CFD Utilities Files

The numodules library contains miscellaneous numerical utilities such as
those used for finite difference derivatives, means & standard deviations,
and linear transformations.

One of the more recent additions, TRAPEZOID_RECURSION, implements the
recurrence relations for a time series mean and standard deviation using
the trapezoidal rule for quadrature as opposed to the rectangle rule.
It was prompted by the need to visualize averaged data in the unsteady
wake flow behind atmospheric entry vehicles.  This method avoids the
potentially large sums encountered over thousands of flow iterations by
the straightforward method.

bernstein_basis.f90    Evaluate Bernstein basis polynomials 0:n at x in [0, 1]
bernstein_polynomial.f90  ! Evaluate a Bernstein polynomial at x(1:nx)
bessel.f               3-pt. differencing utility in LCSFIT & its relatives
binomial_coef.f90      nCr for 0 <= n <= 33 (4-byte integer limit)
bounds.f               Min./max. (so far) across 1 or more 1- or 2-D arrays
brodlie.f              3-pt. differencing utility in LCSFIT & its relatives
butland.f              3-pt. differencing utility in LCSFIT & its relatives
circ_shift.f           Left or right shift in place for a real 1-D array
copy.f                 Simple copy of a real 1-D [sub]array to another one
d4coefs.f              4th-derivative finite differencing utility
deriv3.f               3-pt. differencing utility invoking BESSEL & THREEPT
derivs_123.f90         1st 3 derivs. at x(i) for 3 <= i <= n-2; quartic fit
fd12k.f                1st/2nd derivs. + curvature at (x(i), f(i)), i = 1:n
fd1sid.f               Lower-level 3-point utility used by FD12K
fdcntr.f               Lower-level 3-point utility used by FD12K
fdcurv.f               Lower-level 3-point utility used by FD12K
fivepoint.f            1st 4 derivatives at middle of 5 points, for D4COEFS
gaussian.f             Calc. pts. in a Gaussian distribn., mean 0, sigma 1
getblock.f             Transfer part of a 3-D array to another 3-D array
getrow.f               Transfer part of row i of a 2-D array to a vector
getscale.f             Determine scales/shifts for normalizing x[y[z]] data
getxform.f             Calc. scale, shift for x in [a, b] --> x' in [p, q]
meanx.f                Average of real array via recurrence relation
nmlizx.f               Normalizes/denormalizes real vector to/from [0, 1]
power2.f               Determine if integer l is a power of 2 or not
protect.f              Test for data monotonicity and distinctness
putrow.f               GETROW companion to update [part of] row i of A(:,:)
rverse.f               Reverse order of a real vector, possibly in place
shiftx.f               Add constant to elements of a real vector, in place
sideways_shift.f90     Perturbs abscissas sideways via a 1 +/- SIN2 bump
splitxyz.f90           Split x/y/z cloud in place via cutoff & <|<=|== ..
stdev1p.f              Mean/std. deviation via recurrence relations, 1 pass
stdev2p.f              Mixed-precisn. 2-pass mean/std. dev. for real*4 data
stdevi2.f              Mean & standard deviation for integer*2 A/D data
sumx.f                 Sum of real*4 vector elements (double precisn. adds)
table_coordinates.f90  Expand coords. of rectangular table (2-6 dimensions)
table_derivatives.f90  f'/f" for nf fns. wrt each of ndim coords.; ndim 1-5
threept.f              3-pt. differencing utility in LCSFIT & its relatives
trapezoid_recursion.f90  Update running mean/var.: recursion/trapez. quadr.
usescale.f             Apply scales/shifts determined by GETSCALE
utcopy.f               Variant of COPY that allows for in-place shifting