def velocity_matrix(ra: MatrixVector,
rb: MatrixVector,
rc: MatrixVector,
betm: float = 1.0,
tol: float = 1e-12):
if ra.shape != rb.shape:
return ValueError()
numi = rc.shape[0]
numj = ra.shape[1]
ra = ra.repeat(numi, axis=0)
rb = rb.repeat(numi, axis=0)
rc = rc.repeat(numj, axis=1)
a = rc - ra
b = rc - rb
a.x = a.x / betm
b.x = b.x / betm
am = a.return_magnitude()
bm = b.return_magnitude()
# Velocity from Bound Vortex
adb = elementwise_dot_product(a, b)
abm = multiply(am, bm)
dm = multiply(abm, abm + adb)
axb = elementwise_cross_product(a, b)
axbm = axb.return_magnitude()
chki = (axbm == 0.0)
chki = logical_and(axbm >= -tol, axbm <= tol)
veli = elementwise_multiply(axb, divide(am + bm, dm))
veli.x[chki] = 0.0
veli.y[chki] = 0.0
veli.z[chki] = 0.0
# Velocity from Trailing Vortex A
axx = MatrixVector(zeros(a.shape, dtype=float), a.z, -a.y)
axxm = axx.return_magnitude()
chka = (axxm == 0.0)
vela = elementwise_divide(axx, multiply(am, am - a.x))
vela.x[chka] = 0.0
vela.y[chka] = 0.0
vela.z[chka] = 0.0
# Velocity from Trailing Vortex B
bxx = MatrixVector(zeros(b.shape, dtype=float), b.z, -b.y)
bxxm = bxx.return_magnitude()
chkb = (bxxm == 0.0)
velb = elementwise_divide(bxx, multiply(bm, bm - b.x))
velb.x[chkb] = 0.0
velb.y[chkb] = 0.0
velb.z[chkb] = 0.0
return veli, vela, velb
def vel_doublet_matrix(ov, om, faco):
ov = faco * ov
oxx = MatrixVector(zeros(ov.shape), -ov.z, ov.y)
oxxm = oxx.return_magnitude()
chko = (oxxm == 0.0)
velol = elementwise_divide(oxx, multiply(om, om - ov.x))
velol.x[chko] = 0.0
velol.y[chko] = 0.0
velol.z[chko] = 0.0
return velol
def phi_doublet_matrix(vecs: MatrixVector, rls: MatrixVector, sgnz: matrix):
mags = vecs.return_magnitude()
ms = divide(vecs.x, rls.y)
ths = arctan(ms)
ths[rls.y == 0.0] = piby2
gs = multiply(ms, divide(rls.z, mags))
Js = arctan(gs)
Js[rls.y == 0.0] = piby2
phids = Js - multiply(sgnz, ths)
return phids, mags
def vel_trailing_doublet_matrix(ov, om, faco):
ov: MatrixVector = faco * ov
oxx = MatrixVector(zeros(ov.shape), -ov.z, ov.y)
oxxm = oxx.return_magnitude()
chko = absolute(oxxm) < tol
den = multiply(om, om - ov.x)
chkd = absolute(den) < tol
denr = zeros(ov.shape, dtype=float)
reciprocal(den, where=logical_not(chkd), out=denr)
velol = elementwise_multiply(oxx, denr)
velol.x[chko] = 0.0
velol.y[chko] = 0.0
velol.z[chko] = 0.0
return velol
def phi_doublet_matrix(vecs: MatrixVector, sgnz: matrix):
mags = vecs.return_magnitude()
chkm = mags < tol
chky = absolute(vecs.y) < tol
vecs.y[chky] = 0.0
ms = zeros(mags.shape, dtype=float)
divide(vecs.x, vecs.y, where=logical_not(chky), out=ms)
ths = arctan(ms)
ths[chky] = piby2
ts = zeros(mags.shape, dtype=float)
divide(vecs.z, mags, where=logical_not(chkm), out=ts)
gs = multiply(ms, ts)
Js = arctan(gs)
Js[chky] = piby2
phids = Js - multiply(sgnz, ths)
return phids, mags