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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 \( | x - y |/|y| < \epsilon \). | |
| 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 | 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 \( a = c \). | |
| 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. | |
| 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 | 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 \( dot = u \cdot v \cdot w \). | |
| 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. | |
Variables | |
| real(kind=rp), parameter, public | neko_eps = epsilon(1.0_rp) |
| Machine epsilon \( \epsilon \). | |
| 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()
◆ add2()
◆ add2s1()
◆ add2s2()
◆ add3()
◆ add3s2()
◆ add4()
◆ 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 | ||
| ) |
◆ 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 | ||
| ) |
◆ addcol3()
◆ addcol3s2()
◆ addcol4()
◆ addsqr2s2()
◆ ascol5()
◆ cadd()
◆ cadd2()
◆ cdiv()
◆ cdiv2()
◆ cfill()
◆ cfill_mask()
◆ chsign()
◆ cmult()
◆ cmult2()
◆ col2()
◆ col3()
◆ copy()
◆ cpwmax2()
◆ cpwmax3()
◆ cpwmin2()
◆ cpwmin3()
◆ dabscmp()
◆ drelcmp()
◆ flipvdp()
◆ flipvi4()
◆ glimax()
◆ glimin()
◆ glmax()
◆ glmin()
◆ glsc2()
◆ glsc3()
◆ glsc4()
◆ glsubnorm()
◆ glsum()
◆ invcol1()
◆ invcol2()
◆ invcol3()
◆ invers2()
◆ izero()
◆ masked_copy()
◆ 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_maskthe length of the mask array.n Size of the arrays aandb.n_mask Size of the mask array mask.
Definition at line 268 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 + 1, where mask(0) = n_maskthe length of the mask array.n Size of the array b.n_mask Size of the mask array maskanda.
- Note
- Assumes
n .ge. n_mask.
Definition at line 335 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_maskthe length of the mask array.n Size of the array b.n_mask Size of the mask array maskanda.
- Note
- Assumes
n .ge. n_mask.
Definition at line 312 of file math.f90.
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◆ masked_scatter_copy()
◆ 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 + 1the length of the mask array.n Size of the array maskand arrayb.m Size of the mask array a.
- Note
- Assumes
n .ge. n_mask.
Definition at line 358 of file math.f90.
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◆ math_dstepf()
◆ math_stepf()
◆ matinv3()
◆ 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 | ||
| ) |
◆ p_update()
◆ pwmax2()
◆ pwmax3()
◆ pwmin2()
◆ pwmin3()
◆ qabscmp()
◆ qrelcmp()
◆ reorddp()
◆ reordi4()
◆ rone()
◆ row_zero()
◆ rzero()
◆ sabscmp()
◆ sorti4()
◆ sortrp()
◆ srelcmp()
◆ sub2()
◆ sub3()
◆ subcol3()
◆ subcol4()
◆ swapdp()
◆ swapi4()
◆ 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 | ||
| ) |
◆ vdot2()
◆ 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 | ||
| ) |
