jungem's profile - activity

I added to the code linked above and made it into an @interact that takes one all the way to reduced echelon form: (a formatting issue is having one of the @interacts not in the code box, and messing with the indentation a bit. Be sure to copy-paste the hanging @interact and indent in the nested one.)

@interact def _(row = slider([1..10], label='rows', default = 3) , col = slider([1..10], label='columns', default = 3)):

@interact(layout=dict(top=[['M', 'b']]))

def gauss_method(b= random_matrix(QQ,nrows = row, ncols = 1, algorithm='echelonizable', rank = 1), M=random_matrix(QQ,nrows = row, ncols = col, algorithm='echelonizable', rank = min(row,col)),rescale_leading_entry=True ):

    M=M.augment(b, subdivide = True)
    N=copy(M)
    N=N.rref()

    num_rows=M.nrows()
    num_cols=M.ncols()
    print("Reduced echelon form:")
    show(N)

    print("Steps")
    show(M)

    col = 0   # all cols before this are already done
    for row in range(0,num_rows):
        # ?Need to swap in a nonzero entry from below
        while (col < num_cols
               and M[row][col] == 0):
            for i in M.nonzero_positions_in_column(col):
                if i > row:
                    print " R",row+1,"\;\circlearrowright \; R",i+1
                    M.swap_rows(row,i)
                    show(M)
                    break
            else:
                col += 1

        if col >= num_cols:
            break

        # Now guaranteed M[row][col] != 0
        if (rescale_leading_entry
           and M[row][col] != 1):
            print "",1/M[row][col],"R",row+1
            M.rescale_row(row,1/M[row][col])
            show(M)
        change_flag=False
        for changed_row in range(row+1,num_rows):
            if M[changed_row][col] != 0:
                change_flag=True
                factor=-1*M[changed_row][col]/M[row][col]
                print "",factor," R",changed_row+1,"+R",changed_row
                M.add_multiple_of_row(changed_row,row,factor)
        if change_flag:
            show(M)
        col +=1
    print "Above is the echelon form, let's keep cruising to get the reduced echelon form"

    for changed_row in range(1,num_rows):
        for row in range(0,changed_row):
            factor = -1*M[row][changed_row]
            print "",factor," R",changed_row+1,"+R",row+1
            M.add_multiple_of_row(row,changed_row,factor)
            show(M)