EPS = 10 ** -9
from random import randint
import numpy as np
from numpy.linalg import svd
import sys

def getMatrixFromFile(fileName, flag=False):
  with open(fileName, 'r') as f:
    n = int(f.readline())
    blank = f.readline()
   # b = [float(f.readline()) for i in range(n)]
    lines = f.readlines()
    a = [dict() for i in range(n)]
    for it in lines:
      vals = it.split(',')
      z, x, y = float(vals[0]), int(vals[1]), int(vals[2])
      a[x][y] = a[x].get(y, 0) + z
      if len(a[x]) > 10 and flag:
        print("Matricea contine o linie cu mai mult de 10 elemente!!!")
    checksim(a,n)
    return n, a


def add(a, b, n):
  ans = [dict() for i in range(n)]
  for i in range(n):
    for it in a[i]:
      ans[i][it] = ans[i].get(it, 0) + a[i][it]
    for it in b[i]:
      ans[i][it] = ans[i].get(it, 0) + b[i][it]
  return ans


def mul(a, b, n):
  ans = [dict() for i in range(n)]
  for i in range(n):
    for j in range(n):
      for k in a[i]:
        if j in b[k]:
          ans[i][j] = ans[i].get(j, 0) + a[i][k] * b[k][j]
  return ans


def mulVector(a, b, n):
  ans = [0 for i in range(n)]
  for i in range(n):
    for k in a[i]:
      ans[i] += a[i][k] * b[k]
  return ans


def compareMatrix(a, b, n):
  for i in range(n):
    if len(a[i]) != len(b[i]):
      return False
    for j in a[i]:
      if j not in b[i]:
        return False
      if abs(a[i][j] - b[i][j]) > EPS:
        print(a[i][j], b[i][j])
        return False
  return True



def dotprod(w,v):
  s=0
  for i in range(len(w)):
    s+=w[i]*v[i]
  return s

def vecnorm(v):
  norm=0
  for i in range(len(v)):
    norm+=v[i]**2
  norm=norm**0.5
  return norm

def checksim(a,n):
    c=1
    for i in range(len(a)):
      for j in a[i].keys():
        if i not in a[j].keys() or abs(a[i][j]-a[j][i]) > EPS and i!=j:
          #print("Avem lipsa de simetrie!!!")
          if(c==1):
            print(i,j)
          c=0
    if c==0:
      print("Avem lipsa de simetrie!!!")
    else:
      print("Matrice simetrica")

def powermethod(a,n):
  #get vector
  v=list()
  vv=list()
  k=0
  for i in range(n):
    v.append(randint(0,10000))
    vv.append(0)
  norm=vecnorm(v)
  for i in range(n):
    v[i]=v[i]/norm
  w=mulVector(a,v,n)
  lamb=dotprod(w,v)
  lamv=[lamb*i for i in v]
  test=[w[i]-lamv[i] for i in range(n)]
  #print(test)
  #print(w)
  #print(v)
  #print(len(v))
  while vecnorm(test)>n*EPS and k<=1000000:
    norm=vecnorm(w)
    for i in range(n):
      vv[i]=w[i]/norm
    w=mulVector(a,vv,n)
    lamb1=dotprod(w,vv)
    lamv=[lamb*i for i in v]
    test=[w[i]-lamv[i] for i in range(n)]
    k+=1
    lamb=lamb1
    v=[j for j in vv]
  print(k)
  print(lamb)
  print(vecnorm(test))

def getMatrixFromFile2(fileName):
  with open(fileName, 'r') as f:
    a = [list(map(float, it.split())) for it in f.readlines()]
    return a, len(a), len(a[0])

def genrandomvector(size):
  b=list()
  for i in range(size):
    b.append(randint(0,10000))
  return b

def Ainf(a, n, m):
  aux = [0.0 for i in range(n)]
  for i in range(n):
    for j in range(m):
      aux[i] += a[i,j]
  max=aux[0]
  for i in range(len(aux)):
    if aux[i]>max:
      max=aux[i]
  #print(aux)
  return max

if __name__ == '__main__':
  #print("Matrice proprie")
  #n1, a1 = getMatrixFromFile('a6.txt')
  #print("Matrice laborator")
  #n1, a1 = getMatrixFromFile('m_rar_sim_2018.txt')
  #print(n2, a2)
  #powermethod(a1,n1)
  a,n,m=getMatrixFromFile2('a62.txt')
  u,s,vstar=svd(np.asmatrix(a), full_matrices=True)
  #print("Singular values:")
  #print(s)
  #print(len(s))
  rk=0
  min=s[0]
  max=s[0]
  #print("Rank:")
  sinv=np.zeros((n,m))
  for i in range(len(s)):
    if s[i]!=0:
      rk+=1
      if max<s[i]:
        max=s[i]
      if min>s[i]:
        min=s[i]
      sinv[i][i]+=1/s[i]
  #print(rk)
  #print("Nr conditionare:")
  #print(max/min)
  print("Pseudoinversa:")
  ainv=np.matmul(np.matmul(np.transpose(vstar), np.transpose(np.asmatrix(sinv))),np.transpose(u))
  print(ainv)
 # print(np.linalg.pinv(np.asmatrix(a)))
  b=genrandomvector(n)
  #x, res, rank, ss=np.linalg.lstsq(a, b)
  xx=np.matmul(ainv, b)
  print("Solutie:")
  print(xx)
  #print(xx)
  #print(len(x))
  print("Dati val:")
  k=int(input())
  #print(k)
  while k>rk:
    print("Valoare invalida")
    k=int(input())
  As=np.zeros((n,m))
  for i in range(k):
    cu=u[:,i]
    cv=np.transpose(vstar)[:,i]
    mataux=np.multiply(s[i],np.matmul(cu, np.transpose(cv)))
    As=np.add(As, mataux)
  dif=np.subtract(np.asmatrix(a), As)
  print("Norma")
  #print(np.asmatrix(dif)[1][0])
  print(Ainf(np.asmatrix(dif), n, m))