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GRADPREC.m
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%% main
function opt = GRADPREC(spc,khr,opt)
% function opt = GRADPREC(spc,khr,opt)
%
% GRADPREC described in:
%
% Optimal control gradient precision trade-offs: Application to fast generation of DeepControl libraries for MRI
% Vinding, M.S., et al.
% J Magn Reson. 2021, 333, 107094
% https://doi.org/10.1016/j.jmr.2021.107094
%
% https://github.com/madssakre/GradientPrecision
%
% is an extension to the blOCh optimization framework:
%
% https://github.com/madssakre/blOCh
%
% which has been used in:
%
% Application of the limited-memory quasi-Newton algorithm for multi-dimensional, large flip-angle RF pulses at 7T.
% Vinding, M.S., et al.,
% Magn Reson Mater Phy. 2017, 30, 29-39.
% doi:10.1007/s10334-016-0580-1
%
% Local SAR, global SAR, and power-constrained large-flip-angle pulses with optimal control and virtual observation points.
% Vinding, M.S., et al.,
% Magn Reson Med. 2017, 77, 1, 374-384.
% doi: 10.1002/mrm.26086
%
% Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods.
% Maximov, I. et al.,
% J Magn Reson. 2015, 254, 110-20.
% doi: 10.1016/j.jmr.2015.03.003
%
% Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods.
% Vinding, M.S., et al.,
% J Chem Phys. 2012, 137, 054203.
% doi: 10.1063/1.4739755
%
% and more...
%
% From the adjacent "main.m" you can run GRADPREC with several
% different control gradients with different accuracies. You can find the
% gradient implementations in the "GRAD*" functions below.
%
% Please cite the appropriate papers if you use GRADPREC or blOCh. And it
% comes with no warranty etc.
%
%
%
% Copyright (C) 2021 Mads Sloth Vinding
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
%
%
%
global history opt2 dt
tic_Opt_Wall_Clock_Time = tic;
% adopt variables from other structs to avoid passing entire structs around
opt.R = spc.R;
opt.Rv = spc.Rv;
opt.D = spc.D;
opt.Dv = spc.Dv;
opt.NS = spc.NS;
opt.Dim = spc.Dim;
opt.pTx = spc.pTx;
opt.P = spc.P;
opt.Md = spc.Md;
opt.idxtot = spc.idxtot;
opt.gamma = khr.gamma;
opt.B1_nom_amp_val = spc.B1_nom_amp_val;
opt.B1_nom_amp_unit = spc.B1_nom_amp_unit;
opt.f_B1_val = spc.f_B1_val;
% default parameters.
Par.Grad= 'midpoint';
Par.StoreGrad = 'off';
% Masks in this context refers to indices in the control waveforms that we
% don't optimize but keep fixed. % this is not applicable in all gradient
% types
Par.Mask.RF = 'Off';
Par.Mask.GRA = 'Off';
% This specifies which controls we optimize uv means real and imag RF. s
% means shims, x, y, z means Gx, Gy, Gz. Respectively. Any combination is
% possible e.g. usz.
Par.Controls = 'uv'; % uvxyzs
% for average power and SAR we need to know the pulse duty cycle
Par.Constr.Dutycycle = 0.1;
% about peak RF. This is the one we pay attention to.
Par.Constr.peak_uv.Type = 'bnd';
Par.Constr.peak_uv.Lim = 1000;
Par.Constr.peak_uv.Unit = 'Hz';
Par.Constr.peak_uv.FreeIterations = 10;
Par.Constr.peak_uv.Cope = 'Constr';
% we can constrain the first and final time slices to zero. Ignore for now
Par.Constr.edges_uv.Type = 'bnd';
Par.Constr.edges_uv.Lim = 0;
Par.Constr.edges_uv.Unit = 'W';
Par.Constr.edges_uv.FreeIterations = 0;
Par.Constr.edges_uv.Cope = 'Ignore';
% about average power. Ignore for now
Par.Constr.ave_uv.Type = 'nlc';
Par.Constr.ave_uv.Lim = 1e16;
Par.Constr.ave_uv.Unit = '(rad/s)^2';
Par.Constr.ave_uv.FreeIterations = 10;
Par.Constr.ave_uv.Cope = 'Ignore';
% about jaggedness, not really implemented yet. Ignore
Par.Constr.jag_uv.Type = 'nlc';
Par.Constr.jag_uv.Lim = 1;
Par.Constr.jag_uv.Unit = '(rad/s)^2/s';
Par.Constr.jag_uv.FreeIterations = 10;
Par.Constr.jag_uv.Cope = 'Ignore';
% about peak Grad. This is the one we pay attention to.
Par.Constr.peak_xyz.Type = 'bnd';
Par.Constr.peak_xyz.Lim = 40e-3;
Par.Constr.peak_xyz.Unit = 'T/m';
Par.Constr.peak_xyz.FreeIterations = 10;
Par.Constr.peak_xyz.Cope = 'Constr';
% we can constrain the first and final time slices to zero. Ignore
Par.Constr.edges_xyz.Type = 'bnd';
Par.Constr.edges_xyz.Lim = 0;
Par.Constr.edges_xyz.Unit = 'T/m';
Par.Constr.edges_xyz.FreeIterations = 0;
Par.Constr.edges_xyz.Cope = 'Ignore';
% about peak dGrad/dt. This is the one we pay attention to.
Par.Constr.slew_xyz.Type = 'nlc';
Par.Constr.slew_xyz.Lim = 200;
Par.Constr.slew_xyz.Unit = 'T/m/s';
Par.Constr.slew_xyz.FreeIterations = 10;
Par.Constr.slew_xyz.Cope = 'Constr';
% about RF robustness
Par.Robust.Num = 1; % not che
Par.Robust.Min = 0.9;
Par.Robust.Max = 1.1;
Par.Robust.FWHM = 0.1;
Par.Robust.Distribution = 'lorentzian'; % 'evenly'
Par.Robust.Show = 1;
Par.Robust.FixGradient = 1;
% About right or left handedness. % dont try this at home
Par.Turn = 1;
% Here I exhange default parameters with user specified parameters
opt.Par = NEWPAR(opt.Par,Par);
% about sanity checking controls to optimize
[opt.Par.Controls,opt.Par.PosControls,opt.Par.FixControls] = CONTROLS(opt.Par.Controls);
% about masks in time domain.
if strcmp(opt.Par.Mask.RF,'Off') && strcmp(opt.Par.Mask.GRA,'Off')
opt.mon = [1:opt.N]; %#ok<*NBRAK>
opt.moff = [];
opt.mon_u = [1:opt.N];
opt.mon_v = [1:opt.N];
opt.mon_x = [1:opt.N];
opt.mon_y = [1:opt.N];
opt.mon_z = [1:opt.N];
opt.mon_s = [1:opt.N];
opt.m_u = ones(opt.pTx,opt.N);
opt.m_v = ones(opt.pTx,opt.N);
opt.m_x = ones(1,opt.N);
opt.m_y = ones(1,opt.N);
opt.m_z = ones(1,opt.N);
opt.m_s = ones(opt.NS,opt.N);
elseif strcmp(opt.Par.Mask.RF,'Off') && strcmp(opt.Par.Mask.GRA,'On')
opt.mon = find(opt.m);
opt.moff = find(~opt.m);
opt.mon_u = [1:opt.N];
opt.mon_v = [1:opt.N];
opt.mon_x = opt.mon;
opt.mon_y = opt.mon;
opt.mon_z = opt.mon;
opt.mon_s = [1:opt.N];
opt.m_u = ones(opt.pTx,opt.N);
opt.m_v = ones(opt.pTx,opt.N);
opt.m_x = opt.m;
opt.m_y = opt.m;
opt.m_z = opt.m;
opt.m_s = ones(opt.NS,opt.N);
elseif strcmp(opt.Par.Mask.RF,'On') && strcmp(opt.Par.Mask.GRA,'Off')
opt.mon = find(opt.m);
opt.moff = find(~opt.m);
opt.mon_u = opt.mon;
opt.mon_v = opt.mon;
opt.mon_x = [1:opt.N];
opt.mon_y = [1:opt.N];
opt.mon_z = [1:opt.N];
opt.mon_s = [1:opt.N];
opt.m_u = repmat(opt.m,[opt.pTx,1]);
opt.m_v = repmat(opt.m,[opt.pTx,1]);
opt.m_x = ones(1,opt.N);
opt.m_y = ones(1,opt.N);
opt.m_z = ones(1,opt.N);
opt.m_s = ones(opt.NS,opt.N);
elseif strcmp(opt.Par.Mask.RF,'On') && strcmp(opt.Par.Mask.GRA,'On')
opt.mon = find(opt.m);
opt.moff = find(~opt.m);
opt.mon_u = opt.mon;
opt.mon_v = opt.mon;
opt.mon_x = opt.mon;
opt.mon_y = opt.mon;
opt.mon_z = opt.mon;
opt.mon_s = [1:opt.N];
opt.m_u = repmat(opt.m,[opt.pTx,1]);
opt.m_v = repmat(opt.m,[opt.pTx,1]);
opt.m_x = opt.m;
opt.m_y = opt.m;
opt.m_z = opt.m;
opt.m_s = ones(opt.NS,opt.N);
end
opt = CONSTRAINTSANITY(opt);
[opt.Par.Robust.Values,opt.Par.Robust.Weightings] = RFROBUSTNESS(opt.Par.Robust.Num,opt.Par.Robust.Min,opt.Par.Robust.Max,opt.Par.Robust.Distribution,opt.Par.Robust.FWHM);
opt.k = 0;
opt = CONSTRAINHOW(opt);
opt = ALLOCATE(spc,khr,opt);
opt.s = zeros(opt.NS,opt.N);
arraymask = [];
if contains(opt.Par.Controls,'v')
arraymask = [arraymask,REARRANGE('u','array',opt.m_u)];
end
if contains(opt.Par.Controls,'v')
arraymask = [arraymask,REARRANGE('v','array',opt.m_v)];
end
if contains(opt.Par.Controls,'x')
arraymask = [arraymask,REARRANGE('x','array',opt.m_x)];
end
if contains(opt.Par.Controls,'y')
arraymask = [arraymask,REARRANGE('y','array',opt.m_y)];
end
if contains(opt.Par.Controls,'z')
arraymask = [arraymask,REARRANGE('z','array',opt.m_z)];
end
if contains(opt.Par.Controls,'s')
arraymask = [arraymask,REARRANGE('s','array',opt.m_s)];
end
opt.arraymask = arraymask;
opt.gx = opt.g(1,:);
opt.gy = opt.g(2,:);
opt.gz = opt.g(3,:);
opt.gxo = zeros(1,opt.N,opt.MaxIter+1);
opt.gyo = zeros(1,opt.N,opt.MaxIter+1);
opt.gzo = zeros(1,opt.N,opt.MaxIter+1);
opt.gxo(1,:,1) = opt.gx;
opt.gyo(1,:,1) = opt.gy;
opt.gzo(1,:,1) = opt.gz;
opt.array0 = ARRAY(opt.Par.Controls,opt.u,opt.v,opt.gx,opt.gy,opt.gz,opt.s);
opt.array0(isinf(abs(opt.array0))) = 0;
opt.array0(isnan(opt.array0)) = 0;
opt.max_uv = opt.w1m;
opt.max_g = opt.Par.Constr.peak_xyz.Lim;
[opt.arrayub,opt.arraylb,opt.arraysc] = UB_LB_SC(opt);
opt.array0 = ARRAY2NORM(opt.array0,opt.arraysc);
options=optimset('TolX',opt.TolX,'TolFun',opt.TolFun,'Display','off','MaxIter',opt.MaxIter,'SubproblemAlgorithm','cg',...
'MaxFunEvals',opt.MaxFunEvals,'Algorithm','interior-point','Hessian',{'lbfgs',10},'ScaleProblem','none',...
'GradObj','on','DerivativeCheck',opt.deriv_check,'FinDiffType','central','LargeScale','off','GradConstr','on','OutputFcn',@OUTPUT);
dt = opt.dt;
opt.Go = true;
opt2 = opt;
[opt.array,fval,opt.exitflag,opt.output] =fmincon(@FUN,opt.array0,[],[],[],[],opt.arraylb,opt.arrayub,@CONSTR,options,opt);
fprintf(opt.output.message);
opt.Go = false;
opt.k = 1;
opt.ksafe = history.safeiter;
opt.Par.Constr.sar_l.Viol = history.Constr.sar_l.Viol;
opt.Par.Constr.sar_g.Viol = history.Constr.sar_g.Viol;
opt.Par.Constr.peak_uv.Violu = history.Constr.peak_uv.Violu;
opt.Par.Constr.peak_uv.Violv = history.Constr.peak_uv.Violv;
opt.Par.Constr.ave_uv.Violuv = history.Constr.ave_uv.Violuv;
opt.Par.Constr.jag_uv.Viol = history.Constr.jag_uv.Viol;
opt.Par.Constr.peak_xyz.Violx = history.Constr.peak_xyz.Violx;
opt.Par.Constr.peak_xyz.Violy = history.Constr.peak_xyz.Violy;
opt.Par.Constr.peak_xyz.Violz = history.Constr.peak_xyz.Violz;
opt.Par.Constr.slew_xyz.Violx = history.Constr.slew_xyz.Violx;
opt.Par.Constr.slew_xyz.Violy = history.Constr.slew_xyz.Violy;
opt.Par.Constr.slew_xyz.Violz = history.Constr.slew_xyz.Violz;
Copes = {opt.Par.Constr.peak_uv.Cope,opt.Par.Constr.peak_uv.Cope,opt.Par.Constr.ave_uv.Cope,opt.Par.Constr.jag_uv.Cope,opt.Par.Constr.peak_xyz.Cope,opt.Par.Constr.peak_xyz.Cope,opt.Par.Constr.peak_xyz.Cope,opt.Par.Constr.slew_xyz.Cope,opt.Par.Constr.slew_xyz.Cope,opt.Par.Constr.slew_xyz.Cope}; %,opt.Par.NRMSE.Cope
Viols = [opt.Par.Constr.peak_uv.Violu,opt.Par.Constr.peak_uv.Violv,opt.Par.Constr.ave_uv.Violuv,opt.Par.Constr.jag_uv.Viol,opt.Par.Constr.peak_xyz.Violx,opt.Par.Constr.peak_xyz.Violy,opt.Par.Constr.peak_xyz.Violz,opt.Par.Constr.slew_xyz.Violx,opt.Par.Constr.slew_xyz.Violy,opt.Par.Constr.slew_xyz.Violz]; % ,~opt.Par.NRMSE.Viol
opt.ksafe = KSAFE(opt.ksafe,Copes,Viols);
opt.StopCriteria = history.StopCriteria;
opt.Fun = history.Fun(1:opt.ksafe);
opt.dFun = history.dFun(1:opt.ksafe);
opt.con.peak_u = zeros(1,opt.ksafe);
opt.con.peak_v = zeros(1,opt.ksafe);
opt.con.ave_uv = zeros(1,opt.ksafe);
opt.con.jag_uv = zeros(1,opt.ksafe);
opt.con.peak_x = zeros(1,opt.ksafe);
opt.con.peak_y = zeros(1,opt.ksafe);
opt.con.peak_z = zeros(1,opt.ksafe);
opt.con.slew_x = zeros(1,opt.ksafe);
opt.con.slew_y = zeros(1,opt.ksafe);
opt.con.slew_z = zeros(1,opt.ksafe);
if isfield(history,'Durations')
opt.Durations = history.Durations;
else
opt.Durations = -1;
end
opt.uo = zeros(opt.pTx,opt.N,opt.ksafe);
opt.vo = zeros(opt.pTx,opt.N,opt.ksafe);
opt.gxo = zeros(1,opt.N,opt.ksafe);
opt.gyo = zeros(1,opt.N,opt.ksafe);
opt.gzo = zeros(1,opt.N,opt.ksafe);
for p = 1:opt.ksafe
opt.k = p;
array_scaled = ARRAY2PHYS(history.array(p,:),opt.arraysc);
[u_,v_,gx_,gy_,gz_,s_] = iARRAY(opt.Par.Controls,array_scaled,opt.N,opt.pTx,opt.NS,opt.u,opt.v,opt.gx,opt.gy,opt.gz,opt.s);
opt.uo(:,:,p) = u_;
opt.vo(:,:,p) = v_;
opt.gxo(1,:,p) = gx_;
opt.gyo(1,:,p) = gy_;
opt.gzo(1,:,p) = gz_;
opt.con.peak_u(p) = history.con(p).peak_u;
opt.con.peak_v(p) = history.con(p).peak_v;
opt.con.ave_uv(p) = history.con(p).ave_uv;
opt.con.jag_uv(p) = history.con(p).jag_uv;
opt.con.peak_x(p) = history.con(p).peak_x;
opt.con.peak_y(p) = history.con(p).peak_y;
opt.con.peak_z(p) = history.con(p).peak_z;
opt.con.slew_x(p) = history.con(p).slew_x;
opt.con.slew_y(p) = history.con(p).slew_y;
opt.con.slew_z(p) = history.con(p).slew_z;
end
% for saving
opt.Path2Package = strrep(mfilename('fullpath'),mfilename,'');
opt = rmfield(opt,{'u','v','g','Md','mon','mon_u','mon_v','mon_x','mon_y','mon_z','mon_s','m_u','m_v','m_x','m_y','m_z','m_s','sr','si','w0','yX','yY','yZ','yS','Gm','Sm','L_t','M_t','s','arraymask','gx','gy','gz','array0','arrayub','arraylb','arraysc','array','ksaveintermediate'});
opt.Durations(opt.ksafe+1:end) = [];
clearvars -global history
opt.Opt_Wall_Clock_Time = toc(tic_Opt_Wall_Clock_Time);
opt.Go = false;
end
%% Optimization and physics functions
function [Fun,arraygrad] = FUN(array,opt)
global M_T Duration
array_scaled = ARRAY2PHYS(array,opt.arraysc);
[u,v,gx,gy,gz,s] = iARRAY(opt.Par.Controls,array_scaled,opt.N,opt.pTx,opt.NS,opt.u,opt.v,opt.gx,opt.gy,opt.gz,opt.s);
[M_t,L_t] = PROPAGATE(opt.N,opt.pTx,opt.dt,u,v,gx,gy,gz,s,opt.yX,opt.yY,opt.yZ,opt.yS,opt.sr,opt.si,opt.w0,opt.M_t,opt.L_t,opt.Par.Turn);
if nargout >= 2
tic_One_Iteration = tic;
if strcmp(opt.Par.Grad,'standard_0')
[Gu,Gv] = GRAD_STANDARD_0(opt.Par.Controls,opt.N,opt.P,opt.pTx,opt.dt,opt.sr,opt.si,M_t,L_t);
elseif strcmp(opt.Par.Grad,'standard_1')
[Gu,Gv] = GRAD_STANDARD_1(opt.Par.Controls,opt.N,opt.P,opt.pTx,opt.dt,opt.sr,opt.si,M_t,L_t);
elseif contains(opt.Par.Grad,'midpoint')
[Gu,Gv,Gx,Gy,Gz,Gs] = GRAD_MIDPOINT(opt.Par.Controls,opt.N,opt.P,opt.pTx,opt.NS,opt.dt,opt.yX,opt.yY,opt.yZ,opt.yS,opt.sr,opt.si,M_t,L_t,opt.Par.Turn);
elseif contains(opt.Par.Grad,'exact')
[Gu,Gv,Gx,Gy,Gz,Gs] = GRAD_EXACT(opt.Par.Controls,opt.par_Ncores,opt.N,opt.P,opt.pTx,opt.NS,opt.dt,opt.yX,opt.yY,opt.yZ,opt.yS,opt.sr,opt.si,opt.w0,M_t,L_t,u,v,gx,gy,gz,s,opt.mon_u,opt.mon_v,opt.mon_x,opt.mon_y,opt.mon_z,opt.mon_s,opt.Par.Turn,opt.gamma);
elseif strcmp(opt.Par.Grad,'standard_0_loop')
Gu = GRAD_STANDARD_0_forloop('u',opt.N,opt.pTx,opt.P,opt.dt,opt.sr,opt.si,opt.mon_u,M_t,L_t);
Gv = GRAD_STANDARD_0_forloop('v',opt.N,opt.pTx,opt.P,opt.dt,opt.sr,opt.si,opt.mon_v,M_t,L_t);
elseif strcmp(opt.Par.Grad,'standard_1_loop')
Gu = GRAD_STANDARD_1_forloop('u',opt.N,opt.pTx,opt.P,opt.dt,opt.sr,opt.si,opt.mon_u,M_t,L_t);
Gv = GRAD_STANDARD_1_forloop('v',opt.N,opt.pTx,opt.P,opt.dt,opt.sr,opt.si,opt.mon_v,M_t,L_t);
end
Duration = toc(tic_One_Iteration);
arraygrad = [];
if contains(opt.Par.Controls,'u')
arraygrad = [arraygrad,REARRANGE('u','array',Gu)];
end
if contains(opt.Par.Controls,'v')
arraygrad = [arraygrad,REARRANGE('v','array',Gv)];
end
if contains(opt.Par.Controls,'x')
arraygrad = [arraygrad,REARRANGE('x','array',Gx)];
end
if contains(opt.Par.Controls,'y')
arraygrad = [arraygrad,REARRANGE('y','array',Gy)];
end
if contains(opt.Par.Controls,'z')
arraygrad = [arraygrad,REARRANGE('z','array',Gz)];
end
arraygrad = arraygrad.*opt.arraymask;
arraygrad = ARRAY2PHYS(arraygrad,opt.arraysc);
if strcmp(opt.Par.StoreGrad,'on')
GradFileID = fopen('GradFile1.txt','a');
for h = 1:length(arraygrad)
fprintf(GradFileID,'%02.6e ',arraygrad(h));
end
fprintf(GradFileID,'\n');
fclose(GradFileID);
end
end
M_T = M_t(:,end);
Fun = -EFFICIENCY(opt.Md,M_T,opt.P);
end
function [M_t,L_t] = PROPAGATE(N,pTx,dt,u,v,gx,gy,gz,s,yX,yY,yZ,yS,sr,si,w0,M_t,L_t,Turn)
R11 = cell(1,N);R12 = cell(1,N);R13 = cell(1,N);
R21 = cell(1,N);R22 = cell(1,N);R23 = cell(1,N);
R31 = cell(1,N);R32 = cell(1,N);R33 = cell(1,N);
for n = 1:N
[R11{n},R12{n},R13{n},R21{n},R22{n},R23{n},R31{n},R32{n},R33{n}] = ROTATOR(u,v,gx,gy,gz,s,w0,yX,yY,yZ,yS,pTx,sr,si,dt,n,Turn);
end
for n = 1:N
M_t(:,n+1) = ROTATE(M_t(:,n),R11{n},R12{n},R13{n},R21{n},R22{n},R23{n},R31{n},R32{n},R33{n},'Forward');
end
for n = N:-1:1
L_t(:,n) = ROTATE(L_t(:,n+1),R11{n},R12{n},R13{n},R21{n},R22{n},R23{n},R31{n},R32{n},R33{n},'Backward');
end
end
function [R11,R12,R13,R21,R22,R23,R31,R32,R33] = ROTATOR(u,v,gx,gy,gz,s,w0,yX,yY,yZ,yS,pTx,sr,si,dt,n,varargin)
P = length(w0);
wx = zeros(size(w0));
wy = zeros(size(w0));
for ns = 1:pTx
wx = wx+(sr(:,ns).*u(ns,n)-si(:,ns).*v(ns,n)).*dt;
wy = wy+(si(:,ns).*u(ns,n)+sr(:,ns).*v(ns,n)).*dt;
end
wz = (yX*gx(n) + yY*gy(n) + yZ*gz(n) + w0).*dt;
if nargin == 16
Turn = -1;
elseif nargin >= 16
Turn = varargin{1};
end
switch Turn
case -1
wx = -wx+eps;
wy = -wy+eps;
wz = wz+eps;
case 1
wx = -wx+eps;
wy = -wy+eps;
wz = -wz+eps;
end
theta = sqrt(wx.^2+wy.^2+wz.^2);
x = wx./theta;
y = wy./theta;
z = wz./theta;
c = cos(theta);
s = sin(theta);
C =1-c;
zs = z.*s;
xs = x.*s;
ys = y.*s;
xyC = x.*y.*C;
yzC = y.*z.*C;
xzC = x.*z.*C;
R11 = x.*x.*C+c;
R12 = xyC-zs;
R13 = xzC+ys;
R21 = xyC+zs;
R22 = y.*y.*C+c;
R23 = yzC-xs;
R31 = xzC-ys;
R32 = yzC+xs;
R33 = z.*z.*C+c;
end
function ML_out = ROTATE(ML_in,R11,R12,R13,R21,R22,R23,R31,R32,R33,Type)
[P,N] = size(R11);
ML = ML_in(:)';
ML = reshape(ML,3,P);
ML = permute(ML,[2 1]);
MLx = ML(:,1);
MLy = ML(:,2);
MLz = ML(:,3);
if strcmp(Type,'Forward')
if N > 1
for n = 1:N
MLx_ = R11(:,n).*MLx + R12(:,n).*MLy + R13(:,n).*MLz;
MLy_ = R21(:,n).*MLx + R22(:,n).*MLy + R23(:,n).*MLz;
MLz_ = R31(:,n).*MLx + R32(:,n).*MLy + R33(:,n).*MLz;
MLx = MLx_;
MLy = MLy_;
MLz = MLz_;
end
else
MLx_ = R11.*MLx + R12.*MLy + R13.*MLz;
MLy_ = R21.*MLx + R22.*MLy + R23.*MLz;
MLz_ = R31.*MLx + R32.*MLy + R33.*MLz;
MLx = MLx_;
MLy = MLy_;
MLz = MLz_;
end
elseif strcmp(Type,'Backward')
if N > 1
for n = N:-1:1
MLx_ = R11(:,n).*MLx + R21(:,n).*MLy + R31(:,n).*MLz;
MLy_ = R12(:,n).*MLx + R22(:,n).*MLy + R32(:,n).*MLz;
MLz_ = R13(:,n).*MLx + R23(:,n).*MLy + R33(:,n).*MLz;
MLx = MLx_;
MLy = MLy_;
MLz = MLz_;
end
else
MLx_ = R11.*MLx + R21.*MLy + R31.*MLz;
MLy_ = R12.*MLx + R22.*MLy + R32.*MLz;
MLz_ = R13.*MLx + R23.*MLy + R33.*MLz;
MLx = MLx_;
MLy = MLy_;
MLz = MLz_;
end
end
ML(:,1) = MLx;
ML(:,2) = MLy;
ML(:,3) = MLz;
ML = permute(ML,[2 1]);
ML = reshape(ML,3*P,1);
ML_out = ML(:);
end
function [Eff] = EFFICIENCY(Md,M_T,P,varargin)
A_x = Md(1:3:end);
A_y = Md(2:3:end);
A_z = Md(3:3:end);
B_x = M_T(1:3:end);
B_y = M_T(2:3:end);
B_z = M_T(3:3:end);
Phi = sum(A_x.*B_x+A_y.*B_y+A_z.*B_z);
Eff = Phi/P;
end
function opt = PROGRESS(opt)
Stop = zeros(14,1);
if strcmp(opt.Par.Constr.peak_uv.Cope,'Stop') && opt.Par.Constr.peak_uv.Violu && opt.k > opt.Par.Constr.peak_uv.FreeIterations
Stop(3) = 1;
fprintf('%s: Will stop because rf u peak is violated\n',mfilename);
end
if strcmp(opt.Par.Constr.peak_uv.Cope,'Stop') && opt.Par.Constr.peak_uv.Violv && opt.k > opt.Par.Constr.peak_uv.FreeIterations
Stop(4) = 1;
fprintf('%s: Will stop because rf v peak is violated\n',mfilename);
end
if strcmp(opt.Par.Constr.ave_uv.Cope,'Stop') && opt.Par.Constr.ave_uv.Viol && opt.k > opt.Par.Constr.ave_uv.FreeIterations
Stop(5) = 1;
fprintf('%s: Will stop because uv average is violated\n',mfilename);
end
if strcmp(opt.Par.Constr.peak_xyz.Cope,'Stop') && opt.Par.Constr.peak_xyz.Violx && opt.k > opt.Par.Constr.peak_xyz.FreeIterations
Stop(6) = 1;
fprintf('%s: Will stop because gradient x peak is violated\n',mfilename);
end
if strcmp(opt.Par.Constr.peak_xyz.Cope,'Stop') && opt.Par.Constr.peak_xyz.Violy && opt.k > opt.Par.Constr.peak_xyz.FreeIterations
Stop(7) = 1;
fprintf('%s: Will stop because gradient y peak is violated\n',mfilename);
end
if strcmp(opt.Par.Constr.peak_xyz.Cope,'Stop') && opt.Par.Constr.peak_xyz.Violz && opt.k > opt.Par.Constr.peak_xyz.FreeIterations
Stop(8) = 1;
fprintf('%s: Will stop because gradient z peak is violated\n',mfilename);
end
if strcmp(opt.Par.Constr.slew_xyz.Cope,'Stop') && opt.Par.Constr.slew_xyz.Violx && opt.k > opt.Par.Constr.slew_xyz.FreeIterations
Stop(9) = 1;
fprintf('%s: Will stop because gradient x slew is violated\n',mfilename);
end
if strcmp(opt.Par.Constr.slew_xyz.Cope,'Stop') && opt.Par.Constr.slew_xyz.Violy && opt.k > opt.Par.Constr.slew_xyz.FreeIterations
Stop(10) = 1;
fprintf('%s: Will stop because gradient y slew is violated\n',mfilename);
end
if strcmp(opt.Par.Constr.slew_xyz.Cope,'Stop') && opt.Par.Constr.slew_xyz.Violz && opt.k > opt.Par.Constr.slew_xyz.FreeIterations
Stop(11) = 1;
fprintf('%s: Will stop because gradient z slew is violated\n',mfilename);
end
% save intermediate
if opt.k-1 > 0
if mod(opt.k-1,opt.ksaveintermediate) == 0
% opt.arrayintermed = Rearrange_controls(opt.u,opt.v);
tempsave = opt.Save; % take backup
opt.Save = struct('Bundle','reduced','Data',tempsave.Data,'Controls',tempsave.Controls,'Figures','none','Scripts','none');
try
b6_Save_Job([],[],opt,[]);
catch me
fprintf('%s: %s',mfilename,me.message);
end
opt.Save = tempsave;
% opt.k = tempk;
end
end
if sum(Stop)>0
opt.Go = false;
opt.StopCriteria = Stop;
opt.ksafe = opt.k;
opt.k = opt.k+1;
return
else
opt.StopCriteria = Stop;
opt.Go = true;
opt.ksafe = opt.k;
opt.k = opt.k+1;
end
end
function [stop] = OUTPUT(array,optimValues,state,opt)
global M_T history Duration opt2
stop = false;
switch state
case 'init'
history.array = zeros(opt2.MaxIter,length(array));
history.array(1,:) = array;
history.fval(1)= optimValues.fval;
history.safeiter = optimValues.iteration+1;
array_scaled = ARRAY2PHYS(array,opt.arraysc);
opt2.arrayiintermed = array;
[opt2.u,opt2.v,opt2.gx,opt2.gy,opt2.gz,opt2.s] = iARRAY(opt.Par.Controls,array_scaled,opt.N,opt.pTx,opt.NS,opt.u,opt.v,opt.gx,opt.gy,opt.gz,opt.s);
opt2.M_T = M_T;
history.M_T{1} = M_T;
[Fun] = EFFICIENCY(opt.Md,M_T,opt.P);
[con,opt2] = CONSTR_dummyfunc(opt2);
history.con(1) = con;
opt2.con = history.con;
history.Fun(1) = Fun;
opt2.dFun = [];
opt2 = PROGRESS(opt2);
PRINT(opt2,'all',Fun,con);
opt2.dFun = 0;
history.dFun(1) = opt2.dFun;
history.Constr.sar_l.Viol = opt2.Par.Constr.sar_l.Viol;
history.Constr.sar_g.Viol = opt2.Par.Constr.sar_g.Viol;
history.Constr.peak_uv.Violu = opt2.Par.Constr.peak_uv.Violu;
history.Constr.peak_uv.Violv = opt2.Par.Constr.peak_uv.Violv;
history.Constr.ave_uv.Violuv = opt2.Par.Constr.ave_uv.Violuv;
history.Constr.jag_uv.Viol = opt2.Par.Constr.jag_uv.Viol;
history.Constr.peak_xyz.Violx = opt2.Par.Constr.peak_xyz.Violx;
history.Constr.peak_xyz.Violy= opt2.Par.Constr.peak_xyz.Violy;
history.Constr.peak_xyz.Violz = opt2.Par.Constr.peak_xyz.Violz;
history.Constr.slew_xyz.Violx = opt2.Par.Constr.slew_xyz.Violx;
history.Constr.slew_xyz.Violy = opt2.Par.Constr.slew_xyz.Violy;
history.Constr.slew_xyz.Violz = opt2.Par.Constr.slew_xyz.Violz;
history.StopCriteria = opt2.StopCriteria;
case 'iter'
if optimValues.iteration > 0
iter = optimValues.iteration+1;
history.array(iter,:) = array;
history.fval(iter)= optimValues.fval;
history.M_T{iter} = M_T;
history.safeiter = iter;
array_scaled = ARRAY2PHYS(array,opt.arraysc);
opt2.arrayiintermed = array;
[opt2.u,opt2.v,opt2.gx,opt2.gy,opt2.gz,opt2.s] = iARRAY(opt.Par.Controls,array_scaled,opt.N,opt.pTx,opt.NS,opt.u,opt.v,opt.gx,opt.gy,opt.gz,opt.s);
opt2.M_T = M_T;
[Fun] = EFFICIENCY(opt.Md,M_T,opt.P);
[con,opt2] = CONSTR_dummyfunc(opt2);
history.Fun(iter) = Fun;
history.con(iter) = con;
opt2.con = history.con;
opt2.Fun = history.Fun;
opt2.dFun = history.Fun(iter)-history.Fun(iter-1);
opt2.arrayintermed = array;
opt2 = PROGRESS(opt2);
PRINT(opt2,'all',Fun,con);
history.dFun(iter) = opt2.dFun;
history.Constr.sar_l.Viol = opt2.Par.Constr.sar_l.Viol;
history.Constr.sar_g.Viol = opt2.Par.Constr.sar_g.Viol;
history.Constr.peak_uv.Violu = opt2.Par.Constr.peak_uv.Violu;
history.Constr.peak_uv.Violv = opt2.Par.Constr.peak_uv.Violv;
history.Constr.ave_uv.Violuv = opt2.Par.Constr.ave_uv.Violuv;
history.Constr.jag_uv.Viol = opt2.Par.Constr.jag_uv.Viol;
history.Constr.peak_xyz.Violx = opt2.Par.Constr.peak_xyz.Violx;
history.Constr.peak_xyz.Violy= opt2.Par.Constr.peak_xyz.Violy;
history.Constr.peak_xyz.Violz = opt2.Par.Constr.peak_xyz.Violz;
history.Constr.slew_xyz.Violx = opt2.Par.Constr.slew_xyz.Violx;
history.Constr.slew_xyz.Violy = opt2.Par.Constr.slew_xyz.Violy;
history.Constr.slew_xyz.Violz = opt2.Par.Constr.slew_xyz.Violz;
history.Durations(iter) = Duration;
history.StopCriteria = opt2.StopCriteria;
if ~opt2.Go
stop = true;
end
end
case 'done'
otherwise
end
end
%% midpoint gradient functions
function [Gu,Gv,Gx,Gy,Gz,Gs] = GRAD_MIDPOINT(Controls,N,P,pTx,NS,dt,yX,yY,yZ,yS,sr,si,M_t,L_t,Turn)
if contains(Controls,'u') || contains(Controls,'v')
LzMx = L_t(3:3:end,:).*M_t(1:3:end,:);
LzMy = L_t(3:3:end,:).*M_t(2:3:end,:);
LxMz = L_t(1:3:end,:).*M_t(3:3:end,:);
LyMz = L_t(2:3:end,:).*M_t(3:3:end,:);
end
switch Turn
case -1
if contains(Controls,'x') || contains(Controls,'y') || contains(Controls,'z')
LxMy = -L_t(1:3:end,:).*M_t(2:3:end,:);
LyMx = -L_t(2:3:end,:).*M_t(1:3:end,:);
end
case 1
if contains(Controls,'x') || contains(Controls,'y') || contains(Controls,'z')
LxMy = L_t(1:3:end,:).*M_t(2:3:end,:);
LyMx = L_t(2:3:end,:).*M_t(1:3:end,:);
end
end
if contains(Controls,'u')
Gu = GRAD_u_MIDPOINT(pTx,dt,N,P,si,sr,LzMx,LzMy,LxMz,LyMz);
else
Gu = [];
end
if contains(Controls,'v')
Gv = GRAD_v_MIDPOINT(pTx,dt,N,P,si,sr,LzMx,LzMy,LxMz,LyMz);
else
Gv = [];
end
if contains(Controls,'x')
Gx = GRAD_xyz_MIDPOINT(dt,P,yX,LxMy,LyMx);
else
Gx = [];
end
if contains(Controls,'y')
Gy = GRAD_xyz_MIDPOINT(dt,P,yY,LxMy,LyMx);
else
Gy = [];
end
if contains(Controls,'z')
Gz = GRAD_xyz_MIDPOINT(dt,P,yZ,LxMy,LyMx);
else
Gz = [];
end
Gs = [];
end
function Ga = GRAD_xyz_MIDPOINT(dt,P,yA,LxMy,LyMx)
temp1a=yA.*LxMy;
temp2a = sum(temp1a);
temp1b=yA.*LyMx;
temp2b = sum(temp1b);
Ga = temp2a-temp2b;
Ga = -(Ga(:,1:end-1)+Ga(:,2:end))./2*dt/P;
end
function Gu = GRAD_u_MIDPOINT(pTx,dt,N,P,si,sr,LzMx,LzMy,LxMz,LyMz)
Gu = zeros(pTx,N+1);
for s = 1:pTx
temp1a=si(:,s).*LzMx;
temp2a = sum(temp1a);
temp1b=sr(:,s).*LzMy;
temp2b = sum(temp1b);
temp1c=si(:,s).*LxMz;
temp2c = sum(temp1c);
temp1d=sr(:,s).*LyMz;
temp2d = sum(temp1d);
Gu(s,:) = temp2a-temp2b-temp2c+temp2d;