3247.sagews

import numpy as np

def posmax(A):
    pos=A.argmax()
    N=A.shape[0] #je suppose que A est carree
    lin=index/N
    col=mod(index,N)
    return(lin,col)

def system_lineaire(A,b):
    N=A.shape[0] # matrice carree*
    #on met des zero sur chaque colonne
    for j in range(0,N-1):
        c=abs(A[j:N,j])
        #permutation indices p et j
        #abs est la val absolue
        p=j+c.argmax()
        #ne pas oublier ici le .copy()
        v=A[j,:].copy()
        A[j,:]=A[p,:]
        A[p,:]=v.copy()
        # fin de la permutation
        # permutation de b à ne pas oublier
        t=b[j]
        b[j]=b[p]
        b[p]=t
        pivot=A[j,j]
        for i in range(j+1,N):
            b[i]=b[i]-(A[i,j]/pivot)*b[j]
            A[i,:]=A[i,:]-(A[i,j]/pivot)*A[j,:]
    #resolution du système triangulaire
    for j in range(N-1,0,-1):
        pivot=A[j,j]
        for i in range(j-1,-1,-1):
            b[i]=b[i]-(A[i,j]/pivot)*b[j]
            A[i,:]=A[i,:]-(A[i,j]/pivot)*A[j,:]
    sol=b/A.diagonal()
    return(sol)

A=np.array ([[11.,2.,3.,4.],[5.,6.,7.,108.],[10.,11.,12.,13.],[34.,45.,46.,57.]])
Asauve=A.copy()
b=np.array([2.,3.,4.,5.])

sol=system_lineaire(A,b)
print(sol)

[-0.23176471 -3.97176471 4.18 -0.01176471]

np.dot(Asauve,sol)

array([ 2., 3., 4., 5.])

c=np.array ([[1,2,3],[-35,23,6],[-15,13,16]])

b=abs(c)

b

array([[ 1, 2, 3], [35, 23, 6], [15, 13, 16]])

b.argmax(1)

array([2, 0, 2])

np.argmax?

File: /sagenb/sage_install/sage-4.7/local/lib/python2.6/site-packages/numpy/core/fromnumeric.py

Type: <type ‘function’>

Definition: np.argmax(a, axis=None)

Docstring:

Indices of the maximum values along an axis.

a : array_like

Input array.

axis : int, optional

By default, the index is into the flattened array, otherwise along the specified axis.

index_array : ndarray of ints

Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed.

ndarray.argmax, argmin amax : The maximum value along a given axis. unravel_index : Convert a flat index into an index tuple.

In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned.

>>> a = np.arange(6).reshape(2,3)
>>> a
array([[0, 1, 2],
       [3, 4, 5]])
>>> np.argmax(a)
5
>>> np.argmax(a, axis=0)
array([1, 1, 1])
>>> np.argmax(a, axis=1)
array([2, 2])

>>> b = np.arange(6)
>>> b[1] = 5
>>> b
array([0, 5, 2, 3, 4, 5])
>>> np.argmax(b) # Only the first occurrence is returned.
1