math.F90 File Reference

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Modules
module	math_oct_m
	This module is intended to contain "only mathematical" functions and procedures.

Data Types
interface	math_oct_m::is_close
interface	math_oct_m::diagonal_matrix
interface	math_oct_m::upper_triangular_to_hermitian
interface	math_oct_m::lower_triangular_to_hermitian
interface	math_oct_m::interpolate
	This is the common interface to a simple-minded polynomical interpolation procedure (simple use of the classical formula of Lagrange). More...
interface	math_oct_m::symmetrize_matrix
interface	math_oct_m::log2
interface	math_oct_m::pad

Functions/Subroutines
elemental logical function	math_oct_m::dis_close_scalar (x, y, rtol, atol)
	Are \(x\) and \(y\) equal within a tolerance. More...
elemental logical function	math_oct_m::zis_close_scalar (x, y, rtol, atol)
	Same as dis_close_scalar for complex numbers. More...
pure integer function, dimension(dim, dim)	math_oct_m::idiagonal_matrix (dim, diag)
	Currently only returns a matrix whose diagonal elements are all the same. Note that the real and complex versions are in math_inc.F90. More...
recursive real(real64) function, public	math_oct_m::hermite (n, x)
recursive integer function, public	math_oct_m::factorial (n)
subroutine, public	math_oct_m::ylmr_cmplx (xx, li, mi, ylm)
	Computes spherical harmonics ylm at position (x, y, z) More...
subroutine, public	math_oct_m::ylmr_real (xx, li, mi, ylm)
	This is a Numerical Recipes-based subroutine computes real spherical harmonics ylm at position (x, y, z): ylm = c * plm( cos(theta) ) * sin(m*phi) for m < 0 ylm = c * plm( cos(theta) ) * cos(m*phi) for m >= 0 with (theta,phi) the polar angles of r, c a positive normalization. More...
subroutine, public	math_oct_m::weights (N, M, cc, side)
	Compute the weights for finite-difference calculations: More...
real(real64) pure function, public	math_oct_m::ddelta (i, j)
subroutine, public	math_oct_m::make_idx_set (n, out, length, in)
	Construct out(1:length) = (/1, ..., n/) if in is not present, out(1:length) = in otherwise. More...
logical function, public	math_oct_m::member (n, a)
	Considers a(1:ubound(a, 1)) as an integer set and checks if n is a member of it. More...
subroutine, public	math_oct_m::interpolation_coefficients (nn, xa, xx, cc)
logical pure function, public	math_oct_m::even (n)
	Returns if n is even. More...
logical pure function, public	math_oct_m::odd (n)
	Returns if n is odd. More...
subroutine, public	math_oct_m::cartesian2hyperspherical (x, u)
	Performs a transformation of an n-dimensional vector from Cartesian coordinates to hyperspherical coordinates. More...
subroutine, public	math_oct_m::hyperspherical2cartesian (u, x)
	Performs the inverse transformation of cartesian2hyperspherical. More...
subroutine, public	math_oct_m::hypersphere_grad_matrix (grad_matrix, r, x)
	Gives the hyperspherical gradient matrix, which contains the derivatives of the Cartesian coordinates with respect to the hyperspherical angles. More...
integer(int64) pure function	math_oct_m::pad88 (size, blk)
integer(int64) pure function	math_oct_m::pad48 (size, blk)
integer(int64) pure function	math_oct_m::pad8 (size, blk)
integer pure function	math_oct_m::pad4 (size, blk)
integer pure function, public	math_oct_m::pad_pow2 (size)
	create array size, which is padded to powers of 2 More...
real(real64) pure function	math_oct_m::dlog2 (xx)
integer pure function	math_oct_m::ilog2 (xx)
integer(int64) pure function	math_oct_m::llog2 (xx)
complex(real64) pure function, public	math_oct_m::exponential (z)
	Wrapper for exponential. More...
complex(real64) pure function, public	math_oct_m::phi1 (z)
	Compute phi1(z) = (exp(z)-1)/z. More...
complex(real64) pure function, public	math_oct_m::phi2 (z)
	Compute phi2(z) = (phi1(z)-1)/z = (exp(z) - z - 1)/z^2. More...
real(real64) pure function, public	math_oct_m::square_root (x)
	Wrapper for sqrt. More...
logical function, public	math_oct_m::is_prime (n)
subroutine, public	math_oct_m::generate_rotation_matrix (R, ff, tt)
	Generates a rotation matrix R to rotate a vector f to t. More...
subroutine, public	math_oct_m::numder_ridders (x, h, res, err, f)
	Numerical derivative (Ridder`s algorithm). More...
pure complex(real64) function, dimension(1:3), public	math_oct_m::dzcross_product (a, b)
pure complex(real64) function, dimension(1:3), public	math_oct_m::zdcross_product (a, b)
subroutine, public	math_oct_m::generalized_laguerre_polynomial (np, nn, mm, xx, cx)
subroutine	math_oct_m::dupper_triangular_to_hermitian (nn, aa)
subroutine	math_oct_m::zupper_triangular_to_hermitian (nn, aa)
subroutine	math_oct_m::dlower_triangular_to_hermitian (nn, aa)
subroutine	math_oct_m::zlower_triangular_to_hermitian (nn, aa)
subroutine	math_oct_m::dsymmetrize_matrix (nn, aa)
	symmetrize a real matrix More...
subroutine	math_oct_m::zsymmetrize_matrix (n, a)
	make a complex matrix Hermitian More...
subroutine, public	math_oct_m::dzero_small_elements_matrix (aa, tol)
logical function, public	math_oct_m::is_symmetric (a, tol)
	Check if a 2D array is symmetric. More...
logical pure function, public	math_oct_m::is_diagonal (dim, matrix, tol)
	Returns true is the matrix of size dim x dim is diagonal, given a relative tolerance. More...
subroutine, public	math_oct_m::convert_to_base (num, base, converted)
	convert an integer in base 10 to a different base More...
subroutine, public	math_oct_m::convert_from_base (converted, base, num)
	convert an integer to base 10 from a different base More...
pure complex(real64) function, dimension(dim, dim)	math_oct_m::zdiagonal_matrix (dim, diag)
	Currently only returns a matrix whose diagonal elements are all the same. Note that the integer version is in math.F90. More...
subroutine	math_oct_m::zinterpolate_2 (xa, ya, x, y)
subroutine	math_oct_m::zinterpolate_1 (xa, ya, x, y)
subroutine	math_oct_m::zinterpolate_0 (xa, ya, x, y)
pure complex(real64) function, dimension(1:3), public	math_oct_m::zcross_product (a, b)
pure real(real64) function, dimension(dim, dim)	math_oct_m::ddiagonal_matrix (dim, diag)
	Currently only returns a matrix whose diagonal elements are all the same. Note that the integer version is in math.F90. More...
subroutine	math_oct_m::dinterpolate_2 (xa, ya, x, y)
subroutine	math_oct_m::dinterpolate_1 (xa, ya, x, y)
subroutine	math_oct_m::dinterpolate_0 (xa, ya, x, y)
pure real(real64) function, dimension(1:3), public	math_oct_m::dcross_product (a, b)