def trefftz_plane_velocities(self,
pnts: MatrixVector,
betx: float = 1.0,
bety: float = 1.0,
betz: float = 1.0):
# Trailing Vortex A
agcs = self.relative_mach(pnts,
self.grda,
betx=betx,
bety=bety,
betz=betz)
dirxa = -self.diro
dirza = self.nrm
dirya = dirza**dirxa
alcs = MatrixVector(agcs * dirxa, agcs * dirya, agcs * dirza)
alcs.x = zeros(alcs.shape, dtype=float)
axx = MatrixVector(alcs.x, -alcs.z, alcs.y)
am2 = square(alcs.y) + square(alcs.z)
chkam2 = absolute(am2) < tol
am2r = zeros(pnts.shape, dtype=float)
reciprocal(am2, where=logical_not(chkam2), out=am2r)
faca = -1.0
veldl = elementwise_multiply(axx, am2r) * faca
veldl.x[chkam2] = 0.0
veldl.y[chkam2] = 0.0
veldl.z[chkam2] = 0.0
dirxi = Vector(dirxa.x, dirya.x, dirza.x)
diryi = Vector(dirxa.y, dirya.y, dirza.y)
dirzi = Vector(dirxa.z, dirya.z, dirza.z)
velda = MatrixVector(veldl * dirxi, veldl * diryi,
veldl * dirzi) * faca
# Trailing Vortex B
bgcs = self.relative_mach(pnts,
self.grdb,
betx=betx,
bety=bety,
betz=betz)
dirxb = self.diro
dirzb = self.nrm
diryb = dirzb**dirxb
blcs = MatrixVector(bgcs * dirxb, bgcs * diryb, bgcs * dirzb)
blcs.x = zeros(blcs.shape, dtype=float)
bxx = MatrixVector(blcs.x, -blcs.z, blcs.y)
bm2 = square(blcs.y) + square(blcs.z)
chkbm2 = absolute(bm2) < tol
bm2r = zeros(pnts.shape, dtype=float)
reciprocal(bm2, where=logical_not(chkbm2), out=bm2r)
facb = 1.0
veldl = elementwise_multiply(bxx, bm2r) * facb
veldl.x[chkbm2] = 0.0
veldl.y[chkbm2] = 0.0
veldl.z[chkbm2] = 0.0
dirxi = Vector(dirxb.x, diryb.x, dirzb.x)
diryi = Vector(dirxb.y, diryb.y, dirzb.y)
dirzi = Vector(dirxb.z, diryb.z, dirzb.z)
veldb = MatrixVector(veldl * dirxi, veldl * diryi,
veldl * dirzi) * facb
# Add Together
veld = velda + veldb
return veld / twoPi
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 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_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 fetch_pids_ttol(pnts: MatrixVector, psys: PanelSystem, ztol: float=0.01, ttol: float=0.1):
shp = pnts.shape
pnts = pnts.reshape((-1, 1))
numpnt = pnts.shape[0]
numpnl = len(psys.pnls)
pidm = zeros((1, numpnl), dtype=int)
wintm = zeros((numpnt, numpnl), dtype=bool)
abszm = zeros((numpnt, numpnl), dtype=float)
for pnl in psys.pnls.values():
pidm[0, pnl.ind] = pnl.pid
wintm[:, pnl.ind], abszm[:, pnl.ind] = pnl.within_and_absz_ttol(pnts[:, 0], ttol=ttol)
abszm[wintm is False] = float('inf')
minm = argmin(abszm, axis=1)
minm = array(minm).flatten()
pidm = array(pidm).flatten()
pids = pidm[minm]
pids = matrix([pids], dtype=int).transpose()
indp = arange(numpnt)
minz = array(abszm[indp, minm]).flatten()
minz = matrix([minz], dtype=float).transpose()
chkz = minz < ztol
pids[logical_not(chkz)] = 0
pids = pids.reshape(shp)
chkz = chkz.reshape(shp)
return pids, chkz
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
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 __sub__(self, obj):
from pygeom.matrix3d import MatrixVector
if isinstance(obj, Vector):
x = self.x-obj.x
y = self.y-obj.y
z = self.z-obj.z
return Vector(x, y, z)
elif isinstance(obj, MatrixVector):
x = self.x-obj.x
y = self.y-obj.y
z = self.z-obj.z
return MatrixVector(x, y, z)
def __pow__(self, obj):
from pygeom.matrix3d import MatrixVector
if isinstance(obj, Vector):
x = self.y*obj.z-self.z*obj.y
y = self.z*obj.x-self.x*obj.z
z = self.x*obj.y-self.y*obj.x
return Vector(x, y, z)
elif isinstance(obj, MatrixVector):
x = self.y*obj.z-self.z*obj.y
y = self.z*obj.x-self.x*obj.z
z = self.x*obj.y-self.y*obj.x
return MatrixVector(x, y, z)
def trefftz_plane_velocities(self, pnts: MatrixVector):
rls = self.points_to_local(pnts)
rls.x = zeros(rls.shape, dtype=float)
# ro = Vector(0.0, self.grdo.y, self.grdo.z)
# o = rls-ro
oxx = MatrixVector(rls.x, -rls.z, rls.y)
om2 = square(rls.y) + square(rls.z)
chkom2 = (absolute(om2) < tol)
veldl = elementwise_divide(oxx, om2) * self.faco
veldl.x[chkom2] = 0.0
veldl.y[chkom2] = 0.0
veldl.z[chkom2] = 0.0
veld = self.vectors_to_global(veldl) * self.faco
return veld / twoPi
def __rmul__(self, obj):
from numpy.matlib import matrix
from pygeom.matrix3d import MatrixVector
if isinstance(obj, (Vector, MatrixVector)):
return self.x*obj.x+self.y*obj.y+self.z*obj.z
elif isinstance(obj, matrix):
x = obj*self.x
y = obj*self.y
z = obj*self.z
return MatrixVector(x, y, z)
else:
x = obj*self.x
y = obj*self.y
z = obj*self.z
return Vector(x, y, z)
def within_and_absz_ttol(self, pnts: MatrixVector, ttol: float = 0.1):
shp = pnts.shape
pnts = pnts.reshape((-1, 1))
rgcs = pnts - self.pnto
wint = full(pnts.shape, False)
absz = full(pnts.shape, float('inf'))
for i in range(self.num):
dirx = self.dirxab[0, i]
diry = self.diryab[0, i]
dirz = self.dirzab[0, i]
xy1 = ones((pnts.shape[0], 3), dtype=float)
xy1[:, 1] = rgcs * dirx
xy1[:, 2] = rgcs * diry
t123 = xy1 * self.baryinv[i].transpose()
mint = t123.min(axis=1)
chk = mint > -ttol
wint[chk] = True
abszi = absolute(rgcs * dirz)
abszi[logical_not(chk)] = float('inf')
absz = minimum(absz, abszi)
wint = wint.reshape(shp)
absz = absz.reshape(shp)
return wint, absz
def influence_coefficients(self, pnts: MatrixVector, incvel: bool=True,
betx: float=1.0, bety: float=1.0, betz: float=1.0,
checktol: bool=False):
grdm = self.mach_grids(betx=betx, bety=bety, betz=betz)
vecab = self.edge_vector(grdm)
vecaxb = self.edge_cross(grdm)
dirxab = vecab.to_unit()
dirzab = vecaxb.to_unit()
diryab = elementwise_cross_product(dirzab, dirxab)
nrm = vecaxb.sum().to_unit()
rgcs = self.relative_mach(pnts, self.pnto, betx=betx, bety=bety, betz=betz)
locz = rgcs*nrm
sgnz = ones(locz.shape, dtype=float)
sgnz[locz <= 0.0] = -1.0
vecgcs = []
for i in range(self.num):
vecgcs.append(self.relative_mach(pnts, self.grds[i], betx=betx, bety=bety, betz=betz))
phid = zeros(pnts.shape, dtype=float)
phis = zeros(pnts.shape, dtype=float)
if incvel:
veld = zero_matrix_vector(pnts.shape, dtype=float)
vels = zero_matrix_vector(pnts.shape, dtype=float)
for i in range(self.num):
# Edge Length
dab = vecab[0, i].return_magnitude()
# Local Coordinate System
dirx = dirxab[0, i]
diry = diryab[0, i]
dirz = dirzab[0, i]
# Vector A in Local Coordinate System
veca = vecgcs[i-1]
alcs = MatrixVector(veca*dirx, veca*diry, veca*dirz)
if checktol:
alcs.x[absolute(alcs.x) < tol] = 0.0
alcs.y[absolute(alcs.y) < tol] = 0.0
alcs.z[absolute(alcs.z) < tol] = 0.0
# Vector A Doublet Velocity Potentials
phida, amag = phi_doublet_matrix(alcs, sgnz)
# Vector B in Local Coordinate System
vecb = vecgcs[i]
blcs = MatrixVector(vecb*dirx, vecb*diry, vecb*dirz)
if checktol:
blcs.x[absolute(blcs.x) < tol] = 0.0
blcs.y[absolute(blcs.y) < tol] = 0.0
blcs.z[absolute(blcs.z) < tol] = 0.0
# Vector B Doublet Velocity Potentials
phidb, bmag = phi_doublet_matrix(blcs, sgnz)
# Edge Doublet Velocity Potentials
phidi = phida - phidb
# Edge Source Velocity Potentials
phisi, Qab = phi_source_matrix(amag, bmag, dab, alcs, phidi)
# Add Edge Velocity Potentials
phid += phidi
phis += phisi
# Calculate Edge Velocities
if incvel:
# Velocities in Local Coordinate System
veldi = vel_doublet_matrix(alcs, amag, blcs, bmag)
velsi = vel_source_matrix(Qab, alcs, phidi)
# Transform to Global Coordinate System and Add
dirxi = Vector(dirx.x, diry.x, dirz.x)
diryi = Vector(dirx.y, diry.y, dirz.y)
dirzi = Vector(dirx.z, diry.z, dirz.z)
veld += MatrixVector(veldi*dirxi, veldi*diryi, veldi*dirzi)
vels += MatrixVector(velsi*dirxi, velsi*diryi, velsi*dirzi)
phid = phid/fourPi
phis = phis/fourPi
if incvel:
veld = veld/fourPi
vels = vels/fourPi
output = phid, phis, veld, vels
else:
output = phid, phis
return output
def doublet_influence_coefficients(self,
pnts: MatrixVector,
incvel: bool = True,
betx: float = 1.0,
bety: float = 1.0,
betz: float = 1.0,
checktol: bool = False):
vecab = Vector(self.vecab.x / betx, self.vecab.y / bety,
self.vecab.z / betz)
dirxab = vecab.to_unit()
dirzab = Vector(self.nrm.x, self.nrm.y, self.nrm.z)
diryab = dirzab**dirxab
agcs = self.relative_mach(pnts,
self.grda,
betx=betx,
bety=bety,
betz=betz)
bgcs = self.relative_mach(pnts,
self.grdb,
betx=betx,
bety=bety,
betz=betz)
locz = agcs * self.nrm
sgnz = ones(locz.shape, dtype=float)
sgnz[locz <= 0.0] = -1.0
phid = zeros(pnts.shape, dtype=float)
if incvel:
veld = zero_matrix_vector(pnts.shape, dtype=float)
# Vector A in Local Coordinate System
alcs = MatrixVector(agcs * dirxab, agcs * diryab, agcs * dirzab)
if checktol:
alcs.x[absolute(alcs.x) < tol] = 0.0
alcs.y[absolute(alcs.y) < tol] = 0.0
alcs.z[absolute(alcs.z) < tol] = 0.0
# Vector A Doublet Velocity Potentials
phida, amag = phi_doublet_matrix(alcs, sgnz)
# Vector B in Local Coordinate System
blcs = MatrixVector(bgcs * dirxab, bgcs * diryab, bgcs * dirzab)
if checktol:
blcs.x[absolute(blcs.x) < tol] = 0.0
blcs.y[absolute(blcs.y) < tol] = 0.0
blcs.z[absolute(blcs.z) < tol] = 0.0
# Vector B Doublet Velocity Potentials
phidb, bmag = phi_doublet_matrix(blcs, sgnz)
# Edge Doublet Velocity Potentials
phidi = phida - phidb
# Add Edge Velocity Potentials
phid += phidi
if incvel:
# Bound Edge Velocities in Local Coordinate System
veldi = vel_doublet_matrix(alcs, amag, blcs, bmag)
# Transform to Global Coordinate System and Add
dirxi = Vector(dirxab.x, diryab.x, dirzab.x)
diryi = Vector(dirxab.y, diryab.y, dirzab.y)
dirzi = Vector(dirxab.z, diryab.z, dirzab.z)
veld += MatrixVector(veldi * dirxi, veldi * diryi, veldi * dirzi)
# Trailing Edge A Coordinate Transformation
dirxa = self.diro
dirza = self.nrm
dirya = -dirza**dirxa
alcs = MatrixVector(agcs * dirxa, agcs * dirya, agcs * dirza)
# Trailing Edge A Velocity Potential
phida, amag = phi_doublet_matrix(alcs, sgnz)
phidt = phi_trailing_doublet_matrix(alcs, sgnz)
phidi = phida + phidt
# Add Trailing Edge A Velocity Potentials
phid += phidi
# Trailing Edge B Coordinate Transformation
if incvel:
# Trailing Edge A Velocities in Local Coordinate System
veldi = vel_trailing_doublet_matrix(alcs, amag, 1.0)
# Transform to Global Coordinate System and Add
dirxi = Vector(dirxa.x, dirya.x, dirza.x)
diryi = Vector(dirxa.y, dirya.y, dirza.y)
dirzi = Vector(dirxa.z, dirya.z, dirza.z)
veld += MatrixVector(veldi * dirxi, veldi * diryi, veldi * dirzi)
# Trailing Edge B Coordinate Transformation
dirxb = self.diro
dirzb = self.nrm
diryb = dirzb**dirxb
blcs = MatrixVector(bgcs * dirxb, bgcs * diryb, bgcs * dirzb)
# Trailing Edge B Velocity Potential
phidb, bmag = phi_doublet_matrix(blcs, sgnz)
phidt = phi_trailing_doublet_matrix(blcs, sgnz)
phidi = phidb + phidt
# Add Trailing Edge B Velocity Potentials
phid += phidi
if incvel:
# Trailing Edge B Velocities in Local Coordinate System
veldi = vel_trailing_doublet_matrix(blcs, bmag, 1.0)
# Transform to Global Coordinate System and Add
dirxi = Vector(dirxb.x, diryb.x, dirzb.x)
diryi = Vector(dirxb.y, diryb.y, dirzb.y)
dirzi = Vector(dirxb.z, diryb.z, dirzb.z)
veld += MatrixVector(veldi * dirxi, veldi * diryi, veldi * dirzi)
# Factors and Outputs
phid = phid / fourPi
if incvel:
veld = veld / fourPi
output = phid, veld
else:
output = phid
return output
def vectors_to_global(self, vecs: MatrixVector):
dirx = Vector(self.dirx.x, self.diry.x, self.dirz.x)
diry = Vector(self.dirx.y, self.diry.y, self.dirz.y)
dirz = Vector(self.dirx.z, self.diry.z, self.dirz.z)
return MatrixVector(vecs * dirx, vecs * diry, vecs * dirz)
def points_to_local(self, pnts: MatrixVector, betx: float = 1.0):
vecs = pnts - self.pntc
if betx != 1.0:
vecs.x = vecs.x / betx
return MatrixVector(vecs * self.dirx, vecs * self.diry,
vecs * self.dirz)