update

2025.03.09_matrix_running_time_for_different_num_of_cpu_cores/code_1/make_qsub_files.py

@@ -1,7 +1,7 @@
 import guan  # https://py.guanjihuan.com | install: pip install --upgrade guan
 import numpy as np
 
-cpu_num_array = np.arange(1, 17)
+cpu_num_array = np.arange(1, 9)
 
 sh_filename = 'task'
 task_name = 'test'

2025.03.09_matrix_running_time_for_different_num_of_cpu_cores/code_1/matrix_running_time_for_different_num_of_cpu_cores.py

@@ -6,22 +6,14 @@ The newest version of this code is on the web page: https://www.guanjihuan.com/a
 import numpy as np
 import time
 
-n = 5000
-A = np.random.rand(n, n)
-B = np.random.rand(n, n)
-
+n = 1000
 test_times = 20
 
-# 矩阵行列式
-start_time = time.time()
-for _ in range(test_times):
-    det_A = np.linalg.det(A)
-det_time = (time.time() - start_time)/test_times
-print(f"矩阵行列式时间: {det_time:.3f} 秒")
-
 # 矩阵乘法
 start_time = time.time()
 for _ in range(test_times):
+    A = np.random.rand(n, n)
+    B = np.random.rand(n, n)
     C = np.dot(A, B)
 multiply_time = (time.time() - start_time)/test_times
 print(f"矩阵乘法时间: {multiply_time:.3f} 秒")
@@ -29,27 +21,15 @@ print(f"矩阵乘法时间: {multiply_time:.3f} 秒")
 # 矩阵求逆
 start_time = time.time()
 for _ in range(test_times):
+    A = np.random.rand(n, n)
     inv_A = np.linalg.inv(A)
 inv_time = (time.time() - start_time)/test_times
 print(f"矩阵求逆时间: {inv_time:.3f} 秒")
 
-# 矩阵的秩
-start_time = time.time()
-for _ in range(test_times):
-    rank_A = np.linalg.matrix_rank(A)
-rank_time = (time.time() - start_time)/test_times
-print(f"矩阵的秩时间: {rank_time:.3f} 秒")
-
-# 矩阵的特征值
-start_time = time.time()
-for _ in range(test_times):
-    eigenvalues_A = np.linalg.eigvals(A)
-eigen_time = (time.time() - start_time)/test_times
-print(f"矩阵特征值时间: {eigen_time:.3f} 秒")
-
 # 矩阵的特征值和特征向量
 start_time = time.time()
 for _ in range(test_times):
+    A = np.random.rand(n, n)
     eigenvalues_A, eigenvector_A = np.linalg.eig(A)
 eigen_time = (time.time() - start_time)/test_times
 print(f"矩阵特征值和特征向量时间: {eigen_time:.3f} 秒")

2025.03.09_matrix_running_time_for_different_num_of_cpu_cores/code_1/plot_result_of_running_time1.py

@@ -1,74 +0,0 @@
-import matplotlib.pyplot as plt
-from matplotlib.ticker import MultipleLocator
-import numpy as np
-
-cpu_num_array = np.arange(1, 17)
-
-# n = 5000
-
-time_array_1 = [3.999, 1.679, 1.257, 0.985, 0.699, 0.562, 0.534, 0.525, 0.510, 0.424, 0.409, 0.380, 0.372, 0.339, 0.334, 0.293]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.show()
-
-time_0 = time_array_1[0]
-for i0 in range(len(time_array_1)):
-    time_array_1[i0] = time_0/time_array_1[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()
-
-
-
-time_array_2 = [6.059, 2.723, 2.190, 1.577, 1.169, 0.939, 1.231, 0.958, 1.070, 0.793, 1.208, 0.760, 0.709, 0.677, 0.671, 0.906]
-fig, ax = plt.subplots()
-ax.set_title('np.linalg.inv()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_2, '-o', )
-plt.show()
-
-time_0 = time_array_2[0]
-for i0 in range(len(time_array_2)):
-    time_array_2[i0] = time_0/time_array_2[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.linalg.inv()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_2, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()
-
-
-
-time_array_3 = [95.896, 49.107, 41.703, 38.915, 32.468, 25.804, 40.716, 31.072, 40.045, 26.397, 38.557, 28.684, 28.267, 26.840, 27.381, 34.494]
-fig, ax = plt.subplots()
-ax.set_title('np.linalg.eig()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_3, '-o', )
-plt.show()
-
-time_0 = time_array_3[0]
-for i0 in range(len(time_array_3)):
-    time_array_3[i0] = time_0/time_array_3[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.linalg.eig()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_3, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()

2025.03.09_matrix_running_time_for_different_num_of_cpu_cores/code_1/plot_result_of_running_time2.py

@@ -1,160 +0,0 @@
-import matplotlib.pyplot as plt
-from matplotlib.ticker import MultipleLocator
-import numpy as np
-
-cpu_num_array = np.arange(1, 17)
-
-
-
-# n = 30000
-
-time_array_1 = [1164.522, 648.587, 444.488, 647.176, 298.652, 256.809, 239.630, 231.987, 475.781, 383.823, 410.388, 172.702, 163.727, 144.307, 121.530, 109.636]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.show()
-
-time_0 = time_array_1[0]
-for i0 in range(len(time_array_1)):
-    time_array_1[i0] = time_0/time_array_1[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()
-
-
-
-
-# n = 20000
-
-time_array_1 = [365.730, 209.475, 151.805, 120.739, 104.102, 88.944, 80.475, 70.486, 67.500, 61.404, 53.837, 51.219, 51.542, 84.641, 80.378, 30.629]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.show()
-
-time_0 = time_array_1[0]
-for i0 in range(len(time_array_1)):
-    time_array_1[i0] = time_0/time_array_1[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()
-
-
-
-
-# n = 10000
-
-time_array_1 = [62.485, 36.402, 25.316, 21.785, 17.619, 15.412, 16.718, 10.874, 9.588, 7.004, 6.733, 7.251, 7.248, 4.979, 4.889, 7.037]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.show()
-
-time_0 = time_array_1[0]
-for i0 in range(len(time_array_1)):
-    time_array_1[i0] = time_0/time_array_1[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()
-
-
-
-
-# n = 500
-
-time_array_1 = [0.004053801, 0.002605676, 0.001590664, 0.001103345, 0.001266495, 0.000954730, 0.000930616, 0.000779754, 0.000970088, 0.000651353, 0.000918634, 0.000538209, 0.000716934, 0.000521487, 0.001165715, 0.000764804 ]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.show()
-
-time_0 = time_array_1[0]
-for i0 in range(len(time_array_1)):
-    time_array_1[i0] = time_0/time_array_1[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()
-
-
-
-
-# n = 300
-
-time_array_1 = [0.001144045, 0.000554059, 0.000413136, 0.000385368, 0.000287431, 0.000270178, 0.000268842, 0.000535453, 0.000219275, 0.000219676, 0.000186116, 0.000522058, 0.000146788, 0.000134041, 0.000558532, 0.000135554]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.show()
-
-time_0 = time_array_1[0]
-for i0 in range(len(time_array_1)):
-    time_array_1[i0] = time_0/time_array_1[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()
-
-
-
-
-# n = 100
-
-time_array_1 = [0.000041899, 0.000104283, 0.000138595, 0.000038628, 0.000039540, 0.000029726, 0.000101140, 0.000023468, 0.000061134, 0.000225034, 0.000033439, 0.000075225, 0.000057184, 0.000040229, 0.000104894, 0.000041510]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Time (s)')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.show()
-
-time_0 = time_array_1[0]
-for i0 in range(len(time_array_1)):
-    time_array_1[i0] = time_0/time_array_1[i0]
-fig, ax = plt.subplots()
-ax.set_title('np.dot()')
-ax.set_xlabel('Number of CPU cores')
-ax.set_ylabel('Ratio')
-ax.xaxis.set_major_locator(MultipleLocator(1))
-plt.plot(cpu_num_array, time_array_1, '-o', )
-plt.plot(cpu_num_array, cpu_num_array, '--r')
-plt.show()

2025.03.09_matrix_running_time_for_different_num_of_cpu_cores/code_1/qsub_task.py

@@ -1,7 +1,7 @@
 import numpy as np
 import os
 
-cpu_num_array = np.arange(1, 17)
+cpu_num_array = np.arange(1, 9)
 
 for cpu_num in cpu_num_array:
     os.system(f'qsub task_{cpu_num}.sh')

2025.03.09_matrix_running_time_for_different_num_of_cpu_cores/code_2/matrix_running_time_for_different_num_of_cpu_cores_writing_into_files.py

@@ -8,15 +8,13 @@ import time
 import pickle
 
 n = 1000
-
-A = np.random.rand(n, n)
-B = np.random.rand(n, n)
-
 test_times = 20
 
 # 矩阵乘法
 start_time = time.time()
 for _ in range(test_times):
+    A = np.random.rand(n, n)
+    B = np.random.rand(n, n)
     C = np.dot(A, B)
 multiply_time = (time.time() - start_time)/test_times
 with open(f'multiply_time_n={n}.pkl', 'wb') as f:
@@ -25,6 +23,7 @@ with open(f'multiply_time_n={n}.pkl', 'wb') as f:
 # 矩阵求逆
 start_time = time.time()
 for _ in range(test_times):
+    A = np.random.rand(n, n)
     inv_A = np.linalg.inv(A)
 inv_time = (time.time() - start_time)/test_times
 with open(f'inv_time_n={n}.pkl', 'wb') as f:
@@ -33,6 +32,7 @@ with open(f'inv_time_n={n}.pkl', 'wb') as f:
 # 矩阵的特征值和特征向量
 start_time = time.time()
 for _ in range(test_times):
+    A = np.random.rand(n, n)
     eigenvalues_A, eigenvector_A = np.linalg.eig(A)
 eigen_time = (time.time() - start_time)/test_times
 with open(f'eigen_time_n={n}.pkl', 'wb') as f:

2025.04.03_time_of_fotran_mkl_and_python_numpy/a.f90

@@ -40,10 +40,12 @@ program main
     implicit none
 
     integer, allocatable :: index1(:)
-    integer n, i, j, info, ierr, stage, start, end_val, step, count_start, count_end, count_rate
+    integer n, i, j, info, ierr, stage, start, end_val, step, count_start, count_end, count_rate, test_0, test_times
     double precision, allocatable :: A(:,:)
     double precision time_used
 
+    test_times = 20
+
     ! 定义不同阶段的参数
     do stage = 1, 3
         select case(stage)
@@ -55,9 +57,9 @@ program main
             start = 2000
             end_val = 10000
             step = 1000
-        case(3)  ! 第三阶段：20000-50000，步长10000
+        case(3)  ! 第三阶段：20000-30000，步长10000
             start = 20000
-            end_val = 50000
+            end_val = 30000
             step = 10000
         end select
 
@@ -65,21 +67,25 @@ program main
         do while (n <= end_val)
 
             allocate(index1(n), stat=ierr)
-            call generate_random_matrix(n, A)
-
+            
             call system_clock(count_start, count_rate)
-            call getrf(A, index1, info);  call getri(A, index1, info)  ! 使用 getrf 和 getri 对矩阵求逆。这时候 A 不再是原来的矩阵了，而是求逆后的矩阵。
+            test_0 = 1
+            do while (test_0 <= test_times)
+                call generate_random_matrix(n, A)
+                call getrf(A, index1, info);  call getri(A, index1, info)  ! 使用 getrf 和 getri 对矩阵求逆。这时候 A 不再是原来的矩阵了，而是求逆后的矩阵。
+                deallocate(A, stat=ierr)
+                test_0 = test_0 + 1
+            end do
             call system_clock(count_end)
 
             ! 打印计算时间
             if (count_rate > 0) then
-                time_used = real(count_end - count_start) / real(count_rate)
+                time_used = real(count_end - count_start) / real(count_rate) / test_times
                 write(*, '(a, I6, a, f12.6, a)') 'n = ', n, ' 的计算时间: ', time_used, ' 秒'
             else
                 write(*,*) "无法获取计算时间"
             endif
 
-            deallocate(A, stat=ierr)
             deallocate(index1, stat=ierr)
 
             n = n + step

2025.04.03_time_of_fotran_mkl_and_python_numpy/a.py

@@ -8,11 +8,13 @@ import time
 
 n_array = np.concatenate((np.arange(100, 1000, 100),
                           np.arange(1000, 10000, 1000),
-                          np.arange(10000, 60000, 10000)))
+                          np.arange(10000, 40000, 10000)))
 
 for n in n_array:
-    A = np.random.rand(n, n)
+    test_times = 20
     start_time = time.time()
-    inv_A = np.linalg.inv(A)
-    inv_time = time.time() - start_time
+    for _ in range(test_times):
+        A = np.random.rand(n, n)
+        inv_A = np.linalg.inv(A)
+    inv_time = (time.time() - start_time)/test_times
     print(f"n = {n} 的计算时间: {inv_time:.6f} 秒")

2025.04.03_time_of_fotran_mkl_and_python_numpy/task_fotran.sh

@@ -0,0 +1,4 @@
+#!/bin/sh
+#PBS -N fortran
+#PBS -l nodes=1:ppn=24
+./a.exe

2025.04.03_time_of_fotran_mkl_and_python_numpy/task_python.sh

@@ -0,0 +1,4 @@
+#!/bin/sh
+#PBS -N python
+#PBS -l nodes=1:ppn=24
+python a.py