数値計算入門¶
よいプログラムを書くために注意すべきこと¶
プログラムにコメントを含める
意味のある変数名を使用する
適切なタイプの変数を使用する
定数を定義する
実行に時間がかかる場合は、プログラム全体の部分的な結果と更新を出力します
プログラムを明確にレイアウトする
プログラムを不必要に複雑にしない
最初に関数をインポートする
復習¶
基本的な変数と型¶
integers、float、bollean、complexなど
変数と型¶
通常の変数名は文字で始まる必要があります。慣例により、変数名は小文字で始まり、クラス名は大文字で始まります。
変数名には、英数字 a ～ z、A ～ Z、0 ～ 9、および _ などの一部の特殊文字を含めることができます。
変数名として使用できない Python キーワードがいくつかあります。$ and, as, assert, print……
Python の代入演算子は = です。Python は動的型付け言語であり、C/C++ とは異なり、変数の型を指定する必要はありません
[1]:
a = 1
c = True
d = 1+1.0j
b = 2.0
B = 1.0
print(b, B)
2.0 1.0
[2]:
print(a, type(a))
print(b, type(b))
print(c, type(c))
print(d, type(d))
1 <class 'int'>
2.0 <class 'float'>
True <class 'bool'>
(1+1j) <class 'complex'>
クイズ¶
複素変数の実部と虚部を見つける方法は？
[11]:
complex_number = 1+2.0j
complex_number
[11]:
(1+2j)
[12]:
print(complex_number.real)
print(complex_number.imag)
1.0
2.0
算術演算子と比較演算子¶
ほとんどの算術演算子と比較演算子を使用することができます。
算術演算子 +, -, *, /, // (整数除算), ’**’ 乗数
[5]:
x, y = 1, 2
print(x+y, x-y, x*y, x/y, x//y, y**x)
print(x>y, x==y, x<y)
3 -1 2 0.5 0 2
False False True
[6]:
x = 1
y = 2
x, y = 1, 2
[7]:
# 三角関数 sin, cos
from math import sin, cos, tan, asin
print(sin(x), cos(x))
0.8414709848078965 0.5403023058681398
[8]:
import math
[9]:
help(math)
Help on module math:
NAME
math
MODULE REFERENCE
https://docs.python.org/3.11/library/math.html
The following documentation is automatically generated from the Python
source files. It may be incomplete, incorrect or include features that
are considered implementation detail and may vary between Python
implementations. When in doubt, consult the module reference at the
location listed above.
DESCRIPTION
This module provides access to the mathematical functions
defined by the C standard.
FUNCTIONS
acos(x, /)
Return the arc cosine (measured in radians) of x.
The result is between 0 and pi.
acosh(x, /)
Return the inverse hyperbolic cosine of x.
asin(x, /)
Return the arc sine (measured in radians) of x.
The result is between -pi/2 and pi/2.
asinh(x, /)
Return the inverse hyperbolic sine of x.
atan(x, /)
Return the arc tangent (measured in radians) of x.
The result is between -pi/2 and pi/2.
atan2(y, x, /)
Return the arc tangent (measured in radians) of y/x.
Unlike atan(y/x), the signs of both x and y are considered.
atanh(x, /)
Return the inverse hyperbolic tangent of x.
cbrt(x, /)
Return the cube root of x.
ceil(x, /)
Return the ceiling of x as an Integral.
This is the smallest integer >= x.
comb(n, k, /)
Number of ways to choose k items from n items without repetition and without order.
Evaluates to n! / (k! * (n - k)!) when k <= n and evaluates
to zero when k > n.
Also called the binomial coefficient because it is equivalent
to the coefficient of k-th term in polynomial expansion of the
expression (1 + x)**n.
Raises TypeError if either of the arguments are not integers.
Raises ValueError if either of the arguments are negative.
copysign(x, y, /)
Return a float with the magnitude (absolute value) of x but the sign of y.
On platforms that support signed zeros, copysign(1.0, -0.0)
returns -1.0.
cos(x, /)
Return the cosine of x (measured in radians).
cosh(x, /)
Return the hyperbolic cosine of x.
degrees(x, /)
Convert angle x from radians to degrees.
dist(p, q, /)
Return the Euclidean distance between two points p and q.
The points should be specified as sequences (or iterables) of
coordinates. Both inputs must have the same dimension.
Roughly equivalent to:
sqrt(sum((px - qx) ** 2.0 for px, qx in zip(p, q)))
erf(x, /)
Error function at x.
erfc(x, /)
Complementary error function at x.
exp(x, /)
Return e raised to the power of x.
exp2(x, /)
Return 2 raised to the power of x.
expm1(x, /)
Return exp(x)-1.
This function avoids the loss of precision involved in the direct evaluation of exp(x)-1 for small x.
fabs(x, /)
Return the absolute value of the float x.
factorial(n, /)
Find n!.
Raise a ValueError if x is negative or non-integral.
floor(x, /)
Return the floor of x as an Integral.
This is the largest integer <= x.
fmod(x, y, /)
Return fmod(x, y), according to platform C.
x % y may differ.
frexp(x, /)
Return the mantissa and exponent of x, as pair (m, e).
m is a float and e is an int, such that x = m * 2.**e.
If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.
fsum(seq, /)
Return an accurate floating point sum of values in the iterable seq.
Assumes IEEE-754 floating point arithmetic.
gamma(x, /)
Gamma function at x.
gcd(*integers)
Greatest Common Divisor.
hypot(...)
hypot(*coordinates) -> value
Multidimensional Euclidean distance from the origin to a point.
Roughly equivalent to:
sqrt(sum(x**2 for x in coordinates))
For a two dimensional point (x, y), gives the hypotenuse
using the Pythagorean theorem: sqrt(x*x + y*y).
For example, the hypotenuse of a 3/4/5 right triangle is:
>>> hypot(3.0, 4.0)
5.0
isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)
Determine whether two floating point numbers are close in value.
rel_tol
maximum difference for being considered "close", relative to the
magnitude of the input values
abs_tol
maximum difference for being considered "close", regardless of the
magnitude of the input values
Return True if a is close in value to b, and False otherwise.
For the values to be considered close, the difference between them
must be smaller than at least one of the tolerances.
-inf, inf and NaN behave similarly to the IEEE 754 Standard. That
is, NaN is not close to anything, even itself. inf and -inf are
only close to themselves.
isfinite(x, /)
Return True if x is neither an infinity nor a NaN, and False otherwise.
isinf(x, /)
Return True if x is a positive or negative infinity, and False otherwise.
isnan(x, /)
Return True if x is a NaN (not a number), and False otherwise.
isqrt(n, /)
Return the integer part of the square root of the input.
lcm(*integers)
Least Common Multiple.
ldexp(x, i, /)
Return x * (2**i).
This is essentially the inverse of frexp().
lgamma(x, /)
Natural logarithm of absolute value of Gamma function at x.
log(...)
log(x, [base=math.e])
Return the logarithm of x to the given base.
If the base not specified, returns the natural logarithm (base e) of x.
log10(x, /)
Return the base 10 logarithm of x.
log1p(x, /)
Return the natural logarithm of 1+x (base e).
The result is computed in a way which is accurate for x near zero.
log2(x, /)
Return the base 2 logarithm of x.
modf(x, /)
Return the fractional and integer parts of x.
Both results carry the sign of x and are floats.
nextafter(x, y, /)
Return the next floating-point value after x towards y.
perm(n, k=None, /)
Number of ways to choose k items from n items without repetition and with order.
Evaluates to n! / (n - k)! when k <= n and evaluates
to zero when k > n.
If k is not specified or is None, then k defaults to n
and the function returns n!.
Raises TypeError if either of the arguments are not integers.
Raises ValueError if either of the arguments are negative.
pow(x, y, /)
Return x**y (x to the power of y).
prod(iterable, /, *, start=1)
Calculate the product of all the elements in the input iterable.
The default start value for the product is 1.
When the iterable is empty, return the start value. This function is
intended specifically for use with numeric values and may reject
non-numeric types.
radians(x, /)
Convert angle x from degrees to radians.
remainder(x, y, /)
Difference between x and the closest integer multiple of y.
Return x - n*y where n*y is the closest integer multiple of y.
In the case where x is exactly halfway between two multiples of
y, the nearest even value of n is used. The result is always exact.
sin(x, /)
Return the sine of x (measured in radians).
sinh(x, /)
Return the hyperbolic sine of x.
sqrt(x, /)
Return the square root of x.
tan(x, /)
Return the tangent of x (measured in radians).
tanh(x, /)
Return the hyperbolic tangent of x.
trunc(x, /)
Truncates the Real x to the nearest Integral toward 0.
Uses the __trunc__ magic method.
ulp(x, /)
Return the value of the least significant bit of the float x.
DATA
e = 2.718281828459045
inf = inf
nan = nan
pi = 3.141592653589793
tau = 6.283185307179586
FILE
/Users/iikubo/miniconda3/lib/python3.11/lib-dynload/math.cpython-311-darwin.so
文字列¶
[11]:
Strings = "Welcome to 融合基礎情報学I"
print(Strings, type(Strings))
Welcome to 融合基礎情報学I <class 'str'>
[10]:
# 文字列計算もできます
str1 = 'welcome to'
str2 = ' 融合基礎情報学I'
print(str1+str2)
welcome to 融合基礎情報学I
リスト¶
[12]:
Lists = ['Welcome to 融合基礎情報学']
print(Lists, type(Lists))
['Welcome to 融合基礎情報学'] <class 'list'>
forループ¶
Pythonでは、リストなどの反復可能なオブジェクトと一緒にfor ループが使用されます。
基本的な構文は次のとおりです。
[13]:
for x in [1,2,3]:
print(x)
print(x**2)
print('complete')
1
1
complete
2
4
complete
3
9
complete
条件分岐¶
if文を使って条件により処理を分岐させます。基本的な構文は次のとおりです。
[14]:
x=3
y=3
if (x>=y):
print("true")
else:
print("false")
true
whileループ¶
while文を使って処理を繰り返し行わせることができます。基本的な構文は次のとおりです。
[15]:
i = 0
while True:
print("cycle-----------: ", i, 'nm')
#i = i + 1 works
#i++ not work
i+=1
if i == 10:
break
cycle-----------: 0 nm
cycle-----------: 1 nm
cycle-----------: 2 nm
cycle-----------: 3 nm
cycle-----------: 4 nm
cycle-----------: 5 nm
cycle-----------: 6 nm
cycle-----------: 7 nm
cycle-----------: 8 nm
cycle-----------: 9 nm