def Expand(formula):
try:
A = expand(formula)
anser = LATEX(formula) + "=" + LATEX(A)
except:
anser = "Error"
flash("エラー：もう一度入力してください")
return anser
def factorization(formula):
try:
A = factor(formula)
anser = LATEX(formula) + " = " + LATEX(A)
except:
anser = "Error"
flash("エラー：もう一度入力してください")
return anser
def lim(formula, a):
try:
A = limit(formula, x, sympify(a))
anser = "\lim_{x \\to "+str(a)+"}"+LATEX(formula)+"="+LATEX(A)
except:
anser = "Error"
flash("エラー:もう一度関数を入力してください")
return anser
def Factorial(formula):
try:
A = math.factorial(int(formula))
anser = LATEX(formula)+"! = "+LATEX(A)
except:
anser = "Error"
flash("エラー：もう一度入力してください")
return anser
def Apart(formula):
try:
x = Symbol('x')
anser = apart(formula)
anser = LATEX(formula) + "=" + LATEX(anser)
except:
anser = "Error"
flash("エラー：もう一度入力してください")
return anser
def calculation(matrixA, matrixB, type, k, l):
try:
k, l = [int(k), int(l)]
A, Ar, Ac = MATRIX(matrixA)
B, Br, Bc = MATRIX(matrixB)
if type == "A":
anser = LATEX(A)
elif type == "B":
anser = LATEX(B)
elif type == "kA+lB":
anser = LATEX(k * A + l * B)
type = str(k) + "A+" + str(l) + "B"
elif type == "AB":
anser = LATEX(A * B)
elif type == "BA":
anser = LATEX(B * A)
elif type == "A・B(内積)":
anser = LATEX(B.dot(A))
elif type == "A×B(外積)":
anser = LATEX(A.cross(B))
elif type == "B×A(外積)":
anser = LATEX(B.cross(A))
anser = str(type) + "=" + anser
except:
anser = "Error"
flash("エラー：もう一度入力してください")
return anser
def latex(formula):
try:
anser = LATEX(formula)
return anser
except:
flash("エラー：もう一度入力してください")
return "Error"
def nyquist(formula):
s = symbols('s')
formula = sympify(formula)
formula_2 = lambdify(s, formula, "numpy")
w_list_1 = np.array([-10**(i/100) for i in range(-3000, 3000, 1)])
w_list_2 = np.array([10**(i/100) for i in range(-3000, 3000, 1)])
w_list = np.hstack((w_list_1, w_list_2))
formula_3 = formula_2(1j*w_list)
deg = np.linspace(0, 2*np.pi, 100)
circle_x = np.cos(deg)
circle_y = np.sin(deg)
fig = plt.figure(figsize=(7, 4))
plt.title("$G(s)="+LATEX(formula)+"$")
plt.plot(np.real(formula_3), np.imag(formula_3))
plt.plot(circle_x, circle_y, label="0dB")
plt.plot(-1, 0, marker="x", color="red", label="s=-1+0j")
plt.axhline(y=0, color="black")
plt.axvline(x=0, color="black")
plt.legend()
# canvasにプロットした画像を出力
canvas = FigureCanvasAgg(fig)
png_output = BytesIO()
canvas.print_png(png_output)
data = png_output.getvalue()
# HTML側に渡すレスポンスを生成する
response = make_response(data)
response.headers['Content-Type'] = 'image/png'
response.headers['Content-Length'] = len(data)
return response
def diff_equation(formula):
try:
x = Symbol('x')
y = Function('y')
formula = sympify(formula)
A = dsolve(formula)
Anser = [LATEX(formula) + "=0"]
if (type(A) is list):
for i in range(len(A)):
Anser.append(LATEX(A[i]))
else:
Anser.append(LATEX(A))
except:
Anser = ["Error"]
flash("エラー：もう一度入力してください")
return Anser
def bode(formula, lower_end, upper_end):
s = symbols('s')
formula = sympify(formula)
formula_2 = lambdify(s, formula, "numpy")
title = ""
width = 100
fig = plt.figure()
ax1 = fig.add_subplot(2, 1, 1)
ax2 = fig.add_subplot(2, 1, 2)
# データ作成
w_list = np.array([10**(i/width) for i in range(int(lower_end)*width, int(upper_end)*width, 1)])
g_list = 20*np.log10(np.abs(formula_2(1j*w_list)))
φ_list = np.rad2deg(np.angle(formula_2(1j*w_list)))
φ_list[np.where(φ_list > 0)] = φ_list[np.where(φ_list > 0)]-360
tmpWc = np.average(w_list[np.where(abs(g_list) < 5)])
if(str(tmpWc) != "nan"):
w_list_c = np.array([i/100 for i in range(int((tmpWc-0.3)*100), int((tmpWc+0.3)*100), 1)])
g_list_c = 20*np.log10(np.abs(formula_2(1j*w_list_c)))
Wc = w_list_c[np.argmin(np.abs(g_list_c))]
Pm = 180+np.rad2deg(np.angle(formula_2(1j*Wc)))
ax1.axvline(x=Wc, color="black")
ax2.axvline(x=Wc, color="black")
title += "Wc="+str(round(Wc, 2))+"rad/s, Pm="+str(round(Pm, 2))+"deg, "
tmpWp = np.average(w_list[np.where((-190 < φ_list) & (φ_list < -170))])
if(str(tmpWp) != "nan"):
w_list_p = np.array([i/100 for i in range(int((tmpWp-0.3)*100), int((tmpWp+0.3)*100), 1)])
φ_list_p = np.rad2deg(np.angle(formula_2(1j*w_list_p)))
φ_list_p[np.where(φ_list_p > 0)] = φ_list_p[np.where(φ_list_p > 0)]-360
Wp = w_list_p[np.argmin(np.abs(180+φ_list_p))]
Gm = -20*np.log10(np.abs(formula_2(1j*Wp)))
ax1.axvline(x=Wp, color="black")
ax2.axvline(x=Wp, color="black")
title += "Wπ="+str(round(Wp, 2))+"rad/s, Gm="+str(round(Gm, 2))+"dB, "
ax1.plot(w_list, g_list)
ax2.plot(w_list, φ_list)
ax1.set_xscale("log")
ax2.set_xscale("log")
ax1.axhline(y=0, color="black")
ax2.axhline(y=-180, color="black")
ax1.set_title("$G(s)="+LATEX(formula)+"$")
plt.title(title, y=-0.30)
# canvasにプロットした画像を出力
canvas = FigureCanvasAgg(fig)
png_output = BytesIO()
canvas.print_png(png_output)
data = png_output.getvalue()
# HTML側に渡すレスポンスを生成する
response = make_response(data)
response.headers['Content-Type'] = 'image/png'
response.headers['Content-Length'] = len(data)
return response
def equations(formula, number):
try:
A = solve(formula)
Anser = []
if (number == 1):
for i in range(len(A)):
a = A[i]
for B in a.items():
anser = LATEX(B[0]) + "=" + LATEX(B[1])
Anser.append(anser)
else:
for B in A.items():
anser = LATEX(B[0]) + " = " + LATEX(B[1])
Anser.append(anser)
except:
Anser = ["Error"]
flash("エラー：もう一度入力してください")
return Anser
def laplace(formula, type):
try:
formula = simplify(formula)
if (type == "lap"):
Anser = laplace_transform(formula, t, s)
anser = str(Anser[0]).replace("Heaviside(", "u_s(")
formula = str(formula).replace("Heaviside(", "u_s(")
return "\mathcal{L}[" + LATEX(formula) + "]=" + LATEX(anser)
elif (type == "inv"):
anser = inverse_laplace_transform(formula, s, t)
anser = str(anser).replace("Heaviside(", "u_s(")
formula = str(formula).replace("Heaviside(", "u_s(")
return "\mathcal{L}^{-1}[" + LATEX(formula) + "]=" + LATEX(anser)
else:
flash("type エラー：もう一度入力してください")
return "Error"
except:
flash("エラー：もう一度入力してください")
return "Error"
def taylor(formula, dimension, center):
try:
x = Symbol('x')
f = sympify(formula)
center = float(center)
A = f.subs(x, center)
for number in range(1, int(dimension) + 1, 1):
f = diff(f)
D = f.subs(x, center) / factorial(number)
A += D * (x - center)**number
anser_1 = "f(x)=" + LATEX(formula)
anser_2 = "f(x)≒" + LATEX(A)
Anser = [anser_1, anser_2]
except:
Anser = ["Error", ""]
flash("エラー：もう一度入力してください")
return Anser
def sysio_matrix(matrix_A, matrix_B, matrix_C, matrix_D, matrix_X, formula,
lower_end, upper_end, type):
A, Ar, Ac = MATRIX(matrix_A)
B, Br, Bc = MATRIX(matrix_B)
C, Cr, Cc = MATRIX(matrix_C)
D, Dr, Dc = MATRIX(matrix_D)
X, Xr, Xc = MATRIX(matrix_X)
formula = simplify(formula)
lower_end, upper_end = [float(lower_end), float(upper_end)]
inverse = (s * eye(Ar) - A).inv()
matrix_T = inverse_laplace_transform(inverse, s, t)
print(matrix_T)
anser_1 = matrix_T * X
Integrand = (matrix_T.subs(t, t - τ)) * B * formula
T = integrate(Integrand, τ)
anser_2 = T.subs(τ, t) - T.subs(τ, 0)
anser = LATEX(anser_1 + anser_2)
title = str(factor(anser)).replace("Heaviside(", "u_s(")
# データ作成
T = np.linspace(lower_end, upper_end, num)
Y = np.array([anser.subs(t, T[i]) for i in range(len(T))])
fig = plt.figure(figsize=(7, 4))
plt.plot(T, Y)
plt.xlim(lower_end, upper_end)
plt.title("$y(t)=" + LATEX(title) + "(" + str(lower_end) + "<t<" +
str(upper_end) + ")$")
# canvasにプロットした画像を出力
canvas = FigureCanvasAgg(fig)
png_output = BytesIO()
canvas.print_png(png_output)
data = png_output.getvalue()
# HTML側に渡すレスポンスを生成する
response = make_response(data)
response.headers['Content-Type'] = 'image/png'
response.headers['Content-Length'] = len(data)
return response
def equation(formula, type):
try:
x = Symbol('x')
A = solve(formula, dict=True)
Anser = ["方程式:" + LATEX(formula) + "=0", ""]
if (type == "analytical"):
for i in range(len(A)):
a = A[i]
for B in a.items():
anser = LATEX(B[0]) + "=" + LATEX(B[1])
Anser.append(anser)
elif (type == "numerical"):
for i in range(len(A)):
a = A[i]
for B in a.items():
anser = LATEX(B[0]) + "=" + LATEX(B[1].evalf())
Anser.append(anser)
except:
Anser = ["Error"]
flash("エラー：もう一度入力してください")
return Anser
def derivative(formula, type):
try:
x, y, z = symbols('x y z')
anser = "f_{" + type + "}="
if (type == "x"):
A = diff(formula, x)
elif (type == "y"):
A = diff(formula, y)
elif (type == "z"):
A = diff(formula, z)
elif (type == "xx"):
A = diff(formula, x, x)
elif (type == "yy"):
A = diff(formula, y, y)
elif (type == "zz"):
A = diff(formula, z, z)
elif (type == "xy"):
A = diff(formula, x, y)
elif (type == "yz"):
A = diff(formula, y, x)
elif (type == "zx"):
A = diff(formula, z, x)
elif (type == "grad"):
anser = "\mathrm{grad} f="
A = (diff(formula, x), diff(formula, y), diff(formula, z))
elif (type == "∆"):
anser = "\Delta f="
A = (diff(formula, x, x), diff(formula, y, y), diff(formula, z, z))
anser += LATEX(factor(A))
formula = "f\left(x,y,z \\right)=" + LATEX(formula)
Anser = [formula, anser]
except:
Anser = ["Error", ""]
flash("エラー：もう一度入力してください")
return Anser
def graph(formula_1, lower_end_x, upper_end_x):
x, y = symbols('x y')
formula_1 = sympify(formula_1)
lower_end_x = float(lower_end_x)
upper_end_x = float(upper_end_x)
fig = plt.figure(figsize=(7, 4))
# データ作成
dx = diff(formula_1, x)
dy = diff(formula_1, y)
if ((dx == 0) or (dy == 0)):
X = np.linspace(lower_end_x, upper_end_x, 300)
if ((dx == 0) and (dy == 0)):
Y = lambdify(x, formula_1, "numpy")(lower_end_x) * np.ones(300)
elif (dy == 0):
Y = lambdify(x, formula_1, "numpy")(X)
elif (dx == 0):
Y = lambdify(y, formula_1, "numpy")(X)
ax = fig.add_subplot(111)
ax.plot(X, Y)
else:
s = np.linspace(lower_end_x, upper_end_x, 50)
X, Y = np.meshgrid(s, s)
Z = lambdify((x, y), formula_1, "numpy")(X, Y)
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, cmap=cm.coolwarm)
ax.set_xlabel('x')
ax.set_ylabel('y')
plt.title("$f(x)=" + LATEX(formula_1) + "(" + str(lower_end_x) + "<x,y<" +
str(upper_end_x) + ")$")
# canvasにプロットした画像を出力
canvas = FigureCanvasAgg(fig)
png_output = BytesIO()
canvas.print_png(png_output)
data = png_output.getvalue()
# HTML側に渡すレスポンスを生成する
response = make_response(data)
response.headers['Content-Type'] = 'image/png'
response.headers['Content-Length'] = len(data)
return response
def sysio(formula, formula_2, lower_end, upper_end, type):
formula = simplify(formula)
formula_2 = simplify(formula_2)
lower_end = float(lower_end)
upper_end = float(upper_end)
if (type == "s"):
output = apart(formula * formula_2)
anser = inverse_laplace_transform(output, s, t)
else:
g = simplify(formula).subs(t, t - τ)
u = simplify(formula_2).subs(t, τ)
y = integrate(g * u, τ)
anser = y.subs(τ, t) - y.subs(τ, 0)
anser = str(anser).replace("Heaviside(0)", "0")
anser = simplify(anser)
title = str(factor(anser)).replace("Heaviside(", "u_s(")
# データ作成
T = np.linspace(lower_end, upper_end, num)
Y = np.array([anser.subs(t, T[i]) for i in range(len(T))])
fig = plt.figure(figsize=(7, 4))
plt.plot(T, Y)
plt.xlim(lower_end, upper_end)
plt.title("$y(t)=" + LATEX(title) + "(" + str(lower_end) + "<t<" +
str(upper_end) + ")$")
# canvasにプロットした画像を出力
canvas = FigureCanvasAgg(fig)
png_output = BytesIO()
canvas.print_png(png_output)
data = png_output.getvalue()
# HTML側に渡すレスポンスを生成する
response = make_response(data)
response.headers['Content-Type'] = 'image/png'
response.headers['Content-Length'] = len(data)
return response
def max_min(formula):
try:
x, y = symbols('x y')
formula = sympify(formula)
f_x = diff(formula, x)
f_y = diff(formula, y)
f_xx = diff(formula, x, x)
f_yy = diff(formula, y, y)
f_xy = diff(formula, x, y)
if f_x == 0 or f_y == 0:
if f_x == 0:
var = y
det = f_yy
A = solve(f_y, dict=True)
else:
var = x
det = f_xx
A = solve(f_x, dict=True)
Max_Anser = []
Min_Anser = []
for i in range(len(A)):
a = A[i]
for B in a.items():
b = det.subs(var, B[1])
c = formula.subs(var, B[1])
if b >= 0:
anser = "極小値 f("+LATEX(B[1])+") = "+LATEX(c)
Min_Anser.append(anser)
else:
anser = "極大値 f("+LATEX(B[1])+") = "+LATEX(c)
Max_Anser.append(anser)
Anser = ["f("+LATEX(var)+")="+LATEX(formula)]+Max_Anser+Min_Anser
else:
A = solve([f_x, f_y])
B = []
if type(A) == list:
for i in range(len(A)):
a = A[i]
D = []
for C in a.items():
D.append(C[1])
B.append(D)
else:
D = []
for C in A.items():
D.append(C[1])
B.append(D)
Anser = ["f(x,y)="+LATEX(formula)]
for j in range(len(B)):
a = B[j][0]
b = B[j][1]
D = f_xx*f_yy-(f_xy)**2
D = D.subs([(x, a), (y, b)])
f_xx = f_xx.subs([(x, a), (y, b)])
if D > 0:
if f_xx > 0:
anser = "極小値 f("+LATEX(a)+","+LATEX(b)+")=" + \
LATEX(formula.subs([(x, a), (y, b)]))
else:
anser = "極大値 f("+LATEX(a)+","+LATEX(b)+")=" + \
LATEX(formula.subs([(x, a), (y, b)]))
elif D < 0:
anser = "点("+LATEX(a)+","+LATEX(b)+")で極値をとらない"
else:
anser = "点("+LATEX(a)+","+LATEX(b)+")での極値は判別できない"
Anser.append(anser)
if len(Anser) == 1:
Anser.append("極値をとらない")
except:
Anser = ["Error"]
flash("エラー：もう一度入力してください")
return Anser
def integral(formula, Up, Low, type):
try:
x, y = symbols('x y')
if (type == "multiple_integral_1" or type == "multiple_integral_2"):
A = integrate(formula, (x, Low[0], Up[0]), (y, Low[1], Up[1]))
anser = "\int_{" + LATEX(Low[1]) + "}^{" + LATEX(
Up[1]) + "} \int_{" + LATEX(Low[0]) + "}^{" + LATEX(
Up[0]) + "}" + LATEX(formula) + "dxdy="
if (type == "multiple_integral_1"):
anser += LATEX(A)
elif (type == "multiple_integral_2"):
anser += LATEX(A.evalf())
else:
if (type == "indefinite_integral"):
A = integrate(formula, x)
anser = "\int " + LATEX(formula) + "dx=" + LATEX(A) + "+C"
else:
A = integrate(formula, (x, Low[0], Up[0]))
anser = "\int_{" + LATEX(Low[0]) + "}^{" + LATEX(
Up[0]) + "}" + LATEX(formula) + "dx="
if (type == "definite_integral_1"):
anser += LATEX(A)
elif (type == "definite_integral_2"):
anser += LATEX(A.evalf())
except:
anser = "Error"
flash("エラー:もう一度入力してください")
return anser
def calculation(matrixA, type):
try:
A, Ar, Ac = MATRIX(matrixA)
if type == "A":
anser = "A="+LATEX(A)
elif type == "A^n":
if(Ar == Ac):
P, D = list(A.diagonalize())
for i in range(Ac):
D[i, i] = "("+str(D[i, i])+")^n"
anser = "A^n="+LATEX(P*D*P.inv())
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
elif type == "A^{-1}":
if(Ar == Ac):
anser = "A^{-1}="+LATEX(A.inv())
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
elif type == "A^t":
anser = "A^T="+LATEX(A.transpose())
elif type == "\widetilde{A}":
if(Ar == Ac):
anser = "\widetilde{A}="+LATEX(A.adjugate())
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
elif type == "det(A)":
if(Ar == Ac):
anser = "det(A)="+LATEX(A.det())
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
elif type == "rank(A)":
anser = "rank(A)="+LATEX(A.rank())
elif type == "tr(A)":
if(Ar == Ac):
anser = "tr(A)="+LATEX(A.trace())
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
elif type == "λ":
if(Ar == Ac):
A = A.eigenvals()
anser = ""
for B in A.items():
anser += ("\lambda="+LATEX(B[0])+"(n="+LATEX(B[1])+"), ")
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
elif type == "P":
if(Ar == Ac):
A = list(A.diagonalize())
anser = "P="+LATEX(A[0])
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
elif type == "P^{-1}AP":
if(Ar == Ac):
A = list(A.diagonalize())
anser = "P^{-1}AP="+LATEX(A[1])
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
elif type == "Φ(t)":
if(Ar == Ac):
anser = "Φ(t)="+LATEX((s*eye(Ar)-A).inv())
else:
flash("Error:正方行列を入力してください")
anser = "正方行列を入力してください"
except:
anser = "Error"
flash("エラー：もう一度入力してください")
return anser
def calculation(matrixA, Ar, Ac, type):
try:
Ar, Ac = [int(Ar), int(Ac)]
A = MATRIX(matrixA, Ar, Ac)
if type == "A":
anser = LATEX(A)
elif type == "A^n":
A = list(A.diagonalize())
P = A[0]
D = A[1]
for i in range(0, Ac, 1):
D[i, i] = "(" + str(D[i, i]) + ")^n"
anser = LATEX(P * D * P.inv())
elif type == "A^t":
anser = LATEX(A.transpose())
elif type == "A^{-1}":
anser = LATEX(A.inv())
elif type == "\widetilde{A}":
anser = LATEX(A.adjugate())
elif type == "det(A)":
anser = LATEX(A.det())
elif type == "rank(A)":
anser = LATEX(A.rank())
elif type == "tr(A)":
anser = LATEX(A.trace())
elif type == "λ":
A = A.eigenvals()
anser = ""
for B in A.items():
anser += LATEX(B[0]) + "(n=" + LATEX(B[1]) + "), "
elif type == "P":
A = A.diagonalize()
A = list(A)
anser = LATEX(A[0])
elif type == "P^{-1}AP":
A = A.diagonalize()
A = list(A)
anser = LATEX(A[1])
except:
anser = "Error"
flash("エラー：もう一度入力してください")
return anser
