找到矩陣單位根的（部分）串列

我正在尋找一種方法來構建 1 和 -1 的矩陣平方根串列。只對 2 到 4 維感興趣，我什至不需要一套完整的，只需要一個實用的可用的（意味著我可以在某個時候停止回圈）。這是我（非常）低效的解決方案

def racines(n, dim, field='real'):
    if field == 'real':
        unites = [1, 0, -1]
    elif field == 'complex':
        unites = [1, 0, -1, 1j, -1j]
    if dim == 2:
        liste = [np.array([[a,b], [c,d]]) for a in unites
                 for b in unites for c in unites 
                 for d in unites]
    elif dim == 3:
        liste = [np.array([[a, b, c], [d, e, f], [g, h, i]])
                 for a in unites for b in unites for c in unites 
                 for d in unites for e in unites for f in unites
                 for g in unites for h in unites for i in unites]
    elif dim == 4:
        liste = [np.array([[a,b,c,d], [e,f,g,h], [i,j,k,l], [m,o,p,q]])
                 for a in unites for b in unites for c in unites for d in unites
                 for e in unites for f in unites for g in unites for h in unites
                 for i in unites for j in unites for k in unites for l in unites
                 for m in unites for o in unites for p in unites for q in unites]
    liste = [m for m in liste if np.linalg.det(m) != 0]
    liste = [m for m in liste if np.array_equal(np.matmul(m, m), np.identity(dim, dtype='int')*n)]
return(liste)

運行良好，直到 4d，當然它變得太多處理......如何讓它更快？

uj5u.com熱心網友回復：

你可以遞回地做。例如，如果我想要 0 到 4 之間的 n 個數字的串列，您可以使用

def get_lists(size, max_it, accumulator = [], lists = []):
    if size ==0:
        lists.append(accumulator)
    else:
        for i in range(5):
            if len(lists) == max_it:
                break
            l = accumulator.copy()
            l.append(i)
            get_lists(size-1,max_it, l, lists)

            
def lists(size,max_it=-1):
    l = []  
    get_lists(size,max_it, [], l)
    return l        
print(lists(3,10))

使用 max_it 您想要的不同串列的數量（如果您想要所有串列，則設定為 -1）

uj5u.com熱心網友回復：

對于那些需要它的人，這就是訣竅。仍然不漂亮，但它在 4d 中的運行速度要快得多

def racines(n, dim, field='real'):
    unites = [1, 0, -1]
    if field == 'complex':
        unites  = [1j, -1j]
    elif field != 'real':
        print('Unknown field !')
        return([])
    if dim == 2:
        liste = [np.array([[a,b], [c,d]]) for a in unites
                 for b in unites for c in unites 
                 for d in unites]
    elif dim == 3:
        liste = [np.array([[a, b, c], [d, e, f], [g, h, i]])
                 for a in unites for b in unites for c in unites 
                 for d in unites for e in unites for f in unites
                 for g in unites for h in unites for i in unites]
    elif dim == 4:
        roots_2d = racines(n, 2, field=field)
        neg_roots_2d = racines(-n, 2, field=field)
        other = [np.identity(2, dtype='int'), np.identity(2, dtype='int')*-1, np.zeros([2,2], dtype='int')]
        unites = roots_2d   neg_roots_2d   other
        liste = [np.hstack([np.vstack([a,b]), np.vstack([c,d])])
                 for a in unites for b in unites for c in unites for d in unites]
    else:
        print('No can do !')
        return([])
    liste = [m for m in liste if np.linalg.det(m) != 0]
    liste = [m for m in liste if np.array_equal(np.matmul(m, m), np.identity(dim, dtype='int')*n)]
    return(liste)
# res = racines(1, 4, field='real') # 2.43s
# res = racines(1, 4, field='complex') # 2min 18s

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