf', @(i) simpletimeseries.isframe(i);...
'frame_to', 'crf', @(i) simpletimeseries.isframe(i);...
'qsfirst', true, @islogical;...
'verbose', false, @islogical;...
};
%These parameter are considered when checking if two data sets are
%compatible (and only these).
%NOTICE: needs updated when adding a new data type (if relevant)
compatible_parameter_list={'satname','frame_from','frame_to'};
end
%NOTICE: needs updated when adding a new parameter
properties
%parameters
satname
frame_from
frame_to
qsfirst
verbose
end
%NOTICE: needs updated when adding a new data type
properties(SetAccess=private)
%data types
quat
angi
angri
angai
initialized
end
%calculated only when asked for
properties(Dependent)
time
ang
angr
anga
vector_part
scalar_part
end
methods(Static)
%interface methods to object constants
function out=data_types
out=attitude.data_type_list;
end
function out=parameters(varargin)
persistent v
if isempty(v); v=varargs(attitude.parameter_list); end
out=v.picker(varargin{:});
end
%data source definitions
% function out=nrtdm_product(in)
% switch simpletimeseries.translatesat(in)
% case 'ch'
% out='CH_Basic/Orbit_CH-OG-3-RSO';
% case 'ga'
% out='GA_Basic/Orbit_NAVSOL';
% case 'gb'
% out='GB_Basic/Orbit_NAVSOL';
% case 'sa'
% out='SA_Basic/Orbit_L1B';
% case 'sb'
% out='SB_Basic/Orbit_L1B';
% case 'sc'
% out='SC_Basic/Orbit_L1B';
% otherwise
% error([mfilenane,': unknown NRTDM product for satellite ''',in,''', debug needed!'])
% end
% end
%import data according to format, satname, start and optionally data_dir:
% - valid formats are according to swith loop in this routine
% - valid satnames are according to simpletimeseries.translatesat
% - start is datetime, from which the date in the filename is retrieved
% - data_dir
function obj=import(format,satname,start,varargin)
%save loaded data in appropriate data type
switch format
case 'grace_l1b'
%get datafile
datafile=grace.grace_l1b_filename('SCA1B',satname,start,varargin{:});
%load the data
sts=simpletimeseries.import(datafile,'format','SCA1B');
%ensure quaternions are unitary
sts=sts.assign_y(attitude.quat_unit(sts.y));
args={'quat',sts};
sat=simpletimeseries.translatesatname(satname);
%TODO: check if this correct
frame_from='srf';
frame_to='crf';
qsfirst=true;
otherwise
error(['Cannot handle format ''',format,'''.'])
end
if ~isempty(sts)
obj=attitude(...
args{:},...
'satname', sat,...
'frame_from',frame_from,...
'frame_to', frame_to,...
'qsfirst', qsfirst...
);
else
obj=[];
end
end
%% math
%sets norm of the quaternion equal to 1
function q=quat_unit(q)
scale=sqrt(sum(q.^2,2))*ones(1,4);
if any(scale ~= 1)
q=q./scale;
end
end
%split scalar and vector parts
function [s,v]=quat_split(q,qsfirst)
if qsfirst
s=q(:,1);
v=q(:,2:4);
else
s=q(:,4);
v=q(:,1:3);
end
end
%joins scalar and vector parts
function q=quat_join(s,v,qsfirst)
if qsfirst
q=[s,v];
else
q=[v,s];
end
end
%scales the quaterion so it represents a rotation
function q=quat_scale(q,qsfirst)
[s,v]=attitude.quat_split(q,qsfirst);
q=attitude.quat_join(s,v.*( abs(sin(acos(s))./sqrt(sum(v.^2,2)))*ones(1,3) ),qsfirst);
end
%compute the conjugate quaternion
function q=quat_conj(q,qsfirst)
[s,v]=attitude.quat_split(q,qsfirst);
q=attitude.quat_join(s,-v,qsfirst);
end
%compute quaternion multiplication
function q=quat_mult(q1,q2,qsfirst)
%split
[s1,v1]=attitude.quat_split(q1,qsfirst);
[s2,v2]=attitude.quat_split(q2,qsfirst);
%multiply the scale parts
s=s1.*s2-sum(v1.*v2,2);
%multiply the vector parts
v=[s1.*v2(:,1),s1.*v2(:,2),s1.*v2(:,3)]+...
[s2.*v1(:,1),s2.*v1(:,2),s2.*v1(:,3)]+...
cross(v1,v2);
%join
q=attitude.quat_join(s,v,qsfirst);
end
%compute quaternion derivative
% function dq=quat_diff(q)
% end
%% tests for the current object
function out=test_parameters(field)
switch lower(field)
case 'format'
out='grace_l1b';
case 'satname'
out='gracea';
case 'start'
out=datetime('2010-01-01');
case 'version'
out='02';
otherwise
error(['unknown field ',field,'.'])
end
end
function out=test(method)
if ~exist('method','var') || isempty(method)
method='all';
end
format= attitude.test_parameters('format');
satname=attitude.test_parameters('satname');
start= attitude.test_parameters('start');
test_list={'import','quat','ang','angr'};
switch(method)
case 'all'
for i=1:numel(test_list)
out{i}=attitude.test(test_list{i});
end
case 'import'
out=attitude.import(format,satname,start);
case 'quat'
out=attitude.test('import');
figure
out.quat.plot;
case 'ang'
out=attitude.test('import');
figure
out.ang.plot;
case 'angr'
out=attitude.test('import');
figure
out.angr.plot('zeromean',true);
otherwise
error(['Cannot handle test method ''',method,'''.'])
end
end
end
methods
%% constructor
function obj=attitude(varargin)
p=machinery.inputParser;
%parse the arguments with the names defined in attitude.data_type_list
for j=1:numel(attitude.data_types)
%shorter names
dtn=attitude.data_types{j};
%declare data types
p.addParameter(dtn,[],(@(i) isa(i,'simpletimeseries')));
end
%declare parameters p
[~,p,obj]=varargs.wrap('parser',p,'sinks',{obj},'sources',{attitude.parameters('obj')},varargin{:});
%clean varargin
varargin=cells.vararginclean(varargin,p.Parameters);
% retrieve each data type
for j=1:numel(attitude.data_types)
%shorter names
data_type=attitude.data_types{j};
%skip if this data type is empty
if ~isempty(p.Results.(data_type))
%add new data type
obj=obj.add_data_type(...
data_type,p.Results.(data_type),...
varargin{:}...
);
end
end
%propagate quaternion information to other data types
obj=obj.update_ang;
obj=obj.update_angr;
%initialize internal records
obj.initialized=true;
end
function obj=add_data_type(obj,data_type,data_value)
%simplify things
data_type=lower(data_type);
%parse input
p=machinery.inputParser;
p.addRequired('data_type' ,@(i) ischar(i) && cells.isincluded(attitude.data_types,i));
p.addRequired('data_value',@(i) isa(i,'simpletimeseries'));
% parse it
p.parse(data_type,data_value);
%sanity
assert(isempty(obj.(data_type)),['data of type ''',data_type,''' has already been created. Use another method to append data.'])
%propagate this data type
obj.(data_type)=data_value;
end
function obj=copy_metadata(obj,obj_in,more_parameters,less_parameters)
if ~exist('less_parameters','var')
less_parameters={};
end
if ~exist('more_parameters','var')
more_parameters={};
end
pn=[attitude.parameters('list');more_parameters(:)];
for i=1:numel(pn)
%skip less parameters
if ismember(pn{i},less_parameters)
continue
end
%check if this is a relevant parameter to this object and obj_in
if isprop(obj,pn{i}) && isprop(obj_in,pn{i})
obj.(pn{i})=obj_in.(pn{i});
end
end
%propagate parameters of all non-empty data types
for j=1:numel(attitude.data_types)
%shorter names
data_type=attitude.data_types{j};
%sanity
if xor(isempty(obj.(data_type)),isempty(obj_in.(data_type)))
error(['error propagating metadata of type ',data_type,': it does not exist in both objects.'])
end
%skip if data type is empty
if ~isempty(obj.(data_type))
obj.(data_type)=obj.(data_type).copy_metadata(obj_in.(data_type),more_parameters,less_parameters);
end
end
end
function out=metadata(obj,more_parameters)
if ~exist('more_parameters','var')
more_parameters={};
end
warning off MATLAB:structOnObject
out=varargs(...
structs.filter(struct(obj),[attitude.parameters('list');more_parameters(:)])...
).varargin;
warning on MATLAB:structOnObject
end
function out=varargin(obj,more_parameters)
out=varargs(obj.metadata(more_parameters)).varargin;
end
%% info methods
function print(obj,tab)
if ~exist('tab','var') || isempty(tab)
tab=20;
end
disp(' --- Parameters --- ')
for i=1:numel(attitude.parameters('list'))
%shorter names
p=attitude.parameters('value',i);
disp([p,repmat(' ',1,tab-length(p)),' : ',str.show(obj.(p))])
end
d_list=attitude.data_types;
for i=1:numel(d_list)
%shorter names
d=d_list{i};
if ~isempty(obj.(d))
disp([' --- ',d,' --- '])
obj.(d).print
end
end
end
function msg(obj,in)
if obj.verbose
disp(in)
end
end
%% properties of this object
function obj=update_qsfirst(obj,qsfirst)
%trivial call
if (qsfirst==obj.qsfirst)
return
end
%split scalar/vector parts
[s,v]=attitude.quat_split(obj.quat.y,obj.qsfirst);
%swap scalar/vector parts
if obj.qsfirst && ~qsfirst
obj.quat=obj.quat.assign_y([v,s]);
elseif ~obj.qsfirst && qsfirst
obj.quat=obj.quat.assign_y([s,v]);
end
end
function obj=set.qsfirst(obj,qsfirst)
if ~isempty(obj.initialized) && obj.initialized %#ok<MCSUP>
obj=obj.update_qsfirst(qsfirst);
else
obj.qsfirst=qsfirst;
end
end
%% dependent properties of this object
function s=get.scalar_part(obj)
s=attitude.quat_split(obj.quat,obj.qsfirst);
end
function obj=set.scalar_part(obj,s)
[~,v]=attitude.quat_split(obj.quat,obj.qsfirst);
obj.quat=attitude.quat_join(s,v,obj.qsfirst);
end
function v=get.vector_part(obj)
[~,v]=attitude.quat_split(obj.quat,obj.qsfirst);
end
function obj=set.vector_part(obj,v)
s=attitude.quat_split(obj.quat,obj.qsfirst);
obj.quat=attitude.quat_join(s,v,obj.qsfirst);
end
%% properties of data types
function out=get_dtp(obj,propname)
out=[];
dt=attitude.data_types;
for i=1:numel(dt)
if ~isempty(obj.(dt{i}))
out=obj.(dt{i}).(propname);
break
end
end
assert(~isempty(out),'all data types are empty.')
end
function obj=set_dtp(obj,propname,propvalue)
odt=attitude.data_types;
for i=1:numel(odt)
if ~isempty(obj.(odt{i}))
switch propname
case {'time','t'}
obj.(odt{i})=obj.(odt{i}).interp(t,'interp1_args',{'spline'});
otherwise
obj.(odt{i}).(propname)=propvalue;
end
end
end
obj.check_dtp(propname)
end
function check_dtp(obj,propname)
odt=attitude.data_types;
for i=2:numel(odt)
if ~obj.isempty(odt{i})
switch propname
case {'time','t'}
check=obj.(odt{1}).istequal(obj.(odt{i}));
otherwise
check=cells.isequal(...
cells.set(obj.(odt{1}).(propname),'set'),...
cells.set(obj.(odt{i}).(propname),'set'));
end
assert(check,...
['discrepancy in property ''',propname,''' between data types ''',...
odt{1},''' and ''',odt{i},'''.']...
)
end
end
end
function out=get.time(obj)
out=obj.get_dtp('time');
end
function obj=set.time(obj,value)
obj=obj.set_dtp('time',value);
end
%% euler angles
function obj=update_ang(obj)
assert(~isempty(obj.quat),'cannot compute data type ''ang'' because ''quat'' is empty')
%getting euler angles
y = SpinConv('QtoEA123', obj.update_qsfirst(false).quat.y);
%building object
obj.angi=simpletimeseries(obj.quat.t,y,...
'format','datetime',...
'units',{'deg', 'deg', 'deg'},...
'labels', {'roll','pitch','yaw'},...
'timesystem','gps',...
'descriptor',obj.quat.descriptor...
);
end
function obj=set.ang(obj,ang)
obj.angi=ang;
end
function ang=get.ang(obj)
if isempty(obj.angi)
ang=[];
else
ang=obj.angi;
end
end
%% angular rates
function obj=update_angr(obj)
assert(~isempty(obj.quat),'cannot compute data type ''angr'' because ''quat'' is empty')
%computing quaternion quantities
qj=attitude.quat_conj(obj.quat.y,obj.qsfirst);
%NOTICE: this calls simpledata.diff, but there is also simpletimeseries.deriv (unnecessary)
dq=obj.quat.diff.y;
%compute angular rates in frame_to
y=2*attitude.quat_mult(qj,dq,obj.qsfirst);
%%compute angular rates in frame_from
%y=2*attitude.quat_mult(dq,qj,obj.qsfirst);
if obj.qsfirst
obj.msg([' average of absolute value of scalar part of omega is ',...
num2str(mean(abs(y(~isnan(y(:,1)),1))))])
y=y(:,2:4);
else
obj.msg([' average of absolute value of scalar part of omega is ',...
num2str(mean(abs(y(~isnan(y(:,1)),4))))])
y=y(:,1:3);
end
%building object
obj.angri=simpletimeseries(obj.quat.t,y,...
'format','datetime',...
'units',{'deg/s', 'deg/s', 'deg/s'},...
'labels', {'roll-rate','pitch-rate','yaw-rate'},...
'timesystem','gps',...
'descriptor',obj.quat.descriptor...
);
end
function obj=set.angr(obj,angr)
obj.angri=angr;
end
function angr=get.angr(obj)
if isempty(obj.angri)
angr=[];
else
angr=obj.angri;
end
end
%% angular accelerations
function obj=update_anga(obj)
assert(~isempty(obj.quat),'cannot compute data type ''anga'' because ''quat'' is empty')
%computing quaternion quantities
q=obj.quat.y;
qj=attitude.quat_conj(q,obj.qsfirst);
dq=obj.quat.diff.y;
%compute angular rates in frame_to
y=2*attitude.quat_mult(qj,dq,obj.qsfirst);
%%compute angular rates in frame_from
%y=2*attitude.quat_mult(dq,qj,obj.qsfirst);
if obj.qsfirst
obj.msg([' average of absolute value of scalar part of omega is ',...
num2str(mean(abs(y(~isnan(y(:,1)),1))))])
y=y(:,2:4);
else
obj.msg([' average of absolute value of scalar part of omega is ',...
num2str(mean(abs(y(~isnan(y(:,1)),4))))])
y=y(:,1:3);
end
%building object
obj.angai=simpletimeseries(obj.quat.t,y,...
'format','datetime',...
'units',{'deg/s', 'deg/s', 'deg/s'},...
'labels', {'roll-rate','pitch-rate','yaw-rate'},...
'timesystem','gps',...
'descriptor',obj.quat.descriptor...
);
end
function obj=set.anga(obj,anga)
obj.angai=anga;
end
function anga=get.anga(obj)
if isempty(obj.angai)
anga=[];
else
anga=obj.angai;
end
end
%% object properties
function obj=set.satname(obj,in)
obj.satname=simpletimeseries.translatesat(in);
end
function obj=set.frame_to(obj,in)
obj.frame_to=simpletimeseries.translateframe(in);
end
function obj=set.frame_from(obj,in)
obj.frame_from=simpletimeseries.translateframe(in);
end
%% general data_type scalar get method
function out=get(obj,method,varargin)
%get data types
odt=attitude.data_types;
%make room for outputs
out=cell(size(odt));
%loop over all data types
for i=1:numel(odt)
%check if this data type is not empty
if ~isempty(obj.(odt{i}))
%check if this is a member
if ismethod(obj.(odt{i}),method)
%use the method on it, pass additional arguments
out{i}=obj.(odt{i}).(method)(varargin{:});
%check if this is a property
elseif isprop(obj.(odt{i}),method)
%call this member (varargin is ignored)
out{i}=obj.(odt{i}).(method);
end
end
end
%remove dups and reduce to scalar if possible
out=cells.scalar(cells.rm_duplicates(out),'get');
%need to return something
assert(~isempty(out),'all data types are empty.')
end
%% management
function compatible(obj1,obj2,varargin)
%This method checks if the objectives are referring to the same
%type of data, i.e. the data length is not important.
parameters=attitude.compatible_parameter_list;
for i=1:numel(parameters)
if ~isequal(obj1.(parameters{i}),obj2.(parameters{i}))
error(['discrepancy in parameter ',parameters{i},': ''',...
obj1.(parameters{i}),''' ~= ''',obj2.(parameters{i}),'''.'])
end
end
%check that all data type as compatible as well
odt=attitude.data_types;
for i=1:numel(odt)
if ~isempty(obj1.(odt{i})) && ~isempty(obj2.(odt{i}))
obj1.(odt{i}).compatible(obj2.(odt{i}),varargin{:})
end
end
end
%object obj1 will have the time domain of obj2 (interpolated if needed)
function [obj1,obj2]=consolidate(obj1,obj2,varargin)
%compatibility check
obj1.compatible(obj2,varargin{:})
%consolidate all data types
counter=0;
odt=attitude.data_types;
for i=1:numel(odt)
if ~isempty(obj1.(odt{i})) && ~isempty(obj2.(odt{i}))
[obj1.(odt{i}),obj2.(odt{i})]=obj1.(odt{i}).interp2_lcm(obj2.(odt{i}));
counter=counter+1;
end
end
if counter==0
error('there were no common fields in the input objects.')
end
end
function out=isempty(obj,data_type)
if ~exist('data_type','var') || isempty(data_type)
odt=attitude.data_types;
for i=1:numel(odt)
if ~obj.isempty(odt{i});out=false;return;end
end
out=true;
else
out=isempty(obj.(data_type)) || all(obj.(data_type).y(:)==0);
end
end
%% multiple object manipulation
function[obj1,idx1,idx2]=append(obj1,obj2,varargin)
%append all data types
for i=1:numel(attitude.data_types)
%simplify things
data_type=lower(attitude.data_types{i});
if obj1.isempty(data_type) || obj2.isempty(data_type)
continue
end
%call upstream method
[...
obj1.(data_type),...
idx1.(data_type),...
idx2.(data_type)...
]=obj1.(data_type).append(...
obj2.(data_type),...
varargin{:}...
);
end
end
%% operator
% uses a method from a superclass over all non-empty data types
function obj=op(obj,operation,varargin)
%operation counter
counter=0;
odt=attitude.data_types;
%handle operations between two attitude sets
if numel(varargin)==1 && isa(varargin{1},'attitude')
err_msg='there are no common fields in the input objects';
%shorter names
obj1=varargin{1};
%No need for consolidation, that is done inside the operation
for i=1:numel(odt)
%operate over all non-empty data types
if ~isempty(obj.(odt{i})) && ~isempty(obj1.(odt{i}))
%operate
obj.(odt{i})=obj.(odt{i}).(operation)(obj1.(odt{i}));
counter=counter+1;
end
end
else
err_msg='there are no non-empty fields in the input object';
for i=1:numel(odt)
%operate over all non-empty data types
if ~isempty(obj.(odt{i}))
if isprop(obj.(odt{i}),operation)
%sanity
if numel(varargin)>1
error(['when propagating data to field ',operation,...
' can only handle one input argument, not ',num2str(numel(varargin)),'.'])
end
%propagate
obj.(odt{i}).(operation)=varargin{1};
else
%operate
obj.(odt{i})=obj.(odt{i}).(operation)(varargin{:});
end
counter=counter+1;
end
end
end
if counter==0
error(err_msg)
end
end
%% relative attitude (in the local frame)
function rel=relative(obj1,obj2)
%compute difference
rel=obj1.op('minus',obj2);
end
%TODO: needs testing
function out=periodic_stats(obj,period,varargin)
% separate time series into segments
[ts,idx]=segmentedfreqseries.time_segmented(obj.time,period,seconds(0));
%get stats for all available stat types
odt=attitude.data_types;
for j=1:numel(odt)
if ~isempty(obj.(odt{j}))
% initialize
s.msg=['cutting into segments data of type ''',odt{j},'''.'];s.n=numel(ts);
clear tmp
% propagate segments
for i=1:numel(ts)
%compute statistics
tmp(i)=simpledata(...
ts{i},...
obj.(odt{j}).y(idx{i}(1):idx{i}(2),:),...
'mask',obj.(odt{j}).mask(idx{i}(1):idx{i}(2),:),...
varargin{:}...
).stats('struct'); %#ok<*AGROW>
%inform
s=simpledata.progress(s,i);
end
%propagate
s_list=fields(tmp);
for i=1:numel(s_list)
stats.(odt{j}).(s_list{i})=transpose(reshape(...
[tmp.(s_list{i})],...
numel(tmp(1).(s_list{i})),...
numel(ts)...
));
end
end
end
%build time domain
t=datetime([],[],[]);
for i=1:numel(ts)
t(i)=mean(ts{i});
end
%build argument list
o_list=fields(stats);
args=cell(1,2*numel(o_list));
%propagate all fields in statistics
s_list=fields(tmp);
for i=1:numel(s_list)
%build argument list for this statistic
for j=1:numel(o_list)
args{2*j-1}=o_list{j};
if size(stats.(o_list{j}).(s_list{i}),2)==1
args{2*j }=repmat(stats.(o_list{j}).(s_list{i}),1,attitude.data_type_list.(o_list{j}).size);
elseif size(stats.(o_list{j}).(s_list{i}),2)==attitude.data_type_list.(o_list{j}).size
args{2*j }=stats.(o_list{j}).(s_list{i});
else
error('BUG TRAP: statistic with non-comformant number of columns. Debug needed!')
end
end
%build attitude object for this statistic
out.(s_list{i})=attitude(t,args{:},obj.varargin{:});
end
end
end
end
%% SpinConv
% https://nl.mathworks.com/matlabcentral/fileexchange/41562-spinconv
function OUTPUT = SpinConv(TYPES, INPUT, tol, ichk)
%SpinConv Conversion from a rotation representation type to another
%
% OUT = SpinConv(TYPES, IN, TOL, ICHK) converts a rotation representation
% type (IN) to another (OUT). Supported conversion input/output types are
% as follows:
% 1) Q Rotation quaternions
% 2) EV Euler vector and rotation angle (degrees)
% 3) DCM Direction cosine matrix (a.k.a. rotation matrix)
% 4) EA### Euler angles (12 possible sets) (degrees)
% All representation types accepted as input (IN) and returned as output
% (OUT) by SpinConv are meant to represent the rotation of a 3D
% coordinate system (CS) relative to a rigid body or vector space
% ("alias" transformation), rather than vice-versa ("alibi"
% transformation).
%
% OUT=SpinConv(TYPES,IN) is equivalent to OUT=SpinConv(TYPES,IN,10*eps,1)
% OUT=SpinConv(TYPES,IN,TOL) is equiv. to OUT=SpinConv(TYPES,IN,TOL,1)
%
% Input and output arguments:
%
% TYPES - Single string value that specifies both the input type and
% the desired output type. The allowed values are:
%
% 'DCMtoEA###' 'DCMtoEV' 'DCMtoQ'
% 'EA###toDCM' 'EA###toEV' 'EA###toQ'
% 'EVtoDCM' 'EVtoEA###' 'EVtoQ'
% 'QtoDCM' 'QtoEA###' 'QtoEV'
% 'EA###toEA###'
%
% For cases that involve Euler angles, ### should be
% replaced with the proper order desired. E.g., EA321
% would be Z(yaw)-Y(pitch)-X(roll).
%
% IN - Array of N matrices or N vectors (N>0) corresponding to the
% first entry in the TYPES string, formatted as follows:
%
% DCM - (3×3×N) Array of rotation matrices. Each matrix R
% contains in its rows the versors of the rotated CS
% represented in the original CS, and in its columns the
% versors of the original CS represented in the rotated
% CS. This format is typically used when the column-vector
% convention is adopted: point coordinates are arranged in
% column vectors Vi, and the desired rotation is applied
% by pre-multiplying Vi by R (rotated Vi = R * Vi).
% EA### - [psi,theta,phi] (N×3) row vector list containing, in
% each row, three Euler angles or Tait-Bryan angles.
% (degrees).
% EV - [m1,m2,m3,MU] (N×4) Row vector list containing, in each
% row, the components (m1, m2, m3) of an Euler rotation
% vector (represented in the original CS) and the Euler
% rotation angle about that vector (MU, in degrees).
% Q - [q1,q2,q3,q4] (N×4) Row vector list defining, in each
% row, a rotation quaternion. q4 = cos(MU/2), where MU is
% the Euler angle.
%
% TOL - (Default value: TOL = 10 * eps) Tolerance value for deviations
% from 1. Used to test determinant of rotation matrices or
% length of unit vectors.
% ICHK - (Default value: ICHK = 1) Flag controlling whether
% near-singularity warnings are issued or not.
% ICHK = 0 disables warnings.
% ICHK = 1 enables them.
% OUT - Array of N matrices or N vectors (N > 0) corresponding to the
% second entry in the TYPES string, formatted as shown
% above.
%
% See also SpinCalc, degtorad, rad2deg.
% Version 2.2
% 2013 April 3
%
% Based on:
% SpinCalc, Version 1.3 (MATLAB Central file #20696)
% 2009 June 30
% SpinCalc code by:
% John Fuller
% National Institute of Aerospace
% Hampton, VA 23666
% John.Fuller@nianet.org
% Debugged and optimized for speed by:
% Paolo de Leva
% University "Foro Italico"
% Rome, Italy
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Setting default values for missing input arguments
switch nargin
case 2, tol = 10*eps; ichk = true;
case 3, ichk = true;
case 4
if isequal(ichk, 0), ichk = false;
else, ichk = true;
end
otherwise, narginchk(2, 4); % Allow 2 to 4 input arguments
end
% No TYPES string can be shorter than 4 or longer than 12 chars
len = length(TYPES);
if len>12 || len<4, error('Invalid entry for TYPES input string'); end
% Determine type of conversion from TYPES string
TYPES = upper(TYPES);
index = strfind(TYPES, 'TO');
TYPE.INPUT = TYPES(1 : index-1);
TYPE.OUTPUT = TYPES(index+2 : len);
fields = {'INPUT', 'OUTPUT'}; % 1×2 cell
% Check validity of TYPES string, both for input and output
for f = 1:2
IO = fields{f};
type = TYPE.(IO);
switch type
case {'Q' 'EV' 'DCM'} % Valid TYPE
otherwise
% Check that TYPE is 'EA###'
if length(type)~=5 || ~strcmp(type(1:2), 'EA')
error('Invalid entry for TYPES input string')
end
TYPE.(IO) = 'EA';
EAorder.(IO) = type(3:5);
% Check that all characters in '###' are numbers between 1
% and 3, and that no 2 consecutive characters are equal
order31 = str2num(EAorder.(IO)'); %#ok<ST2NM> % 3×1 double
if isempty(order31) || any ([order31<1; order31>3]) || ...
order31(1)==order31(2) || ...
order31(2)==order31(3)
error('Invalid Euler angle order in TYPES string.')
end
% Type of EA sequence:
% 1) Rotations about three distinct axes
% 2) 1st and 3rd rotation about same axis
if order31(1)==order31(3), EAtype.(IO) = 2;
else , EAtype.(IO) = 1;
end
end
end
% Set N (number of rotations) and check INPUT size
s=size(INPUT);
switch numel(s)
case 2; size1=s(1); size2=s(2);
case 3; size1=s(1); size2=s(2); size3=s(3);
end
switch TYPE.INPUT
case 'DCM' % (3×3×N) Direction cosine matrix
N = size3;
isnot_DCM = false;
if ndims(INPUT)>3 || N==0 || size1~=3 || size2~=3
error('Invalid INPUT size (INPUT must be 3×3×N for DCM type)')
end
case 'EA', v_length=3; Isize='N×3'; isnot_DCM=true;
case 'Q', v_length=4; Isize='N×4'; isnot_DCM=true;
case 'EV', v_length=4; Isize='N×4'; isnot_DCM=true;
end
if isnot_DCM
N = size1;
if ~ismatrix(INPUT) || N==0 || size2~=v_length
error(['Invalid INPUT size (INPUT must be ' ...
Isize ' for ' TYPE.INPUT ' type)'])
end
end
% Determine the quaternions that uniquely describe the rotation prescribed
% by INPUT. OUTPUT will be calculated in the second portion of the code
% from these quaternions.
switch TYPE.INPUT
case 'DCM'
% NOTE: Orthogonal matrixes may have determinant -1 or 1
% DCMs are special orthogonal matrices, with determinant 1
improper = false;
DCM_not_1 = false;
if N == 1
% Computing deviation from orthogonality
delta = INPUT * INPUT' - eye(3); % DCM*DCM' - I
delta = delta(:); % 9×1 <-- 3×3
% Checking determinant of DCM
DET = det(INPUT);
if DET<0, improper=true; end
if ichk && abs(DET-1)>tol, DCM_not_1=true; end
% Permuting INPUT
INPUT = reshape(INPUT, [1 3 3]); % 1×3×3
else
% Computing deviation from orthogonality
delta = multiprod(INPUT, multitransp(INPUT), [1 2]); % DCM*DCM'
delta = bsxfun(@minus, delta, eye(3)); % Subtracting I
delta = delta(:); % 9N×1 <-- 3×3×N
% Checking determinant of DCMs
DET = INPUT(1,1,:).*INPUT(2,2,:).*INPUT(3,3,:) -INPUT(1,1,:).*INPUT(2,3,:).*INPUT(3,2,:)...
+INPUT(1,2,:).*INPUT(2,3,:).*INPUT(3,1,:) -INPUT(1,2,:).*INPUT(2,1,:).*INPUT(3,3,:)...
+INPUT(1,3,:).*INPUT(2,1,:).*INPUT(3,2,:) -INPUT(1,3,:).*INPUT(2,2,:).*INPUT(3,1,:); % 1×1×N
if any(DET<0), improper=true; end
if ichk && any(abs(DET-1)>tol), DCM_not_1=true; end
% Permuting INPUT
INPUT = permute(INPUT, [3 1 2]); % N×3×3
end
% Issuing error messages or warnings
if ichk && any(abs(delta)>tol)
warning('Input DCM is not orthogonal.')
end
if improper, error('Improper input DCM'); end
if DCM_not_1
warning('Input DCM determinant off from 1 by more than tolerance.');
end
% Denominators for 4 distinct types of equivalent Q equations
denom = [1 + INPUT(:,1,1) - INPUT(:,2,2) - INPUT(:,3,3),...
1 - INPUT(:,1,1) + INPUT(:,2,2) - INPUT(:,3,3),...
1 - INPUT(:,1,1) - INPUT(:,2,2) + INPUT(:,3,3),...
1 + INPUT(:,1,1) + INPUT(:,2,2) + INPUT(:,3,3)];
denom = 2 .* sqrt (denom); % N×4
% Choosing for each DCM the equation which uses largest denominator
[maxdenom, index] = max(denom, [], 2); % N×1
clear delta DET denom
Q = NaN(N,4); % N×4
% EQUATION 1
ii = (index==1); % (Logical vector) MAXDENOM==DENOM(:,1)
if any(ii)
Q(ii,:) = [ 0.25 .* maxdenom(ii,1),...
(INPUT(ii,1,2)+INPUT(ii,2,1)) ./ maxdenom(ii,1),...
(INPUT(ii,1,3)+INPUT(ii,3,1)) ./ maxdenom(ii,1),...
(INPUT(ii,2,3)-INPUT(ii,3,2)) ./ maxdenom(ii,1)];
end
% EQUATION 2
ii = (index==2); % (Logical vector) MAXDENOM==DENOM(:,2)
if any(ii)
Q(ii,:) = [(INPUT(ii,1,2)+INPUT(ii,2,1)) ./ maxdenom(ii,1),...
0.25 .* maxdenom(ii,1),...
(INPUT(ii,2,3)+INPUT(ii,3,2)) ./ maxdenom(ii,1),...
(INPUT(ii,3,1)-INPUT(ii,1,3)) ./ maxdenom(ii,1)];
end
% EQUATION 3
ii = (index==3); % (Logical vector) MAXDENOM==DENOM(:,3)
if any(ii)
Q(ii,:) = [(INPUT(ii,1,3)+INPUT(ii,3,1)) ./ maxdenom(ii,1),...
(INPUT(ii,2,3)+INPUT(ii,3,2)) ./ maxdenom(ii,1),...
0.25 .* maxdenom(ii,1),...
(INPUT(ii,1,2)-INPUT(ii,2,1)) ./ maxdenom(ii,1)];
end
% EQUATION 4
ii = (index==4); % (Logical vector) MAXDENOM==DENOM(:,4)
if any(ii)
Q(ii,:) = [(INPUT(ii,2,3)-INPUT(ii,3,2)) ./ maxdenom(ii,1),...
(INPUT(ii,3,1)-INPUT(ii,1,3)) ./ maxdenom(ii,1),...
(INPUT(ii,1,2)-INPUT(ii,2,1)) ./ maxdenom(ii,1),...
0.25 .* maxdenom(ii)];
end
clear INPUT maxdenom index ii
case 'EV'
% Euler vector (EV) and angle MU in degrees
EV = INPUT(:,1:3); % N×3
halfMU = INPUT(:,4) * (pi/360); % (N×1) MU/2 in radians
% Check that input m's constitute unit vector
delta = sqrt(sum(EV.*EV, 2)) - 1; % N×1
if any(abs(delta) > tol)
error('(At least one of the) input Euler vector(s) is not a unit vector')
end