bool testblas(bool silent)
{
bool result;
int pass;
int passcount;
int n;
int i;
int i1;
int i2;
int j;
int j1;
int j2;
int l;
int k;
int r;
int i3;
int j3;
int col1;
int col2;
int row1;
int row2;
ap::real_1d_array x1;
ap::real_1d_array x2;
ap::real_2d_array a;
ap::real_2d_array b;
ap::real_2d_array c1;
ap::real_2d_array c2;
double err;
double e1;
double e2;
double e3;
double v;
double scl1;
double scl2;
double scl3;
bool was1;
bool was2;
bool trans1;
bool trans2;
double threshold;
bool n2errors;
bool hsnerrors;
bool amaxerrors;
bool mverrors;
bool iterrors;
bool cterrors;
bool mmerrors;
bool waserrors;
n2errors = false;
amaxerrors = false;
hsnerrors = false;
mverrors = false;
iterrors = false;
cterrors = false;
mmerrors = false;
waserrors = false;
threshold = 10000*ap::machineepsilon;
//
// Test Norm2
//
passcount = 1000;
e1 = 0;
e2 = 0;
e3 = 0;
scl2 = 0.5*ap::maxrealnumber;
scl3 = 2*ap::minrealnumber;
for(pass = 1; pass <= passcount; pass++)
{
n = 1+ap::randominteger(1000);
i1 = ap::randominteger(10);
i2 = n+i1-1;
x1.setbounds(i1, i2);
x2.setbounds(i1, i2);
for(i = i1; i <= i2; i++)
{
x1(i) = 2*ap::randomreal()-1;
}
v = 0;
for(i = i1; i <= i2; i++)
{
v = v+ap::sqr(x1(i));
}
v = sqrt(v);
e1 = ap::maxreal(e1, fabs(v-vectornorm2(x1, i1, i2)));
for(i = i1; i <= i2; i++)
{
x2(i) = scl2*x1(i);
}
e2 = ap::maxreal(e2, fabs(v*scl2-vectornorm2(x2, i1, i2)));
for(i = i1; i <= i2; i++)
{
x2(i) = scl3*x1(i);
}
e3 = ap::maxreal(e3, fabs(v*scl3-vectornorm2(x2, i1, i2)));
}
e2 = e2/scl2;
e3 = e3/scl3;
n2errors = ap::fp_greater_eq(e1,threshold)||ap::fp_greater_eq(e2,threshold)||ap::fp_greater_eq(e3,threshold);
//
// Testing VectorAbsMax, Column/Row AbsMax
//
x1.setbounds(1, 5);
x1(1) = 2.0;
x1(2) = 0.2;
x1(3) = -1.3;
x1(4) = 0.7;
x1(5) = -3.0;
amaxerrors = vectoridxabsmax(x1, 1, 5)!=5||vectoridxabsmax(x1, 1, 4)!=1||vectoridxabsmax(x1, 2, 4)!=3;
n = 30;
x1.setbounds(1, n);
a.setbounds(1, n, 1, n);
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
a(i,j) = 2*ap::randomreal()-1;
}
}
was1 = false;
was2 = false;
for(pass = 1; pass <= 1000; pass++)
{
j = 1+ap::randominteger(n);
i1 = 1+ap::randominteger(n);
i2 = i1+ap::randominteger(n+1-i1);
ap::vmove(x1.getvector(i1, i2), a.getcolumn(j, i1, i2));
if( vectoridxabsmax(x1, i1, i2)!=columnidxabsmax(a, i1, i2, j) )
{
was1 = true;
}
i = 1+ap::randominteger(n);
j1 = 1+ap::randominteger(n);
j2 = j1+ap::randominteger(n+1-j1);
ap::vmove(&x1(j1), &a(i, j1), ap::vlen(j1,j2));
if( vectoridxabsmax(x1, j1, j2)!=rowidxabsmax(a, j1, j2, i) )
{
was2 = true;
}
}
amaxerrors = amaxerrors||was1||was2;
//
// Testing upper Hessenberg 1-norm
//
a.setbounds(1, 3, 1, 3);
x1.setbounds(1, 3);
a(1,1) = 2;
a(1,2) = 3;
a(1,3) = 1;
a(2,1) = 4;
a(2,2) = -5;
a(2,3) = 8;
a(3,1) = 99;
a(3,2) = 3;
a(3,3) = 1;
hsnerrors = ap::fp_greater(fabs(upperhessenberg1norm(a, 1, 3, 1, 3, x1)-11),threshold);
//
// Testing MatrixVectorMultiply
//
a.setbounds(2, 3, 3, 5);
x1.setbounds(1, 3);
x2.setbounds(1, 2);
a(2,3) = 2;
a(2,4) = -1;
a(2,5) = -1;
a(3,3) = 1;
a(3,4) = -2;
a(3,5) = 2;
x1(1) = 1;
x1(2) = 2;
x1(3) = 1;
x2(1) = -1;
x2(2) = -1;
matrixvectormultiply(a, 2, 3, 3, 5, false, x1, 1, 3, 1.0, x2, 1, 2, 1.0);
matrixvectormultiply(a, 2, 3, 3, 5, true, x2, 1, 2, 1.0, x1, 1, 3, 1.0);
e1 = fabs(x1(1)+5)+fabs(x1(2)-8)+fabs(x1(3)+1)+fabs(x2(1)+2)+fabs(x2(2)+2);
x1(1) = 1;
x1(2) = 2;
x1(3) = 1;
x2(1) = -1;
x2(2) = -1;
matrixvectormultiply(a, 2, 3, 3, 5, false, x1, 1, 3, 1.0, x2, 1, 2, 0.0);
matrixvectormultiply(a, 2, 3, 3, 5, true, x2, 1, 2, 1.0, x1, 1, 3, 0.0);
e2 = fabs(x1(1)+3)+fabs(x1(2)-3)+fabs(x1(3)+1)+fabs(x2(1)+1)+fabs(x2(2)+1);
mverrors = ap::fp_greater_eq(e1+e2,threshold);
//
// testing inplace transpose
//
n = 10;
a.setbounds(1, n, 1, n);
b.setbounds(1, n, 1, n);
x1.setbounds(1, n-1);
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
a(i,j) = ap::randomreal();
}
}
passcount = 10000;
was1 = false;
for(pass = 1; pass <= passcount; pass++)
{
i1 = 1+ap::randominteger(n);
i2 = i1+ap::randominteger(n-i1+1);
j1 = 1+ap::randominteger(n-(i2-i1));
j2 = j1+(i2-i1);
copymatrix(a, i1, i2, j1, j2, b, i1, i2, j1, j2);
inplacetranspose(b, i1, i2, j1, j2, x1);
for(i = i1; i <= i2; i++)
{
for(j = j1; j <= j2; j++)
{
if( ap::fp_neq(a(i,j),b(i1+(j-j1),j1+(i-i1))) )
{
was1 = true;
}
}
}
}
iterrors = was1;
//
// testing copy and transpose
//
n = 10;
a.setbounds(1, n, 1, n);
b.setbounds(1, n, 1, n);
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
a(i,j) = ap::randomreal();
}
}
passcount = 10000;
was1 = false;
for(pass = 1; pass <= passcount; pass++)
{
i1 = 1+ap::randominteger(n);
i2 = i1+ap::randominteger(n-i1+1);
j1 = 1+ap::randominteger(n);
j2 = j1+ap::randominteger(n-j1+1);
copyandtranspose(a, i1, i2, j1, j2, b, j1, j2, i1, i2);
for(i = i1; i <= i2; i++)
{
for(j = j1; j <= j2; j++)
{
if( ap::fp_neq(a(i,j),b(j,i)) )
{
was1 = true;
}
}
}
}
cterrors = was1;
//
// Testing MatrixMatrixMultiply
//
n = 10;
a.setbounds(1, 2*n, 1, 2*n);
b.setbounds(1, 2*n, 1, 2*n);
c1.setbounds(1, 2*n, 1, 2*n);
c2.setbounds(1, 2*n, 1, 2*n);
x1.setbounds(1, n);
x2.setbounds(1, n);
for(i = 1; i <= 2*n; i++)
{
for(j = 1; j <= 2*n; j++)
{
a(i,j) = ap::randomreal();
b(i,j) = ap::randomreal();
}
}
passcount = 1000;
was1 = false;
for(pass = 1; pass <= passcount; pass++)
{
for(i = 1; i <= 2*n; i++)
{
for(j = 1; j <= 2*n; j++)
{
c1(i,j) = 2.1*i+3.1*j;
c2(i,j) = c1(i,j);
}
}
l = 1+ap::randominteger(n);
k = 1+ap::randominteger(n);
r = 1+ap::randominteger(n);
i1 = 1+ap::randominteger(n);
j1 = 1+ap::randominteger(n);
i2 = 1+ap::randominteger(n);
j2 = 1+ap::randominteger(n);
i3 = 1+ap::randominteger(n);
j3 = 1+ap::randominteger(n);
trans1 = ap::fp_greater(ap::randomreal(),0.5);
trans2 = ap::fp_greater(ap::randomreal(),0.5);
if( trans1 )
{
col1 = l;
row1 = k;
}
else
{
col1 = k;
row1 = l;
}
if( trans2 )
{
col2 = k;
row2 = r;
}
else
{
col2 = r;
row2 = k;
}
scl1 = ap::randomreal();
scl2 = ap::randomreal();
matrixmatrixmultiply(a, i1, i1+row1-1, j1, j1+col1-1, trans1, b, i2, i2+row2-1, j2, j2+col2-1, trans2, scl1, c1, i3, i3+l-1, j3, j3+r-1, scl2, x1);
naivematrixmatrixmultiply(a, i1, i1+row1-1, j1, j1+col1-1, trans1, b, i2, i2+row2-1, j2, j2+col2-1, trans2, scl1, c2, i3, i3+l-1, j3, j3+r-1, scl2);
err = 0;
for(i = 1; i <= l; i++)
{
for(j = 1; j <= r; j++)
{
err = ap::maxreal(err, fabs(c1(i3+i-1,j3+j-1)-c2(i3+i-1,j3+j-1)));
}
}
if( ap::fp_greater(err,threshold) )
{
was1 = true;
break;
}
}
mmerrors = was1;
//
// report
//
waserrors = n2errors||amaxerrors||hsnerrors||mverrors||iterrors||cterrors||mmerrors;
if( !silent )
{
printf("TESTING BLAS\n");
printf("VectorNorm2: ");
if( n2errors )
{
printf("FAILED\n");
}
else
{
printf("OK\n");
}
printf("AbsMax (vector/row/column): ");
if( amaxerrors )
{
printf("FAILED\n");
}
else
{
printf("OK\n");
}
printf("UpperHessenberg1Norm: ");
if( hsnerrors )
{
printf("FAILED\n");
}
else
{
printf("OK\n");
}
printf("MatrixVectorMultiply: ");
if( mverrors )
{
printf("FAILED\n");
}
else
{
printf("OK\n");
}
printf("InplaceTranspose: ");
if( iterrors )
{
printf("FAILED\n");
}
else
{
printf("OK\n");
}
printf("CopyAndTranspose: ");
if( cterrors )
{
printf("FAILED\n");
}
else
{
printf("OK\n");
}
printf("MatrixMatrixMultiply: ");
if( mmerrors )
{
printf("FAILED\n");
}
else
{
printf("OK\n");
}
if( waserrors )
{
printf("TEST FAILED\n");
}
else
{
printf("TEST PASSED\n");
}
printf("\n\n");
}
result = !waserrors;
return result;
}
/**
* Compute the ordinary least squares estimation of the solution to a linear regression
*
* @param data The regression input. Each inner vector should be a single variable (so column maj order)
* @param response The response variable.
* @return betas The estimate of regression coefficients
*/
vector<double> LinearRegression::leastSquares(const vector<vector<double> > &data, const vector<double> &response){
int sz = data.size();
if(sz < 0) throw LinearRegressionException();
int indivSz = response.size();
vector<double> betas;
alglib::real_1d_array vecResp;
alglib::real_1d_array vecBetas;
alglib::real_2d_array vecData;
alglib::real_2d_array tempSquare;
alglib::real_1d_array tempWork;
vecResp.setlength(indivSz);
vecBetas.setlength(sz);
vecData.setlength(indivSz,sz);
tempSquare.setlength(sz,sz);
tempWork.setlength(indivSz+1);
// Transfer into the matrices.
for(unsigned int i=0;i<data.size();i++){
for(unsigned int j=0;j < data.at(0).size();j++){
vecData(j,i) = data.at(i).at(j);
}
}
for(unsigned int i=0;i<response.size();i++)
vecResp(i) = response.at(i);
/// X'*X
matrixmatrixmultiply(vecData,0,indivSz-1,0,sz-1,true,
vecData,0,indivSz-1,0,sz-1,false,1.0,
tempSquare,0,sz-1,0,sz-1,0.0,tempWork);
alglib::matinvreport report;
alglib::ae_int_t reportInfo ;
rmatrixinverse(tempSquare, reportInfo, report);
if(reportInfo != 1){
throw LinearRegressionException();
}
if (report.r1 > LINEAR_REGRESSION_CONDITION_NUMBER_LIMIT){
throw ConditionNumberEx(1.0/report.r1);
}
/// X'*beta
matrixvectormultiply(vecData,0,indivSz-1,0,sz-1,true,
vecResp,0,indivSz-1,1.0,
tempWork,0,sz-1,0.0);
/// tempSquare * tempWork
matrixvectormultiply(tempSquare,0,sz-1,0,sz-1,false,
tempWork,0,sz-1,1.0,
vecBetas,0,sz-1,0.0);
for(int i=0;i<sz;i++)
betas.push_back(vecBetas(i));
return betas;
}
/*************************************************************************
Internal linear regression subroutine
*************************************************************************/
static void lrinternal(const ap::real_2d_array& xy,
const ap::real_1d_array& s,
int npoints,
int nvars,
int& info,
linearmodel& lm,
lrreport& ar)
{
ap::real_2d_array a;
ap::real_2d_array u;
ap::real_2d_array vt;
ap::real_2d_array vm;
ap::real_2d_array xym;
ap::real_1d_array b;
ap::real_1d_array sv;
ap::real_1d_array t;
ap::real_1d_array svi;
ap::real_1d_array work;
int i;
int j;
int k;
int ncv;
int na;
int nacv;
double r;
double p;
double epstol;
lrreport ar2;
int offs;
linearmodel tlm;
epstol = 1000;
//
// Check for errors in data
//
if( npoints<nvars||nvars<1 )
{
info = -1;
return;
}
for(i = 0; i <= npoints-1; i++)
{
if( ap::fp_less_eq(s(i),0) )
{
info = -2;
return;
}
}
info = 1;
//
// Create design matrix
//
a.setbounds(0, npoints-1, 0, nvars-1);
b.setbounds(0, npoints-1);
for(i = 0; i <= npoints-1; i++)
{
r = 1/s(i);
ap::vmove(&a(i, 0), &xy(i, 0), ap::vlen(0,nvars-1), r);
b(i) = xy(i,nvars)/s(i);
}
//
// Allocate W:
// W[0] array size
// W[1] version number, 0
// W[2] NVars (minus 1, to be compatible with external representation)
// W[3] coefficients offset
//
lm.w.setbounds(0, 4+nvars-1);
offs = 4;
lm.w(0) = 4+nvars;
lm.w(1) = lrvnum;
lm.w(2) = nvars-1;
lm.w(3) = offs;
//
// Solve problem using SVD:
//
// 0. check for degeneracy (different types)
// 1. A = U*diag(sv)*V'
// 2. T = b'*U
// 3. w = SUM((T[i]/sv[i])*V[..,i])
// 4. cov(wi,wj) = SUM(Vji*Vjk/sv[i]^2,K=1..M)
//
// see $15.4 of "Numerical Recipes in C" for more information
//
t.setbounds(0, nvars-1);
svi.setbounds(0, nvars-1);
ar.c.setbounds(0, nvars-1, 0, nvars-1);
vm.setbounds(0, nvars-1, 0, nvars-1);
if( !rmatrixsvd(a, npoints, nvars, 1, 1, 2, sv, u, vt) )
{
info = -4;
return;
}
if( ap::fp_less_eq(sv(0),0) )
{
//
// Degenerate case: zero design matrix.
//
for(i = offs; i <= offs+nvars-1; i++)
{
lm.w(i) = 0;
}
ar.rmserror = lrrmserror(lm, xy, npoints);
ar.avgerror = lravgerror(lm, xy, npoints);
ar.avgrelerror = lravgrelerror(lm, xy, npoints);
ar.cvrmserror = ar.rmserror;
ar.cvavgerror = ar.avgerror;
ar.cvavgrelerror = ar.avgrelerror;
ar.ncvdefects = 0;
ar.cvdefects.setbounds(0, nvars-1);
ar.c.setbounds(0, nvars-1, 0, nvars-1);
for(i = 0; i <= nvars-1; i++)
{
for(j = 0; j <= nvars-1; j++)
{
ar.c(i,j) = 0;
}
}
return;
}
if( ap::fp_less_eq(sv(nvars-1),epstol*ap::machineepsilon*sv(0)) )
{
//
// Degenerate case, non-zero design matrix.
//
// We can leave it and solve task in SVD least squares fashion.
// Solution and covariance matrix will be obtained correctly,
// but CV error estimates - will not. It is better to reduce
// it to non-degenerate task and to obtain correct CV estimates.
//
for(k = nvars; k >= 1; k--)
{
if( ap::fp_greater(sv(k-1),epstol*ap::machineepsilon*sv(0)) )
{
//
// Reduce
//
xym.setbounds(0, npoints-1, 0, k);
for(i = 0; i <= npoints-1; i++)
{
for(j = 0; j <= k-1; j++)
{
r = ap::vdotproduct(&xy(i, 0), &vt(j, 0), ap::vlen(0,nvars-1));
xym(i,j) = r;
}
xym(i,k) = xy(i,nvars);
}
//
// Solve
//
lrinternal(xym, s, npoints, k, info, tlm, ar2);
if( info!=1 )
{
return;
}
//
// Convert back to un-reduced format
//
for(j = 0; j <= nvars-1; j++)
{
lm.w(offs+j) = 0;
}
for(j = 0; j <= k-1; j++)
{
r = tlm.w(offs+j);
ap::vadd(&lm.w(offs), &vt(j, 0), ap::vlen(offs,offs+nvars-1), r);
}
ar.rmserror = ar2.rmserror;
ar.avgerror = ar2.avgerror;
ar.avgrelerror = ar2.avgrelerror;
ar.cvrmserror = ar2.cvrmserror;
ar.cvavgerror = ar2.cvavgerror;
ar.cvavgrelerror = ar2.cvavgrelerror;
ar.ncvdefects = ar2.ncvdefects;
ar.cvdefects.setbounds(0, nvars-1);
for(j = 0; j <= ar.ncvdefects-1; j++)
{
ar.cvdefects(j) = ar2.cvdefects(j);
}
ar.c.setbounds(0, nvars-1, 0, nvars-1);
work.setbounds(1, nvars);
matrixmatrixmultiply(ar2.c, 0, k-1, 0, k-1, false, vt, 0, k-1, 0, nvars-1, false, 1.0, vm, 0, k-1, 0, nvars-1, 0.0, work);
matrixmatrixmultiply(vt, 0, k-1, 0, nvars-1, true, vm, 0, k-1, 0, nvars-1, false, 1.0, ar.c, 0, nvars-1, 0, nvars-1, 0.0, work);
return;
}
}
info = -255;
return;
}
for(i = 0; i <= nvars-1; i++)
{
if( ap::fp_greater(sv(i),epstol*ap::machineepsilon*sv(0)) )
{
svi(i) = 1/sv(i);
}
else
{
svi(i) = 0;
}
}
for(i = 0; i <= nvars-1; i++)
{
t(i) = 0;
}
for(i = 0; i <= npoints-1; i++)
{
r = b(i);
ap::vadd(&t(0), &u(i, 0), ap::vlen(0,nvars-1), r);
}
for(i = 0; i <= nvars-1; i++)
{
lm.w(offs+i) = 0;
}
for(i = 0; i <= nvars-1; i++)
{
r = t(i)*svi(i);
ap::vadd(&lm.w(offs), &vt(i, 0), ap::vlen(offs,offs+nvars-1), r);
}
for(j = 0; j <= nvars-1; j++)
{
r = svi(j);
ap::vmove(vm.getcolumn(j, 0, nvars-1), vt.getrow(j, 0, nvars-1), r);
}
for(i = 0; i <= nvars-1; i++)
{
for(j = i; j <= nvars-1; j++)
{
r = ap::vdotproduct(&vm(i, 0), &vm(j, 0), ap::vlen(0,nvars-1));
ar.c(i,j) = r;
ar.c(j,i) = r;
}
}
//
// Leave-1-out cross-validation error.
//
// NOTATIONS:
// A design matrix
// A*x = b original linear least squares task
// U*S*V' SVD of A
// ai i-th row of the A
// bi i-th element of the b
// xf solution of the original LLS task
//
// Cross-validation error of i-th element from a sample is
// calculated using following formula:
//
// ERRi = ai*xf - (ai*xf-bi*(ui*ui'))/(1-ui*ui') (1)
//
// This formula can be derived from normal equations of the
// original task
//
// (A'*A)x = A'*b (2)
//
// by applying modification (zeroing out i-th row of A) to (2):
//
// (A-ai)'*(A-ai) = (A-ai)'*b
//
// and using Sherman-Morrison formula for updating matrix inverse
//
// NOTE 1: b is not zeroed out since it is much simpler and
// does not influence final result.
//
// NOTE 2: some design matrices A have such ui that 1-ui*ui'=0.
// Formula (1) can't be applied for such cases and they are skipped
// from CV calculation (which distorts resulting CV estimate).
// But from the properties of U we can conclude that there can
// be no more than NVars such vectors. Usually
// NVars << NPoints, so in a normal case it only slightly
// influences result.
//
ncv = 0;
na = 0;
nacv = 0;
ar.rmserror = 0;
ar.avgerror = 0;
ar.avgrelerror = 0;
ar.cvrmserror = 0;
ar.cvavgerror = 0;
ar.cvavgrelerror = 0;
ar.ncvdefects = 0;
ar.cvdefects.setbounds(0, nvars-1);
for(i = 0; i <= npoints-1; i++)
{
//
// Error on a training set
//
r = ap::vdotproduct(&xy(i, 0), &lm.w(offs), ap::vlen(0,nvars-1));
ar.rmserror = ar.rmserror+ap::sqr(r-xy(i,nvars));
ar.avgerror = ar.avgerror+fabs(r-xy(i,nvars));
if( ap::fp_neq(xy(i,nvars),0) )
{
ar.avgrelerror = ar.avgrelerror+fabs((r-xy(i,nvars))/xy(i,nvars));
na = na+1;
}
//
// Error using fast leave-one-out cross-validation
//
p = ap::vdotproduct(&u(i, 0), &u(i, 0), ap::vlen(0,nvars-1));
if( ap::fp_greater(p,1-epstol*ap::machineepsilon) )
{
ar.cvdefects(ar.ncvdefects) = i;
ar.ncvdefects = ar.ncvdefects+1;
continue;
}
r = s(i)*(r/s(i)-b(i)*p)/(1-p);
ar.cvrmserror = ar.cvrmserror+ap::sqr(r-xy(i,nvars));
ar.cvavgerror = ar.cvavgerror+fabs(r-xy(i,nvars));
if( ap::fp_neq(xy(i,nvars),0) )
{
ar.cvavgrelerror = ar.cvavgrelerror+fabs((r-xy(i,nvars))/xy(i,nvars));
nacv = nacv+1;
}
ncv = ncv+1;
}
if( ncv==0 )
{
//
// Something strange: ALL ui are degenerate.
// Unexpected...
//
info = -255;
return;
}
ar.rmserror = sqrt(ar.rmserror/npoints);
ar.avgerror = ar.avgerror/npoints;
if( na!=0 )
{
ar.avgrelerror = ar.avgrelerror/na;
}
ar.cvrmserror = sqrt(ar.cvrmserror/ncv);
ar.cvavgerror = ar.cvavgerror/ncv;
if( nacv!=0 )
{
ar.cvavgrelerror = ar.cvavgrelerror/nacv;
}
}
/*************************************************************************
N-dimensional multiclass Fisher LDA
Subroutine finds coefficients of linear combinations which optimally separates
training set on classes. It returns N-dimensional basis whose vector are sorted
by quality of training set separation (in descending order).
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 - basis, array[0..NVars-1,0..NVars-1]
columns of matrix stores basis vectors, sorted by
quality of training set separation (in descending order)
-- ALGLIB --
Copyright 31.05.2008 by Bochkanov Sergey
*************************************************************************/
void fisherldan(const ap::real_2d_array& xy,
int npoints,
int nvars,
int nclasses,
int& info,
ap::real_2d_array& w)
{
int i;
int j;
int k;
int m;
double v;
ap::integer_1d_array c;
ap::real_1d_array mu;
ap::real_2d_array muc;
ap::integer_1d_array nc;
ap::real_2d_array sw;
ap::real_2d_array st;
ap::real_2d_array z;
ap::real_2d_array z2;
ap::real_2d_array tm;
ap::real_2d_array sbroot;
ap::real_2d_array a;
ap::real_2d_array xyproj;
ap::real_2d_array wproj;
ap::real_1d_array tf;
ap::real_1d_array d;
ap::real_1d_array d2;
ap::real_1d_array work;
//
// Test data
//
if( npoints<0||nvars<1||nclasses<2 )
{
info = -1;
return;
}
for(i = 0; i <= npoints-1; i++)
{
if( ap::round(xy(i,nvars))<0||ap::round(xy(i,nvars))>=nclasses )
{
info = -2;
return;
}
}
info = 1;
//
// Special case: NPoints<=1
// Degenerate task.
//
if( npoints<=1 )
{
info = 2;
w.setbounds(0, nvars-1, 0, nvars-1);
for(i = 0; i <= nvars-1; i++)
{
for(j = 0; j <= nvars-1; j++)
{
if( i==j )
{
w(i,j) = 1;
}
else
{
w(i,j) = 0;
}
}
}
return;
}
//
// Prepare temporaries
//
tf.setbounds(0, nvars-1);
work.setbounds(1, ap::maxint(nvars, npoints));
//
// Convert class labels from reals to integers (just for convenience)
//
c.setbounds(0, npoints-1);
for(i = 0; i <= npoints-1; i++)
{
c(i) = ap::round(xy(i,nvars));
}
//
// Calculate class sizes and means
//
mu.setbounds(0, nvars-1);
muc.setbounds(0, nclasses-1, 0, nvars-1);
nc.setbounds(0, nclasses-1);
for(j = 0; j <= nvars-1; j++)
{
mu(j) = 0;
}
for(i = 0; i <= nclasses-1; i++)
{
nc(i) = 0;
for(j = 0; j <= nvars-1; j++)
{
muc(i,j) = 0;
}
}
for(i = 0; i <= npoints-1; i++)
{
ap::vadd(&mu(0), 1, &xy(i, 0), 1, ap::vlen(0,nvars-1));
ap::vadd(&muc(c(i), 0), 1, &xy(i, 0), 1, ap::vlen(0,nvars-1));
nc(c(i)) = nc(c(i))+1;
}
for(i = 0; i <= nclasses-1; i++)
{
v = double(1)/double(nc(i));
ap::vmul(&muc(i, 0), 1, ap::vlen(0,nvars-1), v);
}
v = double(1)/double(npoints);
ap::vmul(&mu(0), 1, ap::vlen(0,nvars-1), v);
//
// Create ST matrix
//
st.setbounds(0, nvars-1, 0, nvars-1);
for(i = 0; i <= nvars-1; i++)
{
for(j = 0; j <= nvars-1; j++)
{
st(i,j) = 0;
}
}
for(k = 0; k <= npoints-1; k++)
{
ap::vmove(&tf(0), 1, &xy(k, 0), 1, ap::vlen(0,nvars-1));
ap::vsub(&tf(0), 1, &mu(0), 1, ap::vlen(0,nvars-1));
for(i = 0; i <= nvars-1; i++)
{
v = tf(i);
ap::vadd(&st(i, 0), 1, &tf(0), 1, ap::vlen(0,nvars-1), v);
}
}
//
// Create SW matrix
//
sw.setbounds(0, nvars-1, 0, nvars-1);
for(i = 0; i <= nvars-1; i++)
{
for(j = 0; j <= nvars-1; j++)
{
sw(i,j) = 0;
}
}
for(k = 0; k <= npoints-1; k++)
{
ap::vmove(&tf(0), 1, &xy(k, 0), 1, ap::vlen(0,nvars-1));
ap::vsub(&tf(0), 1, &muc(c(k), 0), 1, ap::vlen(0,nvars-1));
for(i = 0; i <= nvars-1; i++)
{
v = tf(i);
ap::vadd(&sw(i, 0), 1, &tf(0), 1, ap::vlen(0,nvars-1), v);
}
}
//
// Maximize ratio J=(w'*ST*w)/(w'*SW*w).
//
// First, make transition from w to v such that w'*ST*w becomes v'*v:
// v = root(ST)*w = R*w
// R = root(D)*Z'
// w = (root(ST)^-1)*v = RI*v
// RI = Z*inv(root(D))
// J = (v'*v)/(v'*(RI'*SW*RI)*v)
// ST = Z*D*Z'
//
// so we have
//
// J = (v'*v) / (v'*(inv(root(D))*Z'*SW*Z*inv(root(D)))*v) =
// = (v'*v) / (v'*A*v)
//
if( !smatrixevd(st, nvars, 1, true, d, z) )
{
info = -4;
return;
}
w.setbounds(0, nvars-1, 0, nvars-1);
if( ap::fp_less_eq(d(nvars-1),0)||ap::fp_less_eq(d(0),1000*ap::machineepsilon*d(nvars-1)) )
{
//
// Special case: D[NVars-1]<=0
// Degenerate task (all variables takes the same value).
//
if( ap::fp_less_eq(d(nvars-1),0) )
{
info = 2;
for(i = 0; i <= nvars-1; i++)
{
for(j = 0; j <= nvars-1; j++)
{
if( i==j )
{
w(i,j) = 1;
}
else
{
w(i,j) = 0;
}
}
}
return;
}
//
// Special case: degenerate ST matrix, multicollinearity found.
// Since we know ST eigenvalues/vectors we can translate task to
// non-degenerate form.
//
// Let WG is orthogonal basis of the non zero variance subspace
// of the ST and let WZ is orthogonal basis of the zero variance
// subspace.
//
// Projection on WG allows us to use LDA on reduced M-dimensional
// subspace, N-M vectors of WZ allows us to update reduced LDA
// factors to full N-dimensional subspace.
//
m = 0;
for(k = 0; k <= nvars-1; k++)
{
if( ap::fp_less_eq(d(k),1000*ap::machineepsilon*d(nvars-1)) )
{
m = k+1;
}
}
ap::ap_error::make_assertion(m!=0, "FisherLDAN: internal error #1");
xyproj.setbounds(0, npoints-1, 0, nvars-m);
matrixmatrixmultiply(xy, 0, npoints-1, 0, nvars-1, false, z, 0, nvars-1, m, nvars-1, false, 1.0, xyproj, 0, npoints-1, 0, nvars-m-1, 0.0, work);
for(i = 0; i <= npoints-1; i++)
{
xyproj(i,nvars-m) = xy(i,nvars);
}
fisherldan(xyproj, npoints, nvars-m, nclasses, info, wproj);
if( info<0 )
{
return;
}
matrixmatrixmultiply(z, 0, nvars-1, m, nvars-1, false, wproj, 0, nvars-m-1, 0, nvars-m-1, false, 1.0, w, 0, nvars-1, 0, nvars-m-1, 0.0, work);
for(k = nvars-m; k <= nvars-1; k++)
{
ap::vmove(&w(0, k), w.getstride(), &z(0, k-(nvars-m)), z.getstride(), ap::vlen(0,nvars-1));
}
info = 2;
}
else
{
//
// General case: no multicollinearity
//
tm.setbounds(0, nvars-1, 0, nvars-1);
a.setbounds(0, nvars-1, 0, nvars-1);
matrixmatrixmultiply(sw, 0, nvars-1, 0, nvars-1, false, z, 0, nvars-1, 0, nvars-1, false, 1.0, tm, 0, nvars-1, 0, nvars-1, 0.0, work);
matrixmatrixmultiply(z, 0, nvars-1, 0, nvars-1, true, tm, 0, nvars-1, 0, nvars-1, false, 1.0, a, 0, nvars-1, 0, nvars-1, 0.0, work);
for(i = 0; i <= nvars-1; i++)
{
for(j = 0; j <= nvars-1; j++)
{
a(i,j) = a(i,j)/sqrt(d(i)*d(j));
}
}
if( !smatrixevd(a, nvars, 1, true, d2, z2) )
{
info = -4;
return;
}
for(k = 0; k <= nvars-1; k++)
{
for(i = 0; i <= nvars-1; i++)
{
tf(i) = z2(i,k)/sqrt(d(i));
}
for(i = 0; i <= nvars-1; i++)
{
v = ap::vdotproduct(&z(i, 0), 1, &tf(0), 1, ap::vlen(0,nvars-1));
w(i,k) = v;
}
}
}
//
// Post-processing:
// * normalization
// * converting to non-negative form, if possible
//
for(k = 0; k <= nvars-1; k++)
{
v = ap::vdotproduct(&w(0, k), w.getstride(), &w(0, k), w.getstride(), ap::vlen(0,nvars-1));
v = 1/sqrt(v);
ap::vmul(&w(0, k), w.getstride(), ap::vlen(0,nvars-1), v);
v = 0;
for(i = 0; i <= nvars-1; i++)
{
v = v+w(i,k);
}
if( ap::fp_less(v,0) )
{
ap::vmul(&w(0, k), w.getstride(), ap::vlen(0,nvars-1), -1);
}
}
}
/*************************************************************************
Singular value decomposition of a rectangular matrix.
The algorithm calculates the singular value decomposition of a matrix of
size MxN: A = U * S * V^T
The algorithm finds the singular values and, optionally, matrices U and V^T.
The algorithm can find both first min(M,N) columns of matrix U and rows of
matrix V^T (singular vectors), and matrices U and V^T wholly (of sizes MxM
and NxN respectively).
Take into account that the subroutine does not return matrix V but V^T.
Input parameters:
A - matrix to be decomposed.
Array whose indexes range within [0..M-1, 0..N-1].
M - number of rows in matrix A.
N - number of columns in matrix A.
UNeeded - 0, 1 or 2. See the description of the parameter U.
VTNeeded - 0, 1 or 2. See the description of the parameter VT.
AdditionalMemory -
If the parameter:
* equals 0, the algorithm doesn’t use additional
memory (lower requirements, lower performance).
* equals 1, the algorithm uses additional
memory of size min(M,N)*min(M,N) of real numbers.
It often speeds up the algorithm.
* equals 2, the algorithm uses additional
memory of size M*min(M,N) of real numbers.
It allows to get a maximum performance.
The recommended value of the parameter is 2.
Output parameters:
W - contains singular values in descending order.
U - if UNeeded=0, U isn't changed, the left singular vectors
are not calculated.
if Uneeded=1, U contains left singular vectors (first
min(M,N) columns of matrix U). Array whose indexes range
within [0..M-1, 0..Min(M,N)-1].
if UNeeded=2, U contains matrix U wholly. Array whose
indexes range within [0..M-1, 0..M-1].
VT - if VTNeeded=0, VT isn’t changed, the right singular vectors
are not calculated.
if VTNeeded=1, VT contains right singular vectors (first
min(M,N) rows of matrix V^T). Array whose indexes range
within [0..min(M,N)-1, 0..N-1].
if VTNeeded=2, VT contains matrix V^T wholly. Array whose
indexes range within [0..N-1, 0..N-1].
-- ALGLIB --
Copyright 2005 by Bochkanov Sergey
*************************************************************************/
bool rmatrixsvd(ap::real_2d_array a,
int m,
int n,
int uneeded,
int vtneeded,
int additionalmemory,
ap::real_1d_array& w,
ap::real_2d_array& u,
ap::real_2d_array& vt)
{
bool result;
ap::real_1d_array tauq;
ap::real_1d_array taup;
ap::real_1d_array tau;
ap::real_1d_array e;
ap::real_1d_array work;
ap::real_2d_array t2;
bool isupper;
int minmn;
int ncu;
int nrvt;
int nru;
int ncvt;
int i;
int j;
result = true;
if( m==0||n==0 )
{
return result;
}
ap::ap_error::make_assertion(uneeded>=0&&uneeded<=2, "SVDDecomposition: wrong parameters!");
ap::ap_error::make_assertion(vtneeded>=0&&vtneeded<=2, "SVDDecomposition: wrong parameters!");
ap::ap_error::make_assertion(additionalmemory>=0&&additionalmemory<=2, "SVDDecomposition: wrong parameters!");
//
// initialize
//
minmn = ap::minint(m, n);
w.setbounds(1, minmn);
ncu = 0;
nru = 0;
if( uneeded==1 )
{
nru = m;
ncu = minmn;
u.setbounds(0, nru-1, 0, ncu-1);
}
if( uneeded==2 )
{
nru = m;
ncu = m;
u.setbounds(0, nru-1, 0, ncu-1);
}
nrvt = 0;
ncvt = 0;
if( vtneeded==1 )
{
nrvt = minmn;
ncvt = n;
vt.setbounds(0, nrvt-1, 0, ncvt-1);
}
if( vtneeded==2 )
{
nrvt = n;
ncvt = n;
vt.setbounds(0, nrvt-1, 0, ncvt-1);
}
//
// M much larger than N
// Use bidiagonal reduction with QR-decomposition
//
if( ap::fp_greater(m,1.6*n) )
{
if( uneeded==0 )
{
//
// No left singular vectors to be computed
//
rmatrixqr(a, m, n, tau);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= i-1; j++)
{
a(i,j) = 0;
}
}
rmatrixbd(a, n, n, tauq, taup);
rmatrixbdunpackpt(a, n, n, taup, nrvt, vt);
rmatrixbdunpackdiagonals(a, n, n, isupper, w, e);
result = rmatrixbdsvd(w, e, n, isupper, false, u, 0, a, 0, vt, ncvt);
return result;
}
else
{
//
// Left singular vectors (may be full matrix U) to be computed
//
rmatrixqr(a, m, n, tau);
rmatrixqrunpackq(a, m, n, tau, ncu, u);
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= i-1; j++)
{
a(i,j) = 0;
}
}
rmatrixbd(a, n, n, tauq, taup);
rmatrixbdunpackpt(a, n, n, taup, nrvt, vt);
rmatrixbdunpackdiagonals(a, n, n, isupper, w, e);
if( additionalmemory<1 )
{
//
// No additional memory can be used
//
rmatrixbdmultiplybyq(a, n, n, tauq, u, m, n, true, false);
result = rmatrixbdsvd(w, e, n, isupper, false, u, m, a, 0, vt, ncvt);
}
else
{
//
// Large U. Transforming intermediate matrix T2
//
work.setbounds(1, ap::maxint(m, n));
rmatrixbdunpackq(a, n, n, tauq, n, t2);
copymatrix(u, 0, m-1, 0, n-1, a, 0, m-1, 0, n-1);
inplacetranspose(t2, 0, n-1, 0, n-1, work);
result = rmatrixbdsvd(w, e, n, isupper, false, u, 0, t2, n, vt, ncvt);
matrixmatrixmultiply(a, 0, m-1, 0, n-1, false, t2, 0, n-1, 0, n-1, true, 1.0, u, 0, m-1, 0, n-1, 0.0, work);
}
return result;
}
}
//
// N much larger than M
// Use bidiagonal reduction with LQ-decomposition
//
if( ap::fp_greater(n,1.6*m) )
{
if( vtneeded==0 )
{
//
// No right singular vectors to be computed
//
rmatrixlq(a, m, n, tau);
for(i = 0; i <= m-1; i++)
{
for(j = i+1; j <= m-1; j++)
{
a(i,j) = 0;
}
}
rmatrixbd(a, m, m, tauq, taup);
rmatrixbdunpackq(a, m, m, tauq, ncu, u);
rmatrixbdunpackdiagonals(a, m, m, isupper, w, e);
work.setbounds(1, m);
inplacetranspose(u, 0, nru-1, 0, ncu-1, work);
result = rmatrixbdsvd(w, e, m, isupper, false, a, 0, u, nru, vt, 0);
inplacetranspose(u, 0, nru-1, 0, ncu-1, work);
return result;
}
else
{
//
// Right singular vectors (may be full matrix VT) to be computed
//
rmatrixlq(a, m, n, tau);
rmatrixlqunpackq(a, m, n, tau, nrvt, vt);
for(i = 0; i <= m-1; i++)
{
for(j = i+1; j <= m-1; j++)
{
a(i,j) = 0;
}
}
rmatrixbd(a, m, m, tauq, taup);
rmatrixbdunpackq(a, m, m, tauq, ncu, u);
rmatrixbdunpackdiagonals(a, m, m, isupper, w, e);
work.setbounds(1, ap::maxint(m, n));
inplacetranspose(u, 0, nru-1, 0, ncu-1, work);
if( additionalmemory<1 )
{
//
// No additional memory available
//
rmatrixbdmultiplybyp(a, m, m, taup, vt, m, n, false, true);
result = rmatrixbdsvd(w, e, m, isupper, false, a, 0, u, nru, vt, n);
}
else
{
//
// Large VT. Transforming intermediate matrix T2
//
rmatrixbdunpackpt(a, m, m, taup, m, t2);
result = rmatrixbdsvd(w, e, m, isupper, false, a, 0, u, nru, t2, m);
copymatrix(vt, 0, m-1, 0, n-1, a, 0, m-1, 0, n-1);
matrixmatrixmultiply(t2, 0, m-1, 0, m-1, false, a, 0, m-1, 0, n-1, false, 1.0, vt, 0, m-1, 0, n-1, 0.0, work);
}
inplacetranspose(u, 0, nru-1, 0, ncu-1, work);
return result;
}
}
//
// M<=N
// We can use inplace transposition of U to get rid of columnwise operations
//
if( m<=n )
{
rmatrixbd(a, m, n, tauq, taup);
rmatrixbdunpackq(a, m, n, tauq, ncu, u);
rmatrixbdunpackpt(a, m, n, taup, nrvt, vt);
rmatrixbdunpackdiagonals(a, m, n, isupper, w, e);
work.setbounds(1, m);
inplacetranspose(u, 0, nru-1, 0, ncu-1, work);
result = rmatrixbdsvd(w, e, minmn, isupper, false, a, 0, u, nru, vt, ncvt);
inplacetranspose(u, 0, nru-1, 0, ncu-1, work);
return result;
}
//
// Simple bidiagonal reduction
//
rmatrixbd(a, m, n, tauq, taup);
rmatrixbdunpackq(a, m, n, tauq, ncu, u);
rmatrixbdunpackpt(a, m, n, taup, nrvt, vt);
rmatrixbdunpackdiagonals(a, m, n, isupper, w, e);
if( additionalmemory<2||uneeded==0 )
{
//
// We cant use additional memory or there is no need in such operations
//
result = rmatrixbdsvd(w, e, minmn, isupper, false, u, nru, a, 0, vt, ncvt);
}
else
{
//
// We can use additional memory
//
t2.setbounds(0, minmn-1, 0, m-1);
copyandtranspose(u, 0, m-1, 0, minmn-1, t2, 0, minmn-1, 0, m-1);
result = rmatrixbdsvd(w, e, minmn, isupper, false, u, 0, t2, m, vt, ncvt);
copyandtranspose(t2, 0, minmn-1, 0, m-1, u, 0, m-1, 0, minmn-1);
}
return result;
}
/*************************************************************************
Weighted constained linear least squares fitting.
This is variation of LSFitLinearW(), which searchs for min|A*x=b| given
that K additional constaints C*x=bc are satisfied. It reduces original
task to modified one: min|B*y-d| WITHOUT constraints, then LSFitLinearW()
is called.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
W - array[0..N-1] Weights corresponding to function values.
Each summand in square sum of approximation deviations
from given values is multiplied by the square of
corresponding weight.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I,J] - value of J-th basis function in I-th point.
CMatrix - a table of constaints, array[0..K-1,0..M].
I-th row of CMatrix corresponds to I-th linear constraint:
CMatrix[I,0]*C[0] + ... + CMatrix[I,M-1]*C[M-1] = CMatrix[I,M]
N - number of points used. N>=1.
M - number of basis functions, M>=1.
K - number of constraints, 0 <= K < M
K=0 corresponds to absence of constraints.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -3 either too many constraints (M or more),
degenerate constraints (some constraints are
repetead twice) or inconsistent constraints were
specified.
* -1 incorrect N/M/K were specified
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* 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
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
SEE ALSO
LSFitLinear
LSFitLinearC
LSFitLinearWC
-- ALGLIB --
Copyright 07.09.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinearwc(ap::real_1d_array y,
const ap::real_1d_array& w,
const ap::real_2d_array& fmatrix,
ap::real_2d_array cmatrix,
int n,
int m,
int k,
int& info,
ap::real_1d_array& c,
lsfitreport& rep)
{
int i;
int j;
ap::real_1d_array tau;
ap::real_2d_array q;
ap::real_2d_array f2;
ap::real_1d_array tmp;
ap::real_1d_array c0;
double v;
if( n<1||m<1||k<0 )
{
info = -1;
return;
}
if( k>=m )
{
info = -3;
return;
}
//
// Solve
//
if( k==0 )
{
//
// no constraints
//
lsfitlinearinternal(y, w, fmatrix, n, m, info, c, rep);
}
else
{
//
// First, find general form solution of constraints system:
// * factorize C = L*Q
// * unpack Q
// * fill upper part of C with zeros (for RCond)
//
// We got C=C0+Q2'*y where Q2 is lower M-K rows of Q.
//
rmatrixlq(cmatrix, k, m, tau);
rmatrixlqunpackq(cmatrix, k, m, tau, m, q);
for(i = 0; i <= k-1; i++)
{
for(j = i+1; j <= m-1; j++)
{
cmatrix(i,j) = 0.0;
}
}
if( ap::fp_less(rmatrixlurcondinf(cmatrix, k),1000*ap::machineepsilon) )
{
info = -3;
return;
}
tmp.setlength(k);
for(i = 0; i <= k-1; i++)
{
if( i>0 )
{
v = ap::vdotproduct(&cmatrix(i, 0), 1, &tmp(0), 1, ap::vlen(0,i-1));
}
else
{
v = 0;
}
tmp(i) = (cmatrix(i,m)-v)/cmatrix(i,i);
}
c0.setlength(m);
for(i = 0; i <= m-1; i++)
{
c0(i) = 0;
}
for(i = 0; i <= k-1; i++)
{
v = tmp(i);
ap::vadd(&c0(0), 1, &q(i, 0), 1, ap::vlen(0,m-1), v);
}
//
// Second, prepare modified matrix F2 = F*Q2' and solve modified task
//
tmp.setlength(ap::maxint(n, m)+1);
f2.setlength(n, m-k);
matrixvectormultiply(fmatrix, 0, n-1, 0, m-1, false, c0, 0, m-1, -1.0, y, 0, n-1, 1.0);
matrixmatrixmultiply(fmatrix, 0, n-1, 0, m-1, false, q, k, m-1, 0, m-1, true, 1.0, f2, 0, n-1, 0, m-k-1, 0.0, tmp);
lsfitlinearinternal(y, w, f2, n, m-k, info, tmp, rep);
rep.taskrcond = -1;
if( info<=0 )
{
return;
}
//
// then, convert back to original answer: C = C0 + Q2'*Y0
//
c.setlength(m);
ap::vmove(&c(0), 1, &c0(0), 1, ap::vlen(0,m-1));
matrixvectormultiply(q, k, m-1, 0, m-1, true, tmp, 0, m-k-1, 1.0, c, 0, m-1, 1.0);
}
}
/*
* @depricated
*
* NR implementation by RTG.
*
* Note on matrix vector multiplication:
* void matrixmatrixmultiply(const alglib::real_2d_array& a,
* int ai1,
* int ai2,
* int aj1,
* int aj2,
* bool transa,
* const alglib::real_2d_array& b,
* int bi1,
* int bi2,
* int bj1,
* int bj2,
* bool transb,
* double alpha,
* alglib::real_2d_array& c,
* int ci1,
* int ci2,
* int cj1,
* int cj2,
* double beta,
* alglib::real_1d_array& work);
*
* transa is true if transposed.
* Operation is: c = A * alpha * b + beta * C
*
*
* @input const vector<vector<double>> data holds explantory variables. each inner vector is a variable.
* @input const vector<double> response holds response variable.
* @input vector<double> Place to return the information matrix inverse. Column major order.
* Expects correct size.
*/
vector<double> LogisticRegression::newtonRaphsonFast(const vector<vector<double> > &data, const vector<double> &response
, vector<vector<double> > &invInfMatrix, double startVal)
{
vector<double> betas;
// Variables used in the computation:
alglib::real_1d_array tempBetas;
alglib::real_2d_array tempData;
alglib::real_1d_array oldExpY;
alglib::real_2d_array tempDeriv; // holds data' * w * data. Returned in last input param.
alglib::real_1d_array expY;
alglib::real_1d_array adjy;
double stop_var = 1e-10;
int iter = 0;
int maxIter = 200;
int numVars = data.size();
if(numVars < 1){
throw NewtonRaphsonFailureEx();
}
int numSamples = data.at(0).size();
if(numSamples < 1){
throw NewtonRaphsonFailureEx();
}
tempBetas.setlength(numVars);
tempData.setlength(numSamples,numVars);
oldExpY.setlength(numSamples);
expY.setlength(numSamples);
tempDeriv.setlength(numVars,numVars);
adjy.setlength(numSamples);
for(int i=0;i < numVars; i++){
for(int j=0;j < numSamples; j++){
tempData(j,i) = data.at(i).at(j);
}
tempBetas(i) = startVal;
}
for(int i=0;i < numSamples;i++){
oldExpY(i) = -1;
adjy(i) = 0; // makes valgrind happier.
}
while(iter < maxIter){
//data * tempBetas
matrixvectormultiply(tempData, 0, numSamples-1,0,numVars-1,false,
tempBetas, 0, numVars-1, 1.0,
adjy, 0, numSamples-1, 0.0);
for(int i=0;i < numSamples; i++){
expY(i) = 1 / (1 + exp(-adjy(i)));
}
// build deriv.
double deriv = -100000;
for(int i=0;i < numSamples; i++){
if(expY(i) * (1 - expY(i)) > deriv)
deriv = expY(i) * (1 - expY(i));
}
if(stop_var * 0.001 > deriv) deriv = stop_var * 0.001;
// adjy = adjy + (y-expy) ./ deriv
for(int i=0;i<numSamples;i++){
adjy(i) = adjy(i) + (response.at(i) - expY(i)) / deriv;
}
// build data' * w * data
alglib::real_1d_array work;
work.setlength(numSamples); // This temporary workspace must be one larger than the longest
// row or column that will be seen. Otherwise, the program
// crashes or - worse! - corrupts data.
matrixmatrixmultiply(tempData,0,numSamples-1,0,numVars-1,true,
tempData,0,numSamples-1,0,numVars-1,false,deriv,
tempDeriv,0,numVars-1,0,numVars-1,0.0,work);
#if DEBUG_NR
cout << "A' * w * A " << endl;
cout << tempDeriv(0,0) << " " << tempDeriv(0,1) << endl;
cout << tempDeriv(1,0) << " " << tempDeriv(1,1) << endl;
cout << endl;
#endif
alglib::matinvreport report;
alglib::ae_int_t reportInfo;
rmatrixinverse(tempDeriv, reportInfo, report);
if( reportInfo != 1 ){
throw SingularMatrixEx();
}
#if DEBUG_NR
cout << "inv(A' * w * A) " << endl;
cout << tempDeriv(0,0) << " " << tempDeriv(0,1) << endl;
cout << tempDeriv(1,0) << " " << tempDeriv(1,1) << endl;
cout << endl;
#endif
matrixvectormultiply(tempData,0,numSamples-1,0,numVars-1,true,
adjy,0,numSamples-1,deriv,
work,0,numVars-1,0.0);
matrixvectormultiply(tempDeriv,0,numVars-1,0,numVars-1,false,
work,0,numVars-1,1.0,
tempBetas,0,numVars-1,0.0);
#if DEBUG_NR
cout << "Betas ";
for(int i=0;i < numVars;i++) cout << tempBetas(i) << " " ;
cout << endl;
#endif
double stop = 0.0;
for(int i=0;i < numSamples;i++){
stop += abs(expY(i) - oldExpY(i));
}
if (stop < numSamples*stop_var){
break;
}
oldExpY = expY;
iter++;
}
if(iter == maxIter){
throw NewtonRaphsonIterationEx();
}
betas.clear();
for(int i=0;i<numVars;i++){
betas.push_back(tempBetas(i));
}
for(int i=0;i<numVars;i++){
for(int j=0;j<numVars;j++){
invInfMatrix.at(i).at(j) = tempDeriv(i,j);
}
}
return betas;
}
