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| real(doubleprecision) function | mathematicalsubroutines::det (rin) |
| | calculates the determinant of 3x3 matrix rin More...
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| integer function | mathematicalsubroutines::gcd (M, N) |
| | calculates the greast common divisor of (m,n) More...
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| integer function | mathematicalsubroutines::lcm (M, N) |
| | calculates the Least common factor of (m,n) More...
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| integer(8) function | mathematicalsubroutines::factorial (n) |
| | calculates the Factorial(n) More...
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| real function | mathematicalsubroutines::factorial_real (n) |
| | Real version of the factorial function. More...
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| real function | mathematicalsubroutines::doublefactorial_real (n) |
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| integer function | mathematicalsubroutines::binomialcoefficient (n, m) |
| | calculates the BinomialCoefficient(n,m) of integers n and m More...
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| real function | mathematicalsubroutines::binomialcoefficient_real (n, m) |
| | Real number version of the Binomial Coefficient function. More...
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| real function | mathematicalsubroutines::lorentzian (w, w0, width) |
| | calculates the Lorentzian shape at frequency w centered at w0 with width width; integral wrt w equals to unity. More...
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| real function | mathematicalsubroutines::lorentzim (w, w0, width) |
| | calculates the Lorentzian shape at frequency w centered at w0 with width width; integral wrt w equals to unity. \( \frac{1}{\pi} \frac{\gamma}{(\omega - \omega_0)^2 - \gamma^2} \) More...
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| real function | mathematicalsubroutines::lorentzre (w, w0, width) |
| | calculates the real part of Lorentzian shape at frequency w centered at w0 with width width. Magnitude conforms with the imaginary part having integral of unity. More...
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| real function | mathematicalsubroutines::gaussian (w, w0, width) |
| | calculates the real Gaussian shape at frequency w centered at w0 with width width; integral wrt w equals to unity. Magnitude conforms with the integral of unity. More...
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| real function | mathematicalsubroutines::wigner3jm (j1, j2, j3, m1, m2, m3) |
| | calculates the Wigner 3jm symbol for integer arguments j1 j2 j3 m1 m2 m3 More...
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| real function | mathematicalsubroutines::gauntcoefficient (k, l1, m1, l2, m2) |
| | calculates the Gaunt coefficient for intermediate momentum k for the momenta l1,l2 and projections of momenta m1,m2 More...
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| real function | mathematicalsubroutines::pleg (l, m, x) |
| | calculates the m-th adjoint of n-th Legendre polynomial More...
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| real function | mathematicalsubroutines::legendre_polynomial (l, m, x) |
| | General Legendre polynomial function which accepts negative m. More...
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| complex function | mathematicalsubroutines::spherical_function (l, m, teta, phi) |
| | Calculates complex spherical function with Condon-Shortley phase. More...
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| real function | mathematicalsubroutines::upperincompletegammaf (n, x) |
| | Calculates the "upper" incomplete gamma function defined as. More...
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| real function | mathematicalsubroutines::upperincompletegammaf_real (s, x) |
| | Calculates the upper incomplete gamma function defined above for non-integer values of n (renamed to s) More...
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| real function | mathematicalsubroutines::lowerincompletegammaf (n, x) |
| | Calculates the lower incomplete gamma function, the complement to the upper incomplete gamma function, for integer n. More...
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| real function | mathematicalsubroutines::lowerincompletegammaf_real (s, x) |
| | Calculates the lower incomplete gamma function for non-integer values of n (renamed to s) More...
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| complex function | mathematicalsubroutines::ex (M, S, C) |
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| integer function | mathematicalsubroutines::isig (N) |
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| integer function | mathematicalsubroutines::ihvside (n) |
| | Heaviside function on integers. Returns 1 if n >= 0 and 0 otherwise. More...
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| subroutine | mathematicalsubroutines::sdiagv (N, A, D, X) |
| | MATRIX DIAGONALIZATION PROCEDURE WE USED FOR DECADES... IS GOOD DUE TO FACT THAT IT SORTS THE EIGENVALUES. More...
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| subroutine | mathematicalsubroutines::simplex (start, n, EPSILON, scale, iprint, func, finish, valmin) |
| | gradientless minimization of function func. Our DirtyTricks are used to make the interface modern (transmission fo the function by pointer More...
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| subroutine | mathematicalsubroutines::svdcmp (a, m, n, mp, np, w, v) |
| | Singular value decomposition of matrix A. More...
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| subroutine | mathematicalsubroutines::gradient_minimization (pFunction, pFirstDerivative, init_variables, step, prec, reset) |
| | Function allows to find local minimum of function by using gradient optimization methid. More...
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| real function | mathematicalsubroutines::adapt_simpson_int (f, x_min, x_max, iprec, pars) |
| | Performs adaptive Simpson's numerical integration of a real function of one variable. This algorithm finds the optimal number of points required to reach the given accuracy of integration, which usually allows to decrease number of function evaluations compared to standard integration algorithm. More...
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| recursive real function | adapt_simpson_rec (f, a, fa, b, fb, eps, whole, m, fm, depth, pars) |
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| subroutine | simpson_interval (f, a, fa, b, fb, m, fm, intg, pars) |
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| real function, dimension(2) | mathematicalsubroutines::optimize_f_goldensection (f, xmin, xmax, prec, pars) |
| | Finds minimum of a real function of one variable in a given interval using golden-section search method. Can be used for any unimodal function, when the gradients are not known. Returns an interval where the minimum is located with required precision. More...
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| real function | mathematicalsubroutines::opt_scalar_brent (f, xmin, xmax, tol, stat, pars) |
| | Finds minimum of scalar function f bracketed by [xmin, xmax] More...
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| real function | mathematicalsubroutines::solve_scalar_brent (f, xmin, xmax, tol, stat, pars) |
| | Finds simple root of scalar function f bracketed by [xmin, xmax] More...
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| recursive subroutine | mathematicalsubroutines::generalizedlaguerrepolynomialcoefficients (n, l, coef_array) |
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| subroutine | mathematicalsubroutines::getjacobirotationmatrix (space_dim, dim1, dim2, angle, JacobiMatrix) |
| | produces Jacobi rotation matrix for angle angle of the size space_dim x space_dim for a pair of components with numbers dim1, dim2 More...
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| subroutine | mathematicalsubroutines::getfirstderivativeofjacobirotationmatrix (space_dim, dim1, dim2, angle, DerivativeMatrix) |
| | produces first derivative wrt angle of the Jacobi rotation matrix for angle angle of the size space_dim x space_dim for a pair of components with numbers dim1, dim2 More...
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| subroutine | mathematicalsubroutines::getsecondderivativeofjacobirotationmatrix (space_dim, dim1, dim2, angle, DerivativeMatrix) |
| | produces second derivative wrt angle of the Jacobi rotation matrix for angle angle of the size space_dim x space_dim for a pair of components with numbers dim1, dim2 More...
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| subroutine | mathematicalsubroutines::rotate_matrix_left (space_dim, dim1, dim2, angle, mat) |
| | Multiplies the given matrix by a Jacobi rotation matrix from the left. More...
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| subroutine | mathematicalsubroutines::rotate_matrix_right (space_dim, dim1, dim2, angle, mat) |
| | Multiplies the given matrix by a Jacobi rotation matrix from the left. More...
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| subroutine | mathematicalsubroutines::jacobi (n, a, d, v) |
| | Diagonalization of matrix a(n,n) by Jacobi method n is the matrix dimension a(n,n) - matrix d(n) - eigenvalues array v(n,n) – eigenvectors array. More...
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| real function, dimension(n, n) | mathematicalsubroutines::adj_singular (n, M) |
| | Calculates adjugate matrix of the degenerate NxN matrix M (detM = 0). More...
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