【序列比对】Needleman-Wunsch（全局）和Smith-Waterman（局部）算法py实现（多条回溯路径，三叉树思路，超详细注释）
Needleman-Wunsch和Smith-Waterman算法py实现（多条回溯路径）
话不多说，直接上结果图，多条回溯路径。
原理
代码详解（以NW为例）
导入包以及参数设置
import numpy as np
sequence_1 = "AACGTACTCAAGTCT"
sequence_2 = "TCGTACTCTAACGAT"
match = 9
mismatch = -6
gap = -2
创建得分矩阵
- 创建得分矩阵，行数为第一条序列长度加一，列数为第二条序列长度加二
- 创建是否匹配的矩阵，这个矩阵的长宽就分别是两条序列的长度了。如果匹配了，对应的格子就是匹配的得分，反之就是不匹配的得分
- 动态规划的思想算每个格子的得分，每个格子需要考虑其左、上、左上的值，也可以说是考虑序列一、序列二引入空缺或直接匹配的最大值
# 创建得分矩阵，行数为第一条序列长度加一，列数为第二条序列长度加二
Score = np.zeros((len(sequence_1) + 1, len(sequence_2) + 1))
# 创建是否匹配的矩阵，这个矩阵的长宽就分别是两条序列的长度了。如果匹配了，对应的格子就是匹配的得分，反之就是不匹配的得分
Match_or_not = np.zeros((len(sequence_1), len(sequence_2)))
for i in range(len(sequence_1)):
for j in range(len(sequence_2)):
if sequence_1[i] == sequence_2[j]:
Match_or_not[i][j] = match
else:
Match_or_not[i][j] = mismatch
# 填得分矩阵
# 第一步：初始化第一行和第一列
for i in range(len(sequence_1) + 1):
Score[i][0] = i * gap
for j in range(len(sequence_2) + 1):
Score[0][j] = j * gap
# 第二步：动态规划的思想算每个格子的得分，每个格子需要考虑其左、上、左上的值，也可以说是考虑序列一、序列二引入空缺或直接匹配的最大值
for i in range(1, len(sequence_1) + 1):
for j in range(1, len(sequence_2) + 1):
Score[i][j] = max(Score[i - 1][j - 1] + Match_or_not[i - 1][j - 1],
Score[i - 1][j] + gap,
Score[i][j - 1] + gap)
看看得分矩阵长啥样吧
回溯
我们需要考虑的是可能会有多条回溯路径。全局比对的回溯是从右下角开始，左上角结束，其中可能会有分叉点。我们可以把右下角看成是一个树的根，矩阵中的每个值看成是一个节点。每个节点都可能会有三个子节点：左，上，对角线。分别对应了回溯的方向。而整个回溯的过程也就是遍历这颗三叉树的过程，严谨的说是从根节点遍历每个叶子节点的过程。
# 开始回溯
'''
我们需要考虑的是可能会有多条回溯路径。
全局比对的回溯是从右下角开始，左上角结束，其中可能会有分叉点。
我们可以把右下角看成是一个树的根，矩阵中的每个值看成是一个节点。
每个节点都可能会有三个子节点：左，上，对角线。分别对应了回溯的方向。
而整个回溯的过程也就是遍历这颗三叉树的过程，严谨的说是从根节点遍历每个叶子节点的过程。
'''
class Node:
# 用类来建立三叉树节点，属性包括了行、列、得分、左子树、上子树、对角线子树
def __init__(self, row=None, col=None, score=None):
self.row = row
self.col = col
self.score = score
self.left = None
self.up = None
self.diag = None
def isLeaf(self):
# 判断是否是叶子节点
return self.left is None and self.up is None and self.diag is None
# 递归的函数查找从根节点到每个叶节点的路径
# 回溯路径的个数、回溯路径中的行号和列号
traceback_pathway_number = 0
traceback_pathway_row = [[]]
traceback_pathway_col = [[]]
def SaveRootToLeafPaths(Node, path_row, path_col):
# 如果没有子树了
if Node is None:
return
# 包含当前节点的路径
path_row.append(Node.row)
path_col.append(Node.col)
global traceback_pathway_number
global traceback_pathway_row
global traceback_pathway_col
# 如果找到叶节点，保存路径
if isLeaf(Node):
if traceback_pathway_number == 0:
traceback_pathway_row[traceback_pathway_number] = list(path_row)
traceback_pathway_col[traceback_pathway_number] = list(path_col)
else:
traceback_pathway_row += [list(path_row)]
traceback_pathway_col += [list(path_col)]
traceback_pathway_number += 1
# 递归左、上、对角子树
SaveRootToLeafPaths(Node.left, path_row, path_col)
SaveRootToLeafPaths(Node.up, path_row, path_col)
SaveRootToLeafPaths(Node.diag, path_row, path_col)
# 回溯，出栈
path_row.pop()
path_col.pop()
# 建立三叉树，为 Score 矩阵里所有值都找到它的左、上、对角子树，用一个二位列表来存储节点
NodeTree = [[Node() for _ in range(len(sequence_2) + 1)] for _ in range(len(sequence_1) + 1)]
# 先把节点们的行号列号和得分记录下来
for i in range(len(sequence_1) + 1):
for j in range(len(sequence_2) + 1):
NodeTree[i][j].row = i
NodeTree[i][j].col = j
NodeTree[i][j].score = Score[i][j]
# 设置第一列和第一行的节点的上子树和左子树（其实也能在下面这个大循环里设置，但是这样可读性更高）
for i in range(1, len(sequence_1) + 1):
NodeTree[i][0].up = NodeTree[i - 1][0]
for j in range(1, len(sequence_2) + 1):
NodeTree[0][j].left = NodeTree[0][j - 1]
# 设置剩下的节点
for i in range(1, len(sequence_1) + 1):
for j in range(1, len(sequence_2) + 1):
if (Score[i][j] == Score[i - 1][j - 1] + Match_or_not[i - 1][j - 1]):
NodeTree[i][j].diag = NodeTree[i - 1][j - 1]
if (Score[i][j] == Score[i - 1][j] + gap):
NodeTree[i][j].up = NodeTree[i - 1][j]
if (Score[i][j] == Score[i][j - 1] + gap):
NodeTree[i][j].left = NodeTree[i][j - 1]
# 遍历树并保存路径
SaveRootToLeafPaths(NodeTree[len(sequence_1)][len(sequence_2)], [], [])
# 改成numpy的ndarray类型，更加方便！
traceback_pathway_row = np.array(traceback_pathway_row)
traceback_pathway_col = np.array(traceback_pathway_col)
# 记录一下回溯时走不走左边或上边，如果走就记为1，不走就记为0
Go_left = traceback_pathway_col[:, range(traceback_pathway_col.shape[1] - 1)] - traceback_pathway_col[:, range(1,
traceback_pathway_col.shape[
1])]
Go_up = traceback_pathway_row[:, range(traceback_pathway_row.shape[1] - 1)] - traceback_pathway_row[:,
range(1, traceback_pathway_row.shape[1])]
# 用列表来存储序列一和序列二比对后的结果
seq1_align_set = []
seq2_align_set = []
print("总共有{}个比对结果".format(traceback_pathway_number))
for tpn in range(traceback_pathway_number):
'''
下面其实就是经典的nw回溯的代码了，这部分的原理可以参考nw算法回溯的伪代码。
唯一不同的就是我们是多条回溯路径，所以有多少条路经就得循环多少次。
值得一提的是，回溯过去的序列是逆序的，
在python中字符串逆置十分方便，只需要合理利用切片，如：str[::-1]即可。
'''
seq1_align = ''
seq2_align = ''
i = len(sequence_1)
j = len(sequence_2)
k = 0
while i > 0 or j > 0:
if i > 0 and j > 0 and Go_left[tpn][k] and Go_up[tpn][k]:
seq1_align += sequence_1[i - 1]
seq2_align += sequence_2[j - 1]
i -= 1
j -= 1
elif i > 0 and not (Go_left[tpn][k]) and Go_up[tpn][k]:
seq1_align += sequence_1[i - 1]
seq2_align += '-'
i -= 1
elif j > 0 and Go_left[tpn][k] and not (Go_up[tpn][k]):
seq1_align += '-'
seq2_align += sequence_2[j - 1]
j -= 1
k += 1
seq1_align_set += [seq1_align[::-1]]
seq2_align_set += [seq2_align[::-1]]
print("下面是第{}个".format(tpn + 1))
print(seq1_align[::-1])
print(seq2_align[::-1])
print(' ')
输出
总共有15个比对结果
下面是第1个
AA-CGTACTC-AA-G-TCT
–TCGTACTCTAACGAT–
下面是第2个
A-ACGTACTC-AA-G-TCT
-T-CGTACTCTAACGAT–
下面是第3个
-AACGTACTC-AA-G-TCT
T–CGTACTCTAACGAT–
下面是第4个
AA-CGTACTC-AAGTC–T
–TCGTACTCTAA–CGAT
下面是第5个
A-ACGTACTC-AAGTC–T
-T-CGTACTCTAA–CGAT
下面是第6个
-AACGTACTC-AAGTC–T
T–CGTACTCTAA–CGAT
下面是第7个
AA-CGTACTC-AA-GTC-T
–TCGTACTCTAACG–AT
下面是第8个
A-ACGTACTC-AA-GTC-T
-T-CGTACTCTAACG–AT
下面是第9个
-AACGTACTC-AA-GTC-T
T–CGTACTCTAACG–AT
下面是第10个
AA-CGTACTC-AA-GT-CT
–TCGTACTCTAACG-A-T
下面是第11个
A-ACGTACTC-AA-GT-CT
-T-CGTACTCTAACG-A-T
下面是第12个
-AACGTACTC-AA-GT-CT
T–CGTACTCTAACG-A-T
下面是第13个
AA-CGTACTC-AA-G-TCT
–TCGTACTCTAACGA–T
下面是第14个
A-ACGTACTC-AA-G-TCT
-T-CGTACTCTAACGA–T
下面是第15个
-AACGTACTC-AA-G-TCT
T–CGTACTCTAACGA–T
画一下回溯的路径
可视化代码
'''
下面就是得分矩阵的热图以及回溯路径（格子）画出来了
'''
import pandas as pd
import seaborn as sns
from matplotlib import pyplot as plt
Score = pd.DataFrame(Score)
row_name = list(sequence_1)
row_name.insert(0, ' ')
col_name = list(sequence_2)
col_name.insert(0, ' ')
Score.index = row_name
Score.columns = col_name
traceback_way_mat = np.ones([len(sequence_1) + 1, len(sequence_2) + 1])
for i in range(traceback_pathway_row.shape[0]):
traceback_way_mat[traceback_pathway_row[i][:], traceback_pathway_col[i][:]] = 0
ax1 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r", annot=True)
plt.savefig('nw_Heatmap with annotation.png',dpi=300)
plt.show()
ax2 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r")
plt.savefig('nw_Heatmap.png',dpi=300)
plt.show()
ax3 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r", mask=traceback_way_mat)
plt.savefig('nw_Heatmap_traceback',dpi=300)
plt.show()
#%%
# params={'font.family':'serif',
# 'font.serif':'Times New Roman',
# 'font.style':'normal',#'italic'
# 'font.weight':'normal', #or 'blod'
# 'font.size':12,#or large,small
# 'figure.figsize':(6,6)
# }
plt.rcParams['figure.figsize'] = (6, 6)
# plt.rcParams.update(params)
for j in range(traceback_pathway_col.shape[0]):
fig = plt.figure()
ax = plt.axes()
plt.grid(zorder=0, linestyle='-.')
for i in range(traceback_pathway_col.shape[1]-1):
xs = traceback_pathway_col[j][i]
ys = traceback_pathway_row[j][i]
xe = traceback_pathway_col[j][i+1]
ye = traceback_pathway_row[j][i+1]
ax.arrow(xs, ys, xe-xs, ye-ys, length_includes_head=True,head_width=0.3, fc='crimson', ec='hotpink',zorder=10)
ax.set_xlim(-0.5, len(col_name)-0.5)
ax.set_ylim(-0.5, len(col_name)-0.5)
plt.xticks(np.arange(0,len(col_name),1), col_name)
plt.yticks(np.arange(0,len(row_name),1), row_name)
ax.xaxis.set_ticks_position('top')
ax.invert_yaxis()
ax.set_title('No.{}'.format(j+1),fontsize=12,color='k',loc='left',y=0.86,x=0.3,fontweight='bold')
ax.set_title('{}{}{}'.format(seq1_align_set[j],'\n',seq2_align_set[j]),fontsize=16,fontfamily ='monospace',color='k',fontweight='bold',y=0.83,x=0.7)
# plt.rcParams['figure.figsize'] = (6, 6)
plt.savefig('nw_No.{}'.format(j+1)+'.png',dpi=300)
plt.show()
Smith Waterman算法
局部比对的和全局比对差不多，只需再几个小细节上改改就行，大家可以在两个代码之间找找茬~
完整代码
NW
import numpy as np
sequence_1 = "AACGTACTCAAGTCT"
sequence_2 = "TCGTACTCTAACGAT"
match = 9
mismatch = -6
gap = -2
# 创建得分矩阵，行数为第一条序列长度加一，列数为第二条序列长度加二
Score = np.zeros((len(sequence_1) + 1, len(sequence_2) + 1))
# 创建是否匹配的矩阵，这个矩阵的长宽就分别是两条序列的长度了。如果匹配了，对应的格子就是匹配的得分，反之就是不匹配的得分
Match_or_not = np.zeros((len(sequence_1), len(sequence_2)))
for i in range(len(sequence_1)):
for j in range(len(sequence_2)):
if sequence_1[i] == sequence_2[j]:
Match_or_not[i][j] = match
else:
Match_or_not[i][j] = mismatch
# 填得分矩阵
# 第一步：初始化第一行和第一列
for i in range(len(sequence_1) + 1):
Score[i][0] = i * gap
for j in range(len(sequence_2) + 1):
Score[0][j] = j * gap
# 第二步：动态规划的思想算每个格子的得分，每个格子需要考虑其左、上、左上的值，也可以说是考虑序列一、序列二引入空缺或直接匹配的最大值
for i in range(1, len(sequence_1) + 1):
for j in range(1, len(sequence_2) + 1):
Score[i][j] = max(Score[i - 1][j - 1] + Match_or_not[i - 1][j - 1],
Score[i - 1][j] + gap,
Score[i][j - 1] + gap)
# 开始回溯
'''
我们需要考虑的是可能会有多条回溯路径。
全局比对的回溯是从右下角开始，左上角结束，其中可能会有分叉点。
我们可以把右下角看成是一个树的根，矩阵中的每个值看成是一个节点。
每个节点都可能会有三个子节点：左，上，对角线。分别对应了回溯的方向。
而整个回溯的过程也就是遍历这颗三叉树的过程，严谨的说是从根节点遍历每个叶子节点的过程。
'''
class Node:
# 用类来建立三叉树节点，属性包括了行、列、得分、左子树、上子树、对角线子树
def __init__(self, row=None, col=None, score=None):
self.row = row
self.col = col
self.score = score
self.left = None
self.up = None
self.diag = None
def isLeaf(self):
# 判断是否是叶子节点
return self.left is None and self.up is None and self.diag is None
# 递归的函数查找从根节点到每个叶节点的路径
# 回溯路径的个数、回溯路径中的行号和列号
traceback_pathway_number = 0
traceback_pathway_row = [[]]
traceback_pathway_col = [[]]
def SaveRootToLeafPaths(Node, path_row, path_col):
# 如果没有子树了
if Node is None:
return
# 包含当前节点的路径
path_row.append(Node.row)
path_col.append(Node.col)
global traceback_pathway_number
global traceback_pathway_row
global traceback_pathway_col
# 如果找到叶节点，保存路径
if isLeaf(Node):
if traceback_pathway_number == 0:
traceback_pathway_row[traceback_pathway_number] = list(path_row)
traceback_pathway_col[traceback_pathway_number] = list(path_col)
else:
traceback_pathway_row += [list(path_row)]
traceback_pathway_col += [list(path_col)]
traceback_pathway_number += 1
# 递归左、上、对角子树
SaveRootToLeafPaths(Node.left, path_row, path_col)
SaveRootToLeafPaths(Node.up, path_row, path_col)
SaveRootToLeafPaths(Node.diag, path_row, path_col)
# 回溯，出栈
path_row.pop()
path_col.pop()
# 建立三叉树，为 Score 矩阵里所有值都找到它的左、上、对角子树，用一个二位列表来存储节点
NodeTree = [[Node() for _ in range(len(sequence_2) + 1)] for _ in range(len(sequence_1) + 1)]
# 先把节点们的行号列号和得分记录下来
for i in range(len(sequence_1) + 1):
for j in range(len(sequence_2) + 1):
NodeTree[i][j].row = i
NodeTree[i][j].col = j
NodeTree[i][j].score = Score[i][j]
# 设置第一列和第一行的节点的上子树和左子树（其实也能在下面这个大循环里设置，但是这样可读性更高）
for i in range(1, len(sequence_1) + 1):
NodeTree[i][0].up = NodeTree[i - 1][0]
for j in range(1, len(sequence_2) + 1):
NodeTree[0][j].left = NodeTree[0][j - 1]
# 设置剩下的节点
for i in range(1, len(sequence_1) + 1):
for j in range(1, len(sequence_2) + 1):
if (Score[i][j] == Score[i - 1][j - 1] + Match_or_not[i - 1][j - 1]):
NodeTree[i][j].diag = NodeTree[i - 1][j - 1]
if (Score[i][j] == Score[i - 1][j] + gap):
NodeTree[i][j].up = NodeTree[i - 1][j]
if (Score[i][j] == Score[i][j - 1] + gap):
NodeTree[i][j].left = NodeTree[i][j - 1]
# 遍历树并保存路径
SaveRootToLeafPaths(NodeTree[len(sequence_1)][len(sequence_2)], [], [])
# 改成numpy的ndarray类型，更加方便！
traceback_pathway_row = np.array(traceback_pathway_row)
traceback_pathway_col = np.array(traceback_pathway_col)
# 记录一下回溯时走不走左边或上边，如果走就记为1，不走就记为0
Go_left = traceback_pathway_col[:, range(traceback_pathway_col.shape[1] - 1)] - traceback_pathway_col[:, range(1,
traceback_pathway_col.shape[
1])]
Go_up = traceback_pathway_row[:, range(traceback_pathway_row.shape[1] - 1)] - traceback_pathway_row[:,
range(1, traceback_pathway_row.shape[1])]
# 用列表来存储序列一和序列二比对后的结果
seq1_align_set = []
seq2_align_set = []
print("总共有{}个比对结果".format(traceback_pathway_number))
for tpn in range(traceback_pathway_number):
'''
下面其实就是经典的nw回溯的代码了，这部分的原理可以参考nw算法回溯的伪代码。
唯一不同的就是我们是多条回溯路径，所以有多少条路经就得循环多少次。
值得一提的是，回溯过去的序列是逆序的，
在python中字符串逆置十分方便，只需要合理利用切片，如：str[::-1]即可。
'''
seq1_align = ''
seq2_align = ''
i = len(sequence_1)
j = len(sequence_2)
k = 0
while i > 0 or j > 0:
if i > 0 and j > 0 and Go_left[tpn][k] and Go_up[tpn][k]:
seq1_align += sequence_1[i - 1]
seq2_align += sequence_2[j - 1]
i -= 1
j -= 1
elif i > 0 and not (Go_left[tpn][k]) and Go_up[tpn][k]:
seq1_align += sequence_1[i - 1]
seq2_align += '-'
i -= 1
elif j > 0 and Go_left[tpn][k] and not (Go_up[tpn][k]):
seq1_align += '-'
seq2_align += sequence_2[j - 1]
j -= 1
k += 1
seq1_align_set += [seq1_align[::-1]]
seq2_align_set += [seq2_align[::-1]]
print("下面是第{}个".format(tpn + 1))
print(seq1_align[::-1])
print(seq2_align[::-1])
print(' ')
#%%
'''
下面就是得分矩阵的热图以及回溯路径（格子）画出来了
'''
import pandas as pd
import seaborn as sns
from matplotlib import pyplot as plt
Score = pd.DataFrame(Score)
row_name = list(sequence_1)
row_name.insert(0, ' ')
col_name = list(sequence_2)
col_name.insert(0, ' ')
Score.index = row_name
Score.columns = col_name
traceback_way_mat = np.ones([len(sequence_1) + 1, len(sequence_2) + 1])
for i in range(traceback_pathway_row.shape[0]):
traceback_way_mat[traceback_pathway_row[i][:], traceback_pathway_col[i][:]] = 0
ax1 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r", annot=True)
plt.savefig('nw_Heatmap with annotation.png',dpi=300)
plt.show()
ax2 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r")
plt.savefig('nw_Heatmap.png',dpi=300)
plt.show()
ax3 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r", mask=traceback_way_mat)
plt.savefig('nw_Heatmap_traceback',dpi=300)
plt.show()
#%%
# params={'font.family':'serif',
# 'font.serif':'Times New Roman',
# 'font.style':'normal',#'italic'
# 'font.weight':'normal', #or 'blod'
# 'font.size':12,#or large,small
# 'figure.figsize':(6,6)
# }
plt.rcParams['figure.figsize'] = (6, 6)
# plt.rcParams.update(params)
for j in range(traceback_pathway_col.shape[0]):
fig = plt.figure()
ax = plt.axes()
plt.grid(zorder=0, linestyle='-.')
for i in range(traceback_pathway_col.shape[1]-1):
xs = traceback_pathway_col[j][i]
ys = traceback_pathway_row[j][i]
xe = traceback_pathway_col[j][i+1]
ye = traceback_pathway_row[j][i+1]
ax.arrow(xs, ys, xe-xs, ye-ys, length_includes_head=True,head_width=0.3, fc='crimson', ec='hotpink',zorder=10)
ax.set_xlim(-0.5, len(col_name)-0.5)
ax.set_ylim(-0.5, len(col_name)-0.5)
plt.xticks(np.arange(0,len(col_name),1), col_name)
plt.yticks(np.arange(0,len(row_name),1), row_name)
ax.xaxis.set_ticks_position('top')
ax.invert_yaxis()
ax.set_title('No.{}'.format(j+1),fontsize=12,color='k',loc='left',y=0.86,x=0.3,fontweight='bold')
ax.set_title('{}{}{}'.format(seq1_align_set[j],'\n',seq2_align_set[j]),fontsize=16,fontfamily ='monospace',color='k',fontweight='bold',y=0.83,x=0.7)
# plt.rcParams['figure.figsize'] = (6, 6)
plt.savefig('nw_No.{}'.format(j+1)+'.png',dpi=300)
plt.show()
import datetime
print("这是代码执行时间: ",datetime.datetime.now())
SW
import numpy as np
sequence_1 = "AACGTACTCAAGTCT"
sequence_2 = "TCGTACTCTAACGAT"
match = 9
mismatch = -6
gap = -2
# 创建得分矩阵，行数为第一条序列长度加一，列数为第二条序列长度加二
Score = np.zeros((len(sequence_1) + 1, len(sequence_2) + 1))
# 创建是否匹配的矩阵，这个矩阵的长宽就分别是两条序列的长度了。如果匹配了，对应的格子就是匹配的得分，反之就是不匹配的得分
Match_or_not = np.zeros((len(sequence_1), len(sequence_2)))
for i in range(len(sequence_1)):
for j in range(len(sequence_2)):
if sequence_1[i] == sequence_2[j]:
Match_or_not[i][j] = match
else:
Match_or_not[i][j] = mismatch
# 填得分矩阵
# 第一步：初始化第一行和第一列
for i in range(len(sequence_1) + 1):
Score[i][0] = 0
for j in range(len(sequence_2) + 1):
Score[0][j] = 0
# 第二步：动态规划的思想算每个格子的得分，每个格子需要考虑其左、上、左上的值，也可以说是考虑序列一、序列二引入空缺或直接匹配的最大值
for i in range(1, len(sequence_1) + 1):
for j in range(1, len(sequence_2) + 1):
Score[i][j] = max(Score[i - 1][j - 1] + Match_or_not[i - 1][j - 1],
Score[i - 1][j] + gap,
Score[i][j - 1] + gap, 0)
# 开始回溯
'''
我们需要考虑的是可能会有多条回溯路径。
全局比对的回溯是从右下角开始，左上角结束，其中可能会有分叉点。
我们可以把右下角看成是一个树的根，矩阵中的每个值看成是一个节点。
每个节点都可能会有三个子节点：左，上，对角线。分别对应了回溯的方向。
而整个回溯的过程也就是遍历这颗三叉树的过程，严谨的说是从根节点遍历每个叶子节点的过程。
'''
class Node:
# 用类来建立三叉树节点，属性包括了行、列、得分、左子树、上子树、对角线子树
def __init__(self, row=None, col=None, score=None):
self.row = row
self.col = col
self.score = score
self.left = None
self.up = None
self.diag = None
def isLeaf(self):
# 判断是否是叶子节点
return self.left is None and self.up is None and self.diag is None
# 递归的函数查找从根节点到每个叶节点的路径
# 回溯路径的个数、回溯路径中的行号和列号
traceback_pathway_number = 0
traceback_pathway_row = [[]]
traceback_pathway_col = [[]]
def SaveRootToLeafPaths(Node, path_row, path_col):
# 如果没有子树了
if Node is None:
return
# 包含当前节点的路径
path_row.append(Node.row)
path_col.append(Node.col)
global traceback_pathway_number
global traceback_pathway_row
global traceback_pathway_col
# 如果找到叶节点，保存路径
if isLeaf(Node):
if traceback_pathway_number == 0:
traceback_pathway_row[traceback_pathway_number] = list(path_row)
traceback_pathway_col[traceback_pathway_number] = list(path_col)
else:
traceback_pathway_row += [list(path_row)]
traceback_pathway_col += [list(path_col)]
traceback_pathway_number += 1
# 递归左、上、对角子树
SaveRootToLeafPaths(Node.left, path_row, path_col)
SaveRootToLeafPaths(Node.up, path_row, path_col)
SaveRootToLeafPaths(Node.diag, path_row, path_col)
# 回溯，出栈
path_row.pop()
path_col.pop()
# 建立三叉树，为 Score 矩阵里所有值都找到它的左、上、对角子树，用一个二位列表来存储节点
NodeTree = [[Node() for _ in range(len(sequence_2) + 1)] for _ in range(len(sequence_1) + 1)]
# 先把节点们的行号列号和得分记录下来
for i in range(len(sequence_1) + 1):
for j in range(len(sequence_2) + 1):
NodeTree[i][j].row = i
NodeTree[i][j].col = j
NodeTree[i][j].score = Score[i][j]
# 设置第一列和第一行的节点的上子树和左子树（其实也能在下面这个大循环里设置，但是这样可读性更高）
for i in range(1, len(sequence_1) + 1):
NodeTree[i][0].up = NodeTree[i - 1][0]
for j in range(1, len(sequence_2) + 1):
NodeTree[0][j].left = NodeTree[0][j - 1]
# 设置剩下的节点
for i in range(1, len(sequence_1) + 1):
for j in range(1, len(sequence_2) + 1):
if (Score[i][j] == Score[i - 1][j - 1] + Match_or_not[i - 1][j - 1]):
NodeTree[i][j].diag = NodeTree[i - 1][j - 1]
if (Score[i][j] == Score[i - 1][j] + gap):
NodeTree[i][j].up = NodeTree[i - 1][j]
if (Score[i][j] == Score[i][j - 1] + gap):
NodeTree[i][j].left = NodeTree[i][j - 1]
# 遍历树并保存路径
r, c = np.where(Score == np.max(Score))
SaveRootToLeafPaths(NodeTree[int(r)][int(c)], [], [])
# 改成numpy的ndarray类型，更加方便！
traceback_pathway_row = np.array(traceback_pathway_row)
traceback_pathway_col = np.array(traceback_pathway_col)
# 记录一下回溯时走不走左边或上边，如果走就记为1，不走就记为0
Go_left = traceback_pathway_col[:, range(traceback_pathway_col.shape[1] - 1)] - traceback_pathway_col[:, range(1,
traceback_pathway_col.shape[
1])]
Go_up = traceback_pathway_row[:, range(traceback_pathway_row.shape[1] - 1)] - traceback_pathway_row[:,
range(1, traceback_pathway_row.shape[1])]
# 用列表来存储序列一和序列二比对后的结果
seq1_align_set = []
seq2_align_set = []
print("总共有{}个比对结果".format(traceback_pathway_number))
for tpn in range(traceback_pathway_number):
'''
下面其实就是经典的nw回溯的代码了，这部分的原理可以参考nw算法回溯的伪代码。
唯一不同的就是我们是多条回溯路径，所以有多少条路经就得循环多少次。
值得一提的是，回溯过去的序列是逆序的，
在python中字符串逆置十分方便，只需要合理利用切片，如：str[::-1]即可。
'''
seq1_align = ''
seq2_align = ''
i = int(r)
j = int(c)
k = 0
while Score[i][j] > 0:
# waterman修改条件，到零结束
if k < traceback_pathway_col.shape[1] - 1:
if Go_left[tpn][k] and Go_up[tpn][k]:
seq1_align += sequence_1[i - 1]
seq2_align += sequence_2[j - 1]
i -= 1
j -= 1
elif not (Go_left[tpn][k]) and Go_up[tpn][k]:
seq1_align += sequence_1[i - 1]
seq2_align += '-'
i -= 1
elif Go_left[tpn][k] and not (Go_up[tpn][k]):
seq1_align += '-'
seq2_align += sequence_2[j - 1]
j -= 1
k += 1
seq1_align_set += [seq1_align[::-1]]
seq2_align_set += [seq2_align[::-1]]
print("下面是第{}个".format(tpn + 1))
print(seq1_align[::-1])
print(seq2_align[::-1])
print(' ')
#%%
'''
下面就是得分矩阵的热图以及回溯路径（格子）画出来了
'''
import pandas as pd
import seaborn as sns
from matplotlib import pyplot as plt
Score = pd.DataFrame(Score)
row_name = list(sequence_1)
row_name.insert(0, ' ')
col_name = list(sequence_2)
col_name.insert(0, ' ')
Score.index = row_name
Score.columns = col_name
traceback_way_mat = np.ones([len(sequence_1) + 1, len(sequence_2) + 1])
for i in range(traceback_pathway_row.shape[0]):
traceback_way_mat[traceback_pathway_row[i][:], traceback_pathway_col[i][:]] = 0
ax1 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r", annot=True)
plt.savefig('sw_Heatmap with annotation.png',dpi=300)
plt.show()
ax2 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r")
plt.savefig('sw_Heatmap.png',dpi=300)
plt.show()
ax3 = sns.heatmap(Score, linecolor='white', linewidth=0, square=True, cmap="RdBu_r", mask=traceback_way_mat)
plt.savefig('sw_Heatmap_traceback',dpi=300)
plt.show()
#%%
plt.rcParams['figure.figsize'] = (6, 6)
for j in range(traceback_pathway_col.shape[0]):
fig = plt.figure()
ax = plt.axes()
plt.grid(zorder=0, linestyle='-.')
for i in range(traceback_pathway_col.shape[1]-2):
xs = traceback_pathway_col[j][i]
ys = traceback_pathway_row[j][i]
xe = traceback_pathway_col[j][i+1]
ye = traceback_pathway_row[j][i+1]
ax.arrow(xs, ys, xe-xs, ye-ys, length_includes_head=True,head_width=0.3, fc='crimson', ec='hotpink',zorder=10)
ax.set_xlim(-0.5, len(col_name)-0.5)
ax.set_ylim(-0.5, len(col_name)-0.5)
plt.xticks(np.arange(0,len(col_name),1), col_name)
plt.yticks(np.arange(0,len(row_name),1), row_name)
ax.xaxis.set_ticks_position('top')
ax.invert_yaxis()
# ax.set_title('No.{}'.format(j+1),fontsize=12,color='k',loc='left')
ax.set_title('No.{}'.format(j + 1), fontsize=12, color='k', loc='left', y=0.86, x=0.38, fontweight='bold')
ax.set_title('{}{}{}'.format(seq1_align_set[j], '\n', seq2_align_set[j]), fontsize=16, fontfamily='monospace',
color='k', fontweight='bold', y=0.83, x=0.7)
plt.savefig('sw_No.{}'.format(j+1)+'.png',dpi=300)
plt.show()
import datetime
print("这是代码执行时间: ",datetime.datetime.now())