How do i complete this matrix that has n+1 rows and m columns?

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cakey 2014-11-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/162964-how-do-i-complete-this-matrix-that-has-n-1-rows-and-m-columns

编辑： per isakson 2014-11-17

This stops at the 2nd row of the matrix, How can i get the whole matrix? Also, can someone explain what is going on?

function phi_values = phi_part1(a_vec, b_vec, x_vec)
    n = length(a_vec);
    m = length(x_vec);
    phi_values = zeros(n + 1, m);
      phi_values(1, :) = 1 / sqrt(b_vec(1));
      a0 = a_vec(1);
      b1 = b_vec(2);
      phi_values(2, :) = ((x_vec - a0) .* phi_values(1, :)) / sqrt(b1);
      k = 2;
      %%phi_values(k + 1, :)
      bk = b_vec(k + 1);
      bk_minus_1 = b_vec(k);
      ak_minus_1 = a_vec(k);
      left_quantity = ((x_vec - ak_minus_1) .* phi_values(k, :));
      right_quantity = sqrt(bk_minus_1) * phi_values(k - 1, :);
      phi_values(k + 1, :) = (left_quantity - right_quantity) / sqrt(bk);
  end

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Answer 1

per isakson 2014-11-17

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/162964-how-do-i-complete-this-matrix-that-has-n-1-rows-and-m-columns#answer_159177

编辑：per isakson 2014-11-17

在 MATLAB Online 中打开

"stops at the 2nd row of the matrix" &nbsp Firstly, I think it stop at the third row. Why shouldn't it stop after assigning values to three rows? I have indicated with &nbsp|<< n >>| &nbsp the rows, which do these tree assignments.

Secondly, I have added a for-loop, guessed regarding the input values and invoked the function

    a_vec = randi( [1,9], [1,8] );
    b_vec = randi( [1,6], [1,9] );
    x_vec = randi( [1,9], [1,4] );
    phi_values = cssm( a_vec, b_vec, x_vec )
    phi_values =
        0.4472    0.4472    0.4472    0.4472
       -0.3162   -0.3162         0    0.3162
       -0.6455   -0.6455   -0.2582    0.3873
        2.0656    2.0656    0.2582   -0.7746
        5.1430    5.1430    0.8944   -2.9069
        3.8730    3.8730    1.2910   -5.9386
        2.9445    2.9445    2.1939  -13.6832
        1.3943    1.3943    3.6148  -30.7773
       -7.6133   -7.6133   -8.5810   43.3979

where

    function    phi_values = cssm( a_vec, b_vec, x_vec )
        n = length(a_vec);
        m = length(x_vec);
        phi_values = zeros(n + 1, m);
        phi_values(1, :) = 1 / sqrt(b_vec(1));                      % << 1 >>
        a0 = a_vec(1);
        b1 = b_vec(2);
        phi_values(2, :) = ((x_vec - a0) .* phi_values(1, :)) ...
                                          / sqrt(b1);               % << 2 >>
        for k = 2 : n;
            %%phi_values(k + 1, :)
            bk = b_vec(k + 1);
            bk_minus_1 = b_vec(k);
            ak_minus_1 = a_vec(k);
            left_quantity = ((x_vec - ak_minus_1) .* phi_values(k, :));
            right_quantity = sqrt(bk_minus_1) * phi_values(k - 1, :);
            phi_values(k + 1, :) ...
            =   (left_quantity - right_quantity) / sqrt(bk);        % << 3 >>
        end
    end

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cakey 2014-11-17

Oh, so I had to create a loop then? Also, how did you know what to put for the input vectors? In addition, can you tell me what is going on with "left quantity" and "right quantity"? What are they calculating?

per isakson 2014-11-17

编辑：per isakson 2014-11-17

"how did you know what to put for the input vectors" &nbsp I just picked some small numbers. The row, &nbsp bk&nbsp=&nbspb_vec(k + 1);, &nbsp requires that &nbsp b_vec &nbsp is at least one element larger than &nbsp a_vec.

"going on with "left quantity" and "right quantity"?" &nbsp I cannot guess. You should know what this code is supposed to do.

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