static void fillsparsede(ap::real_1d_array& d,
ap::real_1d_array& e,
int n,
double sparcity)
{
int i;
int j;
d.setbounds(0, n-1);
e.setbounds(0, ap::maxint(0, n-2));
for(i = 0; i <= n-1; i++)
{
if( ap::fp_greater_eq(ap::randomreal(),sparcity) )
{
d(i) = 2*ap::randomreal()-1;
}
else
{
d(i) = 0;
}
}
for(i = 0; i <= n-2; i++)
{
if( ap::fp_greater_eq(ap::randomreal(),sparcity) )
{
e(i) = 2*ap::randomreal()-1;
}
else
{
e(i) = 0;
}
}
}
/*************************************************************************
This function generates 1-dimensional equidistant interpolation task with
moderate Lipshitz constant (close to 1.0)
If N=1 then suborutine generates only one point at the middle of [A,B]
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
void taskgenint1dequidist(double a,
double b,
int n,
ap::real_1d_array& x,
ap::real_1d_array& y)
{
int i;
double h;
ap::ap_error::make_assertion(n>=1, "TaskGenInterpolationEqdist1D: N<1!");
x.setlength(n);
y.setlength(n);
if( n>1 )
{
x(0) = a;
y(0) = 2*ap::randomreal()-1;
h = (b-a)/(n-1);
for(i = 1; i <= n-1; i++)
{
x(i) = a+i*h;
y(i) = y(i-1)+(2*ap::randomreal()-1)*h;
}
}
else
{
x(0) = 0.5*(a+b);
y(0) = 2*ap::randomreal()-1;
}
}
bool in_out_variable_1D(const ap::boolean_1d_array& in, const ap::real_1d_array& X, ap::real_1d_array& x, ap::real_1d_array& vector, bool io)
{
// Routine to know the number of variables in/out
int rows = in.gethighbound(0) + 1;
int n_invar=0;
bool flag;
//ap::real_1d_array vector;
vector.setbounds(0,rows-1);
unsigned int k=0;
for (int i=0; i<rows; i++)
{
if (in(i)==io) //to know how many variables are in/out
{
vector(k) = i;
k++;
n_invar++;
}
}
if (n_invar>0)
{
// Routine to extract the in/out variables
x.setbounds(0,n_invar-1);
for (int i=0; i<n_invar; i++)
x(i) = X(static_cast<int>(vector(i)));
flag=TRUE;
}
else
flag=FALSE;
return flag;
}
/*************************************************************************
This function generates 1-dimensional Chebyshev-2 interpolation task with
moderate Lipshitz constant (close to 1.0)
If N=1 then suborutine generates only one point at the middle of [A,B]
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
void taskgenint1dcheb2(double a,
double b,
int n,
ap::real_1d_array& x,
ap::real_1d_array& y)
{
int i;
ap::ap_error::make_assertion(n>=1, "TaskGenInterpolation1DCheb2: N<1!");
x.setlength(n);
y.setlength(n);
if( n>1 )
{
for(i = 0; i <= n-1; i++)
{
x(i) = 0.5*(b+a)+0.5*(b-a)*cos(ap::pi()*i/(n-1));
if( i==0 )
{
y(i) = 2*ap::randomreal()-1;
}
else
{
y(i) = y(i-1)+(2*ap::randomreal()-1)*(x(i)-x(i-1));
}
}
}
else
{
x(0) = 0.5*(a+b);
y(0) = 2*ap::randomreal()-1;
}
}
//===============================
//=====================================================================
void newiteration_residOpticalFlow_mt(int iter, const ap::real_1d_array& x, double f,const ap::real_1d_array& g, void *params)
{
globs_LBFGS_ *glob_param=(globs_LBFGS_*)params;
double normG=0.0;
for(int ii=g.getlowbound();ii<=g.gethighbound();ii++) normG+=g(ii)*g(ii);
normG=sqrt(normG);
cout<<"Iter="<<iter<<";fData="<<glob_param->fData<<";fSmooth="<<glob_param->fSmooth<<";fData+lambda*fSmooth="<<f<<";RMS(g)="<<normG/((double)(g.gethighbound()-g.getlowbound()+1))<<endl;
}
/*************************************************************************
Computation of nodes and weights for a Gauss quadrature formula
The algorithm generates the N-point Gauss quadrature formula with weight
function given by coefficients alpha and beta of a recurrence relation
which generates a system of orthogonal polynomials:
P-1(x) = 0
P0(x) = 1
Pn+1(x) = (x-alpha(n))*Pn(x) - beta(n)*Pn-1(x)
and zeroth moment Mu0
Mu0 = integral(W(x)dx,a,b)
INPUT PARAMETERS:
Alpha – array[0..N-1], alpha coefficients
Beta – array[0..N-1], beta coefficients
Zero-indexed element is not used and may be arbitrary.
Beta[I]>0.
Mu0 – zeroth moment of the weight function.
N – number of nodes of the quadrature formula, N>=1
OUTPUT PARAMETERS:
Info - error code:
* -3 internal eigenproblem solver hasn't converged
* -2 Beta[i]<=0
* -1 incorrect N was passed
* 1 OK
X - array[0..N-1] - array of quadrature nodes,
in ascending order.
W - array[0..N-1] - array of quadrature weights.
-- ALGLIB --
Copyright 2005-2009 by Bochkanov Sergey
*************************************************************************/
void gqgeneraterec(const ap::real_1d_array& alpha,
const ap::real_1d_array& beta,
double mu0,
int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& w)
{
int i;
ap::real_1d_array d;
ap::real_1d_array e;
ap::real_2d_array z;
if( n<1 )
{
info = -1;
return;
}
info = 1;
//
// Initialize
//
d.setlength(n);
e.setlength(n);
for(i = 1; i <= n-1; i++)
{
d(i-1) = alpha(i-1);
if( ap::fp_less_eq(beta(i),0) )
{
info = -2;
return;
}
e(i-1) = sqrt(beta(i));
}
d(n-1) = alpha(n-1);
//
// EVD
//
if( !smatrixtdevd(d, e, n, 3, z) )
{
info = -3;
return;
}
//
// Generate
//
x.setlength(n);
w.setlength(n);
for(i = 1; i <= n; i++)
{
x(i-1) = d(i-1);
w(i-1) = mu0*ap::sqr(z(0,i-1));
}
}
void lbfgslincomb(const int& n,
const double& da,
const ap::real_1d_array& dx,
int sx,
ap::real_1d_array& dy,
int sy)
{
int fx;
int fy;
fx = sx+n-1;
fy = sy+n-1;
ap::vadd(dy.getvector(sy, fy), dx.getvector(sx, fx), da);
}
double lbfgsdotproduct(const int& n,
const ap::real_1d_array& dx,
int sx,
const ap::real_1d_array& dy,
int sy)
{
double result;
double v;
int fx;
int fy;
fx = sx+n-1;
fy = sy+n-1;
v = ap::vdotproduct(dx.getvector(sx, fx), dy.getvector(sy, fy));
result = v;
return result;
}
/*************************************************************************
Serialization of LinearModel strucure
INPUT PARAMETERS:
LM - original
OUTPUT PARAMETERS:
RA - array of real numbers which stores model,
array[0..RLen-1]
RLen - RA lenght
-- ALGLIB --
Copyright 15.03.2009 by Bochkanov Sergey
*************************************************************************/
void lrserialize(const linearmodel& lm, ap::real_1d_array& ra, int& rlen)
{
rlen = ap::round(lm.w(0))+1;
ra.setbounds(0, rlen-1);
ra(0) = lrvnum;
ap::vmove(&ra(1), &lm.w(0), ap::vlen(1,rlen-1));
}
/*************************************************************************
Solving a system of linear equations with a system matrix given by its
LU decomposition.
The algorithm solves a system of linear equations whose matrix is given by
its LU decomposition. In case of a singular matrix, the algorithm returns
False.
The algorithm solves systems with a square matrix only.
Input parameters:
A - LU decomposition of a system matrix in compact form (the
result of the RMatrixLU subroutine).
Pivots - row permutation table (the result of a
RMatrixLU subroutine).
B - right side of a system.
Array whose index ranges within [0..N-1].
N - size of matrix A.
Output parameters:
X - solution of a system.
Array whose index ranges within [0..N-1].
Result:
True, if the matrix is not singular.
False, if the matrux is singular. In this case, X doesn't contain a
solution.
-- ALGLIB --
Copyright 2005-2008 by Bochkanov Sergey
*************************************************************************/
bool rmatrixlusolve(const ap::real_2d_array& a,
const ap::integer_1d_array& pivots,
ap::real_1d_array b,
int n,
ap::real_1d_array& x)
{
bool result;
ap::real_1d_array y;
int i;
int j;
double v;
y.setbounds(0, n-1);
x.setbounds(0, n-1);
result = true;
for(i = 0; i <= n-1; i++)
{
if( a(i,i)==0 )
{
result = false;
return result;
}
}
//
// pivots
//
for(i = 0; i <= n-1; i++)
{
if( pivots(i)!=i )
{
v = b(i);
b(i) = b(pivots(i));
b(pivots(i)) = v;
}
}
//
// Ly = b
//
y(0) = b(0);
for(i = 1; i <= n-1; i++)
{
v = ap::vdotproduct(&a(i, 0), &y(0), ap::vlen(0,i-1));
y(i) = b(i)-v;
}
//
// Ux = y
//
x(n-1) = y(n-1)/a(n-1,n-1);
for(i = n-2; i >= 0; i--)
{
v = ap::vdotproduct(&a(i, i+1), &x(i+1), ap::vlen(i+1,n-1));
x(i) = (y(i)-v)/a(i,i);
}
return result;
}
/*************************************************************************
Unpacks coefficients of linear model.
INPUT PARAMETERS:
LM - linear model in ALGLIB format
OUTPUT PARAMETERS:
V - coefficients, array[0..NVars]
NVars - number of independent variables (one less than number
of coefficients)
-- ALGLIB --
Copyright 30.08.2008 by Bochkanov Sergey
*************************************************************************/
void lrunpack(const linearmodel& lm, ap::real_1d_array& v, int& nvars)
{
int offs;
ap::ap_error::make_assertion(ap::round(lm.w(1))==lrvnum, "LINREG: Incorrect LINREG version!");
nvars = ap::round(lm.w(2));
offs = ap::round(lm.w(3));
v.setbounds(0, nvars);
ap::vmove(&v(0), &lm.w(offs), ap::vlen(0,nvars));
}
/*************************************************************************
Conversion of a series of Chebyshev polynomials to a power series.
Represents A[0]*T0(x) + A[1]*T1(x) + ... + A[N]*Tn(x) as
B[0] + B[1]*X + ... + B[N]*X^N.
Input parameters:
A - Chebyshev series coefficients
N - degree, N>=0
Output parameters
B - power series coefficients
*************************************************************************/
void fromchebyshev(const ap::real_1d_array& a,
const int& n,
ap::real_1d_array& b)
{
int i;
int k;
double e;
double d;
b.setbounds(0, n);
for(i = 0; i <= n; i++)
{
b(i) = 0;
}
d = 0;
i = 0;
do
{
k = i;
do
{
e = b(k);
b(k) = 0;
if( i<=1&&k==i )
{
b(k) = 1;
}
else
{
if( i!=0 )
{
b(k) = 2*d;
}
if( k>i+1 )
{
b(k) = b(k)-b(k-2);
}
}
d = e;
k = k+1;
}
while(k<=n);
d = b(i);
e = 0;
k = i;
while(k<=n)
{
e = e+b(k)*a(k);
k = k+2;
}
b(i) = e;
i = i+1;
}
while(i<=n);
}
/*************************************************************************
Representation of Ln as C[0] + C[1]*X + ... + C[N]*X^N
Input parameters:
N - polynomial degree, n>=0
Output parameters:
C - coefficients
*************************************************************************/
void laguerrecoefficients(const int& n, ap::real_1d_array& c)
{
int i;
c.setbounds(0, n);
c(0) = 1;
for(i = 0; i <= n-1; i++)
{
c(i+1) = -c(i)*(n-i)/(i+1)/(i+1);
}
}
/*************************************************************************
1-dimensional circular real cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (circular).
Algorithm has linearithmic complexity for any M/N.
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrR1DCircular(Signal, Pattern) = Pattern x Signal (using
traditional definition of cross-correlation, denoting cross-correlation
as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - real function to be transformed,
periodic signal containing pattern
N - problem size
Pattern - array[0..M-1] - real function to be transformed,
non-periodic pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - convolution: A*B. array[0..M-1].
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
void corrr1dcircular(const ap::real_1d_array& signal,
int m,
const ap::real_1d_array& pattern,
int n,
ap::real_1d_array& c)
{
ap::real_1d_array p;
ap::real_1d_array b;
int i1;
int i2;
int i;
int j2;
ap::ap_error::make_assertion(n>0&&m>0, "ConvC1DCircular: incorrect N or M!");
//
// normalize task: make M>=N,
// so A will be longer (at least - not shorter) that B.
//
if( m<n )
{
b.setlength(m);
for(i1 = 0; i1 <= m-1; i1++)
{
b(i1) = 0;
}
i1 = 0;
while(i1<n)
{
i2 = ap::minint(i1+m-1, n-1);
j2 = i2-i1;
ap::vadd(&b(0), &pattern(i1), ap::vlen(0,j2));
i1 = i1+m;
}
corrr1dcircular(signal, m, b, m, c);
return;
}
//
// Task is normalized
//
p.setlength(n);
for(i = 0; i <= n-1; i++)
{
p(n-1-i) = pattern(i);
}
convr1dcircular(signal, m, p, n, b);
c.setlength(m);
ap::vmove(&c(0), &b(n-1), ap::vlen(0,m-n));
if( m-n+1<=m-1 )
{
ap::vmove(&c(m-n+1), &b(0), ap::vlen(m-n+1,m-1));
}
}
/*************************************************************************
L-BFGS algorithm results
Called after MinLBFGSIteration() returned False.
INPUT PARAMETERS:
State - algorithm state (used by MinLBFGSIteration).
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -2 rounding errors prevent further improvement.
X contains best point found.
* -1 incorrect parameters were specified
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient norm is no more than EpsG
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* Rep.IterationsCount contains iterations count
* NFEV countains number of function calculations
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgsresults(const minlbfgsstate& state,
ap::real_1d_array& x,
minlbfgsreport& rep)
{
x.setbounds(0, state.n-1);
ap::vmove(&x(0), 1, &state.x(0), 1, ap::vlen(0,state.n-1));
rep.iterationscount = state.repiterationscount;
rep.nfev = state.repnfev;
rep.terminationtype = state.repterminationtype;
}
/*************************************************************************
Serialization of DecisionForest strucure
INPUT PARAMETERS:
DF - original
OUTPUT PARAMETERS:
RA - array of real numbers which stores decision forest,
array[0..RLen-1]
RLen - RA lenght
-- ALGLIB --
Copyright 13.02.2009 by Bochkanov Sergey
*************************************************************************/
void dfserialize(const decisionforest& df, ap::real_1d_array& ra, int& rlen)
{
ra.setbounds(0, df.bufsize+5-1);
ra(0) = dfvnum;
ra(1) = df.nvars;
ra(2) = df.nclasses;
ra(3) = df.ntrees;
ra(4) = df.bufsize;
ap::vmove(&ra(5), 1, &df.trees(0), 1, ap::vlen(5,5+df.bufsize-1));
rlen = 5+df.bufsize;
}
/*************************************************************************
Dense solver.
Similar to RMatrixSolveM() but solves task with one right part (where b/x
are vectors, not matrices).
See RMatrixSolveM() description for more information about subroutine
parameters.
-- ALGLIB --
Copyright 24.08.2009 by Bochkanov Sergey
*************************************************************************/
void rmatrixsolve(const ap::real_2d_array& a,
int n,
const ap::real_1d_array& b,
int& info,
densesolverreport& rep,
ap::real_1d_array& x)
{
ap::real_2d_array bm;
ap::real_2d_array xm;
if( n<=0 )
{
info = -1;
return;
}
bm.setlength(n, 1);
ap::vmove(bm.getcolumn(0, 0, n-1), b.getvector(0, n-1));
rmatrixsolvem(a, n, bm, 1, info, rep, xm);
x.setlength(n);
ap::vmove(x.getvector(0, n-1), xm.getcolumn(0, 0, n-1));
}
/*************************************************************************
Obsolete 1-based subroutine.
See RMatrixBDUnpackDiagonals for 0-based replacement.
*************************************************************************/
void unpackdiagonalsfrombidiagonal(const ap::real_2d_array& b,
int m,
int n,
bool& isupper,
ap::real_1d_array& d,
ap::real_1d_array& e)
{
int i;
isupper = m>=n;
if( m==0||n==0 )
{
return;
}
if( isupper )
{
d.setbounds(1, n);
e.setbounds(1, n);
for(i = 1; i <= n-1; i++)
{
d(i) = b(i,i);
e(i) = b(i,i+1);
}
d(n) = b(n,n);
}
else
{
d.setbounds(1, m);
e.setbounds(1, m);
for(i = 1; i <= m-1; i++)
{
d(i) = b(i,i);
e(i) = b(i+1,i);
}
d(m) = b(m,m);
}
}
/*************************************************************************
Unpacking of the main and secondary diagonals of bidiagonal decomposition
of matrix A.
Input parameters:
B - output of RMatrixBD subroutine.
M - number of rows in matrix B.
N - number of columns in matrix B.
Output parameters:
IsUpper - True, if the matrix is upper bidiagonal.
otherwise IsUpper is False.
D - the main diagonal.
Array whose index ranges within [0..Min(M,N)-1].
E - the secondary diagonal (upper or lower, depending on
the value of IsUpper).
Array index ranges within [0..Min(M,N)-1], the last
element is not used.
-- ALGLIB --
Copyright 2005-2007 by Bochkanov Sergey
*************************************************************************/
void rmatrixbdunpackdiagonals(const ap::real_2d_array& b,
int m,
int n,
bool& isupper,
ap::real_1d_array& d,
ap::real_1d_array& e)
{
int i;
isupper = m>=n;
if( m<=0||n<=0 )
{
return;
}
if( isupper )
{
d.setbounds(0, n-1);
e.setbounds(0, n-1);
for(i = 0; i <= n-2; i++)
{
d(i) = b(i,i);
e(i) = b(i,i+1);
}
d(n-1) = b(n-1,n-1);
}
else
{
d.setbounds(0, m-1);
e.setbounds(0, m-1);
for(i = 0; i <= m-2; i++)
{
d(i) = b(i,i);
e(i) = b(i+1,i);
}
d(m-1) = b(m-1,m-1);
}
}
/*************************************************************************
Representation of Hn as C[0] + C[1]*X + ... + C[N]*X^N
Input parameters:
N - polynomial degree, n>=0
Output parameters:
C - coefficients
*************************************************************************/
void hermitecoefficients(const int& n, ap::real_1d_array& c)
{
int i;
c.setbounds(0, n);
for(i = 0; i <= n; i++)
{
c(i) = 0;
}
c(n) = exp(n*log(double(2)));
for(i = 0; i <= n/2-1; i++)
{
c(n-2*(i+1)) = -c(n-2*i)*(n-2*i)*(n-2*i-1)/4/(i+1);
}
}
/*************************************************************************
Multiclass Fisher LDA
Subroutine finds coefficients of linear combination which optimally separates
training set on classes.
INPUT PARAMETERS:
XY - training set, array[0..NPoints-1,0..NVars].
First NVars columns store values of independent
variables, next column stores number of class (from 0
to NClasses-1) which dataset element belongs to. Fractional
values are rounded to nearest integer.
NPoints - training set size, NPoints>=0
NVars - number of independent variables, NVars>=1
NClasses - number of classes, NClasses>=2
OUTPUT PARAMETERS:
Info - return code:
* -4, if internal EVD subroutine hasn't converged
* -2, if there is a point with class number
outside of [0..NClasses-1].
* -1, if incorrect parameters was passed (NPoints<0,
NVars<1, NClasses<2)
* 1, if task has been solved
* 2, if there was a multicollinearity in training set,
but task has been solved.
W - linear combination coefficients, array[0..NVars-1]
-- ALGLIB --
Copyright 31.05.2008 by Bochkanov Sergey
*************************************************************************/
void fisherlda(const ap::real_2d_array& xy,
int npoints,
int nvars,
int nclasses,
int& info,
ap::real_1d_array& w)
{
ap::real_2d_array w2;
fisherldan(xy, npoints, nvars, nclasses, info, w2);
if( info>0 )
{
w.setbounds(0, nvars-1);
ap::vmove(&w(0), 1, &w2(0, 0), w2.getstride(), ap::vlen(0,nvars-1));
}
}
/*************************************************************************
Nonlinear least squares fitting results.
Called after LSFitNonlinearIteration() returned False.
INPUT PARAMETERS:
State - algorithm state (used by LSFitNonlinearIteration).
OUTPUT PARAMETERS:
Info - completetion code:
* -1 incorrect parameters were specified
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient norm is no more than EpsG
* 5 MaxIts steps was taken
C - array[0..K-1], solution
Rep - optimization report. Following fields are set:
* Rep.TerminationType completetion code:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitnonlinearresults(const lsfitstate& state,
int& info,
ap::real_1d_array& c,
lsfitreport& rep)
{
info = state.repterminationtype;
if( info>0 )
{
c.setlength(state.k);
ap::vmove(&c(0), 1, &state.c(0), 1, ap::vlen(0,state.k-1));
rep.rmserror = state.reprmserror;
rep.avgerror = state.repavgerror;
rep.avgrelerror = state.repavgrelerror;
rep.maxerror = state.repmaxerror;
}
}
void qrdecomposition(ap::real_2d_array& a,
int m,
int n,
ap::real_1d_array& tau)
{
ap::real_1d_array work;
ap::real_1d_array t;
int i;
int k;
int mmip1;
int minmn;
double tmp;
minmn = ap::minint(m, n);
work.setbounds(1, n);
t.setbounds(1, m);
tau.setbounds(1, minmn);
//
// Test the input arguments
//
k = ap::minint(m, n);
for(i = 1; i <= k; i++)
{
//
// Generate elementary reflector H(i) to annihilate A(i+1:m,i)
//
mmip1 = m-i+1;
ap::vmove(t.getvector(1, mmip1), a.getcolumn(i, i, m));
generatereflection(t, mmip1, tmp);
tau(i) = tmp;
ap::vmove(a.getcolumn(i, i, m), t.getvector(1, mmip1));
t(1) = 1;
if( i<n )
{
//
// Apply H(i) to A(i:m,i+1:n) from the left
//
applyreflectionfromtheleft(a, tau(i), t, i, m, i+1, n, work);
}
}
}
/*************************************************************************
Obsolete 1-based subroutine
*************************************************************************/
void shermanmorrisonupdateuv(ap::real_2d_array& inva,
int n,
const ap::real_1d_array& u,
const ap::real_1d_array& v)
{
ap::real_1d_array t1;
ap::real_1d_array t2;
int i;
int j;
double lambda;
double vt;
t1.setbounds(1, n);
t2.setbounds(1, n);
//
// T1 = InvA * U
// Lambda = v * T1
//
for(i = 1; i <= n; i++)
{
vt = ap::vdotproduct(&inva(i, 1), &u(1), ap::vlen(1,n));
t1(i) = vt;
}
lambda = ap::vdotproduct(&v(1), &t1(1), ap::vlen(1,n));
//
// T2 = v*InvA
//
for(j = 1; j <= n; j++)
{
vt = ap::vdotproduct(v.getvector(1, n), inva.getcolumn(j, 1, n));
t2(j) = vt;
}
//
// InvA = InvA - correction
//
for(i = 1; i <= n; i++)
{
vt = t1(i)/(1+lambda);
ap::vsub(&inva(i, 1), &t2(1), ap::vlen(1,n), vt);
}
}
/*************************************************************************
Inverse matrix update by the Sherman-Morrison formula
The algorithm computes the inverse of matrix A+u*v’ by using the given matrix
A^-1 and the vectors u and v.
Input parameters:
InvA - inverse of matrix A.
Array whose indexes range within [0..N-1, 0..N-1].
N - size of matrix A.
U - the vector modifying the matrix.
Array whose index ranges within [0..N-1].
V - the vector modifying the matrix.
Array whose index ranges within [0..N-1].
Output parameters:
InvA - inverse of matrix A + u*v'.
-- ALGLIB --
Copyright 2005 by Bochkanov Sergey
*************************************************************************/
void rmatrixinvupdateuv(ap::real_2d_array& inva,
int n,
const ap::real_1d_array& u,
const ap::real_1d_array& v)
{
ap::real_1d_array t1;
ap::real_1d_array t2;
int i;
int j;
double lambda;
double vt;
t1.setbounds(0, n-1);
t2.setbounds(0, n-1);
//
// T1 = InvA * U
// Lambda = v * T1
//
for(i = 0; i <= n-1; i++)
{
vt = ap::vdotproduct(&inva(i, 0), &u(0), ap::vlen(0,n-1));
t1(i) = vt;
}
lambda = ap::vdotproduct(&v(0), &t1(0), ap::vlen(0,n-1));
//
// T2 = v*InvA
//
for(j = 0; j <= n-1; j++)
{
vt = ap::vdotproduct(v.getvector(0, n-1), inva.getcolumn(j, 0, n-1));
t2(j) = vt;
}
//
// InvA = InvA - correction
//
for(i = 0; i <= n-1; i++)
{
vt = t1(i)/(1+lambda);
ap::vsub(&inva(i, 0), &t2(0), ap::vlen(0,n-1), vt);
}
}
/*************************************************************************
QR decomposition of a rectangular matrix of size MxN
Input parameters:
A - matrix A whose indexes range within [0..M-1, 0..N-1].
M - number of rows in matrix A.
N - number of columns in matrix A.
Output parameters:
A - matrices Q and R in compact form (see below).
Tau - array of scalar factors which are used to form
matrix Q. Array whose index ranges within [0.. Min(M-1,N-1)].
Matrix A is represented as A = QR, where Q is an orthogonal matrix of size
MxM, R - upper triangular (or upper trapezoid) matrix of size M x N.
The elements of matrix R are located on and above the main diagonal of
matrix A. The elements which are located in Tau array and below the main
diagonal of matrix A are used to form matrix Q as follows:
Matrix Q is represented as a product of elementary reflections
Q = H(0)*H(2)*...*H(k-1),
where k = min(m,n), and each H(i) is in the form
H(i) = 1 - tau * v * (v^T)
where tau is a scalar stored in Tau[I]; v - real vector,
so that v(0:i-1) = 0, v(i) = 1, v(i+1:m-1) stored in A(i+1:m-1,i).
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992.
Translation from FORTRAN to pseudocode (AlgoPascal)
by Sergey Bochkanov, ALGLIB project, 2005-2007.
*************************************************************************/
void rmatrixqr(ap::real_2d_array& a, int m, int n, ap::real_1d_array& tau)
{
ap::real_1d_array work;
ap::real_1d_array t;
int i;
int k;
int minmn;
double tmp;
if( m<=0||n<=0 )
{
return;
}
minmn = ap::minint(m, n);
work.setbounds(0, n-1);
t.setbounds(1, m);
tau.setbounds(0, minmn-1);
//
// Test the input arguments
//
k = minmn;
for(i = 0; i <= k-1; i++)
{
//
// Generate elementary reflector H(i) to annihilate A(i+1:m,i)
//
ap::vmove(t.getvector(1, m-i), a.getcolumn(i, i, m-1));
generatereflection(t, m-i, tmp);
tau(i) = tmp;
ap::vmove(a.getcolumn(i, i, m-1), t.getvector(1, m-i));
t(1) = 1;
if( i<n )
{
//
// Apply H(i) to A(i:m-1,i+1:n-1) from the left
//
applyreflectionfromtheleft(a, tau(i), t, i, m-1, i+1, n-1, work);
}
}
}
/*************************************************************************
Representation of Pn as C[0] + C[1]*X + ... + C[N]*X^N
Input parameters:
N - polynomial degree, n>=0
Output parameters:
C - coefficients
*************************************************************************/
void legendrecoefficients(const int& n, ap::real_1d_array& c)
{
int i;
c.setbounds(0, n);
for(i = 0; i <= n; i++)
{
c(i) = 0;
}
c(n) = 1;
for(i = 1; i <= n; i++)
{
c(n) = c(n)*(n+i)/2/i;
}
for(i = 0; i <= n/2-1; i++)
{
c(n-2*(i+1)) = -c(n-2*i)*(n-2*i)*(n-2*i-1)/2/(i+1)/(2*(n-i)-1);
}
}
/*************************************************************************
Conjugate gradient results
Called after MinASA returned False.
INPUT PARAMETERS:
State - algorithm state (used by MinASAIteration).
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -2 rounding errors prevent further improvement.
X contains best point found.
* -1 incorrect parameters were specified
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient norm is no more than EpsG
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* Rep.IterationsCount contains iterations count
* NFEV countains number of function calculations
* ActiveConstraints contains number of active constraints
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minasaresults(const minasastate& state,
ap::real_1d_array& x,
minasareport& rep)
{
int i;
x.setbounds(0, state.n-1);
ap::vmove(&x(0), 1, &state.x(0), 1, ap::vlen(0,state.n-1));
rep.iterationscount = state.repiterationscount;
rep.nfev = state.repnfev;
rep.terminationtype = state.repterminationtype;
rep.activeconstraints = 0;
for(i = 0; i <= state.n-1; i++)
{
if( ap::fp_eq(state.ak(i),0) )
{
rep.activeconstraints = rep.activeconstraints+1;
}
}
}
/*************************************************************************
Representation of Tn as C[0] + C[1]*X + ... + C[N]*X^N
Input parameters:
N - polynomial degree, n>=0
Output parameters:
C - coefficients
*************************************************************************/
void chebyshevcoefficients(const int& n, ap::real_1d_array& c)
{
int i;
c.setbounds(0, n);
for(i = 0; i <= n; i++)
{
c(i) = 0;
}
if( n==0||n==1 )
{
c(n) = 1;
}
else
{
c(n) = exp((n-1)*log(double(2)));
for(i = 0; i <= n/2-1; i++)
{
c(n-2*(i+1)) = -c(n-2*i)*(n-2*i)*(n-2*i-1)/4/(i+1)/(n-i-1);
}
}
}
/*************************************************************************
1-dimensional real cross-correlation.
For given Pattern/Signal returns corr(Pattern,Signal) (non-circular).
Correlation is calculated using reduction to convolution. Algorithm with
max(N,N)*log(max(N,N)) complexity is used (see ConvC1D() for more info
about performance).
IMPORTANT:
for historical reasons subroutine accepts its parameters in reversed
order: CorrR1D(Signal, Pattern) = Pattern x Signal (using traditional
definition of cross-correlation, denoting cross-correlation as "x").
INPUT PARAMETERS
Signal - array[0..N-1] - real function to be transformed,
signal containing pattern
N - problem size
Pattern - array[0..M-1] - real function to be transformed,
pattern to search withing signal
M - problem size
OUTPUT PARAMETERS
R - cross-correlation, array[0..N+M-2]:
* positive lags are stored in R[0..N-1],
R[i] = sum(pattern[j]*signal[i+j]
* negative lags are stored in R[N..N+M-2],
R[N+M-1-i] = sum(pattern[j]*signal[-i+j]
NOTE:
It is assumed that pattern domain is [0..M-1]. If Pattern is non-zero
on [-K..M-1], you can still use this subroutine, just shift result by K.
-- ALGLIB --
Copyright 21.07.2009 by Bochkanov Sergey
*************************************************************************/
void corrr1d(const ap::real_1d_array& signal,
int n,
const ap::real_1d_array& pattern,
int m,
ap::real_1d_array& r)
{
ap::real_1d_array p;
ap::real_1d_array b;
int i;
ap::ap_error::make_assertion(n>0&&m>0, "CorrR1D: incorrect N or M!");
p.setlength(m);
for(i = 0; i <= m-1; i++)
{
p(m-1-i) = pattern(i);
}
convr1d(p, m, signal, n, b);
r.setlength(m+n-1);
ap::vmove(&r(0), &b(m-1), ap::vlen(0,n-1));
if( m+n-2>=n )
{
ap::vmove(&r(n), &b(0), ap::vlen(n,m+n-2));
}
}