math Module Reference

Data Types
interface	abscmp
interface	flipv
interface	relcmp
interface	reord
interface	sort
interface	swap

Functions/Subroutines
pure logical function, public	sabscmp (x, y, tol)
	Return single precision absolute comparison \( | x - y | < \epsilon \).
pure logical function, public	dabscmp (x, y, tol)
	Return double precision absolute comparison \( | x - y | < \epsilon \).
pure logical function	qabscmp (x, y, tol)
	Return double precision absolute comparison \( | x - y | < \epsilon \).
pure logical function	srelcmp (x, y, eps)
	Return single precision relative comparison \( | x - y |<= \epsilon*|y| \).
pure logical function	drelcmp (x, y, eps)
	Return double precision relative comparison \( | x - y |/|y| < \epsilon \).
pure logical function	qrelcmp (x, y, eps)
	Return quad precision relative comparison \( | x - y |/|y| < \epsilon \).
pure real(kind=rp) function, public	lambert_w0 (x, niter)
	Approximate the principal real branch of the Lambert W function for non-negative real x.
subroutine, public	rzero (a, n)
	Zero a real vector.
subroutine, public	izero (a, n)
	Zero an integer vector.
subroutine, public	row_zero (a, m, n, e)
	Sets row e to 0 in matrix a.
subroutine, public	rone (a, n)
	Set all elements to one.
subroutine, public	copy (a, b, n)
	Copy a vector \( a = b \).
subroutine, public	masked_copy_0 (a, b, mask, n, n_mask)
	Copy a masked vector \( a(mask) = b(mask) \).
subroutine, public	masked_copy (a, b, mask, n, n_mask)
	Copy a masked vector \( a(mask) = b(mask) \).
subroutine, public	masked_gather_copy_0 (a, b, mask, n, n_mask)
	Gather a masked vector to reduced contigous vector \( a = b(mask) \).
subroutine, public	face_masked_gather_copy_0 (a, b, mask, facet, lx, ly, lz, n_mask)
	Gather values from a face-local SEM field to a reduced contiguous vector.
subroutine, public	masked_gather_copy (a, b, mask, n, n_mask)
	Gather a masked vector to reduced contigous vector \( a = b(mask) \).
subroutine, public	masked_scatter_copy_0 (a, b, mask, n, n_mask)
	Scatter a contigous vector to masked positions in a target array \( a(mask) = b \).
subroutine, public	masked_scatter_copy (a, b, mask, n, n_mask)
	Scatter a contigous vector to masked positions in a target array \( a(mask) = b \).
subroutine, public	cfill_mask (a, c, n, mask, n_mask)
	Fill a constant to a masked vector. \( a_i = c, for i in mask \).
subroutine, public	cmult (a, c, n)
	Multiplication by constant c \( a = c \cdot a \).
subroutine, public	cmult2 (a, b, c, n)
	Multiplication by constant c \( a = c \cdot b \).
subroutine, public	cdiv (a, c, n)
	Division of constant c by elements of a \( a = c / a \).
subroutine, public	cdiv2 (a, b, c, n)
	Division of constant c by elements of a \( a = c / b \).
subroutine, public	cadd (a, s, n)
	Add a scalar to vector \( a_i = a_i + s \).
subroutine, public	cadd2 (a, b, s, n)
	Add a scalar to vector \( a_i = b_i + s \).
subroutine, public	cfill (a, c, n)
	Set all elements to a constant c \( a = c \).
subroutine, public	cwrap (a, min_val, max_val, n)
	Wrap value around a range [min, max)
real(kind=rp) function, public	glsum (a, n)
	Sum a vector of length n.
real(kind=rp) function, public	glmax (a, n)
	Max of a vector of length n.
real(kind=rp) function, public	glamax (a, n)
	Max of the absolute value of a vector of length n.
integer function, public	glimax (a, n)
	Max of an integer vector of length n.
real(kind=rp) function, public	glmin (a, n)
	Min of a vector of length n.
integer function, public	glimin (a, n)
	Min of an integer vector of length n.
subroutine, public	chsign (a, n)
	Change sign of vector \( a = -a \).
real(kind=rp) function, public	vlamax (vec, n)
	maximum absolute value of a vector of length n, rank-local
real(kind=rp) function, public	vlmax (vec, n)
	maximum value of a vector of length n
real(kind=rp) function, public	vlmin (vec, n)
	minimun value of a vector of length n
subroutine, public	invcol1 (a, n)
	Invert a vector \( a = 1 / a \).
subroutine, public	invcol3 (a, b, c, n)
	Invert a vector \( a = b / c \).
subroutine, public	invers2 (a, b, n)
	Compute inverted vector \( a = 1 / b \).
subroutine, public	vcross (u1, u2, u3, v1, v2, v3, w1, w2, w3, n)
	Compute a cross product \( u = v \times w \) assuming vector components \( u = (u_1, u_2, u_3) \) etc.
subroutine, public	vdot2 (dot, u1, u2, v1, v2, n)
	Compute a dot product \( dot = u \cdot v \) (2-d version) assuming vector components \( u = (u_1, u_2, u_3) \) etc.
subroutine, public	vdot3 (dot, u1, u2, u3, v1, v2, v3, n)
	Compute a dot product \( dot = u \cdot v \) (3-d version) assuming vector components \( u = (u_1, u_2, u_3) \) etc.
real(kind=rp) function, public	vlsc3 (u, v, w, n)
	Compute multiplication sum \( dot = u \cdot v \cdot w \).
real(kind=rp) function, public	vlsc2 (u, v, n)
	Compute multiplication sum \( dot = u \cdot v \).
subroutine, public	add2 (a, b, n)
	Vector addition \( a = a + b \).
subroutine, public	add3 (a, b, c, n)
	Vector addition \( a = b + c \).
subroutine, public	add4 (a, b, c, d, n)
	Vector addition \( a = b + c + d\).
subroutine, public	sub2 (a, b, n)
	Vector substraction \( a = a - b \).
subroutine, public	sub3 (a, b, c, n)
	Vector subtraction \( a = b - c \).
subroutine, public	add2s1 (a, b, c1, n)
	Vector addition with scalar multiplication \( a = c_1 a + b \) (multiplication on first argument)
subroutine, public	add2s2 (a, b, c1, n)
	Vector addition with scalar multiplication \( a = a + c_1 b \) (multiplication on second argument)
subroutine, public	addsqr2s2 (a, b, c1, n)
	Returns \( a = a + c1 * (b * b )\).
subroutine, public	invcol2 (a, b, n)
	Vector division \( a = a / b \).
subroutine, public	col2 (a, b, n)
	Vector multiplication \( a = a \cdot b \).
subroutine, public	col3 (a, b, c, n)
	Vector multiplication with 3 vectors \( a = b \cdot c \).
subroutine, public	subcol3 (a, b, c, n)
	Returns \( a = a - b*c \).
subroutine, public	add3s2 (a, b, c, c1, c2, n)
	Returns \( a = c1 * b + c2 * c \).
subroutine, public	add4s3 (a, b, c, d, c1, c2, c3, n)
	Returns \( a = c1 * b + c2 * c + c3 * d \).
subroutine, public	add5s4 (a, b, c, d, e, c1, c2, c3, c4, n)
	Returns \( a = a + c1 * b + c2 * c + c3 * d + c4 * e\).
subroutine, public	subcol4 (a, b, c, d, n)
	Returns \( a = a - b*c*d \).
subroutine, public	addcol3 (a, b, c, n)
	Returns \( a = a + b*c \).
subroutine, public	addcol4 (a, b, c, d, n)
	Returns \( a = a + b*c*d \).
subroutine, public	addcol3s2 (a, b, c, s, n)
	Returns \( a = a + s(b*c) \).
subroutine, public	ascol5 (a, b, c, d, e, n)
	Returns \( a = b \dot c - d \cdot e \).
subroutine, public	p_update (a, b, c, c1, c2, n)
	Returns \( a = b \dot c1 ( a - c2 \cdot c )\).
subroutine, public	x_update (a, b, c, c1, c2, n)
	Returns \( a = b \dot c1 ( a - c2 \cdot c )\).
real(kind=rp) function, public	glsc2 (a, b, n)
	Weighted inner product \( a^T b \).
real(kind=rp) function, public	glsc3 (a, b, c, n)
	Weighted inner product \( a^T b c \).
real(kind=rp) function, public	glsc4 (a, b, c, d, n)
real(kind=rp) function, public	glsubnorm (a, b, n)
	Returns the norm of the difference of two vectors \( \sqrt{(a-b)^T (a-b)} \).
subroutine	sortrp (a, ind, n)
	Heap Sort for double precision arrays.
subroutine	sorti4 (a, ind, n)
	Heap Sort for single integer arrays.
subroutine	swapdp (b, ind, n)
	sort double precision array acording to ind vector
subroutine	swapi4 (b, ind, n)
	sort single integer array acording to ind vector
subroutine	reorddp (b, ind, n)
	reorder double precision array - inverse of swap
subroutine	reordi4 (b, ind, n)
	reorder single integer array - inverse of swap
subroutine	flipvdp (b, ind, n)
	Flip double precision vector b and ind.
subroutine	flipvi4 (b, ind, n)
	Flip single integer vector b and ind.
subroutine, public	absval (a, n)
	Take the absolute value of an array.
subroutine, public	pwmax2 (a, b, n)
	Point-wise maximum of two vectors \( a = \max(a, b) \).
subroutine, public	pwmax3 (a, b, c, n)
	Point-wise maximum of two vectors \( a = \max(b, c) \).
subroutine, public	cpwmax2 (a, b, n)
	Point-wise maximum of scalar and vector \( a = \max(a, b) \).
subroutine, public	cpwmax3 (a, b, c, n)
	Point-wise maximum of scalar and vector \( a = \max(b, c) \).
subroutine, public	pwmin2 (a, b, n)
	Point-wise minimum of two vectors \( a = \min(a, b) \).
subroutine, public	pwmin3 (a, b, c, n)
	Point-wise minimum of two vectors \( a = \min(b, c) \).
subroutine, public	cpwmin2 (a, b, n)
	Point-wise minimum of scalar and vector \( a = \min(a, b) \).
subroutine, public	cpwmin3 (a, b, c, n)
	Point-wise minimum of scalar and vector \( a = \min(b, c) \).
real(rp) function, dimension(3, 3), public	matinv39 (a11, a12, a13, a21, a22, a23, a31, a32, a33)
real(kind=xp) function, dimension(3, 3), public	matinv3 (a)
	Performs a direct calculation of the inverse of a 3×3 matrix. M33INV and M44INV by David G. Simpson pure function version from https://fortranwiki.org/fortran/show/Matrix+inversion Invert 3x3 matrix.
real(kind=rp) function, public	math_stepf (x)
	Smooth step function S(x) Returns 0 for x <= 0, 1 for x >= 1, and smooth transition in between.
real(kind=rp) function, public	math_dstepf (x)
	Derivative of math_stepf with respect to x: d(stepf)/dx.
subroutine, public	sqrt_inplace (a, n)
	Sqrt a vector \( a = sqrt(a) \).
subroutine, public	power (ap, a, p, n)
	Take the power of a vector \( a^p \).
pure subroutine, public	eig_sym2 (a11, a22, a12, e1, e2)
	Eigenvalues of a symmetric 2x2 matrix, descending.
pure subroutine, public	eig_sym3 (a11, a22, a33, a12, a13, a23, e1, e2, e3)
	Eigenvalues of a symmetric 3x3 matrix, descending.

Variables
real(kind=rp), parameter, public	neko_eps = epsilon(1.0_rp)
	Machine epsilon \( \epsilon \).
real(kind=dp), parameter, public	neko_eps_dp = epsilon(1.0_dp)
real(kind=sp), parameter, public	neko_eps_sp = epsilon(1.0_sp)
real(kind=rp), parameter, public	neko_m_ln2 = log(2.0_rp)
	\( ln(2) \)
real(kind=rp), parameter, public	pi = 4._rp*atan(1._rp)
	\( \pi \)

Function/Subroutine Documentation

absval()

subroutine, public math::absval	(	real(kind=rp), dimension(n), intent(inout)	a,
		integer, intent(in)	n
	)

Parameters

[in,out]	a	vector to be manipulated
[in]	n	array size

Definition at line 1678 of file math.f90.

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add2()

subroutine, public math::add2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 938 of file math.f90.

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add2s1()

subroutine, public math::add2s1	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), intent(in)	c1,
		integer, intent(in)	n
	)

Definition at line 1019 of file math.f90.

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add2s2()

subroutine, public math::add2s2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), intent(in)	c1,
		integer, intent(in)	n
	)

Definition at line 1036 of file math.f90.

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add3()

subroutine, public math::add3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 953 of file math.f90.

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add3s2()

subroutine, public math::add3s2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), intent(in)	c1,
		real(kind=rp), intent(in)	c2,
		integer, intent(in)	n
	)

Definition at line 1131 of file math.f90.

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add4()

subroutine, public math::add4	(	real(kind=rp), dimension(n), intent(out)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), dimension(n), intent(in)	d,
		integer, intent(in)	n
	)

Definition at line 969 of file math.f90.

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add4s3()

subroutine, public math::add4s3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), dimension(n), intent(in)	d,
		real(kind=rp), intent(in)	c1,
		real(kind=rp), intent(in)	c2,
		real(kind=rp), intent(in)	c3,
		integer, intent(in)	n
	)

Definition at line 1148 of file math.f90.

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add5s4()

subroutine, public math::add5s4	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), dimension(n), intent(in)	d,
		real(kind=rp), dimension(n), intent(in)	e,
		real(kind=rp), intent(in)	c1,
		real(kind=rp), intent(in)	c2,
		real(kind=rp), intent(in)	c3,
		real(kind=rp), intent(in)	c4,
		integer, intent(in)	n
	)

Definition at line 1166 of file math.f90.

addcol3()

subroutine, public math::addcol3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1202 of file math.f90.

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addcol3s2()

subroutine, public math::addcol3s2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), intent(in)	s,
		integer, intent(in)	n
	)

Definition at line 1235 of file math.f90.

addcol4()

subroutine, public math::addcol4	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), dimension(n), intent(in)	d,
		integer, intent(in)	n
	)

Definition at line 1218 of file math.f90.

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addsqr2s2()

subroutine, public math::addsqr2s2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), intent(in)	c1,
		integer, intent(in)	n
	)

Definition at line 1052 of file math.f90.

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ascol5()

subroutine, public math::ascol5	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), dimension(n), intent(in)	d,
		real(kind=rp), dimension(n), intent(in)	e,
		integer, intent(in)	n
	)

Definition at line 1252 of file math.f90.

cadd()

subroutine, public math::cadd	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), intent(in)	s,
		integer, intent(in)	n
	)

Definition at line 569 of file math.f90.

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cadd2()

subroutine, public math::cadd2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), intent(in)	s,
		integer, intent(in)	n
	)

Definition at line 584 of file math.f90.

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cdiv()

subroutine, public math::cdiv	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 538 of file math.f90.

cdiv2()

subroutine, public math::cdiv2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 553 of file math.f90.

cfill()

subroutine, public math::cfill	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 600 of file math.f90.

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cfill_mask()

subroutine, public math::cfill_mask	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), intent(in)	c,
		integer, intent(in)	n,
		integer, dimension(n_mask), intent(in)	mask,
		integer, intent(in)	n_mask
	)

Definition at line 491 of file math.f90.

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chsign()

subroutine, public math::chsign	(	real(kind=rp), dimension(n), intent(inout)	a,
		integer, intent(in)	n
	)

Definition at line 749 of file math.f90.

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cmult()

subroutine, public math::cmult	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 507 of file math.f90.

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cmult2()

subroutine, public math::cmult2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 522 of file math.f90.

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col2()

subroutine, public math::col2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 1084 of file math.f90.

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col3()

subroutine, public math::col3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1099 of file math.f90.

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copy()

subroutine, public math::copy	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 294 of file math.f90.

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cpwmax2()

subroutine, public math::cpwmax2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 1725 of file math.f90.

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cpwmax3()

subroutine, public math::cpwmax3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1740 of file math.f90.

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cpwmin2()

subroutine, public math::cpwmin2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 1786 of file math.f90.

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cpwmin3()

subroutine, public math::cpwmin3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1801 of file math.f90.

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cwrap()

subroutine, public math::cwrap	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), intent(in)	min_val,
		real(kind=rp), intent(in)	max_val,
		integer, intent(in)	n
	)

Definition at line 615 of file math.f90.

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dabscmp()

pure logical function, public math::dabscmp	(	real(kind=dp), intent(in)	x,
		real(kind=dp), intent(in)	y,
		real(kind=dp), intent(in), optional	tol
	)

Definition at line 138 of file math.f90.

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drelcmp()

pure logical function math::drelcmp ( real(kind=dp), intent(in)  x, real(kind=dp), intent(in)  y, real(kind=dp), intent(in), optional  eps  )

private

Definition at line 184 of file math.f90.

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eig_sym2()

pure subroutine, public math::eig_sym2	(	real(kind=dp), intent(in)	a11,
		real(kind=dp), intent(in)	a22,
		real(kind=dp), intent(in)	a12,
		real(kind=dp), intent(out)	e1,
		real(kind=dp), intent(out)	e2
	)

Parameters

a11	Diagonal entry (1,1).
a22	Diagonal entry (2,2).
a12	Off-diagonal entry.
e1	The larger eigenvalue.
e2	The smaller eigenvalue.

Definition at line 1951 of file math.f90.

eig_sym3()

pure subroutine, public math::eig_sym3	(	real(kind=dp), intent(in)	a11,
		real(kind=dp), intent(in)	a22,
		real(kind=dp), intent(in)	a33,
		real(kind=dp), intent(in)	a12,
		real(kind=dp), intent(in)	a13,
		real(kind=dp), intent(in)	a23,
		real(kind=dp), intent(out)	e1,
		real(kind=dp), intent(out)	e2,
		real(kind=dp), intent(out)	e3
	)

Closed form via the characteristic polynomial of the deviatoric part, which avoids an iterative solve for what is a per quadrature point diagnostic. A diagonal matrix is handled by the general path and comes back exact; only the isotropic case is special, because the deviatoric scaling is singular there.

Note

The smallest root is a difference of terms of order \( \lambda_{max} \), so its relative accuracy degrades as \( \epsilon \kappa \) – about 1e-10 at the 1e6 condition numbers this is used to detect, which is ample for a threshold test but would not be if \( \kappa \) approached \( 1/\epsilon \). That is why this works in double regardless of what rp is: in a single precision build the same amplification against \( \epsilon_{sp} \) would put a 6% error on \( \kappa \) at 1e6 and lose it entirely near 1e7, exactly where the answer matters most.

Both call sites in coef_metric_condition() pass a matrix scaled to unit magnitude: the geometric factors divided by their largest entry, and the same factors Jacobi scaled to a unit diagonal. The latter is exactly the identity for an orthogonal element, which is why the isotropic branch above is not merely defensive.

Parameters

a11	Diagonal entry (1,1).
a22	Diagonal entry (2,2).
a33	Diagonal entry (3,3).
a12	Off-diagonal entry (1,2).
a13	Off-diagonal entry (1,3).
a23	Off-diagonal entry (2,3).
e1	The largest eigenvalue.
e2	The intermediate eigenvalue.
e3	The smallest eigenvalue.

Definition at line 2002 of file math.f90.

face_masked_gather_copy_0()

subroutine, public math::face_masked_gather_copy_0	(	real(kind=rp), dimension(n_mask), intent(inout)	a,
		real(kind=rp), dimension(:, :, :, :), intent(in)	b,
		integer, dimension(0:n_mask), intent(in)	mask,
		integer, dimension(0:n_mask), intent(in)	facet,
		integer, intent(in)	lx,
		integer, intent(in)	ly,
		integer, intent(in)	lz,
		integer, intent(in)	n_mask
	)

Parameters

a	Destination array of size n_mask.
b	Source face-local array indexed as b(:, :, facet, element).
mask	Mask array of length n_mask + 1, where mask(0) = n_mask.
facet	Facet ids associated with the masked points.
lx	Number of points in the first SEM direction.
ly	Number of points in the second SEM direction.
lz	Number of points in the third SEM direction.
n_mask	Size of the mask and destination arrays.

Definition at line 388 of file math.f90.

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flipvdp()

subroutine math::flipvdp ( real(kind=rp), dimension(n), intent(inout)  b, integer, dimension(n), intent(inout)  ind, integer, intent(in)  n  )

private

Parameters

[in,out]	b	vector to be reordered
[in,out]	ind	permutation array
[in]	n	array size

Definition at line 1619 of file math.f90.

flipvi4()

subroutine math::flipvi4 ( integer(i4), dimension(n), intent(inout)  b, integer, dimension(n), intent(inout)  ind, integer, intent(in)  n  )

private

Parameters

[in,out]	b	vector to be reordered
[in,out]	ind	permutation array
[in]	n	array size

Definition at line 1649 of file math.f90.

glamax()

real(kind=rp) function, public math::glamax	(	real(kind=rp), dimension(n)	a,
		integer, intent(in)	n
	)

Returns \( \max_i |a_i| \) reduced over all ranks.

Definition at line 673 of file math.f90.

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glimax()

integer function, public math::glimax	(	integer, dimension(n)	a,
		integer, intent(in)	n
	)

Definition at line 692 of file math.f90.

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glimin()

integer function, public math::glimin	(	integer, dimension(n)	a,
		integer, intent(in)	n
	)

Definition at line 730 of file math.f90.

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glmax()

real(kind=rp) function, public math::glmax	(	real(kind=rp), dimension(n)	a,
		integer, intent(in)	n
	)

Definition at line 653 of file math.f90.

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glmin()

real(kind=rp) function, public math::glmin	(	real(kind=rp), dimension(n)	a,
		integer, intent(in)	n
	)

Definition at line 711 of file math.f90.

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glsc2()

real(kind=rp) function, public math::glsc2	(	real(kind=rp), dimension(n), intent(in)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 1304 of file math.f90.

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glsc3()

real(kind=rp) function, public math::glsc3	(	real(kind=rp), dimension(n), intent(in)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1325 of file math.f90.

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glsc4()

real(kind=rp) function, public math::glsc4	(	real(kind=rp), dimension(n), intent(in)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), dimension(n), intent(in)	d,
		integer, intent(in)	n
	)

Definition at line 1346 of file math.f90.

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glsubnorm()

real(kind=rp) function, public math::glsubnorm	(	real(kind=rp), dimension(n), intent(in)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 1371 of file math.f90.

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glsum()

real(kind=rp) function, public math::glsum	(	real(kind=rp), dimension(n)	a,
		integer, intent(in)	n
	)

Definition at line 632 of file math.f90.

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invcol1()

subroutine, public math::invcol1	(	real(kind=rp), dimension(n), intent(inout)	a,
		integer, intent(in)	n
	)

Definition at line 809 of file math.f90.

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invcol2()

subroutine, public math::invcol2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 1068 of file math.f90.

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invcol3()

subroutine, public math::invcol3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 823 of file math.f90.

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invers2()

subroutine, public math::invers2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 838 of file math.f90.

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izero()

subroutine, public math::izero	(	integer, dimension(n), intent(inout)	a,
		integer, intent(in)	n
	)

Definition at line 252 of file math.f90.

lambert_w0()

pure real(kind=rp) function, public math::lambert_w0	(	real(kind=rp), intent(in)	x,
		integer, intent(in)	niter
	)

The reference is Iacono and Boyd, DOI: 10.1007/s10444-017-9530-3 The iterative algorithm converges very fast, and 1 iteration is typically sufficient.

Definition at line 217 of file math.f90.

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masked_copy()

subroutine, public math::masked_copy	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, dimension(n_mask)	mask,
		integer, intent(in)	n,
		integer, intent(in)	n_mask
	)

Parameters

a	Destination array of size n.
b	Source array of size n.
mask	Mask array of length n_mask + 1, where mask(0) = n_mask the length of the mask array.
n	Size of the arrays a and b.
n_mask	Size of the mask array mask.

Definition at line 338 of file math.f90.

masked_copy_0()

subroutine, public math::masked_copy_0	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, dimension(0:n_mask)	mask,
		integer, intent(in)	n,
		integer, intent(in)	n_mask
	)

Parameters

a	Destination array of size n.
b	Source array of size n.
mask	Mask array of length n_mask + 1, where mask(0) = n_mask the length of the mask array.
n	Size of the arrays a and b.
n_mask	Size of the mask array mask.

Definition at line 315 of file math.f90.

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masked_gather_copy()

subroutine, public math::masked_gather_copy	(	real(kind=rp), dimension(n_mask), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, dimension(n_mask)	mask,
		integer, intent(in)	n,
		integer, intent(in)	n_mask
	)

Parameters

a	Destination array of size n_mask.
b	Source array of size n.
mask	Mask array of length n_mask. the length of the mask array.
n	Size of the array b.
n_mask	Size of the mask array mask and a.

Note

Assumes n .ge. n_mask.

Definition at line 423 of file math.f90.

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masked_gather_copy_0()

subroutine, public math::masked_gather_copy_0	(	real(kind=rp), dimension(n_mask), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, dimension(0:n_mask)	mask,
		integer, intent(in)	n,
		integer, intent(in)	n_mask
	)

Parameters

a	Destination array of size n_mask.
b	Source array of size n.
mask	Mask array of length n_mask + 1, where mask(0) = n_mask the length of the mask array.
n	Size of the array b.
n_mask	Size of the mask array mask and a.

Note

Assumes n .ge. n_mask.

Definition at line 363 of file math.f90.

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masked_scatter_copy()

subroutine, public math::masked_scatter_copy	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n_mask), intent(in)	b,
		integer, dimension(n_mask)	mask,
		integer, intent(in)	n,
		integer, intent(in)	n_mask
	)

Parameters

a	Destination array of size n.
b	Source array of size n_mask.
mask	Mask array of length n_mask + 1, where mask(0) = n_mask + 1 the length of the mask array.
n	Size of the array maskand array b.
m	Size of the mask array a.

Note

Assumes n .ge. n_mask.

Definition at line 473 of file math.f90.

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masked_scatter_copy_0()

subroutine, public math::masked_scatter_copy_0	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n_mask), intent(in)	b,
		integer, dimension(0:n_mask)	mask,
		integer, intent(in)	n,
		integer, intent(in)	n_mask
	)

Parameters

a	Destination array of size n.
b	Source array of size n_mask.
mask	Mask array of length n_mask + 1, where mask(0) = n_mask + 1 the length of the mask array.
n	Size of the array maskand array b.
m	Size of the mask array a.

Note

Assumes n .ge. n_mask.

Definition at line 448 of file math.f90.

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math_dstepf()

real(kind=rp) function, public math::math_dstepf

(

real(kind=rp), intent(in)

x

)

Definition at line 1889 of file math.f90.

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math_stepf()

real(kind=rp) function, public math::math_stepf

(

real(kind=rp), intent(in)

x

)

Definition at line 1866 of file math.f90.

matinv3()

real(kind=xp) function, dimension(3,3), public math::matinv3

(

real(kind=xp), dimension(3,3), intent(in)

a

)

Definition at line 1840 of file math.f90.

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matinv39()

real(rp) function, dimension(3,3), public math::matinv39	(	real(kind=rp), intent(in)	a11,
		real(kind=rp), intent(in)	a12,
		real(kind=rp), intent(in)	a13,
		real(kind=rp), intent(in)	a21,
		real(kind=rp), intent(in)	a22,
		real(kind=rp), intent(in)	a23,
		real(kind=rp), intent(in)	a31,
		real(kind=rp), intent(in)	a32,
		real(kind=rp), intent(in)	a33
	)

Definition at line 1819 of file math.f90.

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p_update()

subroutine, public math::p_update	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), intent(in)	c1,
		real(kind=rp), intent(in)	c2,
		integer, intent(in)	n
	)

Definition at line 1270 of file math.f90.

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power()

subroutine, public math::power	(	real(kind=rp), dimension(n), intent(inout)	ap,
		real(kind=rp), dimension(n), intent(in)	a,
		real(kind=rp), intent(in)	p,
		integer, intent(in)	n
	)

Definition at line 1930 of file math.f90.

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pwmax2()

subroutine, public math::pwmax2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 1695 of file math.f90.

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pwmax3()

subroutine, public math::pwmax3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1710 of file math.f90.

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pwmin2()

subroutine, public math::pwmin2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 1756 of file math.f90.

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pwmin3()

subroutine, public math::pwmin3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1771 of file math.f90.

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qabscmp()

pure logical function math::qabscmp ( real(kind=qp), intent(in)  x, real(kind=qp), intent(in)  y, real(kind=qp), intent(in), optional  tol  )

private

Definition at line 153 of file math.f90.

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qrelcmp()

pure logical function math::qrelcmp ( real(kind=qp), intent(in)  x, real(kind=qp), intent(in)  y, real(kind=qp), intent(in), optional  eps  )

private

Definition at line 199 of file math.f90.

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reorddp()

subroutine math::reorddp ( real(kind=rp), dimension(n), intent(inout)  b, integer, dimension(n), intent(in)  ind, integer, intent(in)  n  )

private

Parameters

[in,out]	b	vector to be reordered
[in]	ind	permutation array
[in]	n	array size

Definition at line 1565 of file math.f90.

reordi4()

subroutine math::reordi4 ( integer(i4), dimension(n), intent(inout)  b, integer, dimension(n), intent(in)  ind, integer, intent(in)  n  )

private

Parameters

[in,out]	b	vector to be reordered
[in]	ind	permutation array
[in]	n	array size

Definition at line 1592 of file math.f90.

rone()

subroutine, public math::rone	(	real(kind=rp), dimension(n), intent(inout)	a,
		integer, intent(in)	n
	)

Definition at line 280 of file math.f90.

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row_zero()

subroutine, public math::row_zero	(	real(kind=rp), dimension(m,n), intent(inout)	a,
		integer, intent(in)	m,
		integer, intent(in)	n,
		integer, intent(in)	e
	)

Definition at line 266 of file math.f90.

rzero()

subroutine, public math::rzero	(	real(kind=rp), dimension(n), intent(inout)	a,
		integer, intent(in)	n
	)

Definition at line 238 of file math.f90.

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sabscmp()

pure logical function, public math::sabscmp	(	real(kind=sp), intent(in)	x,
		real(kind=sp), intent(in)	y,
		real(kind=sp), intent(in), optional	tol
	)

Definition at line 123 of file math.f90.

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sorti4()

subroutine math::sorti4 ( integer(i4), dimension(n), intent(inout)  a, integer, dimension(n), intent(out)  ind, integer, intent(in)  n  )

private

Following p 231 Num. Rec., 1st Ed.

Parameters

[in,out]	a	vector to be sorted
[out]	ind	permutation array
[in]	n	array size

Definition at line 1455 of file math.f90.

sortrp()

subroutine math::sortrp ( real(kind=rp), dimension(n), intent(inout)  a, integer, dimension(n), intent(out)  ind, integer, intent(in)  n  )

private

Following p 231 Num. Rec., 1st Ed.

Parameters

[in,out]	a	vector to be sorted
[out]	ind	permutation array
[in]	n	array size

Definition at line 1397 of file math.f90.

sqrt_inplace()

subroutine, public math::sqrt_inplace	(	real(kind=rp), dimension(n), intent(inout)	a,
		integer, intent(in)	n
	)

Definition at line 1916 of file math.f90.

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srelcmp()

pure logical function math::srelcmp ( real(kind=sp), intent(in)  x, real(kind=sp), intent(in)  y, real(kind=sp), intent(in), optional  eps  )

private

Definition at line 169 of file math.f90.

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sub2()

subroutine, public math::sub2	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		integer, intent(in)	n
	)

Definition at line 986 of file math.f90.

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sub3()

subroutine, public math::sub3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1001 of file math.f90.

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subcol3()

subroutine, public math::subcol3	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		integer, intent(in)	n
	)

Definition at line 1115 of file math.f90.

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subcol4()

subroutine, public math::subcol4	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), dimension(n), intent(in)	d,
		integer, intent(in)	n
	)

Definition at line 1185 of file math.f90.

swapdp()

subroutine math::swapdp ( real(kind=rp), dimension(n), intent(inout)  b, integer, dimension(n), intent(in)  ind, integer, intent(in)  n  )

private

Parameters

[in,out]	b	vector to be reordered
[in]	ind	permutation array
[in]	n	array size

Definition at line 1511 of file math.f90.

swapi4()

subroutine math::swapi4 ( integer(i4), dimension(n), intent(inout)  b, integer, dimension(n), intent(in)  ind, integer, intent(in)  n  )

private

Parameters

[in,out]	b	vector to be reordered
[in]	ind	permutation array
[in]	n	array size

Definition at line 1538 of file math.f90.

vcross()

subroutine, public math::vcross	(	real(kind=rp), dimension(n), intent(out)	u1,
		real(kind=rp), dimension(n), intent(out)	u2,
		real(kind=rp), dimension(n), intent(out)	u3,
		real(kind=rp), dimension(n), intent(in)	v1,
		real(kind=rp), dimension(n), intent(in)	v2,
		real(kind=rp), dimension(n), intent(in)	v3,
		real(kind=rp), dimension(n), intent(in)	w1,
		real(kind=rp), dimension(n), intent(in)	w2,
		real(kind=rp), dimension(n), intent(in)	w3,
		integer, intent(in)	n
	)

Definition at line 854 of file math.f90.

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vdot2()

subroutine, public math::vdot2	(	real(kind=rp), dimension(n), intent(out)	dot,
		real(kind=rp), dimension(n), intent(in)	u1,
		real(kind=rp), dimension(n), intent(in)	u2,
		real(kind=rp), dimension(n), intent(in)	v1,
		real(kind=rp), dimension(n), intent(in)	v2,
		integer, intent(in)	n
	)

Definition at line 873 of file math.f90.

vdot3()

subroutine, public math::vdot3	(	real(kind=rp), dimension(n), intent(out)	dot,
		real(kind=rp), dimension(n), intent(in)	u1,
		real(kind=rp), dimension(n), intent(in)	u2,
		real(kind=rp), dimension(n), intent(in)	u3,
		real(kind=rp), dimension(n), intent(in)	v1,
		real(kind=rp), dimension(n), intent(in)	v2,
		real(kind=rp), dimension(n), intent(in)	v3,
		integer, intent(in)	n
	)

Definition at line 890 of file math.f90.

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vlamax()

real(kind=rp) function, public math::vlamax	(	real(kind=rp), dimension(n), intent(in)	vec,
		integer	n
	)

Definition at line 763 of file math.f90.

vlmax()

real(kind=rp) function, public math::vlmax	(	real(kind=rp), dimension(n), intent(in)	vec,
		integer	n
	)

Definition at line 778 of file math.f90.

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vlmin()

real(kind=rp) function, public math::vlmin	(	real(kind=rp), dimension(n), intent(in)	vec,
		integer, intent(in)	n
	)

Definition at line 793 of file math.f90.

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vlsc2()

real(kind=rp) function, public math::vlsc2	(	real(kind=rp), dimension(n), intent(in)	u,
		real(kind=rp), dimension(n), intent(in)	v,
		integer, intent(in)	n
	)

Definition at line 922 of file math.f90.

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vlsc3()

real(kind=rp) function, public math::vlsc3	(	real(kind=rp), dimension(n), intent(in)	u,
		real(kind=rp), dimension(n), intent(in)	v,
		real(kind=rp), dimension(n), intent(in)	w,
		integer, intent(in)	n
	)

Definition at line 906 of file math.f90.

x_update()

subroutine, public math::x_update	(	real(kind=rp), dimension(n), intent(inout)	a,
		real(kind=rp), dimension(n), intent(in)	b,
		real(kind=rp), dimension(n), intent(in)	c,
		real(kind=rp), intent(in)	c1,
		real(kind=rp), intent(in)	c2,
		integer, intent(in)	n
	)

Definition at line 1287 of file math.f90.

Variable Documentation

neko_eps

real(kind=rp), parameter, public math::neko_eps = epsilon(1.0_rp)

Definition at line 70 of file math.f90.

neko_eps_dp

real(kind=dp), parameter, public math::neko_eps_dp = epsilon(1.0_dp)

Definition at line 71 of file math.f90.

neko_eps_sp

real(kind=sp), parameter, public math::neko_eps_sp = epsilon(1.0_sp)

Definition at line 72 of file math.f90.

neko_m_ln2

real(kind=rp), parameter, public math::neko_m_ln2 = log(2.0_rp)

Definition at line 75 of file math.f90.

pi

real(kind=rp), parameter, public math::pi = 4._rp*atan(1._rp)

Definition at line 78 of file math.f90.