STKUNIT_UNIT_TEST(norm, string_function)
{
EXCEPTWATCH;
//stk::diag::WriterThrowSafe _write_throw_safe(dw());
//dw().setPrintMask(dw_option_mask.parse(vm["dw"].as<std::string>().c_str()));
//dw().setPrintMask(LOG_NORM+LOG_ALWAYS);
dw().m(LOG_NORM) << "TEST.norm.string_function " << stk::diag::dendl;
LocalFixture fix(4);
mesh::fem::FEMMetaData& metaData = fix.metaData;
mesh::BulkData& bulkData = fix.bulkData;
PerceptMesh& eMesh = fix.eMesh;
//mesh::FieldBase* coords_field = fix.coords_field;
StringFunction sfx = fix.sfx;
ConstantFunction sfx_res = fix.sfx_res;
/// Create the operator that will do the work
/// get the l2 norm
Norm<2> l2Norm(bulkData, &metaData.universal_part(), TURBO_NONE);
l2Norm(sfx, sfx_res);
double sfx_expect = std::sqrt(0.25/3.);
Teuchos::ScalarTraits<double>::seedrandom(12345);
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res.getValue());
int niter=1;
for (int iter=0; iter < niter; iter++)
{
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, eval(Math::random01(), Math::random01(), Math::random01(), 0.0, sfx_res));
}
/// the function to be integrated: (Integral[ abs(x), dxdydz]) =?= (2 * |x|^2/2 @ [0, 0.5]) ==> .25)
Norm<1> l1Norm(bulkData, &metaData.universal_part(), TURBO_NONE);
l1Norm(sfx, sfx_res);
sfx_expect = 0.25;
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res.getValue());
/// the function to be integrated: (Max[ x^2+y^3+z^4, dxdydz]) =?= (@ [-0.5, 0.5]^3 ) ==> .5^2+.5^3+.5^4)
StringFunction sfmax("x^2 + y^3 + z^4", Name("sfmax"), Dimensions(3), Dimensions(1) );
Norm<-1> lInfNorm(bulkData, &metaData.universal_part(), TURBO_NONE);
lInfNorm.setCubDegree(10);
lInfNorm(sfmax, sfx_res);
double sf1=eval(.5,.5,.5,0.0, sfmax);
sfx_expect = 0.5*0.5 + 0.5*0.5*0.5 + 0.5*0.5*0.5*0.5;
std::cout << "sfmax= " << sf1 << " sfx_expect= " << sfx_expect << " sfx_res= " << sfx_res.getValue() << std::endl;
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res.getValue());
/// indirection
StringFunction sfmax_1("sfmax", Name("sfmax_1"), Dimensions(3), Dimensions(1) );
double sf1_1=eval(.5,.5,.5,0.0, sfmax_1);
std::cout << "sfmax_1= " << sf1_1 << " sfx_expect= " << sfx_expect << std::endl;
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sf1_1);
/// the function to be integrated: sqrt(Integral[(x*y*z)^2, dxdydz]) =?= (see unitTest1.py)
StringFunction sfxyz("x*y*z", Name("sfxyz"), Dimensions(3), Dimensions(1) );
l2Norm(sfxyz, sfx_res);
sfx_expect = 0.0240562612162344;
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res.getValue());
/// indirection
std::cout << "tmp srk start..." << std::endl;
StringFunction sfxyz_2("sfxyz", Name("sfxyz_2"), Dimensions(3), Dimensions(1) );
l2Norm(sfxyz_2, sfx_res);
sfx_expect = 0.0240562612162344;
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res.getValue());
/// the function to be integrated (but over a rotated domain): sqrt(Integral[(x*y*z)^2, dxdydz]) =?= (see unitTest2.py)
/// now rotate the mesh
Math::Matrix rmz = Math::rotationMatrix(2, 30);
Math::Matrix rm = rmz;
eMesh.transform_mesh(rm);
l2Norm(sfxyz, sfx_res);
sfx_expect = 0.0178406008037016;
// NOTE: we need extra quadrature accuracy to reproduce this result (cubDegree==4 in IntegratedOp almost gets it right)
// for now, we are satisfied with 2-3 digits
//STKUNIT_EXPECT_DOUBLE_EQ(sfx_res.getValue(), sfx_expect);
if (std::fabs(sfx_res.getValue()-sfx_expect) > 0.01*sfx_expect)
{
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res.getValue());
STKUNIT_EXPECT_TRUE(false);
}
}
/// This test uses a back door to the function that passes in the element to avoid the lookup of the element when the
/// StringFunction contains references to FieldFunctions
void TEST_norm_string_function_turbo_verify_correctness(TurboOption turboOpt)
{
EXCEPTWATCH;
//stk::diag::WriterThrowSafe _write_throw_safe(dw());
//dw().setPrintMask(dw_option_mask.parse(vm["dw"].as<std::string>().c_str()));
//dw().setPrintMask(LOG_NORM+LOG_ALWAYS);
dw().m(LOG_NORM) << "TEST.norm.string_function " << stk::diag::dendl;
LocalFixture fix(4);
mesh::fem::FEMMetaData& metaData = fix.metaData;
mesh::BulkData& bulkData = fix.bulkData;
PerceptMesh& eMesh = fix.eMesh;
mesh::FieldBase* coords_field = fix.coords_field;
StringFunction sfx = fix.sfx;
ConstantFunction sfx_res = fix.sfx_res;
/// create a field function from the existing coordinates field
FieldFunction ff_coords("ff_coords", coords_field, &bulkData,
Dimensions(3), Dimensions(3), FieldFunction::SIMPLE_SEARCH );
/// the function to be integrated: sqrt(Integral[x^2, dxdydz]) =?= sqrt(x^3/3 @ [-0.5, 0.5]) ==> sqrt(0.25/3)
//StringFunction sfx("x", Name("sfx"), Dimensions(3), Dimensions(1) );
ff_coords.add_alias("mc");
//StringFunction sfcm("sqrt(mc[0]*mc[0]+mc[1]*mc[1]+mc[2]*mc[2])", Name("sfcm"), Dimensions(3), Dimensions(1));
StringFunction sfx_mc("mc[0]", Name("sfx_mc"), Dimensions(3), Dimensions(1) );
StringFunction sfx_mc1("mc[0]", Name("sfx_mc1"), Dimensions(3), Dimensions(1) );
if (1)
{
double x = -0.49+0.98*Math::random01();
double y = -0.49+0.98*Math::random01();
double z = -0.49+0.98*Math::random01();
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(eval(x,y,z,0.0, sfx), eval(x,y,z,0.0, sfx_mc));
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(eval(.034,0,0,0.0, sfx), eval(.034,0,0,0.0, sfx_mc));
}
/// A place to hold the result.
/// This is a "writable" function (we may want to make this explicit - StringFunctions are not writable; FieldFunctions are
/// since we interpolate values to them from other functions).
ConstantFunction sfx_res_turbo(0.0, "sfx_res_turbo");
ConstantFunction sfx_res_slow(0.0, "sfx_res_slow");
ConstantFunction sfx_res_fast(0.0, "sfx_res_fast");
ConstantFunction sfx_res_bucket(0.0, "sfx_res_bucket");
// STATE m_element....
/// Create the operator that will do the work
/// get the l2 norm
Norm<2> l2Norm(bulkData, &metaData.universal_part(), TURBO_NONE);
l2Norm(sfx, sfx_res);
Norm<2> l2Norm_turbo(bulkData, &metaData.universal_part(), turboOpt);
Norm<2> l2Norm_turbo_bucket(bulkData, &metaData.universal_part(), TURBO_BUCKET);
Norm<2> l2Norm_turbo1(bulkData, &metaData.universal_part(), turboOpt);
l2Norm_turbo(sfx, sfx_res_turbo);
l2Norm_turbo1(sfx_mc1, sfx_res_fast);
l2Norm_turbo_bucket(sfx_mc1, sfx_res_bucket);
l2Norm(sfx_mc, sfx_res_slow);
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(eval(.023,0,0,0.0, sfx), eval(.023,0,0,0.0, sfx_mc));
double sfx_expect = std::sqrt(0.25/3.);
std::cout << "sfx_expect= " << sfx_expect << std::endl;
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res_bucket.getValue());
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res.getValue());
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res_turbo.getValue());
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res_slow.getValue());
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res_fast.getValue()); //!
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res.getValue());
//Util::pause(true, "13a");
//STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_res_turbo.getValue(), sfx_expect);
STKUNIT_EXPECT_DOUBLE_EQ_APPROX_TOL(sfx_expect, sfx_res_turbo.getValue(), 1.e-8);
//Util::pause(true, "13");
/// the function to be integrated: (Integral[ abs(x), dxdydz]) =?= (2 * |x|^2/2 @ [0, 0.5]) ==> .25)
Norm<1> l1Norm(bulkData, &metaData.universal_part(), TURBO_NONE);
l1Norm(sfx, sfx_res);
Norm<1> l1Norm_turbo(bulkData, &metaData.universal_part(), TURBO_NONE);
l1Norm_turbo(sfx, sfx_res_turbo);
l1Norm_turbo(sfx_mc, sfx_res_fast);
l1Norm(sfx_mc, sfx_res_slow);
sfx_expect = 0.25;
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res.getValue());
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res_turbo.getValue());
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res_slow.getValue());
STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_expect, sfx_res_fast.getValue());
//// ----- here
/// the function to be integrated: sqrt(Integral[(x*y*z)^2, dxdydz]) =?= (see unitTest1.py)
StringFunction sfxyz("x*y*z", Name("sfxyz"), Dimensions(3), Dimensions(1) );
l2Norm(sfxyz, sfx_res);
l2Norm_turbo(sfxyz, sfx_res_turbo);
sfx_expect = 0.0240562612162344;
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res.getValue());
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res_turbo.getValue());
/// the function to be integrated (but over a rotated domain): sqrt(Integral[(x*y*z)^2, dxdydz]) =?= (see unitTest2.py)
/// now rotate the mesh
Math::Matrix rmz = Math::rotationMatrix(2, 30);
Math::Matrix rm = rmz;
eMesh.transform_mesh(rm);
l2Norm(sfxyz, sfx_res);
l2Norm_turbo(sfxyz, sfx_res_turbo);
sfx_expect = 0.0178406008037016;
// NOTE: we need extra quadrature accuracy to reproduce this result (cubDegree==4 in IntegratedOp almost gets it right)
// for now, we are satisfied with 3 digits
//STKUNIT_EXPECT_DOUBLE_EQ_APPROX(sfx_res.getValue(), sfx_expect);
if (std::fabs(sfx_res.getValue()-sfx_expect) > 0.01*sfx_expect)
{
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res.getValue());
STKUNIT_EXPECT_TRUE(false);
}
if (std::fabs(sfx_res_turbo.getValue()-sfx_expect) > 0.01*sfx_expect)
{
STKUNIT_EXPECT_DOUBLE_EQ_APPROX( sfx_expect, sfx_res_turbo.getValue());
STKUNIT_EXPECT_TRUE(false);
}
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
double *v, *ans, s1, s2;
double *ind;
double *x;
double *u, *tmpV, *tmpU, *tmpW;
double up, mid, low, h_s1, lambda0, lambda;
int n, grpNum;
int i, j, k;
if(nlhs != 1)
mexErrMsgTxt("Error: Number of output parameter does not match.");
if(nrhs !=4)
mexErrMsgTxt("Error: Number of input parameter does not match.");
/*
* Input Parameter handle
*/
v = mxGetPr(prhs[0]);
s1 = mxGetScalar(prhs[1]);
s2 = mxGetScalar(prhs[2]);
ind = mxGetPr(prhs[3]);
n = (int)mxGetNumberOfElements(prhs[0]);
grpNum = (int)mxGetNumberOfElements(prhs[3]) - 1;
/*
* Output Parameter handle
*/
plhs[0] = mxCreateDoubleMatrix(n, 1, mxREAL);
ans = mxGetPr(plhs[0]);
/* Temporary variables. */
lambda = lambda0 = .0;
x = (double *)malloc(n * sizeof(double));
tmpV = (double *)malloc(n * sizeof(double));
tmpU = (double *)malloc(grpNum * sizeof(double));
tmpW = (double *)malloc(grpNum * sizeof(double));
if(l1Norm(v, n) <= s1 + 1e-12 && grpNorm(v, ind, grpNum) <= s2 + 1e-12)
{
for(i = 0; i < n; i++)
ans[i] = v[i];
free(x);
free(tmpV);
free(tmpU);
free(tmpW);
return;
}
lambda0 = .0;
eplb(x, &lambda, &k, v, n, s1, lambda0);
if(grpNorm(x, ind, grpNum) < s2 - 1e-12)
{
for(i = 0; i < n; i++)
ans[i] = x[i];
free(x);
free(tmpV);
free(tmpU);
free(tmpW);
return;
}
epglb(x, v, n, s2, ind, grpNum, tmpW, tmpU);
if(l1Norm(x, n) < s1 - 1e-12)
{
for(i = 0; i < n; i++)
ans[i] = x[i];
free(x);
free(tmpV);
free(tmpU);
free(tmpW);
return;
}
up = 1e15, low = 1e-12;
while(up - low > 1e-7)
{
if(low > 1e6 && up - low < 1e-5)
break;
mid = (up + low) / 2;
soft_thresholding(tmpV, v, n, mid);
if(grpNorm(tmpV, ind, grpNum) < s2 - 1e-15)
up = mid;
else{
epglb(x, tmpV, n, s2, ind, grpNum, tmpW, tmpU);
h_s1 = l1Norm(x, n);
if(h_s1 < s1 + 1e-15)
up = mid;
else
low = mid;
}
}
soft_thresholding(tmpV, v, n, up);
epglb(x, tmpV, n, s2, ind, grpNum, tmpW, tmpU);
for(i = 0; i < n; i++)
ans[i] = x[i];
free(x);
free(tmpV);
free(tmpU);
free(tmpW);
}
