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Kindly please help me with the problem as I need to use nlinfit function for fitting unknown parameters but it is showing some error. Although yesterday I was getting some values for parameters to be fitted but now if I am running it is having some issue for the function output to be used in fitted with NaN answer for last iteration only. X data is a concatenated matrix of three columns as independent variable and yk is dependent variable, taua is a matrix of initial guesses of number of parameters to be fitted.
function [yk]=activity_coefficientE(taua,x)
T=523;
alpha12=0.3; alpha13=0.3; alpha21=0.3; alpha23=0.3; alpha31=0.3; alpha32=0.3;
alpha18=0.2; alpha81=0.2; alpha28=0.2; alpha82=0.2; alpha38=0.2; alpha83=0.3;
alpha19=0.2; alpha91=0.2; alpha29=0.2; alpha92=0.2; alpha39=0.2; alpha93=0.2;
alpha110=0.2;alpha101=0.2;alpha210=0.2;alpha102=0.2;alpha310=0.2;alpha103=0.2;
alpha113=0.2;alpha131=0.2;alpha213=0.2;alpha132=0.2;alpha313=0.2;alpha133=0.2;
alpha114=0.2;alpha141=0.2;alpha214=0.2;alpha142=0.2;alpha314=0.2;alpha143=0.2;
alpha115=0.2;alpha151=0.2;alpha215=0.2;alpha152=0.2;alpha315=0.2;alpha153=0.2;
alpha117=0.2;alpha171=0.2;alpha217=0.2;alpha172=0.2;alpha317=0.2;alpha173=0.2;
alpha118=0.2;alpha181=0.2;alpha218=0.2;alpha182=0.2;alpha318=0.2;alpha183=0.2;
alpha810=0.2;alpha915=0.2;alpha1314=0.2;alpha108=0.2;alpha159=0.2;alpha1413=0.2;
alpha1718=0.2;alpha1817=0.2;
tau12=0; tau13=0; tau21=0; tau23=0; tau31=0; tau32=0;
%taua=randi([-5,5],1,112)
tau18=taua(1)+taua(57)/T;
tau81=taua(2)+taua(58)/T;
tau28=taua(3)+taua(59)/T;
tau82=taua(4)+taua(60)/T;
tau38=taua(5)+taua(61)/T;
tau83=taua(6)+taua(62)/T;
tau19=taua(7)+taua(63)/T;
tau91=taua(8)+taua(64)/T;
tau29=taua(9)+taua(65)/T;
tau92=taua(10)+taua(66)/T;
tau39=taua(11)+taua(67)/T;
tau93=taua(12)+taua(68)/T;
tau110=taua(13)+taua(69)/T;
tau101=taua(14)+taua(70)/T;
tau210=taua(15)+taua(71)/T;
tau102=taua(16)+taua(72)/T;
tau310=taua(17)+taua(73)/T;
tau103=taua(18)+taua(74)/T;
tau113=taua(19)+taua(75)/T;
tau131=taua(20)+taua(76)/T;
tau213=taua(21)+taua(77)/T;
tau132=taua(22)+taua(78)/T;
tau313=taua(23)+taua(79)/T;
tau133=taua(24)+taua(80)/T;
tau114=taua(25)+taua(81)/T;
tau141=taua(26)+taua(82)/T;
tau214=taua(27)+taua(83)/T;
tau142=taua(28)+taua(84)/T;
tau314=taua(29)+taua(85)/T;
tau143=taua(30)+taua(86)/T;
tau115=taua(31)+taua(87)/T;
tau151=taua(32)+taua(88)/T;
tau215=taua(33)+taua(89)/T;
tau152=taua(34)+taua(90)/T;
tau315=taua(35)+taua(91)/T;
tau153=taua(36)+taua(92)/T;
tau117=taua(37)+taua(93)/T;
tau171=taua(38)+taua(94)/T;
tau217=taua(39)+taua(95)/T;
tau172=taua(40)+taua(96)/T;
tau317=taua(41)+taua(97)/T;
tau173=taua(42)+taua(98)/T;
tau118=taua(43)+taua(99)/T;
tau181=taua(44)+taua(100)/T;
tau218=taua(45)+taua(101)/T;
tau182=taua(46)+taua(102)/T;
tau318=taua(47)+taua(103)/T;
tau183=taua(48)+taua(104)/T;
tau810=taua(49)+taua(105)/T;
tau108=taua(50)+taua(106)/T;
tau915=taua(51)+taua(107)/T;
tau159=taua(52)+taua(108)/T;
tau1314=taua(53)+taua(109)/T;
tau1413=taua(54)+taua(110)/T;
tau1718=taua(55)+taua(111)/T;
tau1817=taua(56)+taua(112)/T;
G12=exp(-(tau12*alpha12));
G21=exp(-(tau21*alpha21));
G13=exp(-(tau13*alpha13));
G31=exp(-(tau31*alpha31));
G23=exp(-(tau23*alpha23));
G32=exp(-(tau32*alpha32));
G18=exp(-(tau18*alpha18));
G81=exp(-(tau81*alpha81));
G28=exp(-(tau28*alpha28));
G82=exp(-(tau82*alpha82));
G38=exp(-(tau38*alpha83));
G83=exp(-(tau83*alpha83));
G19=exp(-(tau19*alpha19));
G91=exp(-(tau91*alpha91));
G29=exp(-(tau29*alpha29));
G92=exp(-(tau92*alpha92));
G39=exp(-(tau39*alpha39));
G93=exp(-(tau93*alpha93));
G110=exp(-(tau110*alpha110));
G101=exp(-(tau101*alpha101));
G210=exp(-(tau210*alpha210));
G102=exp(-(tau102*alpha102));
G310=exp(-(tau310*alpha310));
G103=exp(-(tau103*alpha103));
G113=exp(-(tau113*alpha113));
G131=exp(-(tau131*alpha131));
G213=exp(-(tau213*alpha213));
G132=exp(-(tau132*alpha132));
G313=exp(-(tau313*alpha313));
G133=exp(-(tau133*alpha133));
G114=exp(-(tau114*alpha114));
G141=exp(-(tau141*alpha141));
G214=exp(-(tau214*alpha214));
G142=exp(-(tau142*alpha142));
G314=exp(-(tau314*alpha314));
G143=exp(-(tau143*alpha143));
G115=exp(-(tau115*alpha115));
G151=exp(-(tau151*alpha151));
G215=exp(-(tau215*alpha215));
G152=exp(-(tau152*alpha152));
G315=exp(-(tau315*alpha315));
G153=exp(-(tau153*alpha153));
G117=exp(-(tau117*alpha117));
G171=exp(-(tau171*alpha171));
G217=exp(-(tau217*alpha217));
G172=exp(-(tau172*alpha172));
G317=exp(-(tau317*alpha317));
G173=exp(-(tau173*alpha173));
G118=exp(-(tau118*alpha118));
G181=exp(-(tau181*alpha181));
G218=exp(-(tau218*alpha218));
G182=exp(-(tau182*alpha182));
G318=exp(-(tau318*alpha318));
G183=exp(-(tau183*alpha183));
G810=exp(-(tau810*alpha810));
G108=exp(-(tau108*alpha108));
G915=exp(-(tau915*alpha915));
G159=exp(-(tau159*alpha159));
G1314=exp(-(tau1314*alpha1314));
G1413=exp(-(tau1413*alpha1413));
G1718=exp(-(tau1718*alpha1718));
G1817=exp(-(tau1817*alpha1817));
%calculating mole fractions of ionic species
x1=x(:,1);
x2=x(:,2);
x3=x(:,3);
%x1=[0.1577 0.1492 0.1462 0.1366 0.1299 0.1180 0.0863 0.0761 0.0550 ];
%x2=[0.8278 0.7945 0.7678 0.7450 0.6979 0.6309 0.4611 0.4114 0.2952 ];
%x3=[0.0145 0.0563 0.0860 0.1184 0.1722 0.2511 0.4526 0.5125 0.6498 ];
A=[0.0674243 0.0773881 0.0843400 0.0865343 0.0899223 0.0882858 0.0715087 0.0643867 0.0483658];
B=[0.0141081 0.0479814 0.0643151 0.0737477 0.0820756 0.0838701 0.0701576 0.0634457 0.0479639];
C=[0.0565665 0.0450072 0.0387724 0.0313828 0.02506094 0.0186280 0.0092734 0.0073438 0.0041595 ];
D=[0.0336447 0.0267694 0.0230611 0.0186659 0.0149058 0.0110795 0.0055157 0.0043679 0.0024739 ];
E=[0.0008148 0.0008756 0.00087131 0.0008794 0.0008711 0.0008441 0.0007384 0.0006997 0.0005980 ];
N=length(A);
x1n=zeros(N,1);x2n=zeros(N,1);x3n=zeros(N,1);
X1=zeros(N,1);X2=zeros(N,1);X3=zeros(N,1);X4=zeros(N,1);X5=zeros(N,1);X6=zeros(N,1);X7=zeros(N,1);
X12=zeros(N,1);X16=zeros(N,1);
for i=1:N
x1n(i)=(x1(i)-A(i)-D(i)-2*E(i)-C(i)+3*B(i))
x2n(i)=(x2(i)-A(i)-C(i)-D(i))
x3n(i)=(x3(i)-B(i))
X1(i)=(x1n(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
X2(i)=(x2n(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
X3(i)=(x3n(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
X4(i)=(A(i)+D(i)+E(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
X5(i)=(C(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
X6(i)=(A(i)-B(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
X7(i)=(B(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
X12(i)=(E(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
X16(i)=(C(i)+D(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)))
end
yc4=X4./(X4+X5);
yc5=X5./(X4+X5);
yc6=X6./(X6+X7+X12+X16);
yc7=X7./(X6+X7+X12+X16);
yc12=X12./(X6+X7+X12+X16);
yc16=X16./(X6+X7+X12+X16);
alpha14=yc6.*alpha18+yc7.*alpha19+yc12.*alpha113+yc16.*alpha117;
%alpha41=alpha14;
alpha24=yc6.*alpha28+yc7.*alpha29+yc12.*alpha213+yc16.*alpha217;
%alpha42=alpha24;
alpha34=yc6.*alpha38+yc7.*alpha39+yc12.*alpha313+yc16.*alpha317;
%alpha43=alpha34;
alpha15=yc6.*alpha110+yc7.*alpha115+yc12.*alpha114+yc16.*alpha118;
%alpha51=alpha15;
alpha25=yc6.*alpha210+yc7.*alpha215+yc12.*alpha214+yc16.*alpha218;
%alpha52=alpha25;
alpha35=yc6.*alpha310+yc7.*alpha315+yc12.*alpha314+yc16.*alpha318;
%alpha53=alpha35;
alpha16=yc4.*alpha81+yc5.*alpha101;
%alpha61=alpha16;
alpha26=yc4.*alpha82+yc5.*alpha102;
%alpha62=alpha26;
alpha36=yc4.*alpha83+yc5.*alpha103;
%alpha63=alpha36;
alpha17=yc4.*alpha91+yc5.*alpha151;
%alpha71=alpha17;
alpha27=yc4.*alpha92+yc5.*alpha152;
%alpha72=alpha27;
alpha37=yc4.*alpha93+yc5.*alpha153;
%alpha73=alpha37;
alpha112=yc4.*alpha131+yc5.*alpha141;
%alpha121=alpha112;
alpha212=yc4.*alpha132+yc5.*alpha142;
%alpha122=alpha212;
alpha312=yc4.*alpha133+yc5.*alpha143;
%alpha123=alpha312;
alpha116=yc4.*alpha171+yc5.*alpha181;
%alpha161=alpha116;
alpha216=yc4.*alpha172+yc5.*alpha182;
%alpha162=alpha216;
alpha316=yc4.*alpha173+yc5.*alpha183;
%alpha163=alpha316;
alpha46=yc5.*alpha810;
%alpha64=alpha46;
alpha47=yc5.*alpha915;
%alpha74=alpha47;
alpha412=yc5.*alpha1314;
%alpha124=alpha412;
alpha416=yc5.*alpha1718;
%alpha164=alpha416;
alpha56=yc4.*alpha108;
%alpha65=alpha56;
alpha57=yc4.*alpha159;
%alpha75=alpha57;
alpha512=yc4.*alpha1413;
%alpha125=alpha512;
alpha516=yc4.*alpha1817;
%alpha165=alpha516;
G14=yc6.*G18+yc7.*G19+yc12.*G113+yc16.*G117;
%G41=G14;
G24=yc6.*G28+yc7.*G29+yc12.*G213+yc16.*G217;
%G42=G24;
G34=yc6.*G38+yc7.*G39+yc12.*G313+yc16.*G317;
%G43=G34;
G15=yc6.*G110+yc7.*G115+yc12.*G114+yc16.*G118;
%G51=G15;
G25=yc6.*G210+yc7.*G215+yc12.*G214+yc16.*G218;
%G52=G25;
G35=yc6.*G310+yc7.*G315+yc12.*G314+yc16.*G318;
%G53=G35;
G16=yc4.*G81+yc5.*G101;
%G61=G16;
G26=yc4.*G82+yc5.*G102;
%G62=G26;
G36=yc4.*G83+yc5.*G103;
%G63=G36;
G17=yc4.*G91+yc5.*G151;
%G71=G17;
G27=yc4.*G92+yc5.*G152;
%G72=G27;
G37=yc4.*G93+yc5.*G153;
%G73=G37;
G112=yc4.*G131+yc5.*G141;
%G121=G112;
G212=yc4.*G132+yc5.*G142;
%G122=G212;
G312=yc4.*G133+yc5.*G143;
%G123=G312;
G116=yc4.*G171+yc5.*G181;
%G161=G116;
G216=yc4.*G172+yc5.*G182;
%G162=G216;
G316=yc4.*G173+yc5.*G183;
%G163=G316;
G46=yc5.*G810;
%G64=G46;
G47=yc5.*G915;
%G74=G47;
G412=yc5.*G1314;
%G124=G412;
G416=yc5.*G1718;
%G164=G416;
G56=yc4.*G108;
%G65=G56;
G57=yc4.*G159;
%G75=G57;
G512=yc4.*G1413;
%G125=G512;
G516=yc4.*G1817;
%G165=G516;
tau14=-log(G14)./alpha14;
%tau41=tau14;
tau24=-log(G24)./alpha24;
%tau42=tau24;
tau34=-log(G34)./alpha34;
%tau43=tau34;
tau15=-log(G15)./alpha15;
%tau51=tau15;
tau25=-log(G25)./alpha25;
%tau52=tau25;
tau35=-log(G35)./alpha35;
%tau53=tau35;
tau16=-log(G16)./alpha16;
%tau61=tau16;
tau26=-log(G26)./alpha26;
%tau62=tau26;
tau36=-log(G36)./alpha36;
%tau63=tau36;
tau17=-log(G17)./alpha17;
%tau71=tau17;
tau27=-log(G27)./alpha27;
%tau72=tau27;
tau37=-log(G37)./alpha37;
%tau73=tau37;
tau112=-log(G112)./alpha112;
%tau121=tau112;
tau212=-log(G212)./alpha212;
%tau122=tau212;
tau312=-log(G312)./alpha312;
%tau123=tau312;
tau116=-log(G116)./alpha116;
%tau161=tau116;
tau216=-log(G216)./alpha216;
%tau162=tau216;
tau316=-log(G316)./alpha316;
%tau163=tau316;
tau46=-log(G46)./alpha46;
%tau64=tau46;
tau47=-log(G47)./alpha47;
%tau74=tau47;
tau412=-log(G412)./alpha412;
%tau124=tau412;
tau416=-log(G416)./alpha416;
%tau164=tau416;
tau56=-log(G56)./alpha56;
%tau65=tau56;
tau57=-log(G57)./alpha57;
%tau75=tau57;
tau512=-log(G512)./alpha512;
%tau125=tau512;
tau516=-log(G516)./alpha516;
%tau165=tau516;
ln_y1_1=G12.*X2.*tau12+ G31.*X3.*tau13+ G14.*X4.*tau14+G15.*X5.*tau15+G16.*X6.*tau16+G17.*X7.*tau17+G112.*X12.*tau112+G116.*X16.*tau116;
ln_y1_2=G12.*X2+ G13.*X3+ G14.*X4+G15.*X5+G16.*X6+G17.*X7+G112.*X12+G116.*X16;
ln_y2_1=G21.*X1.*tau12+ G32.*X3.*tau32+ G24.*X4.*tau24+G25.*X5.*tau25+G26.*X6.*tau26+G27.*X7.*tau27+G212.*X12.*tau212+G216.*X16.*tau216;
ln_y2_2=G12.*X1+ G23.*X3+G24.*X4+G25.*X5+G26.*X6+G27.*X7+G212.*X12+G216.*X16;
ln_y3_1=G13.*X1.*tau13+ G23.*X3.*tau23+ G34.*X4.*tau34+G35.*X5.*tau35+G36.*X6.*tau36+G37.*X7.*tau37+G312.*X12.*tau312+G316.*X16.*tau316;
ln_y3_2=G13.*X1+ G23.*X3+ G34.*X4+G35.*X5+G36.*X6+G37.*X7+G312.*X12+G316.*X16;
ln_y4_1=G14.*X1.*tau14+G24.*X2.*tau24+G34.*X3.*tau34+G46.*X6.*tau46+G47.*X7.*tau47+G412.*X12.*tau412+G416.*X16.*tau416;
ln_y4_2=G14.*X1+G24.*X2+G34.*X3+G46.*X6+G47.*X7+G412.*X12+G416.*X16;
ln_y5_1=G15.*X1.*tau15+G25.*X2.*tau25+G35.*X3.*tau35+G56.*X6.*tau56+G57.*X7.*tau57+G512.*X12.*tau512+G516.*X16.*tau516;
ln_y5_2=G15.*X1+G25.*X2+G35.*X3+G56.*X6+G57.*X7+G512.*X12+G516.*X16;
ln_y6_1=G16.*X1.*tau16+G26.*X2.*tau26+G36.*X3.*tau36+G46.*X4.*tau46+G56.*X5.*tau56;
ln_y6_2=G16.*X1+G26.*X2+G36.*X3+G46.*X4+G56.*X5;
ln_y7_1=G17.*X1.*tau17+G27.*X2.*tau27+G37.*X3.*tau37+G47.*X4.*tau47+G57.*X5.*tau57;
ln_y7_2=G17.*X1+G27.*X2+G37.*X3+G47.*X4+G57.*X5;
ln_y12_1=G112.*X1.*tau112+G212.*X2.*tau212+G312.*X3.*tau312+G412.*X4.*tau412+G512.*X5.*tau512;
ln_y12_2=G112.*X1+G212.*X2+G312.*X3+G412.*X4+G512.*X5;
ln_y16_1=G116.*X1.*tau116+G216.*X2.*tau216+G316.*X3.*tau316+G416.*X4.*tau416+G516.*X5.*tau516;
ln_y16_2=G116.*X1+G216.*X2+G316.*X3+G416.*X4+G516.*X5;
ln_y1_3=(((X2.*G12)./ln_y2_2).*(tau12-(ln_y2_1)./(ln_y2_2)))+(((X3.*G13)./ln_y3_2).*(tau13-(ln_y3_1)./(ln_y3_2)));
ln_y1_4=(((X6.*G16)./ln_y6_2).*(tau16- (ln_y6_1./ln_y6_2))) + (((X7.*G17)./ln_y7_2).*(tau17- (ln_y7_1./ln_y7_2)))+(((X12.*G12)./ln_y12_2).*(tau112- (ln_y12_1./ln_y12_2)))+(((X16.*G16)./ln_y16_2).*(tau116- (ln_y16_1./ln_y16_2)));
ln_y1_5=(((X4.*G14)./ln_y4_2).*(tau14- (ln_y4_1./ln_y4_2))) + (((X5.*G15)./ln_y5_2).*(tau15- (ln_y5_1./ln_y5_2)));
yk=exp((ln_y1_1./ln_y1_2) + ln_y1_3 + ln_y1_4+ ln_y1_5) % activity coefficient for H2O
end
........................................
Another function where above function to be called.....
% calling the function act_coeff to estimate the binary interaction parameters
for i=1:112
filename = 'EagelsDATA.xlsx'; %reading VLE data from excel file
Data = xlsread(filename);
x(:,1) = Data([10:15 17:19],16);
x(:,2) = Data([10:15 17:19],1);
x(:,3)= Data([10:15 17:19],2);
taua=(randi([-5,5],1,112));
yk=[0.0606 (values calculated from above function and will be used for fitting)
0.4327
0.6545
0.9417
1.2570
1.6881
1.9108
1.7777
1.3821]
% taua =[ -2 3 4 -3 -4 1 4 -2 4 -4 -1 4 5 -3 3 2 -5 3 -4
% 1 4 1 5 -1 -1 -3 2 -3 4 3 4 2 5 4 -2 4 3 -1
% 1 0 -5 -5 -5 -3 4 2 1 4 0 2 -3 -4 5 0 -3 2 5
% 1 0 5 1 -3 5 4 1 5 2 3 2 0 -5 -4 -2 1 -2 5
%-5 5 -2 -2 4 1 -1 3 -1 1 5 -1 0 -1 4 5 5 1 4
% 1 0 4 -4 4 0 -1 -2 -5 -3 -4 -5
% -5 0 -2 0 -5] (random values for which yk was calculted from the command
taua= randi([-5,5],1,112))
try % try-catch used to continue the loop without stopping on encountering an error
[taua1]= nlinfit(x,yk,#activity_coefficientE,taua)
catch exception
continue
end
end
I am not able to attach excel sheet here so data from excel sheet is as:
x =[0.1577 0.1492 0.1462 0.1366 0.1299 0.1180 0.0863 0.0761 0.0550; column 1
0.8278 0.7945 0.7678 0.7450 0.6979 0.6309 0.4611 0.4114 0.2952 ; column 2
0.0145 0.0563 0.0860 0.1184 0.1722 0.2511 0.4526 0.5125 0.6498 ]; column 3
I found 3 major problems with what you did.
Problem #1 - errors
The reason you get the error is because your function "activity_coefficientE" can sometimes return NaN or inf values. My suggestion is to look for these values and set the value of "yk" to a large value so that the optimizer in "nlinfit" will stay away from coefficients that produce infinite or NaN values. This is the code at the bottom of the function so that you avoid crashes:
if any(~isfinite(yk))
yk = 10 * ones(size(yk));
end
Problem #2 - random initial guesses
The trouble with using random numbers for your initial conditions is that every time you run it you get a different answer, so sometimes it works and sometimes it doesn't. If you set the random number generator seed, you can get the same random numbers each time you run the script. If you change you seed, you can get a different set of random numbers. I shortened your main script to this, where I try 100 different random seeds (and store the results of each attempt) to see what answers result:
for i=1:100
rng(i)
taua = randi([-5,5],1,112);
taua1(i, :) = nlinfit(x,yk,#activity_coefficientE,taua);
end
Each row of "taua1" is a set of 111 coefficients.
Problem #3 - Trying to fit 9 points with 112 coefficients
Every time nlinfit is called, you get this warning:
Warning: Rank deficient
because you have more coefficients (112) that you are asking nlinfit to find than data points you are fitting (9). It's like trying to find the 2nd order equation that best fits 2 points, there are an infinite number of solutions. When curve fitting you should have more data points than coefficients to make sure you're not fitting noise. You need more data points in "yk" and "x" and/or fewer coefficients to fit. I've done a lot of curve fitting and I've never seen an equation with 112 coefficients, so I am thinking that you are not solving the problem correctly. Perhaps the 112 coefficients aren't really independent or there are 112 data points and 9 coefficients that you want to find.
For completeness, here is my edited version of the activity_coefficientE.m function that I created to work on this solution. In general, I never see Matlab code with this many variables with similar names. Much of this code could be greatly simplified by using vector operations. Most of my changes involve formatting, adding semicolons, and the checks for non-finite values at the end.
function yk=activity_coefficientE(taua,x)
T=523;
alpha12=0.3; alpha13=0.3; alpha21=0.3; alpha23=0.3; alpha31=0.3; alpha32=0.3;
alpha18=0.2; alpha81=0.2; alpha28=0.2; alpha82=0.2; alpha38=0.2; alpha83=0.3;
alpha19=0.2; alpha91=0.2; alpha29=0.2; alpha92=0.2; alpha39=0.2; alpha93=0.2;
alpha110=0.2;alpha101=0.2;alpha210=0.2;alpha102=0.2;alpha310=0.2;alpha103=0.2;
alpha113=0.2;alpha131=0.2;alpha213=0.2;alpha132=0.2;alpha313=0.2;alpha133=0.2;
alpha114=0.2;alpha141=0.2;alpha214=0.2;alpha142=0.2;alpha314=0.2;alpha143=0.2;
alpha115=0.2;alpha151=0.2;alpha215=0.2;alpha152=0.2;alpha315=0.2;alpha153=0.2;
alpha117=0.2;alpha171=0.2;alpha217=0.2;alpha172=0.2;alpha317=0.2;alpha173=0.2;
alpha118=0.2;alpha181=0.2;alpha218=0.2;alpha182=0.2;alpha318=0.2;alpha183=0.2;
alpha810=0.2;alpha915=0.2;alpha1314=0.2;alpha108=0.2;alpha159=0.2;alpha1413=0.2;
alpha1718=0.2;alpha1817=0.2;
tau12=0; tau13=0; tau21=0; tau23=0; tau31=0; tau32=0;
tau18=taua(1)+taua(57)/T;
tau81=taua(2)+taua(58)/T;
tau28=taua(3)+taua(59)/T;
tau82=taua(4)+taua(60)/T;
tau38=taua(5)+taua(61)/T;
tau83=taua(6)+taua(62)/T;
tau19=taua(7)+taua(63)/T;
tau91=taua(8)+taua(64)/T;
tau29=taua(9)+taua(65)/T;
tau92=taua(10)+taua(66)/T;
tau39=taua(11)+taua(67)/T;
tau93=taua(12)+taua(68)/T;
tau110=taua(13)+taua(69)/T;
tau101=taua(14)+taua(70)/T;
tau210=taua(15)+taua(71)/T;
tau102=taua(16)+taua(72)/T;
tau310=taua(17)+taua(73)/T;
tau103=taua(18)+taua(74)/T;
tau113=taua(19)+taua(75)/T;
tau131=taua(20)+taua(76)/T;
tau213=taua(21)+taua(77)/T;
tau132=taua(22)+taua(78)/T;
tau313=taua(23)+taua(79)/T;
tau133=taua(24)+taua(80)/T;
tau114=taua(25)+taua(81)/T;
tau141=taua(26)+taua(82)/T;
tau214=taua(27)+taua(83)/T;
tau142=taua(28)+taua(84)/T;
tau314=taua(29)+taua(85)/T;
tau143=taua(30)+taua(86)/T;
tau115=taua(31)+taua(87)/T;
tau151=taua(32)+taua(88)/T;
tau215=taua(33)+taua(89)/T;
tau152=taua(34)+taua(90)/T;
tau315=taua(35)+taua(91)/T;
tau153=taua(36)+taua(92)/T;
tau117=taua(37)+taua(93)/T;
tau171=taua(38)+taua(94)/T;
tau217=taua(39)+taua(95)/T;
tau172=taua(40)+taua(96)/T;
tau317=taua(41)+taua(97)/T;
tau173=taua(42)+taua(98)/T;
tau118=taua(43)+taua(99)/T;
tau181=taua(44)+taua(100)/T;
tau218=taua(45)+taua(101)/T;
tau182=taua(46)+taua(102)/T;
tau318=taua(47)+taua(103)/T;
tau183=taua(48)+taua(104)/T;
tau810=taua(49)+taua(105)/T;
tau108=taua(50)+taua(106)/T;
tau915=taua(51)+taua(107)/T;
tau159=taua(52)+taua(108)/T;
tau1314=taua(53)+taua(109)/T;
tau1413=taua(54)+taua(110)/T;
tau1718=taua(55)+taua(111)/T;
tau1817=taua(56)+taua(112)/T;
G12=exp(-(tau12*alpha12));
G21=exp(-(tau21*alpha21));
G13=exp(-(tau13*alpha13));
G31=exp(-(tau31*alpha31));
G23=exp(-(tau23*alpha23));
G32=exp(-(tau32*alpha32));
G18=exp(-(tau18*alpha18));
G81=exp(-(tau81*alpha81));
G28=exp(-(tau28*alpha28));
G82=exp(-(tau82*alpha82));
G38=exp(-(tau38*alpha83));
G83=exp(-(tau83*alpha83));
G19=exp(-(tau19*alpha19));
G91=exp(-(tau91*alpha91));
G29=exp(-(tau29*alpha29));
G92=exp(-(tau92*alpha92));
G39=exp(-(tau39*alpha39));
G93=exp(-(tau93*alpha93));
G110=exp(-(tau110*alpha110));
G101=exp(-(tau101*alpha101));
G210=exp(-(tau210*alpha210));
G102=exp(-(tau102*alpha102));
G310=exp(-(tau310*alpha310));
G103=exp(-(tau103*alpha103));
G113=exp(-(tau113*alpha113));
G131=exp(-(tau131*alpha131));
G213=exp(-(tau213*alpha213));
G132=exp(-(tau132*alpha132));
G313=exp(-(tau313*alpha313));
G133=exp(-(tau133*alpha133));
G114=exp(-(tau114*alpha114));
G141=exp(-(tau141*alpha141));
G214=exp(-(tau214*alpha214));
G142=exp(-(tau142*alpha142));
G314=exp(-(tau314*alpha314));
G143=exp(-(tau143*alpha143));
G115=exp(-(tau115*alpha115));
G151=exp(-(tau151*alpha151));
G215=exp(-(tau215*alpha215));
G152=exp(-(tau152*alpha152));
G315=exp(-(tau315*alpha315));
G153=exp(-(tau153*alpha153));
G117=exp(-(tau117*alpha117));
G171=exp(-(tau171*alpha171));
G217=exp(-(tau217*alpha217));
G172=exp(-(tau172*alpha172));
G317=exp(-(tau317*alpha317));
G173=exp(-(tau173*alpha173));
G118=exp(-(tau118*alpha118));
G181=exp(-(tau181*alpha181));
G218=exp(-(tau218*alpha218));
G182=exp(-(tau182*alpha182));
G318=exp(-(tau318*alpha318));
G183=exp(-(tau183*alpha183));
G810=exp(-(tau810*alpha810));
G108=exp(-(tau108*alpha108));
G915=exp(-(tau915*alpha915));
G159=exp(-(tau159*alpha159));
G1314=exp(-(tau1314*alpha1314));
G1413=exp(-(tau1413*alpha1413));
G1718=exp(-(tau1718*alpha1718));
G1817=exp(-(tau1817*alpha1817));
%calculating mole fractions of ionic species
x1=x(:,1);
x2=x(:,2);
x3=x(:,3);
A=[0.0674243 0.0773881 0.0843400 0.0865343 0.0899223 0.0882858 0.0715087 0.0643867 0.0483658];
B=[0.0141081 0.0479814 0.0643151 0.0737477 0.0820756 0.0838701 0.0701576 0.0634457 0.0479639];
C=[0.0565665 0.0450072 0.0387724 0.0313828 0.02506094 0.0186280 0.0092734 0.0073438 0.0041595 ];
D=[0.0336447 0.0267694 0.0230611 0.0186659 0.0149058 0.0110795 0.0055157 0.0043679 0.0024739 ];
E=[0.0008148 0.0008756 0.00087131 0.0008794 0.0008711 0.0008441 0.0007384 0.0006997 0.0005980 ];
N=length(A);
x1n=zeros(N,1);x2n=zeros(N,1);x3n=zeros(N,1);
X1=zeros(N,1);X2=zeros(N,1);X3=zeros(N,1);X4=zeros(N,1);X5=zeros(N,1);X6=zeros(N,1);X7=zeros(N,1);
X12=zeros(N,1);X16=zeros(N,1);
for i=1:N
x1n(i)=(x1(i)-A(i)-D(i)-2*E(i)-C(i)+3*B(i));
x2n(i)=(x2(i)-A(i)-C(i)-D(i));
x3n(i)=(x3(i)-B(i));
X1(i)=(x1n(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
X2(i)=(x2n(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
X3(i)=(x3n(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
X4(i)=(A(i)+D(i)+E(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
X5(i)=(C(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
X6(i)=(A(i)-B(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
X7(i)=(B(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
X12(i)=(E(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
X16(i)=(C(i)+D(i)/(x1n(i)+x2n(i)+x3n(i)+2*A(i)+4*B(i)+2*C(i)+2*D(i)+2*E(i)));
end
yc4=X4./(X4+X5);
yc5=X5./(X4+X5);
yc6=X6./(X6+X7+X12+X16);
yc7=X7./(X6+X7+X12+X16);
yc12=X12./(X6+X7+X12+X16);
yc16=X16./(X6+X7+X12+X16);
alpha14=yc6.*alpha18+yc7.*alpha19+yc12.*alpha113+yc16.*alpha117;
alpha24=yc6.*alpha28+yc7.*alpha29+yc12.*alpha213+yc16.*alpha217;
alpha34=yc6.*alpha38+yc7.*alpha39+yc12.*alpha313+yc16.*alpha317;
alpha15=yc6.*alpha110+yc7.*alpha115+yc12.*alpha114+yc16.*alpha118;
alpha25=yc6.*alpha210+yc7.*alpha215+yc12.*alpha214+yc16.*alpha218;
alpha35=yc6.*alpha310+yc7.*alpha315+yc12.*alpha314+yc16.*alpha318;
alpha16=yc4.*alpha81+yc5.*alpha101;
alpha26=yc4.*alpha82+yc5.*alpha102;
alpha36=yc4.*alpha83+yc5.*alpha103;
alpha17=yc4.*alpha91+yc5.*alpha151;
alpha27=yc4.*alpha92+yc5.*alpha152;
alpha37=yc4.*alpha93+yc5.*alpha153;
alpha112=yc4.*alpha131+yc5.*alpha141;
alpha212=yc4.*alpha132+yc5.*alpha142;
alpha312=yc4.*alpha133+yc5.*alpha143;
alpha116=yc4.*alpha171+yc5.*alpha181;
alpha216=yc4.*alpha172+yc5.*alpha182;
alpha316=yc4.*alpha173+yc5.*alpha183;
alpha46=yc5.*alpha810;
alpha47=yc5.*alpha915;
alpha412=yc5.*alpha1314;
alpha416=yc5.*alpha1718;
alpha56=yc4.*alpha108;
alpha57=yc4.*alpha159;
alpha512=yc4.*alpha1413;
alpha516=yc4.*alpha1817;
G14=yc6.*G18+yc7.*G19+yc12.*G113+yc16.*G117;
G24=yc6.*G28+yc7.*G29+yc12.*G213+yc16.*G217;
G34=yc6.*G38+yc7.*G39+yc12.*G313+yc16.*G317;
G15=yc6.*G110+yc7.*G115+yc12.*G114+yc16.*G118;
G25=yc6.*G210+yc7.*G215+yc12.*G214+yc16.*G218;
G35=yc6.*G310+yc7.*G315+yc12.*G314+yc16.*G318;
G16=yc4.*G81+yc5.*G101;
G26=yc4.*G82+yc5.*G102;
G36=yc4.*G83+yc5.*G103;
G17=yc4.*G91+yc5.*G151;
G27=yc4.*G92+yc5.*G152;
G37=yc4.*G93+yc5.*G153;
G112=yc4.*G131+yc5.*G141;
G212=yc4.*G132+yc5.*G142;
G312=yc4.*G133+yc5.*G143;
G116=yc4.*G171+yc5.*G181;
G216=yc4.*G172+yc5.*G182;
G316=yc4.*G173+yc5.*G183;
G46=yc5.*G810;
G47=yc5.*G915;
G412=yc5.*G1314;
G416=yc5.*G1718;
G56=yc4.*G108;
G57=yc4.*G159;
G512=yc4.*G1413;
G516=yc4.*G1817;
tau14=-log(G14)./alpha14;
tau24=-log(G24)./alpha24;
tau34=-log(G34)./alpha34;
tau15=-log(G15)./alpha15;
tau25=-log(G25)./alpha25;
tau35=-log(G35)./alpha35;
tau16=-log(G16)./alpha16;
tau26=-log(G26)./alpha26;
tau36=-log(G36)./alpha36;
tau17=-log(G17)./alpha17;
tau27=-log(G27)./alpha27;
tau37=-log(G37)./alpha37;
tau112=-log(G112)./alpha112;
tau212=-log(G212)./alpha212;
tau312=-log(G312)./alpha312;
tau116=-log(G116)./alpha116;
tau216=-log(G216)./alpha216;
tau316=-log(G316)./alpha316;
tau46=-log(G46)./alpha46;
tau47=-log(G47)./alpha47;
tau412=-log(G412)./alpha412;
tau416=-log(G416)./alpha416;
tau56=-log(G56)./alpha56;
tau57=-log(G57)./alpha57;
tau512=-log(G512)./alpha512;
tau516=-log(G516)./alpha516;
ln_y1_1=G12.*X2.*tau12+ G31.*X3.*tau13+ G14.*X4.*tau14+G15.*X5.*tau15+G16.*X6.*tau16+G17.*X7.*tau17+G112.*X12.*tau112+G116.*X16.*tau116;
ln_y1_2=G12.*X2+ G13.*X3+ G14.*X4+G15.*X5+G16.*X6+G17.*X7+G112.*X12+G116.*X16;
ln_y2_1=G21.*X1.*tau12+ G32.*X3.*tau32+ G24.*X4.*tau24+G25.*X5.*tau25+G26.*X6.*tau26+G27.*X7.*tau27+G212.*X12.*tau212+G216.*X16.*tau216;
ln_y2_2=G12.*X1+ G23.*X3+G24.*X4+G25.*X5+G26.*X6+G27.*X7+G212.*X12+G216.*X16;
ln_y3_1=G13.*X1.*tau13+ G23.*X3.*tau23+ G34.*X4.*tau34+G35.*X5.*tau35+G36.*X6.*tau36+G37.*X7.*tau37+G312.*X12.*tau312+G316.*X16.*tau316;
ln_y3_2=G13.*X1+ G23.*X3+ G34.*X4+G35.*X5+G36.*X6+G37.*X7+G312.*X12+G316.*X16;
ln_y4_1=G14.*X1.*tau14+G24.*X2.*tau24+G34.*X3.*tau34+G46.*X6.*tau46+G47.*X7.*tau47+G412.*X12.*tau412+G416.*X16.*tau416;
ln_y4_2=G14.*X1+G24.*X2+G34.*X3+G46.*X6+G47.*X7+G412.*X12+G416.*X16;
ln_y5_1=G15.*X1.*tau15+G25.*X2.*tau25+G35.*X3.*tau35+G56.*X6.*tau56+G57.*X7.*tau57+G512.*X12.*tau512+G516.*X16.*tau516;
ln_y5_2=G15.*X1+G25.*X2+G35.*X3+G56.*X6+G57.*X7+G512.*X12+G516.*X16;
ln_y6_1=G16.*X1.*tau16+G26.*X2.*tau26+G36.*X3.*tau36+G46.*X4.*tau46+G56.*X5.*tau56;
ln_y6_2=G16.*X1+G26.*X2+G36.*X3+G46.*X4+G56.*X5;
ln_y7_1=G17.*X1.*tau17+G27.*X2.*tau27+G37.*X3.*tau37+G47.*X4.*tau47+G57.*X5.*tau57;
ln_y7_2=G17.*X1+G27.*X2+G37.*X3+G47.*X4+G57.*X5;
ln_y12_1=G112.*X1.*tau112+G212.*X2.*tau212+G312.*X3.*tau312+G412.*X4.*tau412+G512.*X5.*tau512;
ln_y12_2=G112.*X1+G212.*X2+G312.*X3+G412.*X4+G512.*X5;
ln_y16_1=G116.*X1.*tau116+G216.*X2.*tau216+G316.*X3.*tau316+G416.*X4.*tau416+G516.*X5.*tau516;
ln_y16_2=G116.*X1+G216.*X2+G316.*X3+G416.*X4+G516.*X5;
ln_y1_3=(((X2.*G12)./ln_y2_2).*(tau12-(ln_y2_1)./(ln_y2_2)))+(((X3.*G13)./ln_y3_2).*(tau13-(ln_y3_1)./(ln_y3_2)));
ln_y1_4=(((X6.*G16)./ln_y6_2).*(tau16- (ln_y6_1./ln_y6_2))) + (((X7.*G17)./ln_y7_2).*(tau17- (ln_y7_1./ln_y7_2)))+(((X12.*G12)./ln_y12_2).*(tau112- (ln_y12_1./ln_y12_2)))+(((X16.*G16)./ln_y16_2).*(tau116- (ln_y16_1./ln_y16_2)));
ln_y1_5=(((X4.*G14)./ln_y4_2).*(tau14- (ln_y4_1./ln_y4_2))) + (((X5.*G15)./ln_y5_2).*(tau15- (ln_y5_1./ln_y5_2)));
yk=exp((ln_y1_1./ln_y1_2) + ln_y1_3 + ln_y1_4+ ln_y1_5)'; % activity coefficient for H2O
if any(~isfinite(yk))
yk = 10 * ones(size(yk));
end
everyone,
I'm trying to do some calculations and plot the results, but it seems that these are too heavy for Maxima. When I try to calculate N1 and N2 the program crashes when parameter j is too high or when I try to plot them, the program displays the following error message: "Heap exhausted, game over." What should I do? I've seen some people saying to try to compile Maxima with ccl, but I don't know how to do it or if it will work.
I usually receive error messages like:
Message from maxima's stderr stream: Heap exhausted during garbage collection: 0 bytes available, 16 requested.
Gen Boxed Unboxed LgBox LgUnbox Pin Alloc Waste Trig WP GCs Mem-age
0 0 0 0 0 0 0 0 20971520 0 0 0,0000
1 0 0 0 0 0 0 0 20971520 0 0 0,0000
2 0 0 0 0 0 0 0 20971520 0 0 0,0000
3 16417 2 0 0 43 1075328496 707088 293986768 16419 1 0,8032
4 13432 21 0 1141 70 955593760 838624 2000000 14594 0 0,2673
5 0 0 0 0 0 0 0 2000000 0 0 0,0000
6 741 184 34 28 0 63259792 1424240 2000000 987 0 0,0000
7 0 0 0 0 0 0 0 2000000 0 0 0,0000
Total bytes allocated = 2094182048
Dynamic-space-size bytes = 2097152000
GC control variables:
*GC-INHIBIT* = true
*GC-PENDING* = true
*STOP-FOR-GC-PENDING* = false
fatal error encountered in SBCL pid 13884(tid 0000000001236360):
Heap exhausted, game over.
Here goes the code:
enter code here
a: 80$;
b: 6*a$;
h1: 80$;
t: 2$;
j: 5$;
carga: 250$;
sig: -carga/2$;
n: 2*q*%pi/b$;
m: i*%pi/a$;
i: 2*p-1$;
i1: 2*p1-1$;
/*i1: p1$;*/
Φ: a/b$;
τ: cosh(x) - (x/sinh(x))$;
σ: sinh(x) - (x/cosh(x))$;
Ψ: sinh(x)/τ$;
Χ: cosh(x)/σ$;
Λ0: 1/(((i/2)^2+Φ^2*q^2)^2)$;
Λ1: sum((((i/2)^3*subst([x=(i*%pi/(2*Φ))],Ψ))/(((i/2)^2+Φ^2*q1^2)^2))*Λ0, p, 1, j)$;
Λ2: sum(((q1^3*subst([x=(q1*%pi*Φ)],Χ))/(((i/2)^2+Φ^2*q1^2)^2))*Λ1, q1, 1, j)$;
Λ3: sum((((i/2)^3*subst([x=(i*%pi/(2*Φ))],Ψ))/(((i/2)^2+Φ^2*q1^2)^2))*Λ2, p, 1, j)$;
Λ4: sum(((q1^3*subst([x=(q1*%pi*Φ)],Χ))/(((i/2)^2+Φ^2*q1^2)^2))*Λ3, q1, 1, j)$;
Λ5: sum((((i/2)^3*subst([x=(i*%pi/(2*Φ))],Ψ))/(((i/2)^2+Φ^2*q1^2)^2))*Λ4, p, 1, j)$;
Ζ0: sum(((q^3*subst([x=(q*%pi*Φ)],Χ))/(((i1/2)^2+Φ^2*q^2)^2))*Λ0, q, 1, j)$;
Ζ2: sum(((q^3*subst([x=(q*%pi*Φ)],Χ))/(((i1/2)^2+Φ^2*q^2)^2))*Λ2, q, 1, j)$;
Ζ4: sum(((q^3*subst([x=(q*%pi*Φ)],Χ))/(((i1/2)^2+Φ^2*q^2)^2))*Λ4, q, 1, j)$;
E: 200000$;
ν: 0.3$;
λ: (ν*E)/((1+ν)*(1-2*ν))$;
μ: E/(2*(1+ν))$;
a0: float(1/(b/2)*integrate(0, y, -(b/2), -h1/2)+1/b*integrate(sig, y, -h1/2, h1/2)+1/(b/2)*integrate(0, y, h1/2, (b/2)))$;
aq: float(1/(b/2)*integrate(0*cos(q*y*%pi/(b/2)), y, -(b/2), - h1/2)+1/(b/2)*integrate(sig*cos(q*y*%pi/(b/2)), y, -h1/2, h1/2)+1/(b/2)*integrate(0*cos(q*y*%pi/(b/2)), y, h1/2, (b/2)))$;
aq1: float(1/(b/2)*integrate(0*cos(q1*y*%pi/(b/2)), y, -(b/2), - h1/2)+1/(b/2)*integrate(sig*cos(q1*y*%pi/(b/2)), y, -h1/2, h1/2)+1/(b/2)*integrate(0*cos(q1*y*%pi/(b/2)), y, h1/2, (b/2)))$;
Bq: aq/((λ+μ)*subst([x=q*%pi*Φ],σ))+((16*Φ^4*q^2*(-1)^q)/((λ+μ)*%pi^2*subst([x=q*%pi*Φ],σ)))*sum(q1*aq1*(-1) ^q1*subst([x=q1*%pi*Φ],Χ)*(Λ1+(16*Φ^4/(%pi^2))*Λ3+((16*Φ^4/(%pi^2))^2)*Λ5), q1, 1, j)+(8*λ*Φ^3*q^2*(-1)^q*a0)/((λ+μ)*(λ+2*μ)*(%pi^3)*subst([x=q*%pi*Φ],σ))*sum(subst([x=i*%pi/(2*Φ)],Ψ)/(i/ 2)*(Λ0+(16*Φ^4/(%pi^2))*Λ2+((16*Φ^4/(%pi^2))^2)*Λ4), p, 1, j)$;
βp: -(2*λ*a0*(-1)^((i-1)/2))/((λ+μ)*(λ+2*μ)*(i/2)^2*%pi^2*subst([x=i*%pi/(2*Φ)],τ))-((32*λ*Φ^4*(i/2)^2*a0*(-1)^((i-1)/2))/((λ+μ)*(λ+2*μ)*%pi^2*subst([x=i*%pi/(2*Φ)],τ)))*sum(((subst([x=i1*%pi/(2*Φ)],Ψ))/(i1/2))*(Ζ0+Ζ2*((16*Φ^4)/%pi^2)+Ζ4*(((16*Φ^4)/%pi^2)^2)),p1,1,j)-((4*Φ*(i/2)^2*(-1)^((i-1)/2))/((λ+μ)*%pi*subst([x=i*%pi/(2*Φ)],τ)))*sum(q*aq*(-1)^q*subst([x=q*%pi*Φ],Χ)*(Λ0+Λ2*(16*Φ^4/%pi^2)+Λ4*(16*Φ^4/%pi^2)^2),q,1,j)$;
N1: (2*a0/a)*x+(λ+μ)*sum(Bq*((1+((n*a*sinh(n*a/2))/(2*cosh(n*a/2))))*sinh(n*x)-n*x*cosh(n*x))*cos(n*y),q,1,j)+(λ+μ)*sum(βp*((1-((m*b*cosh(m*b/2))/(2*sinh(m*b/2))))*cosh(m*y)+m*y*sinh(m*y))*sin(m*x),p,1,j)$;
N2: ((2*λ*a0)/(a*(λ+2*μ)))*x+(λ+μ)*sum(Bq*((1-((n*a*sinh(n*a/2))/(2*cosh(n*a/2))))*sinh(n*x)+n*x*cosh(n*x))*cos(n*y),q,1,j)+(λ+μ)*sum(βp*((1+((m*b*cosh(m*b/2))/(2*sinh(m*b/2))))*cosh(m*y)-m*y*sinh(m*y))*sin(m*x),p,1,j);
wxplot3d(N1, [x,-a/2,a/2], [y,-b/2,b/2])$;
wxplot3d(N2, [x,-a/2,a/2], [y,-b/2,b/2])$;
This is not a complete answer, since I don't know how this should work with wxMaxima: I would suggest that you ask the developers. However it's too long for a comment and I think might be useful to people, and it does answer the question of how you solve the heap-size limit for Maxima itself when using SBCL, at least when run on Linux or some other platform with a command-line.
As a note, I suspect that the underlying problem is not the heap size, but that the calculation is blowing up in some horrible way: the best fix is probably to understand what's blowing up and fix that. See Robert Dodier's answer, which is probably going to be a lot more helpful. However, if heap size is the problem, this is how you deal with it for Maxima.
The trick is that you can tell SBCL what the heap limit should be by passing it the --dynamic-space-size <MB> argument, and you can pas arguments through the maxima wrapper to do this.
Here is a transcript of Maxima, being run on Linux, with SBCL as a back end (this is a version built from source: the packaged version will I assume be the same):
$ maxima
Maxima 5.43.2 http://maxima.sourceforge.net
using Lisp SBCL 2.0.0
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) :lisp (sb-ext:dynamic-space-size)
1073741824
So, on this system the defaule heap limit is 1GB (this is SBCL's default limit on the platform).
Now we can pass the -X <lisp options> aka --lisp-options=<lisp options> option to the maxima wrapper to pass the appropriate option through to sbcl:
$ maxima -X '--dynamic-space-size 2000'
Lisp options: (--dynamic-space-size 2000)
Maxima 5.43.2 http://maxima.sourceforge.net
using Lisp SBCL 2.0.0
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) :lisp (sb-ext:dynamic-space-size)
2097152000
As you can see this has doubled the heap size.
If someone knows the answer for wxMaxima then please do add an edit to this answer: I can't experiment it because all my Linux VMs are headless.
Also not a complete answer here, but some more notes and pointers which I hope will help.
To make the problem easier for Maxima to digest, use only exact numbers (integers and ratios), and avoid float and numer. (Plotting functions will apply float and numer automatically.) I changed 0.3 to 3/10 and cut out the calls to float.
Also, try setting j to a smaller number (I tried j equal to 1) to try to work all the way through the problem before increasing it to 5 again.
Also, replace all sum and integrate with 'sum and 'integrate (i.e. noun expressions instead of verb expressions). Take a look at the summands and integrands to see if they look right. You can evaluate the sums and/or integrals or both via ev(expr, sum) or ev(expr, integrate) or ev(expr, nouns) to evaluate 'sum, 'integrate, or all noun expressions, respectively.
With j equal to 1, I get the following expression for N1:
(2500000*((-(13*cosh(%pi/6)
*((8503056*cosh(%pi/6)^2*sinh(3*%pi)^2)
/(9765625*%pi^4
*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))^2
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi))^2)
+(52488*cosh(%pi/6)*sinh(3*%pi))
/(15625*%pi^2*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi)))
+324/25))
/(120000*%pi^2*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi))))
+(13*sinh(3*%pi)
*((2754990144*cosh(%pi/6)^3*sinh(3*%pi)^2)
/(244140625*%pi^4
*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))^3
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi))^2)
+(17006112*cosh(%pi/6)^2*sinh(3*%pi))
/(390625*%pi^2
*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))^2
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi)))
+(104976*cosh(%pi/6))
/(625*(sinh(%pi/6)-%pi/(6*cosh(%pi/6))))))
/(22680000*%pi^2*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi))^2)
+13/(35000*%pi^2*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi))))
*sin((%pi*(2*p-1)*x)/80)
*((%pi*(2*p-1)*y*sinh((%pi*(2*p-1)*y)/80))/80
+(1-(3*%pi*(2*p-1)*cosh(3*%pi*(2*p-1)))
/sinh(3*%pi*(2*p-1)))
*cosh((%pi*(2*p-1)*y)/80)))
/13
+(2500000*((-(13*cosh(%pi/6)
*((344373768*cosh(%pi/6)^2*sinh(3*%pi)^3)
/(244140625*%pi^4
*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))
^2
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi))
^3)
+(2125764*cosh(%pi/6)*sinh(3*%pi)^2)
/(390625*%pi^2
*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi))^2)
+(13122*sinh(3*%pi))
/(625*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi)))))
/(1620000*%pi^3*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))^2))
+(13*sinh(3*%pi)
*((8503056*cosh(%pi/6)^2*sinh(3*%pi)^2)
/(9765625*%pi^4
*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))^2
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi))^2)
+(52488*cosh(%pi/6)*sinh(3*%pi))
/(15625*%pi^2*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi)))
+324/25))
/(3780000*%pi^3*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))
*(cosh(3*%pi)-(3*%pi)/sinh(3*%pi)))
-13/(20000*%pi*(sinh(%pi/6)-%pi/(6*cosh(%pi/6)))))
*(((%pi*sinh(%pi/6))/(6*cosh(%pi/6))+1)
*sinh((%pi*x)/240)
-(%pi*x*cosh((%pi*x)/240))/240)*cos((%pi*y)/240))
/13-(25*x)/48$
Now in order to plot that, it should be a function of x and y only. However listofvars reports that it contains x, y, and p. Hmm. I see that βp has a summation over p1 but it contains Ζ0, which contains Λ0, which contains p. Is the summation over p1 supposed to be over p? Is the summand supposed to contain p1 instead of p?
Likewise it appears that N2, after evaluating the sums and integrals with j equal to 1, contains p.
Maybe you need to rework the formulas somewhat? I don't know what the correct form might be.
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i have 2 reflection coefficient equations R1 and R2 from K with condition absolute must below 1, i use if command for this situation .But when i plot the graph the absolute reflection coefficient still above 1. (K is matrix with 1 column and 201 row)
R1=K+sqrt(K.^2-1);
R2=K-sqrt(K.^2-1);
if abs(R1)<1
r=R1;
else
r=R2;
end
this is the K in excel
real imaginer
-0.7536 0.0512
-0.802 0.0426
-0.8496 0.0408
-0.8872 0.0327
-0.927 0.0338
-0.9575 0.0242
-0.979 0.0174
-0.9977 0.0113
-10,031 0.0029
-10,012 -0.007
-0.9876 -0.0167
-0.9654 -0.0249
-0.9299 -0.0401
-0.8797 -0.0488
-0.8176 -0.0623
-0.7297 -0.0782
-0.6458 -0.0865
-0.5351 -0.1051
-0.4098 -0.1197
-0.2701 -0.1349
-0.1177 -0.1489
0.0536 -0.1699
0.213 -0.1853
0.3933 -0.1921
0.5519 -0.1857
0.7128 -0.1896
0.8511 -0.1712
0.9468 -0.1452
10,222 -0.0943
10,375 -0.04
10,134 0.0365
0.9361 0.1255
0.8122 0.2168
0.6622 0.3108
0.4657 0.3774
0.2577 0.4497
0.0431 0.4775
-0.1463 0.5093
-0.3442 0.4999
-0.5203 0.4782
-0.6692 0.4417
-0.7781 0.3822
-0.8856 0.3293
-0.9703 0.2615
-10,187 0.193
-10,524 0.1254
-10,614 0.0557
-10,539 -0.0016
-10,297 -0.0698
-0.9879 -0.1212
-0.9355 -0.1829
-0.8721 -0.2298
-0.8011 -0.2783
-0.7232 -0.325
-0.6401 -0.3586
-0.5455 -0.4008
-0.4429 -0.43
-0.3524 -0.4433
-0.2455 -0.4769
-0.1336 -0.4863
-0.0391 -0.5073
0.0779 -0.5105
0.1776 -0.5196
0.2869 -0.5152
0.3893 -0.5084
0.4831 -0.4978
0.5888 -0.4907
0.6822 -0.4574
0.7614 -0.4381
0.8484 -0.4017
0.9098 -0.3585
0.9771 -0.3172
10,268 -0.2607
10,667 -0.2102
10,969 -0.1464
11,115 -0.0724
11,141 -0.0019
10,981 0.0838
10,645 0.1546
10,135 0.2457
0.9409 0.3332
0.8657 0.4061
0.7519 0.4973
0.6426 0.5635
0.5072 0.6302
0.3633 0.6782
0.2148 0.7161
0.0382 0.7573
-0.1051 0.7395
-0.273 0.7359
-0.4273 0.7154
-0.5653 0.6794
-0.6971 0.6279
-0.8202 0.555
-0.905 0.493
-0.9996 0.4155
-10,716 0.3239
-11,006 0.2549
-11,444 0.1479
-11,464 0.0722
-11,493 -0.0031
-11,282 -0.0814
-11,040 -0.1603
-10,645 -0.2219
-10,187 -0.2787
-0.9514 -0.3223
-0.8878 -0.3841
-0.8225 -0.42
-0.7415 -0.4606
-0.6607 -0.4889
-0.5577 -0.5319
-0.482 -0.5512
-0.3775 -0.5614
-0.2918 -0.5798
-0.1621 -0.5712
-0.0979 -0.5917
0.0149 -0.5559
0.1062 -0.5734
0.2142 -0.5648
0.3159 -0.5363
0.3844 -0.5302
0.5019 -0.5066
0.5805 -0.4709
0.6626 -0.4506
0.7482 -0.4117
0.8005 -0.363
0.8799 -0.3378
0.9349 -0.2889
0.9883 -0.2449
10,306 -0.1946
10,643 -0.1373
10,870 -0.1025
10,935 -0.0389
10,840 0.0184
10,732 0.0639
10,333 0.1274
0.9906 0.1739
0.9243 0.2293
0.8455 0.2752
0.7527 0.3035
0.6292 0.3394
0.5384 0.3524
0.3808 0.3845
0.2509 0.4067
0.0931 0.4004
-0.0423 0.3839
-0.2123 0.377
-0.3666 0.3537
-0.4838 0.3309
-0.6157 0.288
-0.7211 0.2604
-0.8322 0.2172
-0.8947 0.1791
-0.9618 0.1366
-10,024 0.0932
-10,299 0.0493
-10,415 0.0099
-10,333 -0.0243
-10,092 -0.0612
-0.9798 -0.0906
-0.9321 -0.1302
-0.8796 -0.1472
-0.8121 -0.17
-0.7414 -0.1886
-0.6649 -0.2019
-0.5907 -0.2149
-0.4793 -0.2271
-0.4011 -0.2224
-0.3121 -0.2408
-0.1948 -0.2343
-0.0997 -0.2322
0.008 -0.2328
0.1304 -0.2224
0.2662 -0.2213
0.4093 -0.2298
0.553 -0.2406
0.7094 -0.3018
0.8613 -0.383
0.9745 -0.5634
0.9796 -0.8226
0.7781 -0.9412
0.6424 -0.8495
0.6264 -0.8147
0.6071 -0.6706
0.6682 -0.6029
0.6759 -0.5596
0.71 -0.5218
0.7479 -0.4825
0.7691 -0.4476
0.8264 -0.4056
0.8412 -0.3912
0.8511 -0.3813
0.8689 -0.3425
0.899 -0.3375
0.8827 -0.3198
0.9024 -0.3164
0.929 -0.2876
0.9106 -0.2855
0.9695 -0.2079
10,342 -0.5353
0.8692 -0.5046
I am not 100% sure exactly what you are asking, but I believe the problem you are experiencing is that r is above 1?
K is an imaginary number, where the first column is the real part and the second column is the imaginary part, do I have that correctly? So the first K value is -0.7536+0.0512i, right?
Ok, so did you perhaps intend to cycle through each position of the R1 matrix and see if each one was less than 1. Because right now what you are doing is saying if any values in the entire R1 vector are less than 1, then r equals to the entire R2 vector.
If you want to go through each position in the vector, you should do this:
R1=K+sqrt(K.^2-1);
R2=K-sqrt(K.^2-1);
l=length(R1);
for p=1:l
if abs(R1(p))<1
r(p)=R1(p);
else
r(p)=R2(p);
end
end
I am trying to use sequentialfs on a logistic regression in order to determine the variables to include. I have tried to modify the answer from here Sequential feature selection Matlab in order to make it work, but the handle part is tricky to me!
I am using
[b, dev, stats] = glmfit(X_train,y_train,'binomial','link','logit')
in order to fit a model, and then I use
y_hat = glmval(b,X_test,'logit');
to evaluate the model output. I have tried to make a handle
f = #(X_test, y_test)...
(sum(y_test ~= round(glmval(b,X_test,'logit'))))
Which just says that I have "Too many input arguments", when I use
sequentialfs(f,X,y)
Can anyone help identify the relevant variables? A data set is below, where all variables will be deemed relevant, but the real problem is of a much larger scale which leads to overparametrization of the model.
X=
0,0305780001742986 0,0293310740486058 0,0289653631914407 0,0313646568650811 0,0308948854477814 0,0298740323895053
0,0221062699789144 0,0213746063391538 0,0196872068542263 0,0209915418572080 0,0206064713419377 0,0198587113064423
0,0275588428138312 0,0273957214651399 0,0291622596392042 0,0313729847567230 0,0314439993783026 0,0307137185244424
0,0262451954064372 0,0230629198767100 0,0251192876802874 0,0243459679829053 0,0235752627390268 0,0245208219450122
0,0232074343987232 0,0272778269415268 0,0288725913067116 0,0274565324127577 0,0283032894902223 0,0287391056368953
0,0237589488887855 0,0251929947662669 0,0209989755767701 0,0146662148369109 0,0193830305676060 0,0198900627308170
0,0275142606053146 0,0311683593689258 0,0287109246912083 0,0307544961383919 0,0293964246310913 0,0291758079280418
0,0284337063240141 0,0249820611584738 0,0261664330153102 0,0270312804219022 0,0269178494606530 0,0273467522864029
0,0279150521116060 0,0314021886143824 0,0291020356476994 0,0278247389567505 0,0294200854382611 0,0306460336509255
0,0270622115094110 0,0317795784913586 0,0278283619288299 0,0307757941373800 0,0292513615541838 0,0283900407512898
0,0270275432108930 0,0330384417745352 0,0323886885104962 0,0330255939800101 0,0329789138848656 0,0333091935226094
0,0263417729025468 0,0243442097895390 0,0253328659546050 0,0270828343149025 0,0262845355278762 0,0257915212526289
0,0247503544929709 0,0282150822748136 0,0282408722769508 0,0306907484707723 0,0284025718962319 0,0280291257508206
0,0282116130443164 0,0259317921438547 0,0316179116969559 0,0300579055064814 0,0315134680888256 0,0299693403497154
0,0221040769734790 0,0232354360252008 0,0231588261739581 0,0240414200785524 0,0209509517094598 0,0223174875964419
0,0264965936690525 0,0312918915850473 0,0297480867085914 0,0349060220702562 0,0307640365732823 0,0299291946182921
0,0283027112468824 0,0288419304885060 0,0275801208398665 0,0239401671924088 0,0263296648119700 0,0260497226349653
0,0298063469363023 0,0253535298515575 0,0245113899712628 0,0158158669753461 0,0228044538675689 0,0221885556611738
0,0276409442724517 0,0283430130710139 0,0303893043659674 0,0314511518633802 0,0315673022208602 0,0302375851656905
0,0270849987059202 0,0312381323489334 0,0301662309393833 0,0290482017036615 0,0299207348490636 0,0295746114571195
0,0225683074444599 0,0297455473987182 0,0241145950178924 0,0233857691372279 0,0259911200866772 0,0248345888658664
0,0267870191916224 0,0254332496269710 0,0270915983261551 0,0263567311441536 0,0267470932454238 0,0279742674970829
0,0271933786309775 0,0274722435013798 0,0249484244285920 0,0301299698898670 0,0255527349811283 0,0263901147510067
0,0262114755708772 0,0168593285634855 0,0205147916736994 0,0227484518393022 0,0187327306255277 0,0197581601499656
0,0314796048983783 0,0281771847088388 0,0318159664952504 0,0325586660052902 0,0315277330661507 0,0324593871738733
0,0265694239044569 0,0239306067986609 0,0263341531447523 0,0277011505766640 0,0274385429019891 0,0258861916796922
0,0248731179403750 0,0253801474063385 0,0258606627949811 0,0234446644496543 0,0262626821946271 0,0265908368467206
0,0268335079060221 0,0327877888534457 0,0292050848084788 0,0286811931594028 0,0288058286572012 0,0297311873407772
0,0289655102183149 0,0297912585631799 0,0289955796469846 0,0301374575223736 0,0286017508461882 0,0294957275181626
0,0291599221376467 0,0284752300175276 0,0294302899166185 0,0291600417637315 0,0304544724881292 0,0299842921064845
0,0306574107981617 0,0282562949634004 0,0290757741762068 0,0266759231631069 0,0276079132984815 0,0283490628634946
0,0251419690541645 0,0190208495552799 0,0219740565645893 0,0229700198654972 0,0231913971059666 0,0218104715761714
0,0279646047804379 0,0213712975401601 0,0266486742241442 0,0282351537040943 0,0256010069497723 0,0254151479565295
0,0291819765619095 0,0274841050997730 0,0277287252877124 0,0253910521460239 0,0270103968729900 0,0280719282161061
0,0267034888169756 0,0230641558482702 0,0254891453796317 0,0246876229024146 0,0232209026694445 0,0255548967304529
0,0282525579813869 0,0275995431014968 0,0263616638576222 0,0282844384170093 0,0262147272435204 0,0257109782177451
0,0293098464976821 0,0323503780295293 0,0266630772869637 0,0228075737924046 0,0263296732877124 0,0254313353506367
y=
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
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0
The function you use for sequentialfs should take in four variables. Yours only accepts two:
criterion = fun(XTRAIN,ytrain,XTEST,ytest)
This is because, even though you give only two variables, X and y, sequentialfs splits these into a training and testing subset (straight from the docs):
Starting from an empty feature set, sequentialfs creates candidate
feature subsets by sequentially adding each of the features not yet
selected. For each candidate feature subset, sequentialfs performs
10-fold cross-validation by repeatedly calling fun with different
training subsets of X and y, XTRAIN and ytrain, and test subsets of X
and y, XTEST and ytest
So the function passed for sequentialfs must take both the training and test subsets, e.g.:
function criterion = my_function(X_train,y_train,X_test,y_test)
[b, dev, stats] = glmfit(X_train,y_train,'binomial','link','logit')
y_hat = glmval(b,X_test,'logit');
criterion = sum(y_test ~= round(y_hat));
end
If this function is on your path you can pass it as #my_function, you don't have to make an anonymous function to get a handle.
I am new in prolog. I have found breadth first search program in the internet which is search for routes between cities. I want to extend the program to store and calculate distances. But I can't figure out how to do it.
The original code:
move(loc(omaha), loc(chicago)).
move(loc(omaha), loc(denver)).
move(loc(chicago), loc(denver)).
move(loc(chicago), loc(los_angeles)).
move(loc(chicago), loc(omaha)).
move(loc(denver), loc(los_angeles)).
move(loc(denver), loc(omaha)).
move(loc(los_angeles), loc(chicago)).
move(loc(los_angeles), loc(denver)).
bfs(State, Goal, Path) :-
bfs_help([[State]], Goal, RevPath), reverse(RevPath, Path).
bfs_help([[Goal|Path]|_], Goal, [Goal|Path]).
bfs_help([Path|RestPaths], Goal, SolnPath) :-
extend(Path, NewPaths),
append(RestPaths, NewPaths, TotalPaths),
bfs_help(TotalPaths, Goal, SolnPath).
extend([State|Path], NewPaths) :-
bagof([NextState,State|Path],
(move(State, NextState), not(member(NextState, [State|Path]))),
NewPaths), !.
extend(_, []).
Output:
1 ?- bfs(loc(omaha), loc(chicago), X).
X = [loc(omaha), loc(chicago)] ;
X = [loc(omaha), loc(denver), loc(los_angeles), loc(chicago)] ;
false.
I have tried this:
bfs(A,B,Path,D) :-
bfs(A,B,Path),
path_distance(Path,D).
path_distance([_], 0).
path_distance([A,B|Cs], S1) :-
move(A,B,D),
path_distance(Cs,S2),
S1 is S2+D.
bfs(A,B, Path) :-
bfs_help([[A]], B, RevPath), reverse(RevPath, Path).
bfs_help([[Goal|Path]|_], Goal, [Goal|Path]).
bfs_help([Path|RestPaths], Goal, SolnPath) :-
extend(Path, NewPaths),
append(RestPaths, NewPaths, TotalPaths),
bfs_help(TotalPaths, Goal, SolnPath).
extend([State|Path], NewPaths) :-
bagof([NextState,State|Path],
(move(State, NextState,_), not(member(NextState, [State|Path]))),
NewPaths), !.
extend(_, []).
Output:
5 ?- bfs(loc(omaha), loc(chicago), X,D).
false.
What i want:
1 ?- bfs(loc(omaha), loc(chicago), X, D).
X = [loc(omaha), loc(chicago)] ;
D = 1
X = [loc(omaha), loc(denver), loc(los_angeles), loc(chicago)] ;
D = 6
false.
Please anyone help me to solve this problem!
Sorry for my english.
It seems cheapest to define a relation path_distance/2. That is not the most elegant way,
but it should serve your purpose:
bfs(A,B,Path,D) :-
bfs(A,B,Path),
path_distance(Path,D).
path_distance([_], 0).
path_distance([A,B|Cs], S1) :-
move(A,B,D),
path_distance([B|Cs],S2),
S1 is S2+D.
You might also reconsider bfs/3 a bit. The query
?- bfs(A,B, Path).
Gives rather odd results.
Both move/2 and move/3 are now used. Thus:
move(A,B) :-
move(A,B,_).
move(loc(omaha), loc(chicago),1).
move(loc(omaha), loc(denver),2).
move(loc(chicago), loc(denver),1).
move(loc(chicago), loc(los_angeles),2).
move(loc(chicago), loc(omaha),1).
move(loc(denver), loc(los_angeles),2).
move(loc(denver), loc(omaha),1).
move(loc(los_angeles), loc(chicago),2).
move(loc(los_angeles), loc(denver),3).