def example(xdata=np.array([-2, -1, 0, 1, 2]),
ydata=np.array([0, 0.2, 0.5, 0.8, 1])):
basis = [1, lambda x: x]
A = np.array([[b(x) if hasattr(b, '__call__') else b for b in basis]
for x in xdata])
lsp = LeastSquareProblem(xdata, ydata, basis='1,x,x^3')
G = A.T @ A
b = A.T @ ydata
a = np.linalg.solve(G, b)
neq = mymat.MyMat(G) | (mymat.MyMat(b)).T
neq = neq.tolineq()
template = '法方程为\n\[{{normeq}}\]\n系数为{{coef}}, 拟合函数为${{function}}$.'
parameter = {'normeq': neq, 'coef': a, 'function': np.poly1d(a)}
lsp.solution = exam.Solution(template, parameter)
return lsp
def example():
A = mymat.MyMat('1,6,5;6,37,23;5,23,75')
p = CholeskyProblem(A)
template = '分解过程为${{process}$.\n\n答案为$L={{L}}$.'
cd = la.CholeskyDecompsition(A)
p.solution = exam.Solution(template, parameter={'L': 'L'}, solver=cd)
return p
def example():
matrix = mymat.MyMat('1,2;3,3')
p = ChasingProblem(matrix)
template = '分解过程为${{process}}$.'
cd = la.ChasingDecompsition(A)
p.solution = exam.Solution(template, parameter={}, solver=cd)
return p
def example3(m=3, n=4, lb=-4, ub=5):
A = mymat.MyMat.randint(m, n, lb, ub)
A[:, 1] = mymat.MyMat([[1], [0], [0]])
B = A.copy()
B.row_transform2(1, 2).row_transform3(2, 1, 2).row_transform3(3, 1, -1)
template = '${{matrixB}}$经初等变换${{transform}}$变成${{matrixA}}$.'
parameter = {'matrixA': A, 'transform': '?,?', 'matrixB': B}
return ElementaryTransformProblem(template, parameter)
def random():
matrix = mymat.MyMat.randint(3, 3, lb=-6, ub=6)
parameter = {'matrix': mymat.MyMat(matrix)}
pmp = PowerMethodProblem(parameter=parameter)
template = '计算过程如下:\n{{process}}\n矩阵${{matrix}}$的主特征值约为${{answer}}$.'
parameter = {'answer': 'l', 'matrix': 'A'}
pm = mymath.eigenvalue.PowerMethod(matrix)
pmp.solution = exam.Solution(template, parameter, solver=pm)
return pmp
def example():
matrix = np.array([[1, 1, 0.5], [1, 1, 0.25], [0.5, 0.25, 2]])
parameter = {'matrix': mymat.MyMat(matrix)}
pmp = PowerMethodProblem(parameter=parameter)
template = '计算过程如下:\n{{process}}\n矩阵${{matrix}}$的主特征值约为${{answer}}$.'
parameter = {'matrix': 'A', 'answer': ''}
pm = mymath.eigenvalue.PowerMethod(matrix)
pmp.solution = exam.Solution(template, parameter, solver=pm)
return pmp
def makeup(m=3, lb=-3, ub=3):
A = mymat.MyMat.randint(m, m, lb, ub)
L = A.tril()[:, :m]
U = A.itriu()
for k in range(m):
if L[k, k] == 0:
L[k, k] = np.random.randint(lb, ub)
A = mymat.MyMat((L * U).tolist(), dtype=np.float64)
return InverseMatrixProblem.fromMatrix(A)
def makeup(m=3, n=4, lb=-5, ub=5):
A = mymat.MyMat.randint(m, n, lb, ub)
L = A.tril()[:, :m]
U = A.itriu()
for k in range(m):
if L[k, k] == 0:
L[k, k] = np.random.randint(lb, ub)
A = mymat.MyMat((L * U).tolist(), dtype=np.float64).tofrac()
return GaussEliminationProblem.fromMatrix(A)
def makeup(m=3, n=3, lb=-5, ub=5):
A = mymat.MyMat.randint(m, n, lb, ub)
L = A.tril()[:, :m]
U = A.itriu()
for k in range(m):
if L[k, k] == 0:
L[k, k] = np.random.randint(lb, ub)
A = mymat.MyMat((L * U).tolist(), dtype=np.float64).tofrac()
b = mymat.MyMat.randint(3, 1, lb, ub).tofrac()
return LinearEquationProblem.fromEquation(mymat.LinearEquation(A, b))
def example():
A1 = mymat.MyMat.randint(1, 3, -5, 6)
A2 = mymat.MyMat.randint(2, 1, -5, 6)
A = mymat.MyMat(LA.block_diag(A1, A2))
B1 = mymat.MyMat.randint(3, 2, -5, 6)
B2 = mymat.MyMat.zeros(1, 2)
B = np.vstack((B1, B2))
template = '用分块矩阵的方法计算${{matrixA}}{{matrixB}}$. (用线条注明分块方案)'
parameter = {'matrixA': A.tofrac(), 'matrixB': B.tofrac()}
return MatrixMultiplicationProblem(template, parameter)
def example():
A = mymat.MyMat('1, 2, 3;2, 5, 8;3, 8, 14').tofrac()
p = LUDecompsitionProblem(A)
template = '分解过程为${{process}}$.\n\n答案为$L={{L}},U={{U}}$.'
lu = la.LUDecompsition(A)
p.solution = exam.Solution(template,
parameter={
'L': 'L',
'U': 'U'
},
solver=lu)
return p
def example():
A = mymat.MyMat('-1 & 2 & -1\\-2 & 2 & 2\\-2 & 5 & -3').tofrac()
return InverseMatrixProblem.fromMatrix(A)
def example():
A = mymat.MyMat([[3, -3, 3], [-3, 4, 0], [3, -4, -4]])
b = mymat.MyMat([1, -1, 1])
return LinearEquationProblem.fromEquation(mymat.LinearEquation(A, b))
def example():
A = mymat.MyMat(
'3, 0, -12, 3; -3, -4, 16, 17; -5, -4, 21, 30').tofrac()
return GaussEliminationProblem.fromMatrix(A)
