From 45f294868d364901b08e3212e7171142d3cbad5f Mon Sep 17 00:00:00 2001 From: Jie Li Date: Fri, 15 Sep 2023 16:42:27 +0800 Subject: [PATCH 1/5] add precision tests for sphbesj; provide standard test data. --- source/module_base/test/CMakeLists.txt | 1 + source/module_base/test/data/bj.bin | Bin 0 -> 480000 bytes source/module_base/test/data/gen_bessel.m | 17 +++ source/module_base/test/data/sphbes.m | 16 +++ source/module_base/test/math_sphbes_test.cpp | 135 ++++++++++++++----- 5 files changed, 133 insertions(+), 36 deletions(-) create mode 100644 source/module_base/test/data/bj.bin create mode 100644 source/module_base/test/data/gen_bessel.m create mode 100644 source/module_base/test/data/sphbes.m diff --git a/source/module_base/test/CMakeLists.txt b/source/module_base/test/CMakeLists.txt index 0aa703eddf..e5181603e7 100644 --- a/source/module_base/test/CMakeLists.txt +++ b/source/module_base/test/CMakeLists.txt @@ -1,4 +1,5 @@ remove_definitions(-D__MPI) +install(DIRECTORY data 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Bessel function +% q: the argument of the Bessel function +% rc: the cutoff radius +% nr: the number of points to be generated +%% Case: q = 0.1; rc = 50; nr = 5000; l_lo = 0; l_hi=11; +function [X, Val] = gen_bessel(q, rc, nr, l_lo, l_hi) + X = linspace(0, rc, nr+1) * q; + X = X(2:nr+1); + Val = zeros(nr, l_hi-l_lo+1); + for l = l_lo:l_hi + Val(:, l-l_lo+1) = sphbes(l, X); + end + Val = reshape(Val, 1, []); +end + + diff --git a/source/module_base/test/data/sphbes.m b/source/module_base/test/data/sphbes.m new file mode 100644 index 0000000000..047d3fef27 --- /dev/null +++ b/source/module_base/test/data/sphbes.m @@ -0,0 +1,16 @@ +function js = sphbes(nu, x) +% returns the spherical Bessel functions jnu(x) +% x is a vector or it may be a matrix if nu is a scalar +% if nu is a row and x a column vector, the output js is a matrix + +[~, lnu] = size(nu); +xm = repmat(x, 1, lnu); +% special case handle: x = 0 +js(~xm) = 0; +% general case +nzind = find(xm); +js(nzind) = sqrt(pi ./(2* xm(nzind))) .* besselj(nu + 0.5, x(nzind)); + + + + diff --git a/source/module_base/test/math_sphbes_test.cpp b/source/module_base/test/math_sphbes_test.cpp index a56892f3d6..725e2cc290 100644 --- a/source/module_base/test/math_sphbes_test.cpp +++ b/source/module_base/test/math_sphbes_test.cpp @@ -1,5 +1,6 @@ #include"../math_sphbes.h" #include +#include #ifdef __MPI #include"mpi.h" @@ -8,7 +9,7 @@ #include"gtest/gtest.h" #define doublethreshold 1e-7 - +#define MAX(x, y) ((x) > (y) ? (x) : (y)) /************************************************ * unit test of class Integral @@ -197,48 +198,110 @@ TEST_F(Sphbes,SphericalBesselRoots) } -TEST_F(Sphbes, SeriesAndRecurrence) +// TEST_F(Sphbes, SeriesAndRecurrence) +// { +// // This test checks whether Spherical_Bessel and sphbesj agree with each other +// // on a coarse grid for a range of l and q values. +// // +// // NOTE: this test should be removed once Spherical_Bessel is removed from the code. +// int lmax = 8; +// int nr = 5000; +// double rcut = 50; +// double dr = rcut / (nr - 1); +// double* r = new double[nr]; +// for (int i = 0; i < nr; ++i) +// { +// r[i] = i * dr; +// } + +// double* jl_old = new double[nr]; +// double* jl_new = new double[nr]; +// for (int l = 0; l <= lmax; ++l) +// { +// for (double q = 0.1; q < 10; q += 0.1) +// { +// ModuleBase::Sphbes::Spherical_Bessel(nr, r, q, l, jl_old); +// ModuleBase::Sphbes::sphbesj(nr, r, q, l, jl_new); +// for (int i = 0; i < nr; ++i) +// { +// EXPECT_NEAR(jl_old[i], jl_new[i], 1e-12); +// } + +// // derivative +// ModuleBase::Sphbes::dSpherical_Bessel_dx(nr, r, q, l, jl_old); +// ModuleBase::Sphbes::dsphbesj(nr, r, q, l, jl_new); +// for (int i = 0; i < nr; ++i) +// { +// EXPECT_NEAR(jl_old[i], jl_new[i], 1e-12); +// } +// } +// } + +// delete[] r; +// delete[] jl_old; +// delete[] jl_new; +// } + +TEST_F(Sphbes, SphericalBesselPrecision) { - // This test checks whether Spherical_Bessel and sphbesj agree with each other + // This test checks whether sphbesj agrees with the Matlab implementation // on a coarse grid for a range of l and q values. - // - // NOTE: this test should be removed once Spherical_Bessel is removed from the code. - int lmax = 8; - int nr = 5000; - double rcut = 50; - double dr = rcut / (nr - 1); - double* r = new double[nr]; - for (int i = 0; i < nr; ++i) + const double q = 0.1; + const double rcut = 50; + const int nr = 5000; + const int l_lo = 0, l_hi = 11; + const double dr = rcut / nr; + double* r = new double[nr + 10]; + double* Y = new double[nr * (l_hi - l_lo + 1) + 10]; + // fill Y with zeros + for (int i = 0; i < nr * (l_hi - l_lo + 1) + 10; ++i) { - r[i] = i * dr; + Y[i] = 0.0; } - double* jl_old = new double[nr]; - double* jl_new = new double[nr]; - for (int l = 0; l <= lmax; ++l) + // case 0: x = 0, l = 0 + EXPECT_NEAR(ModuleBase::Sphbes::sphbesj(0,0), 1.0, 1e-12); + // case 1: x = 0, l = 1, ... , 11 + for (int l = 1; l <= l_hi; ++l) { - for (double q = 0.1; q < 10; q += 0.1) - { - ModuleBase::Sphbes::Spherical_Bessel(nr, r, q, 0, jl_old); - ModuleBase::Sphbes::sphbesj(nr, r, q, 0, jl_new); - for (int i = 0; i < nr; ++i) - { - EXPECT_NEAR(jl_old[i], jl_new[i], 1e-12); - } - - // derivative - ModuleBase::Sphbes::dSpherical_Bessel_dx(nr, r, q, 0, jl_old); - ModuleBase::Sphbes::dsphbesj(nr, r, q, 0, jl_new); - for (int i = 0; i < nr; ++i) - { - EXPECT_NEAR(jl_old[i], jl_new[i], 1e-12); - } - } + EXPECT_NEAR(ModuleBase::Sphbes::sphbesj(l,0), 0.0, 1e-12); + } + // case 2: wide range of x and l + double y; + // read reference data + std::ifstream fin("data/bj.bin", std::ios::binary); + int i = 0; + while (fin.read(reinterpret_cast(&y), sizeof(double))){ + Y[i] = y; ++i; + // if (Y[i] == 0) {std::cout << "i: " << i << std::endl; break;} } + //std::cout << i << std::endl; + fin.close(); - delete[] r; - delete[] jl_old; - delete[] jl_new; + for(int i = 0; i < nr; ++i){ + r[i] = (i + 1) * dr; + } + + // test for new sphbesj + for (int l = l_lo; l <= l_hi; ++l) + { + for(int i = 0; i< nr; ++i){ + EXPECT_NEAR(ModuleBase::Sphbes::sphbesj(l, r[i] * q), Y[l * nr + i], 1e-12); + } + } + // test for old Bessel + // most of l cases precision failed to achieve 1e-12 + double* jl_old = new double[nr + 10]; + for (int l = l_lo; l <= l_hi; ++l) + { + ModuleBase::Sphbes::Spherical_Bessel(nr, r, q, l, jl_old); + double errs = 0.0; + for(int i = 0; i< nr; ++i){ + errs += MAX(jl_old[i] - Y[l * nr + i], Y[l * nr + i] - jl_old[i]); + } + // std::cout << " l = " << l << ", errors: " << std::scientific << errs / nr << std::endl; + } + } int main(int argc, char **argv) @@ -266,4 +329,4 @@ TEST_F(Sphbes,SphericalBesselsjp) EXPECT_EQ(sjp[iii], 1.0); } delete [] sjp; -} +} \ No newline at end of file From 11ae16124cdd777068ccc9fd4f44c5ec6626d59f Mon Sep 17 00:00:00 2001 From: Jie Li Date: Mon, 18 Sep 2023 17:42:50 +0800 Subject: [PATCH 2/5] add test points near zero in a log grid with base 2 --- source/module_base/test/data/bjx.bin | Bin 0 -> 1536 bytes source/module_base/test/data/gen_bessel.m | 16 +++--- .../module_base/test/data/gen_bessel_grid.m | 17 +++++++ source/module_base/test/math_sphbes_test.cpp | 47 ++++++++++++++---- 4 files changed, 61 insertions(+), 19 deletions(-) create mode 100644 source/module_base/test/data/bjx.bin create mode 100644 source/module_base/test/data/gen_bessel_grid.m diff --git a/source/module_base/test/data/bjx.bin b/source/module_base/test/data/bjx.bin new file mode 100644 index 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zLi{*nFFtV+(u{vS8F^n*(*9ewU#g&|XK1`Vl7c>RLLb>HWmEC?7%?a{kk3!&l>{Z6 zY>8W19h43d^Jf=c4@%v-x$^d!pk&bP+&--~C{<{mEfhh8_C-M&n4R$C@qDlWf2R8e z#PNTVkOwvCdStg+_!4PQC)H~Y@Ai(O`*!sv*}coDSLV*QrQXZr4*%rhv);kvh-v?Q z;PlQXsz;ui==7e|DWVssoZg@|BRNXr^d@P8qq4!H3GsKV;7dGpQ$EPxx8n|hd76d; W$Ome_6B)0*UV+@GD!zccHT8dz)7!iN literal 0 HcmV?d00001 diff --git a/source/module_base/test/data/gen_bessel.m b/source/module_base/test/data/gen_bessel.m index fe2f3d53e6..2ae185a586 100644 --- a/source/module_base/test/data/gen_bessel.m +++ b/source/module_base/test/data/gen_bessel.m @@ -1,17 +1,13 @@ % GEN_BESSEL Generate a Bessel function of the first kind. -% l: order of the Bessel function -% q: the argument of the Bessel function -% rc: the cutoff radius -% nr: the number of points to be generated -%% Case: q = 0.1; rc = 50; nr = 5000; l_lo = 0; l_hi=11; -function [X, Val] = gen_bessel(q, rc, nr, l_lo, l_hi) - X = linspace(0, rc, nr+1) * q; - X = X(2:nr+1); - Val = zeros(nr, l_hi-l_lo+1); +% X: function domain of the Bessel function +% l_lo, l_hi: euqation order of the Bessel function +%% Case: X = 2.^[-5:-1:-20]; l_lo = 0; l_hi=11; +function Val = gen_bessel(X, l_lo, l_hi) + [~, n] = size(X); + Val = zeros(n, l_hi-l_lo+1); for l = l_lo:l_hi Val(:, l-l_lo+1) = sphbes(l, X); end Val = reshape(Val, 1, []); end - diff --git a/source/module_base/test/data/gen_bessel_grid.m b/source/module_base/test/data/gen_bessel_grid.m new file mode 100644 index 0000000000..b9c628bb28 --- /dev/null +++ b/source/module_base/test/data/gen_bessel_grid.m @@ -0,0 +1,17 @@ +% GEN_BESSEL_GRID Generate a Bessel function of the first kind in grid. +% q: the argument of the Bessel function +% rc: the cutoff radius +% nr: the number of points to be generated +% l_lo, l_hi: order of the Bessel function +%% Case: q = 0.1; rc = 50; nr = 5000; l_lo = 0; l_hi=11; +function [X, Val] = gen_bessel_grid(q, rc, nr, l_lo, l_hi) + X = linspace(0, rc, nr+1) * q; + X = X(2:nr+1); + Val = zeros(nr, l_hi-l_lo+1); + for l = l_lo:l_hi + Val(:, l-l_lo+1) = sphbes(l, X); + end + Val = reshape(Val, 1, []); +end + + diff --git a/source/module_base/test/math_sphbes_test.cpp b/source/module_base/test/math_sphbes_test.cpp index 725e2cc290..04090da8e2 100644 --- a/source/module_base/test/math_sphbes_test.cpp +++ b/source/module_base/test/math_sphbes_test.cpp @@ -242,7 +242,7 @@ TEST_F(Sphbes,SphericalBesselRoots) // delete[] jl_new; // } -TEST_F(Sphbes, SphericalBesselPrecision) +TEST_F(Sphbes, SphericalBesselPrecisionGrid) { // This test checks whether sphbesj agrees with the Matlab implementation // on a coarse grid for a range of l and q values. @@ -253,11 +253,6 @@ TEST_F(Sphbes, SphericalBesselPrecision) const double dr = rcut / nr; double* r = new double[nr + 10]; double* Y = new double[nr * (l_hi - l_lo + 1) + 10]; - // fill Y with zeros - for (int i = 0; i < nr * (l_hi - l_lo + 1) + 10; ++i) - { - Y[i] = 0.0; - } // case 0: x = 0, l = 0 EXPECT_NEAR(ModuleBase::Sphbes::sphbesj(0,0), 1.0, 1e-12); @@ -273,9 +268,7 @@ TEST_F(Sphbes, SphericalBesselPrecision) int i = 0; while (fin.read(reinterpret_cast(&y), sizeof(double))){ Y[i] = y; ++i; - // if (Y[i] == 0) {std::cout << "i: " << i << std::endl; break;} } - //std::cout << i << std::endl; fin.close(); for(int i = 0; i < nr; ++i){ @@ -301,7 +294,43 @@ TEST_F(Sphbes, SphericalBesselPrecision) } // std::cout << " l = " << l << ", errors: " << std::scientific << errs / nr << std::endl; } - + delete[] r; + delete[] Y; + delete[] jl_old; +} + +TEST_F(Sphbes, SphericalBesselPrecisionNearZero) +{ + // This test checks whether sphbesj agrees with the Matlab implementation + // when x is near zero point for a range of l. + const int n = 16; + const int l_lo = 0, l_hi = 11; + double* x = new double[n + 10]; + double* Y = new double[n * (l_hi - l_lo + 1) + 10]; + + // read reference data + double y; + std::ifstream fin("data/bjx.bin", std::ios::binary); + int i = 0; + while (fin.read(reinterpret_cast(&y), sizeof(double))){ + Y[i] = y; ++i; + } + fin.close(); + // generate x + x[0] = 1.0 / (1 << 5); + for(int i = 1; i < n; i++){ + x[i] = x[i-1] / 2; + } + + // test for sphbesj near zero + for (int l = l_lo; l <= l_hi; ++l) + { + for(int i = 0; i< n; ++i){ + EXPECT_NEAR(ModuleBase::Sphbes::sphbesj(l, x[i]), Y[l * n + i], 1e-12); + } + } + delete[] x; + delete[] Y; } int main(int argc, char **argv) From 39d2610a9837c00d8a27ebaa0213246cde7034e6 Mon Sep 17 00:00:00 2001 From: Jie Li Date: Mon, 18 Sep 2023 21:07:02 +0800 Subject: [PATCH 3/5] add gold standard from octave --- source/module_base/test/data/bj.bin | Bin 480000 -> 0 bytes source/module_base/test/data/bjo.bin | Bin 0 -> 480000 bytes source/module_base/test/data/bjx.bin | Bin 1536 -> 0 bytes source/module_base/test/data/bjxo.bin | Bin 0 -> 1536 bytes source/module_base/test/math_sphbes_test.cpp | 8 ++++---- 5 files changed, 4 insertions(+), 4 deletions(-) delete mode 100644 source/module_base/test/data/bj.bin create mode 100644 source/module_base/test/data/bjo.bin delete mode 100644 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whether sphbesj agrees with the Octave implementation // when x is near zero point for a range of l. const int n = 16; const int l_lo = 0, l_hi = 11; @@ -310,7 +310,7 @@ TEST_F(Sphbes, SphericalBesselPrecisionNearZero) // read reference data double y; - std::ifstream fin("data/bjx.bin", std::ios::binary); + std::ifstream fin("data/bjxo.bin", std::ios::binary); int i = 0; while (fin.read(reinterpret_cast(&y), sizeof(double))){ Y[i] = y; ++i; From 6f2e4faf756a352ce018a7d118675d34d2abf7f5 Mon Sep 17 00:00:00 2001 From: Jie Li Date: Tue, 19 Sep 2023 17:27:36 +0800 Subject: [PATCH 4/5] add notes in sphbes.m --- source/module_base/test/data/sphbes.m | 20 +++++++++----------- 1 file changed, 9 insertions(+), 11 deletions(-) diff --git a/source/module_base/test/data/sphbes.m b/source/module_base/test/data/sphbes.m index 047d3fef27..246917eacf 100644 --- a/source/module_base/test/data/sphbes.m +++ b/source/module_base/test/data/sphbes.m @@ -1,15 +1,13 @@ +% SPHBES: Computes the Spherical Bessel functions of the first kind +% nu: euqation order, specified as a scalar, vector, matrix, or multidimensional array. +% x: function domain, specified as a scalar, vector, matrix, or multidimensional array. function js = sphbes(nu, x) -% returns the spherical Bessel functions jnu(x) -% x is a vector or it may be a matrix if nu is a scalar -% if nu is a row and x a column vector, the output js is a matrix - -[~, lnu] = size(nu); -xm = repmat(x, 1, lnu); -% special case handle: x = 0 -js(~xm) = 0; -% general case -nzind = find(xm); -js(nzind) = sqrt(pi ./(2* xm(nzind))) .* besselj(nu + 0.5, x(nzind)); + % special case handle: x = 0 + js(~x) = 0; + % general case + nzind = find(x); + js(nzind) = sqrt(pi ./(2* xm(nzind))) .* besselj(nu + 0.5, x(nzind)); +end From 4a2817d30395bb258921ae3713aae4dbee493d6f Mon Sep 17 00:00:00 2001 From: Jie Li Date: Wed, 20 Sep 2023 14:20:04 +0800 Subject: [PATCH 5/5] remove octave scripts --- source/module_base/test/data/gen_bessel.m | 13 ------------- source/module_base/test/data/gen_bessel_grid.m | 17 ----------------- source/module_base/test/data/sphbes.m | 14 -------------- 3 files changed, 44 deletions(-) delete mode 100644 source/module_base/test/data/gen_bessel.m delete mode 100644 source/module_base/test/data/gen_bessel_grid.m delete mode 100644 source/module_base/test/data/sphbes.m diff --git a/source/module_base/test/data/gen_bessel.m b/source/module_base/test/data/gen_bessel.m deleted file mode 100644 index 2ae185a586..0000000000 --- a/source/module_base/test/data/gen_bessel.m +++ /dev/null @@ -1,13 +0,0 @@ -% GEN_BESSEL Generate a Bessel function of the first kind. -% X: function domain of the Bessel function -% l_lo, l_hi: euqation order of the Bessel function -%% Case: X = 2.^[-5:-1:-20]; l_lo = 0; l_hi=11; -function Val = gen_bessel(X, l_lo, l_hi) - [~, n] = size(X); - Val = zeros(n, l_hi-l_lo+1); - for l = l_lo:l_hi - Val(:, l-l_lo+1) = sphbes(l, X); - end - Val = reshape(Val, 1, []); -end - diff --git a/source/module_base/test/data/gen_bessel_grid.m b/source/module_base/test/data/gen_bessel_grid.m deleted file mode 100644 index b9c628bb28..0000000000 --- a/source/module_base/test/data/gen_bessel_grid.m +++ /dev/null @@ -1,17 +0,0 @@ -% GEN_BESSEL_GRID Generate a Bessel function of the first kind in grid. -% q: the argument of the Bessel function -% rc: the cutoff radius -% nr: the number of points to be generated -% l_lo, l_hi: order of the Bessel function -%% Case: q = 0.1; rc = 50; nr = 5000; l_lo = 0; l_hi=11; -function [X, Val] = gen_bessel_grid(q, rc, nr, l_lo, l_hi) - X = linspace(0, rc, nr+1) * q; - X = X(2:nr+1); - Val = zeros(nr, l_hi-l_lo+1); - for l = l_lo:l_hi - Val(:, l-l_lo+1) = sphbes(l, X); - end - Val = reshape(Val, 1, []); -end - - diff --git a/source/module_base/test/data/sphbes.m b/source/module_base/test/data/sphbes.m deleted file mode 100644 index 246917eacf..0000000000 --- a/source/module_base/test/data/sphbes.m +++ /dev/null @@ -1,14 +0,0 @@ -% SPHBES: Computes the Spherical Bessel functions of the first kind -% nu: euqation order, specified as a scalar, vector, matrix, or multidimensional array. -% x: function domain, specified as a scalar, vector, matrix, or multidimensional array. -function js = sphbes(nu, x) - % special case handle: x = 0 - js(~x) = 0; - % general case - nzind = find(x); - js(nzind) = sqrt(pi ./(2* xm(nzind))) .* besselj(nu + 0.5, x(nzind)); -end - - - -

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