0
$\begingroup$

I have a huge array of matrices that looks like this W1[[All,All,-1]]={{20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20., 20.}, {20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1, 20.1}, {20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2, 20.2}, {20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3, 20.3}, {20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4, 20.4}, {20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5, 20.5}, {20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6, 20.6}, {20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7, 20.7}, {20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8, 20.8}, {20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9, 20.9}, {21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21., 21.}, {21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1, 21.1}, {21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2, 21.2}, {21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3, 21.3}, {21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4, 21.4}, {21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5, 21.5}, {21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6, 21.6}, {21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7, 21.7}, {21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8, 21.8}, {21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9, 21.9}, {22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22., 22.}, {22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1, 22.1}, {22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2, 22.2}, {22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3, 22.3}, {22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4, 22.4}, {22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5, 22.5}, {22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6, 22.6}, {22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7, 22.7}, {22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8, 22.8}, {22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9, 22.9}, {23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23., 23.}, {23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1, 23.1}, {23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2, 23.2}, {23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3, 23.3}, {23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4, 23.4}, {23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5, 23.5}, {23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6, 23.6}, {23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7, 23.7}, {23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8, 23.8}, {23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9, 23.9}, {24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24., 24.}, {24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1, 24.1}, {24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2, 24.2}, {24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3, 24.3}, {24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4, 24.4}, {24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5, 24.5}, {24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6, 24.6}, {24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7, 24.7}, {24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8, 24.8}, {24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9, 24.9}, {25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25., 25.}, {25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1, 25.1}, {25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2, 25.2}, {25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3, 25.3}, {25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4, 25.4}, {25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5, 25.5}, {25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6, 25.6}, {25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7, 25.7}, {25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8, 25.8}, {25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9, 25.9}, {26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26., 26.}, {26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1, 26.1}, {26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2, 26.2}, {26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3, 26.3}, {26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4, 26.4}, {26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5, 26.5}, {26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6, 26.6}, {26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7, 26.7}, {26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8, 26.8}, {26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9, 26.9}, {27., 27., 27., 27., 27., 27., 27., 27., 27., 27., 27., 27., 27., 27.}, {27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1, 27.1}, {27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2, 27.2}, {27.3, 27.3, 27.3, 27.3, 27.3, 27.3, 27.3, 27.3, 27.3, 27.3, 27.3, 27.3, 27.3, 27.3}, {27.4, 27.4, 27.4, 27.4, 27.4, 27.4, 27.4, 27.4, 27.4, 27.4, 27.4, 27.4, 27.4, 27.4}, {27.5, 27.5, 27.5, 27.5, 27.5, 27.5, 27.5, 27.5, 27.5, 27.5, 27.5, 27.5, 27.5, 27.5}, {27.6, 27.6, 27.6, 27.6, 27.6, 27.6, 27.6, 27.6, 27.6, 27.6, 27.6, 27.6, 27.6}, {27.7, 27.7, 27.7, 27.7, 27.7, 27.7, 27.7, 27.7, 27.7, 27.7, 27.7}, {27.8, 27.8, 27.8, 27.8, 27.8, 27.8, 27.8, 27.8, 27.8, 27.8, 27.8}, {27.9, 27.9, 27.9, 27.9, 27.9, 27.9, 27.9, 27.9, 27.9, 27.9}, {28., 28., 28., 28., 28., 28., 28., 28., 28., 28.}, {28.1, 28.1, 28.1, 28.1, 28.1, 28.1, 28.1, 28.1, 28.1, 28.1}, {28.2, 28.2, 28.2, 28.2, 28.2, 28.2, 28.2, 28.2}, {28.3, 28.3, 28.3, 28.3, 28.3, 28.3, 28.3, 28.3}, {28.4, 28.4, 28.4, 28.4, 28.4}, {28.5, 28.5, 28.5, 28.5}, {28.6, 28.6, 28.6, 28.6, 28.6}, {28.7, 28.7, 28.7, 28.7, 28.7, 28.7}, {28.8, 28.8, 28.8, 28.8, 28.8, 28.8}, {28.9, 28.9, 28.9, 28.9, 28.9, 28.9}, {29., 29., 29., 29., 29., 29.}, {29.1, 29.1, 29.1, 29.1, 29.1, 29.1}, {29.2, 29.2, 29.2, 29.2, 29.2, 29.2}, {29.3, 29.3, 29.3, 29.3, 29.3}, {29.4, 29.4, 29.4, 29.4, 29.4}, {29.5, 29.5, 29.5, 29.5}, {29.6, 29.6, 29.6}, {29.7, 29.7, 29.7}, {29.8, 29.8}, {29.9, 29.9}, {30., 30.}}

I can make a histogram with LogCount along the Y axis

enter image description here

I am trying to replace the bins with a smooth histogram. I tried using SmoothKernelDistribution but I am getting error messages, perhaps due to the presence of matrices as an array?

Is there a way to do this?

To be more precise, I just want to make a smooth histogram of the binned histogram that I have shown. The X-axis have values that are repeated in each matrix, and the Y- axis is the Log of its frequency.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
4
$\begingroup$

The large list contains a lot of redundant data, but I think what you want is something like this: calling your list w, first simplify it by defining 

u = Length /@ w

{17, 19, 21, 22, 21, 21, 22, 19, 24, 26, 27, 31, 35, 34, 29, 26, 29, 33, 31, 35, 35, 31, 32, 32, 37, 38, 31, 26, 27, 30, 28, 36, 35, 34, 35, 36, 37, 32, 35, 39, 39, 44, 38, 40, 38, 39, 40, 44, 45, 44, 42, 45, 39, 42, 44, 44, 40, 38, 35, 35, 33, 30, 27, 23, 24, 23, 21, 19, 17, 16, 14, 17, 16, 14, 14, 14, 13, 11, 11, 10, 10, 10, 8, 8, 5, 4, 5, 6, 6, 6, 6, 6, 6, 5, 5, 4, 3, 3, 2, 2, 2}

Then use SmoothHistogram: 

SmoothHistogram[u]

smooth

Here I assume that you want a smoothed histogram of the number of entries in each sub-list (all entries being identical, there doesn't seem to be any other interpretation).

Edit

Maybe I was misled by your mention of SmoothKernelDistribution, and what you really want is just an interpolation like this:

f = ListInterpolation[u];

Plot[f[t], {t, 1, Length[u]}]

interp

This is the "smoothed" (continuous) version of the bar chart you show in the question, except not using a logarithmic scale. To get there, just replace Plot by LogPlot above.

Edit 2

Here is what I now think the question is asking for:

v = Flatten[w];
SmoothHistogram[v, .15, ScalingFunctions->"Log", Frame -> True, 
  PlotRange -> {{Min[v], Max[v]}, All}]

loghisto

Here, I used the option ScalingFunctions->"Log" to produce a logarithmic plot. The downside of this approach is that the vertical axis isn't labeled by the original frequency data, so it's harder to interpret.

If you want the more natural labeling, then it looks like the circle closes and we're back to the function SmoothKernelDistribution that you already mentioned in the question. This approach becomes necessary because I can then combine it with LogPlot to get this:

sv = SmoothKernelDistribution[v, .15]

(* ==> DataDistribution[<<"SmoothKernel">>, {2482}] *)

LogPlot[PDF[sv, x], {x, 20, 30}, Frame -> True]

logplotSv

So to use SmoothKernelDistribution with your data, you have to Flatten the large list first, and then use PDF to obtain a function from that distribution which can be plotted. As the plot function, you can then choose LogPlot to get the desired vertical scale.

Improve this answer
$\endgroup$
4
  • $\begingroup$ Thank you for your response. I was really looking for the SmoothHistogram option, however on searching I found this mathematica.stackexchange.com/questions/33231/… and that's why I was talking about SmoothKernelDistribution. Yes, the bin height is the frequency of each matrix. However, how do I make the Y-axis log? Also, I would like to have the x-axis show the values like 20, 20.1 ... and then the Y axis to show the frequency of that value. $\endgroup$
    – HuShu
    Commented Apr 3, 2015 at 4:30
  • $\begingroup$ Still not sure if I understand your question, but I updated my answer with what I now think you want. $\endgroup$
    – Jens
    Commented Apr 4, 2015 at 0:03
  • $\begingroup$ Yes, that's what I was after. Thanks. But is there a way to replace the Y axis with a log scale, and the numbers being the frequency instead of the probability? $\endgroup$
    – HuShu
    Commented Apr 4, 2015 at 0:42
  • $\begingroup$ Ah, I just copied the wrong image - the last command I posted already does produce a log scale, but the image was without log scale... However, I suspect you are still looking for a different thing. You want the y axis still labeled by the actual frequency, as opposed to the logarithm of the frequency, right? In that case, I'll make another edit... $\endgroup$
    – Jens
    Commented Apr 4, 2015 at 2:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.