Dim aa As Double, bb As Double '分别接收findway有根区间两端值的变量
Dim x(1) As Double '分别接收ercigenway的根
'1.0 ercigenway 求二次方程实根 -已测试
Private Sub ercigenway(a As Single, b As Single, c As Single) 'a、b、c对应为二次方程的系数
Dim d As Double
d = b ^ 2 - 4 * a * c
If d < 0 Then
MsgBox "Δ小于0，没有实根", , "消息"
x(0) = 0: x(1) = 0
ElseIf d = 0 Then
x(0) = -b / (2 * a): x(1) = x(0)
Else
x(0) = (-b - Sgn(b) * Sqr(d)) / (2 * a): x(1) = c / (a * x(0))
End If
End Sub
'2.1 findway 等步长扫描有根区间 -已测试
Private Sub findway(ByVal a As Single, ByVal b As Single, h As Double) 'a、b分别为待扫描区间端点，h为步长
Dim a1 As Double
a1 = a
Do
If f(a1) * f(a1 + h) <= 0 Then
aa = a1: bb = a1 + h
Exit Sub
End If
a1 = a1 + h
Loop While a1 < b
If a1 > b Then
MsgBox "没有找到有根区间，请换更小的步长试一下"
Exit Sub
End If
End Sub
'2.2 erfenfun 二分法求根 -已测试
Private Function erfenfun(ByVal a As Single, ByVal b As Single, eps As Double) 'a、b为有根区间端点，eps为误差
Dim x0 As Double, x1 As Double, x2 As Double, f0 As Double, f1 As Double, f2 As Double
x1 = a: x2 = b
Do
x0 = (x1 + x2) / 2
f0 = f(x0)
If f0 = 0 Then
Exit Do
Else
f1 = f(x1): f2 = f(x2)
If f0 * f1 < 0 Then
x2 = x0
Else
x1 = x0
End If
End If
Loop While Abs(x1 - x2) > eps
x0 = (x1 + x2) / 2
erfenfun = x0
End Function
'2.4 newtonfxfun Newton切线法 -已测试
Private Function newtonfxfun(ByVal x0 As Double, eps As Double) As Double 'x0为附近根，eps为误差
Dim x1 As Double, f0 As Double, f1 As Double
x1 = x0
Do
x0 = x1
f0 = f(x0): f1 = fd(x0) 'fd表示f的导函数
If Abs(f1) < eps Then
x1 = x0: Exit Do
End If
x1 = x0 - f0 / f1
Loop Until Abs(x1 - x0) < eps
newtonfxfun = x1
End Function
'2.3 stediedaifun Seffensen加速迭代法 (方程形式为x-f(x)=0) -已测试
Private Function stediedaifun(ByVal x0 As Double, eps1 As Double, eps2 As Double) As Double 'x0为解析解附近的根，eps1为输出结果误差，eps2为迭代能否继续判断标准
Dim y As Double, z As Double, x1 As Double
x1 = x0
Do
x0 = x1
y = f(x0): z = f(y)
If Abs(z - 2 * y + x0) < eps2 Then
MsgBox "为满足eps2条件，不能继续迭代"
Exit Function
End If
x1 = x0 - (y - x0) ^ 2 / (z - 2 * y + x0)
Loop Until Abs(x1 - x0) < eps1
stediedaifun = x1
End Function
'2.5 newtonfxnfun n次代数方程Newton切线法 -已测试
Private Function newtonfxnfun(a() As Single, eps As Double, x0 As Double) As Double 'a()分别存储按降幂排列的方程的n个系数，eps为误差，x0为附近根
Dim k As Integer, n As Integer, f0 As Double, f1 As Double, x1 As Double
n = UBound(a)
x1 = x0
Do
x0 = x1
f0 = a(0): f1 = f0
For k = 1 To n - 1
f0 = a(k) + f0 * x0
f1 = f0 + f1 * x0
Next k
f0 = a(n) + f0 * x0
x1 = x0 - f0 / f1
Loop Until Abs(x1 - x0) < eps
newtonfxnfun = x1
End Function
'2.6 linecutfun 弦截法 -已测试
Private Function linecutfun(ByVal x0 As Double, ByVal x1 As Double, eps As Double, n As Long) As Double 'n为迭代次数限制，x0、x1为有根区间端点，eps为误差
Dim f0 As Double, f1 As Double, f2 As Double
Dim x2 As Double, i As Long
f0 = f(x0): f1 = f(x1)
For i = 1 To n
x2 = x1 - (x1 - x0) * f1 / (f1 - f0)
f2 = f(x2)
If Abs(f2) < eps Then
Exit For
End If
x0 = x1: x1 = x2: f0 = f1: f1 = f2
Next i
If i = n + 1 Then
MsgBox "要求的计算次数太低，没有达到精度要求"
End If
linecutfun = x2
End Function
'4.1 lagrangeczfun 拉格朗日插值法 -已测试
Private Function lagrangeczfun(a() As Double, ByVal u As Double) As Double 'a(1,n)存储n+1个节点，u为插值点
Dim i As Integer, j As Integer, n As Integer
Dim l As Double, v As Double
v = 0
n = UBound(a, 2)
For j = 0 To n
l = 1#
For i = 0 To n
If i = j Then GoTo hulue
l = l * (u - a(0, i)) / (a(0, j) - a(0, i))
hulue:
Next i
v = v + l * a(1, j)
Next j
lagrangeczfun = v
End Function
'4.2 newtonczfun newton插值法 -已测试
Private Function newtonczfun(a() As Double, u As Double) As Double 'a(1,n)存储n+1个节点，u为插值点
Dim n As Integer, i As Integer, j As Integer, k As Integer
Dim z() As Double, f() As Double, v As Double
n = UBound(a, 2)
ReDim z(n), f(n)
For i = 0 To n
z(i) = a(1, i)
Next i
For i = 1 To n
k = k + 1
For j = i To n
f(j) = (z(j) - z(j - 1)) / (a(0, j) - a(0, j - k))
Next j
For j = i To n
z(j) = f(j)
Next j
Next i
f(0) = a(1, 0)
v = 0
For i = n To 0 Step -1
v = v * (u - a(0, i)) + f(i)
Next i
newtonczfun = v
End Function
'4.3 hermiteczfun Hermite插值法 -已测试
Private Function hermiteczfun(a() As Double, fd() As Double, u As Double) As Double 'a(1,n)存储n+1个节点，fd(n)存储n+1个节点处导数值，u为插值点
Dim l() As Double, ld() As Double, g() As Double, h() As Double, aim As Double
Dim n As Integer, i As Integer, j As Integer
n = UBound(a)
ReDim l(n), ld(n), g(n), h(n)
aim = 0
For i = 0 To n
l(i) = 1: ld(i) = 0
For j = 0 To n
If j = i Then GoTo hulue
l(i) = l(i) * (u - a(0, j)) / (a(0, i) - a(0, j))
ld(i) = ld(i) + 1 / (a(0, i) - a(0, j))
hulue:
Next j
g(i) = (1 + 2 * (a(0, i) - u) * ld(i)) * l(i) * l(i)
h(i) = (u - a(0, i)) * l(i) * l(i)
aim = aim + g(i) * a(1, i) + h(i) * fd(i)
Next i
hermiteczfun = aim
End Function
'5.2.1 tixingjffun 变步长梯形积分法 -已测试
Private Function tixingjffun(a As Single, b As Single, eps As Double, m As Long) As Double 'a、b分别为积分上下限，eps为误差，m为最大计算次数
Dim h As Double, t1 As Double, t2 As Double, t As Double, hh As Double
Dim n As Long: n = 1
h = b - a: t1 = h * (f(a) + f(b)) / 2
Do
t = 0
For i = 1 To n
t = t + f(a + (i - 0.5) * h)
Next i
hh = h * t
t2 = (t1 + hh) / 2
If Abs(t2 - t1) < eps Then Exit Do
t1 = t2: h = h / 2: n = 2 * n
Loop Until n > 2 * m
If n > 2 * m Then
MsgBox "计算次数预定太小，不能达到误差要求"
End If
tixingjffun = t2
End Function
'5.2.2 simpsonjffun 变步长Simpson积分法 -已测试
Private Function simpsonjffun(a As Single, b As Single, eps As Double, m As Long) As Double 'a、b分别为积分上下限，eps为误差，m为最大计算次数
Dim n As Long, i As Long
Dim h As Double, t1 As Double, t2 As Double, hh As Double, s1 As Double, s2 As Double
n = 1: h = b - a: t1 = h * (f(a) + f(b)) / 2
hh = h * (f((a + b) / 2)): s1 = (t1 + 2 * hh) / 3
Do
n = 2 * n: h = h / 2: t2 = (t1 + hh) / 2
t = 0
For i = 1 To n
t = t + f(a + (i - 0.5) * h)
Next i
hh = t * h
s2 = (t1 + 2 * hh) / 3
If Abs(s2 - s1) < eps Then Exit Do
t1 = t2: s1 = s2
Loop Until n > m
If n > m Then MsgBox "计算次数预定太小，不能达到误差要求"
simpsonjffun = s2
End Function
'5.3 Rombergjffun Romberg积分法
Private Function rombergjffun(a As Single, b As Single, eps As Double) As Double
Dim k As Integer, n As Integer, h As Double
k = 0: n = 1: h = b - a
End Function
'5.5.1 ds1fun 求一阶导数 -已测试
Private Function ds1fun(x0 As Single, eps As Double) As Double 'x0为求导点，eps为误差
Dim h As Double, t1 As Double, t2 As Double
h = 1: t1 = (f(x0 + h) - f(x0 - h)) / (2 * h)
h = h / 2: t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)
Do While Abs(t2 - t1) > eps
t1 = t2
h = h / 2
t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)
Loop
ds1fun = t2
End Function
'5.5.2 ds2fun 求二阶导数 -已测试
Private Function ds2fun(x0 As Single, eps As Double) As Double 'x0为求导点，eps为误差
Dim h As Double, t1 As Double, t2 As Double
h = 1: t1 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)
h = h / 2: t2 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)
Do While Abs(t2 - t1) > eps
t1 = t2
h = h / 2
t2 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)
Loop
ds2fun = t2
End Function
Dim x(1) As Double '分别接收ercigenway的根
'1.0 ercigenway 求二次方程实根 -已测试
Private Sub ercigenway(a As Single, b As Single, c As Single) 'a、b、c对应为二次方程的系数
Dim d As Double
d = b ^ 2 - 4 * a * c
If d < 0 Then
MsgBox "Δ小于0，没有实根", , "消息"
x(0) = 0: x(1) = 0
ElseIf d = 0 Then
x(0) = -b / (2 * a): x(1) = x(0)
Else
x(0) = (-b - Sgn(b) * Sqr(d)) / (2 * a): x(1) = c / (a * x(0))
End If
End Sub
'2.1 findway 等步长扫描有根区间 -已测试
Private Sub findway(ByVal a As Single, ByVal b As Single, h As Double) 'a、b分别为待扫描区间端点，h为步长
Dim a1 As Double
a1 = a
Do
If f(a1) * f(a1 + h) <= 0 Then
aa = a1: bb = a1 + h
Exit Sub
End If
a1 = a1 + h
Loop While a1 < b
If a1 > b Then
MsgBox "没有找到有根区间，请换更小的步长试一下"
Exit Sub
End If
End Sub
'2.2 erfenfun 二分法求根 -已测试
Private Function erfenfun(ByVal a As Single, ByVal b As Single, eps As Double) 'a、b为有根区间端点，eps为误差
Dim x0 As Double, x1 As Double, x2 As Double, f0 As Double, f1 As Double, f2 As Double
x1 = a: x2 = b
Do
x0 = (x1 + x2) / 2
f0 = f(x0)
If f0 = 0 Then
Exit Do
Else
f1 = f(x1): f2 = f(x2)
If f0 * f1 < 0 Then
x2 = x0
Else
x1 = x0
End If
End If
Loop While Abs(x1 - x2) > eps
x0 = (x1 + x2) / 2
erfenfun = x0
End Function
'2.4 newtonfxfun Newton切线法 -已测试
Private Function newtonfxfun(ByVal x0 As Double, eps As Double) As Double 'x0为附近根，eps为误差
Dim x1 As Double, f0 As Double, f1 As Double
x1 = x0
Do
x0 = x1
f0 = f(x0): f1 = fd(x0) 'fd表示f的导函数
If Abs(f1) < eps Then
x1 = x0: Exit Do
End If
x1 = x0 - f0 / f1
Loop Until Abs(x1 - x0) < eps
newtonfxfun = x1
End Function
'2.3 stediedaifun Seffensen加速迭代法 (方程形式为x-f(x)=0) -已测试
Private Function stediedaifun(ByVal x0 As Double, eps1 As Double, eps2 As Double) As Double 'x0为解析解附近的根，eps1为输出结果误差，eps2为迭代能否继续判断标准
Dim y As Double, z As Double, x1 As Double
x1 = x0
Do
x0 = x1
y = f(x0): z = f(y)
If Abs(z - 2 * y + x0) < eps2 Then
MsgBox "为满足eps2条件，不能继续迭代"
Exit Function
End If
x1 = x0 - (y - x0) ^ 2 / (z - 2 * y + x0)
Loop Until Abs(x1 - x0) < eps1
stediedaifun = x1
End Function
'2.5 newtonfxnfun n次代数方程Newton切线法 -已测试
Private Function newtonfxnfun(a() As Single, eps As Double, x0 As Double) As Double 'a()分别存储按降幂排列的方程的n个系数，eps为误差，x0为附近根
Dim k As Integer, n As Integer, f0 As Double, f1 As Double, x1 As Double
n = UBound(a)
x1 = x0
Do
x0 = x1
f0 = a(0): f1 = f0
For k = 1 To n - 1
f0 = a(k) + f0 * x0
f1 = f0 + f1 * x0
Next k
f0 = a(n) + f0 * x0
x1 = x0 - f0 / f1
Loop Until Abs(x1 - x0) < eps
newtonfxnfun = x1
End Function
'2.6 linecutfun 弦截法 -已测试
Private Function linecutfun(ByVal x0 As Double, ByVal x1 As Double, eps As Double, n As Long) As Double 'n为迭代次数限制，x0、x1为有根区间端点，eps为误差
Dim f0 As Double, f1 As Double, f2 As Double
Dim x2 As Double, i As Long
f0 = f(x0): f1 = f(x1)
For i = 1 To n
x2 = x1 - (x1 - x0) * f1 / (f1 - f0)
f2 = f(x2)
If Abs(f2) < eps Then
Exit For
End If
x0 = x1: x1 = x2: f0 = f1: f1 = f2
Next i
If i = n + 1 Then
MsgBox "要求的计算次数太低，没有达到精度要求"
End If
linecutfun = x2
End Function
'4.1 lagrangeczfun 拉格朗日插值法 -已测试
Private Function lagrangeczfun(a() As Double, ByVal u As Double) As Double 'a(1,n)存储n+1个节点，u为插值点
Dim i As Integer, j As Integer, n As Integer
Dim l As Double, v As Double
v = 0
n = UBound(a, 2)
For j = 0 To n
l = 1#
For i = 0 To n
If i = j Then GoTo hulue
l = l * (u - a(0, i)) / (a(0, j) - a(0, i))
hulue:
Next i
v = v + l * a(1, j)
Next j
lagrangeczfun = v
End Function
'4.2 newtonczfun newton插值法 -已测试
Private Function newtonczfun(a() As Double, u As Double) As Double 'a(1,n)存储n+1个节点，u为插值点
Dim n As Integer, i As Integer, j As Integer, k As Integer
Dim z() As Double, f() As Double, v As Double
n = UBound(a, 2)
ReDim z(n), f(n)
For i = 0 To n
z(i) = a(1, i)
Next i
For i = 1 To n
k = k + 1
For j = i To n
f(j) = (z(j) - z(j - 1)) / (a(0, j) - a(0, j - k))
Next j
For j = i To n
z(j) = f(j)
Next j
Next i
f(0) = a(1, 0)
v = 0
For i = n To 0 Step -1
v = v * (u - a(0, i)) + f(i)
Next i
newtonczfun = v
End Function
'4.3 hermiteczfun Hermite插值法 -已测试
Private Function hermiteczfun(a() As Double, fd() As Double, u As Double) As Double 'a(1,n)存储n+1个节点，fd(n)存储n+1个节点处导数值，u为插值点
Dim l() As Double, ld() As Double, g() As Double, h() As Double, aim As Double
Dim n As Integer, i As Integer, j As Integer
n = UBound(a)
ReDim l(n), ld(n), g(n), h(n)
aim = 0
For i = 0 To n
l(i) = 1: ld(i) = 0
For j = 0 To n
If j = i Then GoTo hulue
l(i) = l(i) * (u - a(0, j)) / (a(0, i) - a(0, j))
ld(i) = ld(i) + 1 / (a(0, i) - a(0, j))
hulue:
Next j
g(i) = (1 + 2 * (a(0, i) - u) * ld(i)) * l(i) * l(i)
h(i) = (u - a(0, i)) * l(i) * l(i)
aim = aim + g(i) * a(1, i) + h(i) * fd(i)
Next i
hermiteczfun = aim
End Function
'5.2.1 tixingjffun 变步长梯形积分法 -已测试
Private Function tixingjffun(a As Single, b As Single, eps As Double, m As Long) As Double 'a、b分别为积分上下限，eps为误差，m为最大计算次数
Dim h As Double, t1 As Double, t2 As Double, t As Double, hh As Double
Dim n As Long: n = 1
h = b - a: t1 = h * (f(a) + f(b)) / 2
Do
t = 0
For i = 1 To n
t = t + f(a + (i - 0.5) * h)
Next i
hh = h * t
t2 = (t1 + hh) / 2
If Abs(t2 - t1) < eps Then Exit Do
t1 = t2: h = h / 2: n = 2 * n
Loop Until n > 2 * m
If n > 2 * m Then
MsgBox "计算次数预定太小，不能达到误差要求"
End If
tixingjffun = t2
End Function
'5.2.2 simpsonjffun 变步长Simpson积分法 -已测试
Private Function simpsonjffun(a As Single, b As Single, eps As Double, m As Long) As Double 'a、b分别为积分上下限，eps为误差，m为最大计算次数
Dim n As Long, i As Long
Dim h As Double, t1 As Double, t2 As Double, hh As Double, s1 As Double, s2 As Double
n = 1: h = b - a: t1 = h * (f(a) + f(b)) / 2
hh = h * (f((a + b) / 2)): s1 = (t1 + 2 * hh) / 3
Do
n = 2 * n: h = h / 2: t2 = (t1 + hh) / 2
t = 0
For i = 1 To n
t = t + f(a + (i - 0.5) * h)
Next i
hh = t * h
s2 = (t1 + 2 * hh) / 3
If Abs(s2 - s1) < eps Then Exit Do
t1 = t2: s1 = s2
Loop Until n > m
If n > m Then MsgBox "计算次数预定太小，不能达到误差要求"
simpsonjffun = s2
End Function
'5.3 Rombergjffun Romberg积分法
Private Function rombergjffun(a As Single, b As Single, eps As Double) As Double
Dim k As Integer, n As Integer, h As Double
k = 0: n = 1: h = b - a
End Function
'5.5.1 ds1fun 求一阶导数 -已测试
Private Function ds1fun(x0 As Single, eps As Double) As Double 'x0为求导点，eps为误差
Dim h As Double, t1 As Double, t2 As Double
h = 1: t1 = (f(x0 + h) - f(x0 - h)) / (2 * h)
h = h / 2: t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)
Do While Abs(t2 - t1) > eps
t1 = t2
h = h / 2
t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)
Loop
ds1fun = t2
End Function
'5.5.2 ds2fun 求二阶导数 -已测试
Private Function ds2fun(x0 As Single, eps As Double) As Double 'x0为求导点，eps为误差
Dim h As Double, t1 As Double, t2 As Double
h = 1: t1 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)
h = h / 2: t2 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)
Do While Abs(t2 - t1) > eps
t1 = t2
h = h / 2
t2 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)
Loop
ds2fun = t2
End Function
