test_GNumerics.cpp 23 KB
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711
/***************************************************************************
 *                test_GNumerics.cpp  -  test numerics modules             *
 * ----------------------------------------------------------------------- *
 *  copyright (C) 2010-2020 by Jurgen Knodlseder                           *
 * ----------------------------------------------------------------------- *
 *                                                                         *
 *  This program is free software: you can redistribute it and/or modify   *
 *  it under the terms of the GNU General Public License as published by   *
 *  the Free Software Foundation, either version 3 of the License, or      *
 *  (at your option) any later version.                                    *
 *                                                                         *
 *  This program is distributed in the hope that it will be useful,        *
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of         *
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the          *
 *  GNU General Public License for more details.                           *
 *                                                                         *
 *  You should have received a copy of the GNU General Public License      *
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.  *
 *                                                                         *
 ***************************************************************************/
/**
 * @file test_GNumerics.cpp
 * @brief Unit tests implementation for numerics module
 * @author Juergen Knoedlseder
 */

/* __ Includes ___________________________________________________________ */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <ostream>
#include <stdexcept>
#include <stdlib.h>
#include "test_GNumerics.hpp"

/* __ Namespaces _________________________________________________________ */

/* __ Globals ____________________________________________________________ */


/***********************************************************************//**
 * @brief Set tests
 ***************************************************************************/
void TestGNumerics::set(void)
{
    //set name
    name("GNumerics");

    // Set parameters
    m_sigma = 2.5;

    // Append tests
    append(static_cast<pfunction>(&TestGNumerics::test_math),
           "Test GMath");
    append(static_cast<pfunction>(&TestGNumerics::test_ndarray),
           "Test GNdarray");
    append(static_cast<pfunction>(&TestGNumerics::test_fft),
           "Test GFft");
    append(static_cast<pfunction>(&TestGNumerics::test_function),
           "Test GFunction");
    append(static_cast<pfunction>(&TestGNumerics::test_functions),
           "Test GFunctions");
    append(static_cast<pfunction>(&TestGNumerics::test_integral),
           "Test GIntegral");
    append(static_cast<pfunction>(&TestGNumerics::test_integrals),
           "Test GIntegrals");
    append(static_cast<pfunction>(&TestGNumerics::test_romberg_integration),
           "Test Romberg integration");
    append(static_cast<pfunction>(&TestGNumerics::test_adaptive_simpson_integration),
           "Test adaptive Simpson integration");
    append(static_cast<pfunction>(&TestGNumerics::test_gauss_kronrod_integration),
           "Test Gauss-Kronrod integration");

    // Return
    return;
}


/***********************************************************************//**
 * @brief Clone test suite
 *
 * @return Pointer to deep copy of test suite.
 ***************************************************************************/
TestGNumerics* TestGNumerics::clone(void) const
{
    // Clone test suite
    return new TestGNumerics(*this);
}


/***********************************************************************//**
 * @brief Test mathematics functions
 ***************************************************************************/
void TestGNumerics::test_math(void)
{
    // Test acos function
    test_value(gammalib::acos(0.0), 1.57079633);
    test_value(gammalib::acos(0.37), 1.19178731);

    // Test atan2 function
    test_value(gammalib::atan2( 1.0, 2.0),  0.463647609001);
    test_value(gammalib::atan2( 1.0,-3.0),  2.819842099193);
    test_value(gammalib::atan2(-2.0,-3.0), -2.553590050042);
    test_value(gammalib::atan2(-2.0, 1.0), -1.107148717794);

    // Test cosd function
    test_value(gammalib::cosd(  0.0),  1.0);
    test_value(gammalib::cosd( 33.0),  0.83867057);
    test_value(gammalib::cosd(178.1), -0.99945022);

    // Test sind function
    test_value(gammalib::sind(  0.0), 0.0);
    test_value(gammalib::sind( 33.0), 0.54463904);
    test_value(gammalib::sind(178.1), 0.03315518);

    // Test tand function
    test_value(gammalib::tand(-10.0), -0.176326980708);
    test_value(gammalib::tand( 12.0),  0.21255656167);
    test_value(gammalib::tand(178.1), -0.0331734166041);

    // Test asind function
    test_value(gammalib::asind(0.0), 0.0);
    test_value(gammalib::asind(0.37), 21.7156172833);

    // Test acosd function
    test_value(gammalib::acosd(0.0), 90.0);
    test_value(gammalib::acosd(0.37), 68.28438272);

    // Test atan2d function
    test_value(gammalib::atan2d( 1.0, 2.0),   26.5650511771);
    test_value(gammalib::atan2d( 1.0,-3.0),  161.565051177);
    test_value(gammalib::atan2d(-2.0,-3.0), -146.309932474);
    test_value(gammalib::atan2d(-2.0, 1.0),  -63.4349488229);

    // Test sincosd function
    double s;
    double c;
    gammalib::sincosd(33.0, &s, &c);
    test_value(s, 0.54463904);
    test_value(c, 0.83867057);

    // Test logarithm of gamma function
    test_value(gammalib::gammln(0.5), 0.572364942925);
    test_value(gammalib::gammln(1.5), -0.120782237635);

    // Test error function
    test_value(gammalib::erf(0.0), 0.0);
    test_value(gammalib::erf(1.0), 0.8427008);
    test_value(gammalib::erf(2.0), 0.9953223);

    // Test complementary error function
    test_value(gammalib::erfc(0.0), 1.0);
    test_value(gammalib::erfc(0.1), 0.887537084);
    test_value(gammalib::erfc(0.8), 0.257899035);

    // Test inverse error function
    test_value(gammalib::erfinv(0.3), 0.2724627147);
    test_value(gammalib::erfinv(0.9), 1.1630871537);

    // Test modulo function
    test_value(gammalib::modulo(3.1, 2.8), 0.3);
    test_value(gammalib::modulo(-5.7, 1.37), 1.15);

    // Test power law integration
    test_value(gammalib::plaw_integral(2.0, 3.0, 9.0, 5.0), 29.112577);
    test_value(gammalib::plaw_integral(2.0, 9.0, 9.0, 2.0), 27.073393);
    test_value(gammalib::plaw_integral(2.0, 9.0, 5.0, 2.0), 12.471065);

    // Test Gaussian integration
    test_value(gammalib::gauss_integral(0.0, 1.0),  0.341344746069);
    test_value(gammalib::gauss_integral(-1.0, 1.0), 0.682689492137086);
    test_value(gammalib::gauss_integral(-2.0, 2.0), 0.954499736103642);
    test_value(gammalib::gauss_integral(-3.0, 3.0), 0.997300203936740);

    // Exit test
    return;
}


/***********************************************************************//**
 * @brief Test n-dimensional array
 ***************************************************************************/
void TestGNumerics::test_ndarray(void)
{
    // Test void constructor
    GNdarray nd0;
    test_value(nd0.size(), 0);
    test_value(nd0.dim(), 0);

    // Test 1-dimensional array
    GNdarray nd1(3);
    test_value(nd1.size(), 3);
    test_value(nd1.dim(), 1);
    test_value(nd1.shape()[0], 3);
    for (int i = 0; i < 3; ++i) {
        nd1(i) = double(i);
        test_value(nd1.at(i), double(i));
    }

    // Test 2-dimensional array
    GNdarray nd2(3,2);
    test_value(nd2.size(), 6);
    test_value(nd2.dim(), 2);
    test_value(nd2.shape()[0], 3);
    test_value(nd2.shape()[1], 2);
    for (int ix = 0; ix < 3; ++ix) {
        for (int iy = 0; iy < 2; ++iy) {
            double ref = double(ix)+double(iy);
            nd2(ix,iy) = ref;
            test_value(nd2.at(ix,iy), ref);
        }
    }
    // Test 3-dimensional array
    GNdarray nd3(2,2,2);
    test_value(nd3.size(), 8);
    test_value(nd3.dim(), 3);
    test_value(nd3.shape()[0], 2);
    test_value(nd3.shape()[1], 2);
    test_value(nd3.shape()[2], 2);
    for (int ix = 0; ix < 2; ++ix) {
        for (int iy = 0; iy < 2; ++iy) {
            for (int iz = 0; iz < 2; ++iz) {
                double ref    = double(ix)+double(iy)+double(iz);
                nd3(ix,iy,iz) = ref;
                test_value(nd3.at(ix,iy,iz), ref);
            }
        }
    }

    // Test n-dimensional array
    std::vector<int> n(5,2);
    GNdarray ndn(n);
    test_value(ndn.size(), 32);
    test_value(ndn.dim(), 5);
    for (int i = 0; i < 5; ++i) {
        test_value(ndn.shape()[i], 2);
    }
    std::vector<int> itest(5,1);
    ndn(itest) = 3.1415;
    test_value(ndn.at(itest), 3.1415);

    // Setup arrays for operator tests
    GNdarray nda(1,2);
    nda(0,0) = 3.0;
    nda(0,1) = 5.5;
    GNdarray ndb = nda;
    GNdarray ndc = nda + ndb;

    // Test operator=
    test_value(ndb(0,0), 3.0);
    test_value(ndb(0,1), 5.5);

    // Test operator== and operator!=
    test_assert(nda == ndb, "Test operator==");
    test_assert(nda != ndc, "Test operator!=");

    // Test array operator+=
    nda += ndb;
    test_value(nda(0,0),  6.0);
    test_value(nda(0,1), 11.0);

    // Test array operator-=
    nda -= ndb;
    test_value(nda(0,0), 3.0);
    test_value(nda(0,1), 5.5);

    // Test value operator+=
    nda += 1.5;
    test_value(nda(0,0), 4.5);
    test_value(nda(0,1), 7.0);

    // Test value operator-=
    nda -= 1.5;
    test_value(nda(0,0), 3.0);
    test_value(nda(0,1), 5.5);

    // Test value operator*=
    nda *= 3.0;
    test_value(nda(0,0),  9.0);
    test_value(nda(0,1), 16.5);

    // Test value operator/=
    nda /= 3.0;
    test_value(nda(0,0), 3.0);
    test_value(nda(0,1), 5.5);

    // Test operator-
    GNdarray ndd = -nda;
    test_value(ndd(0,0), -3.0);
    test_value(ndd(0,1), -5.5);

    // Test operator+(GNdarray,GNdarray)
    ndd = nda + ndb;
    test_value(ndd(0,0),  6.0);
    test_value(ndd(0,1), 11.0);

    // Test operator+(GNdarray,double) and operator+(double,GNdarray)
    ndd = nda + 1.5;
    test_value(ndd(0,0), 4.5);
    test_value(ndd(0,1), 7.0);
    ndd = 1.5 + nda;
    test_value(ndd(0,0), 4.5);
    test_value(ndd(0,1), 7.0);

    // Test operator-(GNdarray,GNdarray)
    ndd = nda - ndb;
    test_value(ndd(0,0), 0.0);
    test_value(ndd(0,1), 0.0);

    // Test operator-(GNdarray,double) and operator-(double,GNdarray)
    ndd = nda - 1.5;
    test_value(ndd(0,0), 1.5);
    test_value(ndd(0,1), 4.0);
    ndd = 1.5 - nda;
    test_value(ndd(0,0), -1.5);
    test_value(ndd(0,1), -4.0);

    // Test operator*(GNdarray,double) and operator*(double,GNdarray)
    ndd = nda * 3.0;
    test_value(ndd(0,0),  9.0);
    test_value(ndd(0,1), 16.5);
    ndd = 3.0 * nda;
    test_value(ndd(0,0),  9.0);
    test_value(ndd(0,1), 16.5);

    // Test operator/(GNdarray,double)
    ndd = nda / 3.0;
    test_value(ndd(0,0),     1.0);
    test_value(ndd(0,1), 5.5/3.0);

    // Test friend functions
    test_value(min(nda), 3.0);
    test_value(max(nda), 5.5);
    test_value(sum(nda), 8.5);
    test_value(acos(nda)(0,0), std::acos(3.0));
    test_value(acos(nda)(0,1), std::acos(5.5));
    test_value(acosh(nda)(0,0), acosh(3.0));
    test_value(acosh(nda)(0,1), acosh(5.5));
    test_value(asin(nda)(0,0), std::asin(3.0));
    test_value(asin(nda)(0,1), std::asin(5.5));
    test_value(asinh(nda)(0,0), asinh(3.0));
    test_value(asinh(nda)(0,1), asinh(5.5));
    test_value(atan(nda)(0,0), std::atan(3.0));
    test_value(atan(nda)(0,1), std::atan(5.5));
    test_value(atanh(nda)(0,0), atanh(3.0));
    test_value(atanh(nda)(0,1), atanh(5.5));
    test_value(cos(nda)(0,0), std::cos(3.0));
    test_value(cos(nda)(0,1), std::cos(5.5));
    test_value(cosh(nda)(0,0), std::cosh(3.0));
    test_value(cosh(nda)(0,1), std::cosh(5.5));
    test_value(exp(nda)(0,0), std::exp(3.0));
    test_value(exp(nda)(0,1), std::exp(5.5));
    test_value(abs(nda)(0,0), std::abs(3.0));
    test_value(abs(nda)(0,1), std::abs(5.5));
    test_value(log(nda)(0,0), std::log(3.0));
    test_value(log(nda)(0,1), std::log(5.5));
    test_value(log10(nda)(0,0), std::log10(3.0));
    test_value(log10(nda)(0,1), std::log10(5.5));
    test_value(sin(nda)(0,0), std::sin(3.0));
    test_value(sin(nda)(0,1), std::sin(5.5));
    test_value(sinh(nda)(0,0), std::sinh(3.0));
    test_value(sinh(nda)(0,1), std::sinh(5.5));
    test_value(sqrt(nda)(0,0), std::sqrt(3.0));
    test_value(sqrt(nda)(0,1), std::sqrt(5.5));
    test_value(tan(nda)(0,0), std::tan(3.0));
    test_value(tan(nda)(0,1), std::tan(5.5));
    test_value(tanh(nda)(0,0), std::tanh(3.0));
    test_value(tanh(nda)(0,1), std::tanh(5.5));
    test_value(pow(nda,3.0)(0,0), std::pow(3.0,3.0));
    test_value(pow(nda,3.0)(0,1), std::pow(5.5,3.0));

    // Exit test
    return;
}


/***********************************************************************//**
 * @brief Test Fast Fourier Transform
 ***************************************************************************/
void TestGNumerics::test_fft(void)
{
    // Test 1-dimensional FFT
    for (int n = 2; n < 12; ++n) {

        // Skip n=8,9,10 since they can be factorised
        if (n > 7 && n < 11) {
            continue;
        }

        // Allocate 1-dimensional array
        GNdarray array(n);

        // Set one elements
        array(n/2) = 1.0;

        // Allocate FFT
        GFft fft(array);

        // Backward transformation
        GNdarray back = fft.backward();

        // Check FFT results
        check_fft1(array, fft, back);

    } // endfor: looped over array lengths

    // Test 2-dimensional FFT
    GNdarray array2(8,9);
    array2(4,4) = 1.0;
    GFft     fft2(array2);
    GNdarray back2 = fft2.backward();
    check_fft2(array2, fft2, back2);

    // Exit test
    return;
}


/***********************************************************************//**
 * @brief Check 1-dimensional Fast Fourier Transform
 *
 * @param[in] array Input array.
 * @param[in] fft Fast Fourier Transform of input array.
 * @param[in] back Backward transform of FFT (should be equal to input array)
 ***************************************************************************/
void TestGNumerics::check_fft1(const GNdarray& array,
                               const GFft&     fft,
                               const GNdarray& back)
{
    // Get normalisation factor
    double norm = 1.0 / double(array.size());

    // Compute reference value and compare with FFT result
    for (int k = 0; k < array.size(); ++k) {
        double ref_real = 0.0;
        double ref_imag = 0.0;
        for (int n = 0; n < array.size(); ++n) {
            double x = -gammalib::twopi * k * n * norm;
            ref_real += array(n) * std::cos(x);
            ref_imag += array(n) * std::sin(x);
        }
        std::complex<double> ref(ref_real, ref_imag);
        test_value(fft(k), ref);
    }

    // Test backward transformation
    for (int k = 0; k < array.size(); ++k) {
        test_value(back(k), array(k));
    }

    // Exit test
    return;
}


/***********************************************************************//**
 * @brief Check 2-dimensional Fast Fourier Transform
 *
 * @param[in] array Input array.
 * @param[in] fft Fast Fourier Transform of input array.
 * @param[in] back Backward transform of FFT (should be equal to input array)
 ***************************************************************************/
void TestGNumerics::check_fft2(const GNdarray& array,
                               const GFft&     fft,
                               const GNdarray& back)
{
    // Get normalisation factor
    double normM = 1.0 / double(array.shape()[0]);
    double normN = 1.0 / double(array.shape()[1]);

    // Compute reference value and compare with FFT result
    for (int k = 0; k < array.shape()[0]; ++k) {
        for (int l = 0; l < array.shape()[1]; ++l) {
            double ref_real = 0.0;
            double ref_imag = 0.0;
            for (int n = 0; n < array.shape()[1]; ++n) {
                double sum_real = 0.0;
                double sum_imag = 0.0;
                for (int m = 0; m < array.shape()[0]; ++m) {
                    double x = -gammalib::twopi * m * k * normM;
                    sum_real += array(m,n) * std::cos(x);
                    sum_imag += array(m,n) * std::sin(x);
                }
                double y = -gammalib::twopi * n * l * normN;
                ref_real += (sum_real * std::cos(y) - sum_imag * std::sin(y));
                ref_imag += (sum_real * std::sin(y) + sum_imag * std::cos(y));
            }
            std::complex<double> ref(ref_real, ref_imag);
            test_value(fft(k,l), ref);
        }
    }

    // Test backward transformation
    for (int k = 0; k < array.size(); ++k) {
        test_value(back(k), array(k));
    }

    // Exit test
    return;
}


/***********************************************************************//**
 * @brief Test GFunction class
 ***************************************************************************/
void TestGNumerics::test_function(void)
{
    // Allocate function
    Gauss function(m_sigma);

    // Test function value
    test_value(function.eval(0.0), 0.159576912, "Check function value at x=0");
    test_value(function.eval(1.0), 0.147308056, "Check function value at x=1");

    // Exit test
    return;
}


/***********************************************************************//**
 * @brief Test GFunctions class
 ***************************************************************************/
void TestGNumerics::test_functions(void)
{
    // Set sigma array
    GVector sigma(3);
    sigma[0] = 1.0;
    sigma[1] = 2.0;
    sigma[2] = 4.0;

    // Allocate functions
    GaussArray functions(sigma);

    // Evaluate functions for x=0
    GVector result = functions.eval(0.0);

    // Test function values
    test_value(result[0], 0.39894228, "Check function[0] value at x=0");
    test_value(result[1], 0.19947114, "Check function[1] value at x=0");
    test_value(result[2], 0.09973557, "Check function[2] value at x=0");

    // Evaluate functions for x=1
    result = functions.eval(1.0);

    // Test function values
    test_value(result[0], 0.24197072, "Check function[0] value at x=1");
    test_value(result[1], 0.17603266, "Check function[1] value at x=1");
    test_value(result[2], 0.09666703, "Check function[2] value at x=1");

    // Exit test
    return;
}

/***********************************************************************//**
 * @brief Test GIntegral class
 ***************************************************************************/
void TestGNumerics::test_integral(void)
{
    // Test integral and integrand allocation
    Gauss     integrand(m_sigma);
    GIntegral integral(&integrand);

    // Exit test
    return;
}


/***********************************************************************//**
 * @brief Test GIntegrals class
 ***************************************************************************/
void TestGNumerics::test_integrals(void)
{
    // Set sigma array
    GVector sigma(3);
    sigma[0] = 1.0;
    sigma[1] = 2.0;
    sigma[2] = 4.0;

    // Test kernels and integrals allocation
    GaussArray kernels(sigma);
    GIntegrals integrals(&kernels);
    test_value(integrals.iter(), 0, "Check initial iterations");
    test_value(integrals.calls(), 0, "Check initial calls");

    // Integrate over the entire Gaussian
    GVector result = integrals.romberg(-40.0, 40.0);
    test_value(result[0], 1.0, 1.0e-6, "Check full integration result for (0,0)");
    test_value(result[1], 1.0, 1.0e-6, "Check full integration result for (0,1)");
    test_value(result[2], 1.0, 1.0e-6, "Check full integration result for (0,2)");

    // Test [-1,1] integration
    result = integrals.romberg(-1.0, 1.0);
    test_value(result[0], 0.68268948, 1.0e-6,
               "Check [-1,1] integration result for (0,0)");
    test_value(result[1], 0.38292492, 1.0e-6,
               "Check [-1,1] integration result for (0,1)");
    test_value(result[2], 0.19741265, 1.0e-6,
               "Check [-1,1] integration result for (0,2)");

    // Exit test
    return;
}


/***********************************************************************//**
 * @brief Test Romberg integration
 ***************************************************************************/
void TestGNumerics::test_romberg_integration(void)
{
    // Set-up integral
    Gauss     integrand(m_sigma);
    GIntegral integral(&integrand);

    // Integrate over the entire Gaussian
    double result = integral.romberg(-10.0*m_sigma, 10.0*m_sigma);
    test_value(result, 1.0, 1.0e-6, "Check full integration result");

    // Test [-1sigma, 1sigma]
    result = integral.romberg(-m_sigma, m_sigma);
    test_value(result, 0.68268948, 1.0e-6,
               "Check [-1sigma, 1sigma] integration results");

    // Test [0.0, 1sigma]
    result = integral.romberg(0.0, m_sigma);
    test_value(result, 0.34134475, 1.0e-6,
               "Check [0, 1sigma] integration results");

    // Return
    return;
}


/***********************************************************************//**
 * @brief Test adaptive Simpson integration
 ***************************************************************************/
void TestGNumerics::test_adaptive_simpson_integration(void)
{
    // Set-up integral
    Gauss     integrand(m_sigma);
    GIntegral integral(&integrand);

    // Integrate over the entire Gaussian
    double result = integral.adaptive_simpson(-10.0*m_sigma, 10.0*m_sigma);
    test_value(result, 1.0, 1.0e-6, "Check full integration result");

    // Test [-1sigma, 1sigma]
    result = integral.adaptive_simpson(-m_sigma, m_sigma);
    test_value(result, 0.68268948, 1.0e-6,
               "Check [-1sigma, 1sigma] integration results");


    // Test [0.0, 1sigma]
    result = integral.adaptive_simpson(0.0, m_sigma);
    test_value(result, 0.34134475, 1.0e-6,
               "Check [0, 1sigma] integration results");

    // Return
    return;
}


/***********************************************************************//**
 * @brief Test Gauss-Kronrod integration
 ***************************************************************************/
void TestGNumerics::test_gauss_kronrod_integration(void)
{
    // Set-up integral
    Gauss     integrand(m_sigma);
    GIntegral integral(&integrand);

    // Integrate over the entire Gaussian
    double result = integral.gauss_kronrod(-10.0*m_sigma, 10.0*m_sigma);
    test_value(result, 1.0, 1.0e-6, "Check full integration result");

    // Test [-1sigma, 1sigma]
    result = integral.gauss_kronrod(-m_sigma, m_sigma);
    test_value(result, 0.68268948, 1.0e-6,
               "Check [-1sigma, 1sigma] integration results");

    // Test [0.0, 1sigma]
    result = integral.gauss_kronrod(0.0, m_sigma);
    test_value(result, 0.34134475, 1.0e-6,
               "Check [0, 1sigma] integration results");

    // Return
    return;
}


/***********************************************************************//**
 * @brief Main test function
 ***************************************************************************/
int main(void)
{
    GTestSuites testsuite("GNumerics");

    // Create a test suite
    TestGNumerics test;

    // Append to the container
    testsuite.append(test);

    // Run
    bool success = testsuite.run();

    // save xml report
    testsuite.save("reports/GNumerics.xml");

    // Return
    return (success ? 0:1);
}