def testShapefunctions( ):
poly = g.Mesh( 3 )
n0 = poly.createNode( 0.0, 0.0, 0.0 )
n1 = poly.createNode( 1.0, 0.0, 0.0 )
n2 = poly.createNode( 0.0, 1.0, 0.0 )
n3 = poly.createNode( 0.0, 0.0, 0.5 )
poly.createTetrahedron( n0, n1, n2, n3 )
prism = poly.createP2Mesh()
u = g.RVector( prism.nodeCount(), 0.0 )
u[ 5 ] = 1.0
prism.addExportData( "u", u )
#n3 = poly.createNode( 1.0, 1.0, 0.0 )
#poly.createTriangle( n0, n1, n3 )
#prism = g.createMesh3D( poly, g.asvector( np.linspace( 0, -1, 2 ) ) )
#prism.exportVTK( "prism" )
#mesh2 = g.createMesh2D( g.asvector( np.linspace( 0, 1, 10 ) ),
#g.asvector( np.linspace( 0, 1, 10 ) ) )
#mesh2 = mesh2.createH2Mesh()
#g.interpolate( prism, mesh2 )
#ax = g.viewer.showMesh( mesh2, mesh2.exportData('u'), filled = True, showLater = True )
mesh3 = g.createMesh3D( g.asvector( np.linspace( 0, 1, 11 ) ),
g.asvector( np.linspace( 0, 1, 11 ) ),
g.asvector( np.linspace( 0, 1, 11 ) ) )
grads = g.stdVectorRVector3( )
c = prism.cell( 0 )
uc = g.RVector( mesh3.nodeCount() )
for n in mesh3.nodes():
p = c.shape().xyz( n.pos() )
if not c.shape().isInside( p ):
grads.append( g.RVector3( 0.0, 0.0, 0.0 ) )
uc[ n.id() ] = 0.0
continue
uc[ n.id() ] = c.pot( p, u )
print uc[ n.id() ]
gr = c.grad( p, u )
grads.append( gr )
g.interpolate( prism, mesh3 )
mesh3.addExportData( 'ua', uc )
mesh3.exportVTK( "prismHex", grads )
P.show()
def test3d():
'''
'''
# test1.
mesh = pg.Mesh(3)
mesh.importSTL('sphere.stl')
mesh.scale(pg.RVector3(4.0, 4.0, 4.0))
mesh.translate(pg.RVector3(0.0, 0.0, -5.0))
print(mesh)
mesh.exportVTK('sphere.vtk')
alpha = 24
v = 8.2
epsilon = 1e-12
gamma = (100 * epsilon)**(1. / v)
d = alpha / (gamma * np.sqrt(2))
d = 0
p = pg.RVector3(d, d, 0.0)
x = np.arange(-15, 15, 1.)
spnts = pg.stdVectorRVector3()
for i in x:
spnts.append(pg.RVector3(i, 0.0))
gz = pg.RVector(len(x), 0.0)
for i, p in enumerate(spnts):
for face in mesh.boundaries():
Z = 0
norm = face.norm()
# cos( n, z )
for j in range(face.nodeCount()):
A = face.node(j)
B = face.node((j + 1) % face.nodeCount())
Z += lineIntegralZ3D(A.pos() - p, B.pos() - p, norm)
gz[i] += Z
gz = gz * 2000 * 6.67384e-11 * 1e5
gAna = analyticalSphere(spnts,
radius=2.0,
pos=pg.RVector3(0.0, 0.0, -5.0),
dDensity=2000)
ax1, ax2 = getaxes()
ax1.plot(x, gAna, '-x', label='Analytical Sphere')
ax1.plot(x, gz, label='polyhedral')
ax1.legend()
ax2.set_xlim([x[0], x[-1]])
ax2.grid()
def testShapefunctions():
poly = g.Mesh(3)
n0 = poly.createNode(0.0, 0.0, 0.0)
n1 = poly.createNode(1.0, 0.0, 0.0)
n2 = poly.createNode(0.0, 1.0, 0.0)
n3 = poly.createNode(0.0, 0.0, 0.5)
poly.createTetrahedron(n0, n1, n2, n3)
prism = poly.createP2Mesh()
u = g.RVector(prism.nodeCount(), 0.0)
u[5] = 1.0
prism.addExportData("u", u)
#n3 = poly.createNode( 1.0, 1.0, 0.0 )
#poly.createTriangle( n0, n1, n3 )
#prism = g.createMesh3D( poly, g.asvector( np.linspace( 0, -1, 2 ) ) )
#prism.exportVTK( "prism" )
#mesh2 = g.createMesh2D( g.asvector( np.linspace( 0, 1, 10 ) ),
#g.asvector( np.linspace( 0, 1, 10 ) ) )
#mesh2 = mesh2.createH2Mesh()
#g.interpolate( prism, mesh2 )
#ax = g.viewer.showMesh( mesh2, mesh2.exportData('u'), filled = True, showLater = True )
mesh3 = g.createMesh3D(g.asvector(np.linspace(0, 1, 11)),
g.asvector(np.linspace(0, 1, 11)),
g.asvector(np.linspace(0, 1, 11)))
grads = g.stdVectorRVector3()
c = prism.cell(0)
uc = g.RVector(mesh3.nodeCount())
for n in mesh3.nodes():
p = c.shape().xyz(n.pos())
if not c.shape().isInside(p):
grads.append(g.RVector3(0.0, 0.0, 0.0))
uc[n.id()] = 0.0
continue
uc[n.id()] = c.pot(p, u)
print uc[n.id()]
gr = c.grad(p, u)
grads.append(gr)
g.interpolate(prism, mesh3)
mesh3.addExportData('ua', uc)
mesh3.exportVTK("prismHex", grads)
P.show()
def test3d():
'''
'''
# test1.
mesh = g.Mesh( 3 )
mesh.importSTL( 'sphere.stl' )
mesh.scale( g.RVector3( 4.0, 4.0, 4.0 ) )
mesh.translate( g.RVector3( 0.0, 0.0, -5.0 ) )
print mesh
mesh.exportVTK('sphere.vtk' )
alpha = 24
v = 8.2
epsilon = 1e-12
gamma = ( 100 * epsilon )** 1./v
d = alpha / ( gamma * np.sqrt( 2 ) )
d = 0
p = g.RVector3( d, d, 0.0 )
x = P.arange( -15, 15, 1. );
spnts = g.stdVectorRVector3()
for i in x:
spnts.append( g.RVector3( i, 0.000 ) )
gz = g.RVector( len(x), 0.0 )
for i, p in enumerate( spnts ):
for face in mesh.boundaries():
Z = 0
norm = face.norm()
# cos( n, z )
for j in range( face.nodeCount( ) ):
A = face.node( j )
B = face.node( (j+1)%face.nodeCount( ) )
Z += lineIntegralZ3D( A.pos() -p , B.pos() -p, norm )
gz[ i ] += Z
gz = gz * 2000 * 6.67384e-11 * 1e5
gAna = analyticalSphere( spnts, radius = 2.0, pos = g.RVector3( 0.0, 0.0, -5.0 ), dDensity = 2000 )
ax1, ax2 = getaxes()
ax1.plot( x, gAna, '-x', label = 'Analytical Sphere' )
ax1.plot( x, gz, label = 'polyhedral' )
ax1.legend()
ax2.set_xlim( [ x[0], x[-1] ] )
ax2.grid()
H8_6 = E2_2R * E2_1S * E2_2T H8_7 = E2_2R * E2_2S * E2_2T H8_8 = E2_1R * E2_2S * E2_2T P15_6 = T3_3 * E2_2T * (2. * (T3_3 + E2_2T) + -3.) P15_7 = T6_4 * E2_1T P15_8 = T6_5 * E2_1T P15_9 = T6_6 * E2_1T P15_10 = T6_4 * E2_2T P15_11 = T6_5 * E2_2T P15_12 = T6_6 * E2_2T P15_13 = T3_1 * E3_3T P15_14 = T3_2 * E3_3T P15_15 = T3_3 * E3_3T pnts = g.stdVectorRVector3() # quad pnts.append(g.RVector3(0.0, 0.0)) pnts.append(g.RVector3(1.0, 0.0)) pnts.append(g.RVector3(1.0, 1.0)) pnts.append(g.RVector3(0.0, 1.0)) pnts.append(g.RVector3(0.5, 0.5)) #pnts.append(g.RVector3(0.5, 0.0)) #pnts.append(g.RVector3(1.0, 0.5)) #pnts.append(g.RVector3(0.5, 1.0)) #pnts.append(g.RVector3(0.0, 0.5)) ## tri #pnts.append(g.RVector3(0.0, 0.0)) #pnts.append(g.RVector3(1.0, 0.0))
def test2d():
mesh = pg.Mesh("mesh/world2d.bms")
print (mesh)
xMin = mesh.boundingBox().min()[0]
yMax = mesh.boundingBox().max()[0]
x = np.arange(xMin, yMax, 1.0)
mesh.createNeighbourInfos()
rho = pg.RVector(len(mesh.cellAttributes()), 1.0) * 2000.0
rho.setVal(0.0, pg.find(mesh.cellAttributes() == 1.0))
swatch = pg.Stopwatch(True)
pnts = []
spnts = pg.stdVectorRVector3()
for i in x:
pnts.append(pg.RVector3(i, 0.0001))
spnts.append(pg.RVector3(i, 0.0001))
# gzC, GC = calcGCells(pnts, mesh, rho, 1)
gzC = pg.calcGCells(spnts, mesh, rho, 1)
print ("calcGCells", swatch.duration(True))
# gzB, GB = calcGBounds(pnts, mesh, rho)
# gzB = pg.calcGBounds(spnts, mesh, rho)
# print("calcGBounds", swatch.duration(True))
gZ_Mesh = gzC
ax1, ax2 = getaxes()
# sphere analytical solution
gAna = analyticalCircle2D(spnts, radius=2.0, pos=pg.RVector3(0.0, -5.0), dDensity=2000)
gAna2 = analyticalCircle2D(spnts, radius=2.0, pos=pg.RVector3(5.0, -5.0), dDensity=2000)
gAna = gAna + gAna2
ax1.plot(x, gAna, "-x", label="analytical")
ax1.plot(x, gZ_Mesh, label="WonBevis1987-mesh")
print (gAna / gZ_Mesh)
# rho=GB[0]/mesh.cellSizes()
drawModel(ax2, mesh, rho)
for i in (0, 1):
drawSelectedMeshBoundaries(ax2, mesh.findBoundaryByMarker(i), color=(1.0, 1.0, 1.0, 1.0), linewidth=0.3)
# sphere polygone
radius = 2.0
depth = 5.0
poly1 = pg.stdVectorRVector3()
poly2 = pg.stdVectorRVector3()
nSegment = 124
for i in range(nSegment):
xp = np.sin((i + 1) * (2.0 * np.pi) / nSegment)
yp = np.cos((i + 1) * (2.0 * np.pi) / nSegment)
poly1.append(pg.RVector3(xp * radius, yp * radius - depth))
poly2.append(pg.RVector3(xp * radius + 5.0, yp * radius - depth))
gZ_Poly = calcPolydgdz(spnts, poly1, 2000)
gZ_Poly += calcPolydgdz(spnts, poly2, 2000)
ax1.plot(x, gZ_Poly, label="WonBevis1987-Poly")
ax2.plot(pg.x(poly1), pg.y(poly1), color="red")
ax2.plot(pg.x(poly2), pg.y(poly2), color="red")
ax2.plot(pg.x(spnts), pg.y(spnts), marker="x", color="black")
# test some special case
for i, p in enumerate(poly1):
poly1[i] = pg.RVector3(poly1[i] - pg.RVector3(5.0, -6.0))
ax2.plot(pg.x(poly1), pg.y(poly1), color="green")
gz = calcPolydgdz(spnts, poly1, 2000)
ax1.plot(x, gz, label="Special Case", color="green")
ax1.set_ylabel("dg/dz [mGal]")
ax2.set_ylabel("Tiefe [m]")
ax1.legend()
ax2.set_xlim([x[0], x[-1]])
ax2.grid()
A = mesh.createNode(pg.RVector3(-1.0, -1.0))
B = mesh.createNode(pg.RVector3(-2.0, -1.0))
C = mesh.createNode(pg.RVector3(-2.0, -2.0))
D = mesh.createNode(pg.RVector3(-1.0, -2.0))
mesh.createTriangle(A, B, C)
# mesh.createQuadrangle(A, B, C, D)
mesh.scale(pg.RVector3(3.0, 3.0))
# mesh.createTriangle(A, B, D)
print mesh.cellSizes()
x = np.arange(-10, 10, 1.0)
rho = pg.RVector(len(mesh.cellAttributes()), 1.0) * 2000.0
print (rho)
pnts = pg.stdVectorRVector3()
for i in x:
pnts.append(pg.RVector3(i, 0.0001))
gzNum = []
gzNum.append(pg.calcGCells(pnts, mesh, rho, 0)[0])
# plt.plot(x, gzNum[0], label=str(0))
for i in range(1, 10):
gzNum.append(pg.calcGCells(pnts, mesh, rho, i)[0])
err = pg.abs(gzNum[i] / gzNum[0] - 1.0) * 100.0
plt.semilogy(x, err, label=str(i))
def test2d():
mesh = g.Mesh( 'mesh/world2d.bms' )
print mesh
xMin = mesh.boundingBox( ).min()[0]
yMax = mesh.boundingBox( ).max()[0]
x = P.arange( xMin, yMax, 1. );
mesh.createNeighbourInfos()
rho = g.RVector( len( mesh.cellAttributes() ), 1. ) * 2000.0
rho.setVal( 0.0, g.find( mesh.cellAttributes() == 1.0 ) )
swatch = g.Stopwatch( True )
pnts = []
spnts = g.stdVectorRVector3()
for i in x:
pnts.append( g.RVector3( i, 0.0001 ) )
spnts.append( g.RVector3( i, 0.0001 ) )
#gzC, GC = calcGCells( pnts, mesh, rho, 1 )
gzC = g.calcGCells( spnts , mesh, rho, 1 )
print "calcGCells", swatch.duration( True )
#gzB, GB = calcGBounds( pnts, mesh, rho )
gzB = g.calcGBounds( spnts , mesh, rho )
print "calcGBounds", swatch.duration( True )
gZ_Mesh = gzC
ax1, ax2 = getaxes()
# sphere analytical solution
gAna = analyticalCircle2D( spnts, radius = 2.0, pos = g.RVector3( 0.0, -5.0 ), dDensity = 2000 )
gAna2 = analyticalCircle2D( spnts, radius = 2.0, pos = g.RVector3( 5.0, -5.0 ), dDensity = 2000 )
gAna = gAna + gAna2
ax1.plot( x, gAna, '-x', label= 'Analytisch' )
ax1.plot( x, gZ_Mesh, label= 'WonBevis1987-mesh' )
print gAna / gZ_Mesh
#rho=GB[0]/mesh.cellSizes()
gci = drawModel( ax2, mesh, rho )
drawSelectedMeshBoundaries( ax2, mesh.findBoundaryByMarker( 0 )
, color = ( 1.0, 1.0, 1.0, 1.0 )
, linewidth = 0.3 )
drawSelectedMeshBoundaries( ax2, mesh.findBoundaryByMarker( 1 )
, color = ( 1.0, 1.0, 1.0, 1.0 )
, linewidth = 0.3 )
# sphere polygone
radius = 2.
depth = 5.
poly1 = g.stdVectorRVector3()
poly2 = g.stdVectorRVector3()
nSegment=124
for i in range( nSegment ):
xp = np.sin( (i+1) * ( 2. * np.pi ) / nSegment )
yp = np.cos( (i+1) * ( 2. * np.pi ) / nSegment )
poly1.append( g.RVector3( xp * radius, yp * radius - depth ) )
poly2.append( g.RVector3( xp * radius + 5., yp * radius - depth ) )
gZ_Poly = calcPolydgdz( spnts, poly1, 2000 )
gZ_Poly += calcPolydgdz( spnts, poly2, 2000 )
ax1.plot( x, gZ_Poly, label= 'WonBevis1987-Poly' )
ax2.plot( g.x( poly1 ), g.y( poly1 ), color = 'red' )
ax2.plot( g.x( poly2 ), g.y( poly2 ), color = 'red' )
ax2.plot( g.x( spnts ), g.y( spnts ), marker = 'x', color = 'black' )
# test some special case
for i, p in enumerate( poly1 ):
poly1[i] = g.RVector3( poly1[i] - g.RVector3( 5.0, -6. ) )
ax2.plot( g.x( poly1 ), g.y( poly1 ), color = 'green' )
gz = calcPolydgdz( spnts, poly1, 2000 )
ax1.plot( x, gz, label= 'Special Case', color = 'green' )
ax1.set_ylabel( 'dg/dz [mGal]' )
ax2.set_ylabel( 'Tiefe [m]' )
ax1.legend()
ax2.set_xlim( [ x[0], x[-1] ] )
ax2.grid()
A = mesh.createNode( g.RVector3( -1., -1. ) )
B = mesh.createNode( g.RVector3( -2., -1. ) )
C = mesh.createNode( g.RVector3( -2., -2. ) )
D = mesh.createNode( g.RVector3( -1., -2. ) )
mesh.createTriangle( A, B, C)
#mesh.createQuadrangle( A, B, C, D)
mesh.scale( g.RVector3( 3., 3. ) )
#mesh.createTriangle( A, B, D)
print mesh.cellSizes()
x = np.arange( -10, 10, 1. );
rho = g.RVector( len( mesh.cellAttributes() ), 1. ) * 2000.0
print rho
pnts = g.stdVectorRVector3()
for i in x:
pnts.append( g.RVector3( i, 0.0001 ) )
gzNum = []
gzNum.append( g.calcGCells( pnts, mesh, rho, 0 )[0] )
#P.plot(x, gzNum[0], label = str(0) )
for i in range( 1, 10 ):
gzNum.append( g.calcGCells( pnts, mesh, rho, i )[0] )
err = g.abs(gzNum[i]/gzNum[0]-1.)*100.
P.semilogy(x, err, label = str(i) )
def drawShapes( ax, mesh, u ):
#ax.set_aspect( 'equal' )
N = 11
mesh3 = g.createMesh3D( g.asvector( np.linspace( 0, 1, N ) ),
g.asvector( np.linspace( 0, 1, N ) ),
g.asvector( np.linspace( 0, 1, N ) ) )
uc = g.RVector( mesh3.nodeCount( ) )
grads = g.stdVectorRVector3( )
pnts = g.stdVectorRVector3( )
c = mesh.cell( 0 )
imax=g.find( u == max( u ) )[0]
N = c.createShapeFunctions()[ imax ]
print imax, N
# print imax, c.shape().createShapeFunctions()[imax]
for i in range( c.nodeCount() ):
print c.rst( i ), N( c.rst( i ) )
# draw nodes
for i in range( c.nodeCount() ):
col = 'black'
if i == imax:
col = 'red'
#ax.plot( [c.node( i ).pos()[0], c.node( i ).pos()[0] ],
#[c.node( i ).pos()[1], c.node( i ).pos()[1] ],
#[c.node( i ).pos()[2], c.node( i ).pos()[2] ],
#'.', markersize = 15, linewidth=0, color=col )
newNode = []
for i in range( mesh3.nodeCount( ) ):
p = c.shape().xyz( mesh3.node( i ).pos() )
newNode.append( p )
#ax.plot( p[0], p[1], '.', zorder=10, color='black', markersize = 1 )
if not c.shape().isInside( p ):
uc[ i ] = -99.0
grads.append( g.RVector3( 0.0, 0.0 ) )
continue
uc[ i ] = c.pot( p, u )
gr = c.grad( p, u ).normalise()
grads.append( gr )
#ax.plot( [ p[ 0 ], p[ 0 ] + gr[ 0 ]*0.1 ],
#[ p[ 1 ], p[ 1 ] + gr[ 1 ]*0.1 ],
#[ p[ 2 ], p[ 2 ] + gr[ 2 ]*0.1 ], '-', color='black' )
#pnts.append( p )
#print len(pnts)
#Z = np.ma.masked_where( uc == -99., uc )
##ax.plot( g.x(pnts), g.y(pnts), g.z(pnts), '.' )
for i, n in enumerate( mesh3.nodes() ):
n.setPos( newNode[ i ] )
mesh3.addExportData( 'u', uc.setVal( 0.0, g.find( uc == -99 ) ) )
name = 'cell' + str( c.nodeCount() ) + '-' + str( imax )
print "write ", name
mesh3.exportVTK( name, grads )
def test2d():
mesh = pg.Mesh('mesh/world2d.bms')
print(mesh)
xMin = mesh.boundingBox().min()[0]
yMax = mesh.boundingBox().max()[0]
x = np.arange(xMin, yMax, 1.)
mesh.createNeighbourInfos()
rho = pg.RVector(len(mesh.cellAttributes()), 1.) * 2000.0
rho.setVal(0.0, pg.find(mesh.cellAttributes() == 1.0))
swatch = pg.Stopwatch(True)
pnts = []
spnts = pg.stdVectorRVector3()
for i in x:
pnts.append(pg.RVector3(i, 0.0001))
spnts.append(pg.RVector3(i, 0.0001))
# gzC, GC = calcGCells(pnts, mesh, rho, 1)
gzC = pg.calcGCells(spnts, mesh, rho, 1)
print("calcGCells", swatch.duration(True))
# gzB, GB = calcGBounds(pnts, mesh, rho)
# gzB = pg.calcGBounds(spnts, mesh, rho)
# print("calcGBounds", swatch.duration(True))
gZ_Mesh = gzC
ax1, ax2 = getaxes()
# sphere analytical solution
gAna = analyticalCircle2D(spnts,
radius=2.0,
pos=pg.RVector3(0.0, -5.0),
dDensity=2000)
gAna2 = analyticalCircle2D(spnts,
radius=2.0,
pos=pg.RVector3(5.0, -5.0),
dDensity=2000)
gAna = gAna + gAna2
ax1.plot(x, gAna, '-x', label='analytical')
ax1.plot(x, gZ_Mesh, label='WonBevis1987-mesh')
print(gAna / gZ_Mesh)
# rho=GB[0]/mesh.cellSizes()
drawModel(ax2, mesh, rho)
for i in (0, 1):
drawSelectedMeshBoundaries(ax2,
mesh.findBoundaryByMarker(i),
color=(1.0, 1.0, 1.0, 1.0),
linewidth=0.3)
# sphere polygone
radius = 2.
depth = 5.
poly1 = pg.stdVectorRVector3()
poly2 = pg.stdVectorRVector3()
nSegment = 124
for i in range(nSegment):
xp = np.sin((i + 1) * (2. * np.pi) / nSegment)
yp = np.cos((i + 1) * (2. * np.pi) / nSegment)
poly1.append(pg.RVector3(xp * radius, yp * radius - depth))
poly2.append(pg.RVector3(xp * radius + 5., yp * radius - depth))
gZ_Poly = calcPolydgdz(spnts, poly1, 2000)
gZ_Poly += calcPolydgdz(spnts, poly2, 2000)
ax1.plot(x, gZ_Poly, label='WonBevis1987-Poly')
ax2.plot(pg.x(poly1), pg.y(poly1), color='red')
ax2.plot(pg.x(poly2), pg.y(poly2), color='red')
ax2.plot(pg.x(spnts), pg.y(spnts), marker='x', color='black')
# test some special case
for i, p in enumerate(poly1):
poly1[i] = pg.RVector3(poly1[i] - pg.RVector3(5.0, -6.))
ax2.plot(pg.x(poly1), pg.y(poly1), color='green')
gz = calcPolydgdz(spnts, poly1, 2000)
ax1.plot(x, gz, label='Special Case', color='green')
ax1.set_ylabel('dg/dz [mGal]')
ax2.set_ylabel('Tiefe [m]')
ax1.legend()
ax2.set_xlim([x[0], x[-1]])
ax2.grid()
A = mesh.createNode(pg.RVector3(-1., -1.))
B = mesh.createNode(pg.RVector3(-2., -1.))
C = mesh.createNode(pg.RVector3(-2., -2.))
D = mesh.createNode(pg.RVector3(-1., -2.))
mesh.createTriangle(A, B, C)
# mesh.createQuadrangle(A, B, C, D)
mesh.scale(pg.RVector3(3., 3.))
# mesh.createTriangle(A, B, D)
print mesh.cellSizes()
x = np.arange(-10, 10, 1.)
rho = pg.RVector(len(mesh.cellAttributes()), 1.) * 2000.0
print(rho)
pnts = pg.stdVectorRVector3()
for i in x:
pnts.append(pg.RVector3(i, 0.0001))
gzNum = []
gzNum.append(pg.calcGCells(pnts, mesh, rho, 0)[0])
# plt.plot(x, gzNum[0], label=str(0))
for i in range(1, 10):
gzNum.append(pg.calcGCells(pnts, mesh, rho, i)[0])
err = pg.abs(gzNum[i] / gzNum[0] - 1.) * 100.
plt.semilogy(x, err, label=str(i))
