/** ecologically parameterized logistic function with carrying capacity K; random effects vectorized
\param t independent variable; data vector
\param K carrying capacity; differentiable vector in a random effects model
\param r growth rate; differentiable vector in a random effects model
\param n0 initial population size at t=0; differentiable vector in a random effects model
\return \f$ \frac{K}{1+(\frac{K}{n0}-1)e^{-rt}} \f$
\ingroup ECOL
**/
df1b2vector logisticK( const dvector& t, const df1b2vector& K, const df1b2vector& r, const df1b2vector& n0)
{
df1b2vector y;
y=elem_div(K, 1.0 + elem_prod(elem_div(K, n0)-1.0, exp(-1.0*elem_prod(r,t))));
return(y);
}
/** generalized Ricker function, first parameerization; random effects vectorized
\param x independent variable; data vector
\param x0 ; differentiable vector in a random effects model
\param A ; differentiable vector in a random effects model
\param alpha ; differentiable vector in a random effects model
\return \f$ A(\frac{x}{x0}e^{(1.0-\frac{x}{x0})})^{\alpha} \f$
\ingroup ECOL
**/
df1b2vector generalized_Ricker1(const dvector& x, const df1b2vector& x0, const df1b2vector& A, const df1b2vector& alpha)
{
df1b2vector y;
y=elem_prod(A, pow(elem_prod(elem_div(x, x0), exp(1.0-elem_div(x, x0))), alpha));
return(y);
}
/** ecologically parameterized logistic function with carrying capacity K; vectorized
\param t independent variable; data vector
\param K carrying capacity; differentiable vector
\param r growth rate; differentiable vector
\param n0 initial population size at t=0; differentiable vector
\return \f$ \frac{K}{1+(\frac{K}{n0}-1)e^{-rt}} \f$
\ingroup ECOL
**/
dvar_vector logisticK( const dvector& t, const dvar_vector& K, const dvar_vector& r, const dvar_vector& n0)
{
RETURN_ARRAYS_INCREMENT();
dvar_vector y;
y=elem_div(K, 1.0 + elem_prod(elem_div(K, n0)-1.0, exp(-1.0*elem_prod(r,t))));
RETURN_ARRAYS_DECREMENT();
return (y);
}
/** generalized Ricker function, first parameerization; vectorized
\param x independent variable; data vector
\param x0 ; differentiable vector
\param A ; differentiable vector
\param alpha ; differentiable scalar
\return \f$ A(\frac{x}{x0}e^{(1.0-\frac{x}{x0})})^{\alpha} \f$
\ingroup ECOL
**/
dvar_vector generalized_Ricker1(const dvector& x, const dvar_vector& x0, const dvar_vector& A, const prevariable& alpha)
{
RETURN_ARRAYS_INCREMENT();
dvar_vector y;
y=elem_prod(A, pow(elem_prod(elem_div(x, x0), exp(1.0-elem_div(x, x0))), alpha));
RETURN_ARRAYS_DECREMENT();
return (y);
}
/** logistic function; random effects vectorized
\param x independent variable; data vector
\param a ; differentiable vector in a random effects model
\param b ; differentiable vector in a random effects model
\return \f$ \frac{e^{a+bx}}{(1+e^{a+bx})} \f$
\ingroup ECOL
**/
df1b2vector logistic(const dvector& x, const df1b2vector& a, const df1b2vector& b)
{
df1b2vector y;
y=elem_div(exp(a+elem_prod(b,x)), 1.0+exp(a+elem_prod(b,x)));
return(y);
}
/** Shepherd function random effects vectorized
\param x independent variable; data vector
\param a ; differentiable scalar in a random effects model
\param b ; differentiable vector in a random effects model
\param c ; differentiable vector in a random effects model
\return \f$ \frac{ax}{b+x^c} \f$
\ingroup ECOL
**/
df1b2vector Shepherd(const dvector& x, const df1b2variable& a, const df1b2vector& b, const df1b2vector& c)
{
df1b2vector y;
y=a*elem_div(x, (b+pow(x,c)));
return(y);
}
/** Shepherd function random effects vectorized
\param x independent variable; data vector
\param a ; differentiable vector in a random effects model
\param b ; differentiable vector in a random effects model
\param c ; differentiable vector in a random effects model
\return \f$ \frac{ax}{b+x^c} \f$
\ingroup ECOL
**/
df1b2vector Shepherd(const dvector& x, const df1b2vector& a, const df1b2vector& b, const df1b2vector& c)
{
df1b2vector y;
y=elem_prod(a, elem_div(x, (b+pow(x,c))));
return(y);
}
/** ecologically parameterized logistic function with carrying capacity K; random effects vectorized
\param t independent variable; data vector
\param K carrying capacity; differentiable vector in a random effects model
\param r growth rate; differentiable scalar in a random effects model
\param n0 initial population size at t=0; differentiable scalar in a random effects model
\return \f$ \frac{K}{1+(\frac{K}{n0}-1)e^{-rt}} \f$
\ingroup ECOL
**/
df1b2vector logisticK( const dvector& t, const df1b2vector& K, const df1b2variable& r, const df1b2variable& n0)
{
df1b2vector y;
y=elem_div(K, 1.0 + elem_prod(K/n0-1.0, exp(-r*t)));
return(y);
}
/** logistic function; random effects vectorized
\param x independent variable; data vector
\param a ; differentiable vector in a random effects model
\param b ; differentiable scalar in a random effects model
\return \f$ \frac{e^{a+bx}}{(1+e^{a+bx})} \f$
\ingroup ECOL
**/
df1b2vector logistic(const dvector& x, const df1b2vector& a, const df1b2variable& b)
{
df1b2vector y;
y=elem_div(exp(a+b*x), 1.0+exp(a+b*x));
return(y);
}
dvariable dnorm(const dvector& x, const dvar_vector& mu, const dvar_vector& std)
{
double pi=3.14159265358979323844;
int n=size_count(x);
dvar_vector var=square(std);
dvar_vector SS=square(x-mu);
return(0.5*n*log(2.*pi)+sum(log(std))+0.5*sum(elem_div(SS,var)));
}
/** ecologically parameterized logistic function with carrying capacity K; vectorized
\param t independent variable; data vector
\param K carrying capacity; differentiable vector
\param r growth rate; differentiable scalar
\param n0 initial population size at t=0; differentiable scalar
\return \f$ \frac{K}{1+(\frac{K}{n0}-1)e^{-rt}} \f$
\ingroup ECOL
**/
dvar_vector logisticK( const dvector& t, const dvar_vector& K, const prevariable& r, const prevariable& n0)
{
RETURN_ARRAYS_INCREMENT();
dvar_vector y;
y=elem_div(K, 1.0 + elem_prod(K/n0-1.0, exp(-r*t)));
RETURN_ARRAYS_DECREMENT();
return (y);
}
double eff_N(const dvector& pobs, const dvar_vector& phat)
{
pobs += 0.0001;
phat += 0.0001;
dvar_vector rtmp = elem_div((pobs-phat),sqrt(elem_prod(phat,(1-phat))));
double vtmp;
vtmp = value(norm2(rtmp)/size_count(rtmp));
return 1./vtmp;
}
/** logistic function; vectorized
\param x independent variable; data vector
\param a ; differentiable vector
\param b ; differentiable vector
\return \f$ \frac{e^{a+bx}}{(1+e^{a+bx})} \f$
\ingroup ECOL
**/
dvar_vector logistic(const dvector& x, const dvar_vector& a, const dvar_vector& b)
{
RETURN_ARRAYS_INCREMENT();
dvar_vector y;
y=elem_div(exp(a+elem_prod(b,x)), 1.0+exp(a+elem_prod(b,x)));
RETURN_ARRAYS_DECREMENT();
return (y);
}
/** Shepherd function vectorized
\param x independent variable; data vector
\param a ; differentiable vector
\param b ; differentiable vector
\param c ; differentiable scalar
\return \f$ \frac{ax}{b+x^c} \f$
\ingroup ECOL
**/
dvar_vector Shepherd(const dvector& x, const dvar_vector& a, const dvar_vector& b, const prevariable& c)
{
RETURN_ARRAYS_INCREMENT();
dvar_vector y;
y=elem_prod(a, elem_div(x, (b+pow(x,c))));
RETURN_ARRAYS_DECREMENT();
return (y);
}
/** logistic function; vectorized
\param x independent variable; data vector
\param a ; differentiable vector
\param b ; differentiable scalar
\return \f$ \frac{e^{a+bx}}{(1+e^{a+bx})} \f$
\ingroup ECOL
**/
dvar_vector logistic(const dvector& x, const dvar_vector& a, const prevariable& b)
{
RETURN_ARRAYS_INCREMENT();
dvar_vector y;
y=elem_div(exp(a+b*x), 1.0+exp(a+b*x));
RETURN_ARRAYS_DECREMENT();
return (y);
}
dvector norm_res(const dvector& pred, const dvector& obs, double m)
{
RETURN_ARRAYS_INCREMENT();
pred += 0.0001;
obs += 0.0001;
dvector nr(1,size_count(obs));
nr = elem_div(obs-pred,sqrt(elem_prod(pred,(1.-pred))/m));
RETURN_ARRAYS_DECREMENT();
return nr;
}
void model_parameters::userfunction(void)
{
obj_fun =0.0;
int Gtype, L;
FMpar = mfexp(logFM); // estimated F/M
SL50 = mfexp(logSL50);
Delta = mfexp(logDelta);
Vul = 1.0/(1+mfexp(-log(19)*(LenBins-SL50)/Delta));
MkL = Mk * pow(Linf/LenBins, Mpow);
FkL = FMpar * Mk * Vul;
for (Gtype=1;Gtype<=NGTG;Gtype++) {
MKLMat(Gtype) = MkL + kslope*(DiffLinfs(Gtype) - Linf);
ZKLMat(Gtype) = MKLMat(Gtype) + FkL;
currMkL = MKLMat(Gtype);
currZkL = ZKLMat(Gtype);
PUnFished = 0;
PFished = 0;
NUnFished = 0;
NFished = 0 ;
PUnFished(1) = RecProbs(Gtype);
PFished(1) = RecProbs(Gtype);
GTGLinf = DiffLinfs(Gtype);
for (L=2;L<=NLenMids+1;L++) {
if (LenBins(L) < GTGLinf) {
PUnFished(L) = PUnFished(L-1) * pow(((GTGLinf-LenBins(L))/(GTGLinf-LenBins(L-1))),currMkL(L-1));
PFished(L) = PFished(L-1) * pow(((GTGLinf-LenBins(L))/(GTGLinf-LenBins(L-1))),currZkL(L-1));
}
if (LenBins(L) >= GTGLinf) {
PUnFished(L) = 0;
PFished(L) = 0;
}
}
for (L=1;L<=NLenMids;L++) {
NUnFished(L) = (PUnFished(L) - PUnFished(L+1))/currMkL(L);
NFished(L) = (PFished(L) - PFished(L+1))/currZkL(L);
}
UnfishedMatrix(Gtype) = NUnFished;
FishedMatrix(Gtype) = NFished;
EP0_gtg(Gtype) = sum(elem_prod(NUnFished, Fec));
EPf_gtg(Gtype) = sum(elem_prod(NFished, Fec));
}
EP0 = sum(EP0_gtg);
EPf = sum(EPf_gtg);
SPR = EPf/EP0;
PredUnfishedComp = colsum(UnfishedMatrix);
PredUnfishedComp = PredUnfishedComp/sum(PredUnfishedComp);
// cout<<"hello"<<endl;
PredFishedComp = colsum(FishedMatrix);
PredFishedComp = PredFishedComp/sum(PredFishedComp);
PredLenComp = colsum(FishedMatrix);
PredLenComp = elem_prod(PredLenComp, 1.0/(1+mfexp(-log(19)*(LenMids-SL50)/Delta)));
PredLenComp = PredLenComp/sum(PredLenComp);
SL95 = SL50 + Delta;
obj_fun = -sum(elem_prod(ObsLength, log(elem_div(PredLenComp+0.00000001,ObsLength+0.00000001)))); // AP from ADMB living doc
}
dvariable dstudent_t( const dvar_vector& residual, const dvar_vector& df)
{
RETURN_ARRAYS_INCREMENT();
double pi = 3.141593;
dvar_vector t1 = 0.5*(df+1);
dvar_vector t2 = gammln(t1);
dvar_vector t3 = 0.5*log(df*pi)+gammln(0.5*df);
dvar_vector t4 = elem_prod(t1,log(1+elem_div(square(residual),df)));
dvariable pdf = sum(t3+t4-t2);
RETURN_ARRAYS_DECREMENT();
return( pdf );
}
dvariable initial_params::reset1(const dvar_vector& _x, const dvector& g)
{
dvar_vector& x=(dvar_vector&) _x;
int ii=1;
dvariable pen=0.0;
x=elem_div(x,g);
for (int i=0;i<num_initial_params;i++)
{
//if ((varsptr[i])->phase_start <= current_phase)
if (withinbound(0,(varsptr[i])->phase_start,current_phase))
(varsptr[i])->set_value(x,ii,pen);
}
return pen;
}
/**
* Description not yet available.
* \param
*/
dmatrix elem_div(const dmatrix& m, const dmatrix& m2)
{
ivector cmin(m.rowmin(),m.rowmax());
ivector cmax(m.rowmin(),m.rowmax());
int i;
for (i=m.rowmin();i<=m.rowmax();i++)
{
cmin(i)=m(i).indexmin();
cmax(i)=m(i).indexmax();
}
dmatrix tmp(m.rowmin(),m.rowmax(),cmin,cmax);
for (i=m.rowmin();i<=m.rowmax();i++)
{
tmp(i)=elem_div(m(i),m2(i));
}
return tmp;
}
dvariable mult_likelihood(const dmatrix &o, const dvar_matrix &p, dvar_matrix &nu,
const dvariable &log_vn)
{
// kludge to ensure observed and predicted matrixes are the same size
if(o.colsize()!=p.colsize() || o.rowsize()!=p.rowsize())
{
cerr<<"Error in multivariate_t_likelihood, observed and predicted matrixes"
" are not the same size\n";
ad_exit(1);
}
dvariable vn = mfexp(log_vn);
dvariable ff = 0.0;
int r1 = o.rowmin();
int r2 = o.rowmax();
int c1 = o.colmin();
int c2 = o.colmax();
for(int i = r1; i <= r2; i++ )
{
dvar_vector sobs = vn * o(i)/sum(o(i)); //scale observed numbers by effective sample size.
ff -= gammln(vn);
for(int j = c1; j <= c2; j++ )
{
if( value(sobs(j)) > 0.0 )
ff += gammln(sobs(j));
}
ff -= sobs * log(TINY + p(i));
dvar_vector o1=o(i)/sum(o(i));
dvar_vector p1=p(i)/sum(p(i));
nu(i) = elem_div(o1-p1,sqrt(elem_prod(p1,1.-p1)/vn));
}
// exit(1);
return ff;
}
vec filter_spectrum(const vec &a, const vec &b, int nfft)
{
vec s = sqr(abs(elem_div(fft(to_cvec(a), nfft), fft(to_cvec(b), nfft))));
s.set_size(nfft / 2 + 1, true);
return s;
}