bool NLPDirectTester::finite_diff_check(
NLPDirect *nlp
,const Vector &xo
,const Vector *xl
,const Vector *xu
,const Vector *c
,const Vector *Gf
,const Vector *py
,const Vector *rGf
,const MatrixOp *GcU
,const MatrixOp *D
,const MatrixOp *Uz
,bool print_all_warnings
,std::ostream *out
) const
{
using std::setw;
using std::endl;
using std::right;
using AbstractLinAlgPack::sum;
using AbstractLinAlgPack::dot;
using AbstractLinAlgPack::Vp_StV;
using AbstractLinAlgPack::random_vector;
using AbstractLinAlgPack::assert_print_nan_inf;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::V_StMtV;
using LinAlgOpPack::Vp_MtV;
using LinAlgOpPack::M_StM;
using LinAlgOpPack::M_StMtM;
typedef VectorSpace::vec_mut_ptr_t vec_mut_ptr_t;
// using AbstractLinAlgPack::TestingPack::CompareDenseVectors;
// using AbstractLinAlgPack::TestingPack::CompareDenseSparseMatrices;
using TestingHelperPack::update_success;
bool success = true, preformed_fd;
if(out) {
*out << std::boolalpha
<< std::endl
<< "*********************************************************\n"
<< "*** NLPDirectTester::finite_diff_check(...) ***\n"
<< "*********************************************************\n";
}
const Range1D
var_dep = nlp->var_dep(),
var_indep = nlp->var_indep(),
con_decomp = nlp->con_decomp(),
con_undecomp = nlp->con_undecomp();
NLP::vec_space_ptr_t
space_x = nlp->space_x(),
space_c = nlp->space_c();
// //////////////////////////////////////////////
// Validate the input
TEST_FOR_EXCEPTION(
py && !c, std::invalid_argument
,"NLPDirectTester::finite_diff_check(...) : "
"Error, if py!=NULL then c!=NULL must also be true!" );
const CalcFiniteDiffProd
&fd_deriv_prod = this->calc_fd_prod();
const value_type
rand_y_l = -1.0, rand_y_u = 1.0,
small_num = ::sqrt(std::numeric_limits<value_type>::epsilon());
try {
// ///////////////////////////////////////////////
// (1) Check Gf
if(Gf) {
switch( Gf_testing_method() ) {
case FD_COMPUTE_ALL: {
// Compute FDGf outright
TEST_FOR_EXCEPT(true); // ToDo: update above!
break;
}
case FD_DIRECTIONAL: {
// Compute FDGF'*y using random y's
if(out)
*out
<< "\nComparing products Gf'*y with finite difference values FDGf'*y for "
<< "random y's ...\n";
vec_mut_ptr_t y = space_x->create_member();
value_type max_warning_viol = 0.0;
int num_warning_viol = 0;
const int num_fd_directions_used = ( num_fd_directions() > 0 ? num_fd_directions() : 1 );
for( int direc_i = 1; direc_i <= num_fd_directions_used; ++direc_i ) {
if( num_fd_directions() > 0 ) {
random_vector( rand_y_l, rand_y_u, y.get() );
if(out)
*out
<< "\n****"
<< "\n**** Random directional vector " << direc_i << " ( ||y||_1 / n = "
<< (y->norm_1() / y->dim()) << " )"
<< "\n***\n";
}
else {
*y = 1.0;
if(out)
*out
<< "\n****"
<< "\n**** Ones vector y ( ||y||_1 / n = "<<(y->norm_1()/y->dim())<<" )"
<< "\n***\n";
}
value_type
Gf_y = dot( *Gf, *y ),
FDGf_y;
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*y,NULL,NULL,true,nlp,&FDGf_y,NULL,out,dump_all(),dump_all()
);
if( !preformed_fd )
goto FD_NOT_PREFORMED;
assert_print_nan_inf(FDGf_y, "FDGf'*y",true,out);
const value_type
calc_err = ::fabs( ( Gf_y - FDGf_y )/( ::fabs(Gf_y) + ::fabs(FDGf_y) + small_num ) );
if( calc_err >= Gf_warning_tol() ) {
max_warning_viol = my_max( max_warning_viol, calc_err );
++num_warning_viol;
}
if(out)
*out
<< "\nrel_err(Gf'*y,FDGf'*y) = "
<< "rel_err(" << Gf_y << "," << FDGf_y << ") = "
<< calc_err << endl;
if( calc_err >= Gf_error_tol() ) {
if(out) {
*out
<< "Error, above relative error exceeded Gf_error_tol = " << Gf_error_tol() << endl;
if(dump_all()) {
*out << "\ny =\n" << *y;
}
}
}
}
if(out && num_warning_viol)
*out
<< "\nThere were " << num_warning_viol << " warning tolerance "
<< "violations out of num_fd_directions = " << num_fd_directions()
<< " computations of FDGf'*y\n"
<< "and the maximum violation was " << max_warning_viol
<< " > Gf_waring_tol = " << Gf_warning_tol() << endl;
break;
}
default:
TEST_FOR_EXCEPT(true); // Invalid value
}
}
// /////////////////////////////////////////////
// (2) Check py = -inv(C)*c
//
// We want to check;
//
// FDC * (inv(C)*c) \approx c
// \_________/
// -py
//
// We can compute this as:
//
// FDC * py = [ FDC, FDN ] * [ -py ; 0 ]
// \__________/
// FDA'
//
// t1 = [ -py ; 0 ]
//
// t2 = FDA'*t1
//
// Compare t2 \approx c
//
if(py) {
if(out)
*out
<< "\nComparing c with finite difference product FDA'*[ -py; 0 ] = -FDC*py ...\n";
// t1 = [ -py ; 0 ]
VectorSpace::vec_mut_ptr_t
t1 = space_x->create_member();
V_StV( t1->sub_view(var_dep).get(), -1.0, *py );
*t1->sub_view(var_indep) = 0.0;
// t2 = FDA'*t1
VectorSpace::vec_mut_ptr_t
t2 = nlp->space_c()->create_member();
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*t1,NULL,NULL,true,nlp,NULL,t2.get(),out,dump_all(),dump_all()
);
if( !preformed_fd )
goto FD_NOT_PREFORMED;
const value_type
sum_c = sum(*c),
sum_t2 = sum(*t2);
assert_print_nan_inf(sum_t2, "sum(-FDC*py)",true,out);
const value_type
calc_err = ::fabs( ( sum_c - sum_t2 )/( ::fabs(sum_c) + ::fabs(sum_t2) + small_num ) );
if(out)
*out
<< "\nrel_err(sum(c),sum(-FDC*py)) = "
<< "rel_err(" << sum_c << "," << sum_t2 << ") = "
<< calc_err << endl;
if( calc_err >= Gc_error_tol() ) {
if(out)
*out
<< "Error, above relative error exceeded Gc_error_tol = " << Gc_error_tol() << endl;
if(print_all_warnings)
*out << "\nt1 = [ -py; 0 ] =\n" << *t1
<< "\nt2 = FDA'*t1 = -FDC*py =\n" << *t2;
update_success( false, &success );
}
if( calc_err >= Gc_warning_tol() ) {
if(out)
*out
<< "\nWarning, above relative error exceeded Gc_warning_tol = " << Gc_warning_tol() << endl;
}
}
// /////////////////////////////////////////////
// (3) Check D = -inv(C)*N
if(D) {
switch( Gc_testing_method() ) {
case FD_COMPUTE_ALL: {
//
// Compute FDN outright and check
// -FDC * D \aprox FDN
//
// We want to compute:
//
// FDC * -D = [ FDC, FDN ] * [ -D; 0 ]
// \__________/
// FDA'
//
// To compute the above we perform:
//
// T = FDA' * [ -D; 0 ] (one column at a time)
//
// Compare T \approx FDN
//
/*
// FDN
DMatrix FDN(m,n-m);
fd_deriv_computer.calc_deriv( xo, xl, xu
, Range1D(m+1,n), nlp, NULL
, &FDN() ,BLAS_Cpp::trans, out );
// T = FDA' * [ -D; 0 ] (one column at a time)
DMatrix T(m,n-m);
DVector t(n);
t(m+1,n) = 0.0;
for( int s = 1; s <= n-m; ++s ) {
// t = [ -D(:,s); 0 ]
V_StV( &t(1,m), -1.0, D->col(s) );
// T(:,s) = FDA' * t
fd_deriv_prod.calc_deriv_product(
xo,xl,xu,t(),NULL,NULL,nlp,NULL,&T.col(s),out);
}
// Compare T \approx FDN
if(out)
*out
<< "\nChecking the computed D = -inv(C)*N\n"
<< "where D(i,j) = (-FDC*D)(i,j), dM(i,j) = FDN(i,j) ...\n";
result = comp_M.comp(
T(), FDN, BLAS_Cpp::no_trans
, CompareDenseSparseMatrices::FULL_MATRIX
, CompareDenseSparseMatrices::REL_ERR_BY_COL
, Gc_warning_tol(), Gc_error_tol()
, print_all_warnings, out );
update_success( result, &success );
if(!result) return false;
*/
TEST_FOR_EXCEPT(true); // Todo: Implement above!
break;
}
case FD_DIRECTIONAL: {
//
// Compute -FDC * D * v \aprox FDN * v
// for random v's
//
// We will compute this as:
//
// t1 = [ 0; y ] <: R^(n)
//
// t2 = FDA' * t1 ( FDN * y ) <: R^(m)
//
// t1 = [ -D * y ; 0 ] <: R^(n)
//
// t3 = FDA' * t1 ( -FDC * D * y ) <: R^(m)
//
// Compare t2 \approx t3
//
if(out)
*out
<< "\nComparing finite difference products -FDC*D*y with FDN*y for "
"random vectors y ...\n";
VectorSpace::vec_mut_ptr_t
y = space_x->sub_space(var_indep)->create_member(),
t1 = space_x->create_member(),
t2 = space_c->create_member(),
t3 = space_c->create_member();
value_type max_warning_viol = 0.0;
int num_warning_viol = 0;
const int num_fd_directions_used = ( num_fd_directions() > 0 ? num_fd_directions() : 1 );
for( int direc_i = 1; direc_i <= num_fd_directions_used; ++direc_i ) {
if( num_fd_directions() > 0 ) {
random_vector( rand_y_l, rand_y_u, y.get() );
if(out)
*out
<< "\n****"
<< "\n**** Random directional vector " << direc_i << " ( ||y||_1 / n = "
<< (y->norm_1() / y->dim()) << " )"
<< "\n***\n";
}
else {
*y = 1.0;
if(out)
*out
<< "\n****"
<< "\n**** Ones vector y ( ||y||_1 / n = "<<(y->norm_1()/y->dim())<<" )"
<< "\n***\n";
}
// t1 = [ 0; y ] <: R^(n)
*t1->sub_view(var_dep) = 0.0;
*t1->sub_view(var_indep) = *y;
// t2 = FDA' * t1 ( FDN * y ) <: R^(m)
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*t1,NULL,NULL,true,nlp,NULL,t2.get(),out,dump_all(),dump_all()
);
if( !preformed_fd )
goto FD_NOT_PREFORMED;
// t1 = [ -D * y ; 0 ] <: R^(n)
V_StMtV( t1->sub_view(var_dep).get(), -1.0, *D, BLAS_Cpp::no_trans, *y );
*t1->sub_view(var_indep) = 0.0;
// t3 = FDA' * t1 ( -FDC * D * y ) <: R^(m)
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*t1,NULL,NULL,true,nlp,NULL,t3.get(),out,dump_all(),dump_all()
);
// Compare t2 \approx t3
const value_type
sum_t2 = sum(*t2),
sum_t3 = sum(*t3);
const value_type
calc_err = ::fabs( ( sum_t2 - sum_t3 )/( ::fabs(sum_t2) + ::fabs(sum_t3) + small_num ) );
if(out)
*out
<< "\nrel_err(sum(-FDC*D*y),sum(FDN*y)) = "
<< "rel_err(" << sum_t3 << "," << sum_t2 << ") = "
<< calc_err << endl;
if( calc_err >= Gc_warning_tol() ) {
max_warning_viol = my_max( max_warning_viol, calc_err );
++num_warning_viol;
}
if( calc_err >= Gc_error_tol() ) {
if(out)
*out
<< "Error, above relative error exceeded Gc_error_tol = " << Gc_error_tol() << endl
<< "Stoping the tests!\n";
if(print_all_warnings)
*out << "\ny =\n" << *y
<< "\nt1 = [ -D*y; 0 ] =\n" << *t1
<< "\nt2 = FDA' * [ 0; y ] = FDN * y =\n" << *t2
<< "\nt3 = FDA' * t1 = -FDC * D * y =\n" << *t3;
update_success( false, &success );
}
}
if(out && num_warning_viol)
*out
<< "\nThere were " << num_warning_viol << " warning tolerance "
<< "violations out of num_fd_directions = " << num_fd_directions()
<< " computations of sum(FDC*D*y) and sum(FDN*y)\n"
<< "and the maximum relative iolation was " << max_warning_viol
<< " > Gc_waring_tol = " << Gc_warning_tol() << endl;
break;
}
default:
TEST_FOR_EXCEPT(true);
}
}
// ///////////////////////////////////////////////
// (4) Check rGf = Gf(var_indep) + D'*Gf(var_dep)
if(rGf) {
if( Gf && D ) {
if(out)
*out
<< "\nComparing rGf_tmp = Gf(var_indep) - D'*Gf(var_dep) with rGf ...\n";
VectorSpace::vec_mut_ptr_t
rGf_tmp = space_x->sub_space(var_indep)->create_member();
*rGf_tmp = *Gf->sub_view(var_indep);
Vp_MtV( rGf_tmp.get(), *D, BLAS_Cpp::trans, *Gf->sub_view(var_dep) );
const value_type
sum_rGf_tmp = sum(*rGf_tmp),
sum_rGf = sum(*rGf);
const value_type
calc_err = ::fabs( ( sum_rGf_tmp - sum_rGf )/( ::fabs(sum_rGf_tmp) + ::fabs(sum_rGf) + small_num ) );
if(out)
*out
<< "\nrel_err(sum(rGf_tmp),sum(rGf)) = "
<< "rel_err(" << sum_rGf_tmp << "," << sum_rGf << ") = "
<< calc_err << endl;
if( calc_err >= Gc_error_tol() ) {
if(out)
*out
<< "Error, above relative error exceeded Gc_error_tol = " << Gc_error_tol() << endl;
if(print_all_warnings)
*out << "\nrGf_tmp =\n" << *rGf_tmp
<< "\nrGf =\n" << *rGf;
update_success( false, &success );
}
if( calc_err >= Gc_warning_tol() ) {
if(out)
*out
<< "\nWarning, above relative error exceeded Gc_warning_tol = "
<< Gc_warning_tol() << endl;
}
}
else if( D ) {
if(out)
*out
<< "\nComparing rGf'*y with the finite difference product"
<< " fd_prod(f,[D*y;y]) for random vectors y ...\n";
VectorSpace::vec_mut_ptr_t
y = space_x->sub_space(var_indep)->create_member(),
t = space_x->create_member();
value_type max_warning_viol = 0.0;
int num_warning_viol = 0;
const int num_fd_directions_used = ( num_fd_directions() > 0 ? num_fd_directions() : 1 );
for( int direc_i = 1; direc_i <= num_fd_directions_used; ++direc_i ) {
if( num_fd_directions() > 0 ) {
random_vector( rand_y_l, rand_y_u, y.get() );
if(out)
*out
<< "\n****"
<< "\n**** Random directional vector " << direc_i << " ( ||y||_1 / n = "
<< (y->norm_1() / y->dim()) << " )"
<< "\n***\n";
}
else {
*y = 1.0;
if(out)
*out
<< "\n****"
<< "\n**** Ones vector y ( ||y||_1 / n = "<<(y->norm_1()/y->dim())<<" )"
<< "\n***\n";
}
// t = [ D*y; y ]
LinAlgOpPack::V_MtV(&*t->sub_view(var_dep),*D,BLAS_Cpp::no_trans,*y);
*t->sub_view(var_indep) = *y;
value_type fd_rGf_y = 0.0;
// fd_Gf_y
preformed_fd = fd_deriv_prod.calc_deriv_product(
xo,xl,xu
,*t,NULL,NULL,true,nlp,&fd_rGf_y,NULL,out,dump_all(),dump_all()
);
if( !preformed_fd )
goto FD_NOT_PREFORMED;
if(out) *out << "fd_prod(f,[D*y;y]) = " << fd_rGf_y << "\n";
// rGf_y = rGf'*y
const value_type rGf_y = dot(*rGf,*y);
if(out) *out << "rGf'*y = " << rGf_y << "\n";
// Compare fd_rGf_y and rGf*y
const value_type
calc_err = ::fabs( ( rGf_y - fd_rGf_y )/( ::fabs(rGf_y) + ::fabs(fd_rGf_y) + small_num ) );
if( calc_err >= Gc_warning_tol() ) {
max_warning_viol = my_max( max_warning_viol, calc_err );
++num_warning_viol;
}
if(out)
*out
<< "\nrel_err(rGf'*y,fd_prod(f,[D*y;y])) = "
<< "rel_err(" << fd_rGf_y << "," << rGf_y << ") = "
<< calc_err << endl;
if( calc_err >= Gf_error_tol() ) {
if(out)
*out << "Error, above relative error exceeded Gc_error_tol = " << Gc_error_tol() << endl;
if(print_all_warnings)
*out << "\ny =\n" << *y
<< "\nt = [ D*y; y ] =\n" << *t;
update_success( false, &success );
}
}
}
else {
TEST_FOR_EXCEPT(true); // ToDo: Test rGf without D? (This is not going to be easy!)
}
}
// ///////////////////////////////////////////////////
// (5) Check GcU, and/or Uz (for undecomposed equalities)
if(GcU || Uz) {
TEST_FOR_EXCEPT(true); // ToDo: Implement!
}
FD_NOT_PREFORMED:
if(!preformed_fd) {
if(out)
*out
<< "\nError, the finite difference computation was not preformed due to cramped bounds\n"
<< "Finite difference test failed!\n" << endl;
return false;
}
} // end try
catch( const AbstractLinAlgPack::NaNInfException& except ) {
if(out)
*out
<< "Error, found a NaN or Inf. Stoping tests\n";
success = false;
}
if( out ) {
if( success )
*out
<< "\nCongradulations, all the finite difference errors where within the\n"
"specified error tolerances!\n";
else
*out
<< "\nOh no, at least one of the above finite difference tests failed!\n";
}
return success;
}
bool MatrixOpNonsingTester::test_matrix(
const MatrixOpNonsing &M
,const char M_name[]
,std::ostream *out
)
{
namespace rcp = MemMngPack;
using BLAS_Cpp::no_trans;
using BLAS_Cpp::trans;
using BLAS_Cpp::left;
using BLAS_Cpp::right;
using AbstractLinAlgPack::sum;
using AbstractLinAlgPack::dot;
using AbstractLinAlgPack::Vp_StV;
using AbstractLinAlgPack::assert_print_nan_inf;
using AbstractLinAlgPack::random_vector;
using LinAlgOpPack::V_StMtV;
using LinAlgOpPack::V_MtV;
using LinAlgOpPack::V_StV;
using LinAlgOpPack::V_VpV;
using LinAlgOpPack::Vp_V;
// ToDo: Check the preconditions
bool success = true, result, lresult;
const value_type
rand_y_l = -1.0,
rand_y_u = 1.0,
small_num = ::pow(std::numeric_limits<value_type>::epsilon(),0.25),
alpha = 2.0;
//
// Perform the tests
//
if(out && print_tests() >= PRINT_BASIC)
*out
<< "\nCheck: alpha*op(op(inv("<<M_name<<"))*op("<<M_name<<"))*v == alpha*v ...";
if(out && print_tests() > PRINT_BASIC)
*out << std::endl;
VectorSpace::vec_mut_ptr_t
v_c1 = M.space_cols().create_member(),
v_c2 = M.space_cols().create_member(),
v_r1 = M.space_rows().create_member(),
v_r2 = M.space_rows().create_member();
// Side of the matrix inverse
const BLAS_Cpp::Side a_side[2] = { BLAS_Cpp::left, BLAS_Cpp::right };
// If the matrices are transposed or not
const BLAS_Cpp::Transp a_trans[2] = { BLAS_Cpp::no_trans, BLAS_Cpp::trans };
for( int side_i = 0; side_i < 2; ++side_i ) {
for( int trans_i = 0; trans_i < 2; ++trans_i ) {
const BLAS_Cpp::Side t_side = a_side[side_i];
const BLAS_Cpp::Transp t_trans = a_trans[trans_i];
if(out && print_tests() >= PRINT_MORE)
*out
<< "\n" << side_i+1 << "." << trans_i+1 << ") "
<< "Check: (t2 = "<<(t_side==left?"inv(":"alpha * ")<< M_name<<(t_trans==trans?"\'":"")<<(t_side==left?")":"")
<< " * (t1 = "<<(t_side==right?"inv(":"alpha * ")<<M_name<<(t_trans==trans?"\'":"")<<(t_side==right?")":"")
<< " * v)) == alpha * v ...";
if(out && print_tests() > PRINT_MORE)
*out << std::endl;
result = true;
VectorMutable
*v = NULL,
*t1 = NULL,
*t2 = NULL;
if( (t_side == left && t_trans == no_trans) || (t_side == right && t_trans == trans) ) {
// (inv(R)*R*v or R'*inv(R')*v
v = v_r1.get();
t1 = v_c1.get();
t2 = v_r2.get();
}
else {
// (inv(R')*R'*v or R*inv(R)*v
v = v_c1.get();
t1 = v_r1.get();
t2 = v_c2.get();
}
for( int k = 1; k <= num_random_tests(); ++k ) {
lresult = true;
random_vector( rand_y_l, rand_y_u, v );
if(out && print_tests() >= PRINT_ALL) {
*out
<< "\n"<<side_i+1<<"."<<trans_i+1<<"."<<k<<") random vector " << k
<< " ( ||v||_1 / n = " << (v->norm_1() / v->dim()) << " )\n";
if(dump_all() && print_tests() >= PRINT_ALL)
*out << "\nv =\n" << *v;
}
// t1
if( t_side == right ) {
// t1 = inv(op(M))*v
V_InvMtV( t1, M, t_trans, *v );
}
else {
// t1 = alpha*op(M)*v
V_StMtV( t1, alpha, M, t_trans, *v );
}
// t2
if( t_side == left ) {
// t2 = inv(op(M))*t1
V_InvMtV( t2, M, t_trans, *t1 );
}
else {
// t2 = alpha*op(M)*t1
V_StMtV( t2, alpha, M, t_trans, *t1 );
}
const value_type
sum_t2 = sum(*t2),
sum_av = alpha*sum(*v);
assert_print_nan_inf(sum_t2, "sum(t2)",true,out);
assert_print_nan_inf(sum_av, "sum(alpha*t1)",true,out);
const value_type
calc_err = ::fabs( ( sum_av - sum_t2 )
/( ::fabs(sum_av) + ::fabs(sum_t2) + small_num ) );
if(out && print_tests() >= PRINT_ALL)
*out
<< "\nrel_err(sum(alpha*v),sum(t2)) = "
<< "rel_err(" << sum_av << "," << sum_t2 << ") = "
<< calc_err << std::endl;
if( calc_err >= warning_tol() ) {
if(out && print_tests() >= PRINT_ALL)
*out
<< std::endl
<< ( calc_err >= error_tol() ? "Error" : "Warning" )
<< ", rel_err(sum(alpha*v),sum(t2)) = "
<< "rel_err(" << sum_av << "," << sum_t2 << ") = "
<< calc_err
<< " exceeded "
<< ( calc_err >= error_tol() ? "error_tol" : "warning_tol" )
<< " = "
<< ( calc_err >= error_tol() ? error_tol() : warning_tol() )
<< std::endl;
if(calc_err >= error_tol()) {
if(dump_all() && print_tests() >= PRINT_ALL) {
*out << "\nalpha = " << alpha << std::endl;
*out << "\nv =\n" << *v;
*out << "\nt1 =\n" << *t2;
*out << "\nt2 =\n" << *t2;
}
lresult = false;
}
}
if(!lresult) result = false;
}
if(!result) success = false;
if( out && print_tests() == PRINT_MORE )
*out << " : " << ( result ? "passed" : "failed" )
<< std::endl;
}
}
if( out && print_tests() == PRINT_BASIC )
*out << " : " << ( success ? "passed" : "failed" );
return success;
}
