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Matrix broadcasting was added to matlab’s recent editions. This is an important step for vectorizing codes. Proper usage of broadcasting reduces memory allocation requirements for matrix matrix operations.
Below we add together a 1 by 3 and 4 by 1 array, that should not work. With broadcasting, it is assumed that we will mesh the arrays and then sum up the meshed matrixes.
clear all
ar_A = [1,2,3];
ar_B = [4,3,2,1]';
disp(size(ar_A));
1 3
disp(size(ar_B));
4 1
mt_A_B_broadcast = ar_A + ar_B;
disp(mt_A_B_broadcast);
5 6 7
4 5 6
3 4 5
2 3 4
mt_A_B_broadcast_product = ar_A.*ar_B;
disp(mt_A_B_broadcast_product);
4 8 12
3 6 9
2 4 6
1 2 3Below we add together a 1 by 3 and 4 by 3 matrix, that should not work. With broadcasting, it is assumed that we will repeat the array four times, duplicating the single row four times, so the matrix dimensions match up.
clear all
ar_A = [1,2,3];
mt_B = [4,3,2,1;5,4,3,2;6,5,4,3]';
disp(size(ar_A));
1 3
disp(size(mt_B));
4 3
mt_A_B_broadcast = ar_A + mt_B;
disp(mt_A_B_broadcast);
5 7 9
4 6 8
3 5 7
2 4 6
mt_A_B_broadcast_product = ar_A.*mt_B;
disp(mt_A_B_broadcast_product);
4 10 18
3 8 15
2 6 12
1 4 9Below we add together a 4 by 1 and 4 by 3 matrix, that should not work. With broadcasting, it is assumed that we will repeat the column three times, duplicating the single column three times, so the matrix dimensions match up.
clear all
ar_A = [4,3,2,1]';
mt_B = [4,3,2,1;5,4,3,2;6,5,4,3]';
disp(size(ar_A));
4 1
disp(size(mt_B));
4 3
mt_A_B_broadcast = ar_A + mt_B;
disp(mt_A_B_broadcast);
8 9 10
6 7 8
4 5 6
2 3 4
mt_A_B_broadcast_product = ar_A.*mt_B;
disp(mt_A_B_broadcast_product);
16 20 24
9 12 15
4 6 8
1 2 3clear all
ar_w_perc = [0.1,0.5,0.9]
ar_w_perc = 1x3
0.1000 0.5000 0.9000
ar_w_level = [-2,0,2]
ar_w_level = 1x3
-2 0 2
fl_b_bd = -4
fl_b_bd = -4
ar_k_max = ar_w_level - fl_b_bd
ar_k_max = 1x3
2 4 6
ar_ak_perc = [0.1,0.3,0.7,0.9]
ar_ak_perc = 1x4
0.1000 0.3000 0.7000 0.9000
mt_k = (ar_k_max'*ar_ak_perc)'
mt_k = 4x3
0.2000 0.4000 0.6000
0.6000 1.2000 1.8000
1.4000 2.8000 4.2000
1.8000 3.6000 5.4000
mt_a = (ar_w_level - mt_k)
mt_a = 4x3
-2.2000 -0.4000 1.4000
-2.6000 -1.2000 0.2000
-3.4000 -2.8000 -2.2000
-3.8000 -3.6000 -3.4000clear all
% Same as above
ar_w_level = [-2,-1,-0.1]
ar_w_level = 1x3
-2.0000 -1.0000 -0.1000
fl_b_bd = -4
fl_b_bd = -4
ar_k_max = ar_w_level - fl_b_bd
ar_k_max = 1x3
2.0000 3.0000 3.9000
ar_ak_perc = [0.001, 0.1,0.3,0.7,0.9, 0.999]
ar_ak_perc = 1x6
0.0010 0.1000 0.3000 0.7000 0.9000 0.9990
mt_k = (ar_k_max'*ar_ak_perc)'
mt_k = 6x3
0.0020 0.0030 0.0039
0.2000 0.3000 0.3900
0.6000 0.9000 1.1700
1.4000 2.1000 2.7300
1.8000 2.7000 3.5100
1.9980 2.9970 3.8961
mt_a = (ar_w_level - mt_k)
mt_a = 6x3
-2.0020 -1.0030 -0.1039
-2.2000 -1.3000 -0.4900
-2.6000 -1.9000 -1.2700
-3.4000 -3.1000 -2.8300
-3.8000 -3.7000 -3.6100
-3.9980 -3.9970 -3.9961
% fraction of borrowing for bridge loan
ar_coh_bridge_perc = [0, 0.5, 0.999];
% Expand matrix to include coh percentage dimension
mt_k = repmat(mt_k, [1, length(ar_coh_bridge_perc)])
mt_k = 6x9
0.0020 0.0030 0.0039 0.0020 0.0030 0.0039 0.0020 0.0030 0.0039
0.2000 0.3000 0.3900 0.2000 0.3000 0.3900 0.2000 0.3000 0.3900
0.6000 0.9000 1.1700 0.6000 0.9000 1.1700 0.6000 0.9000 1.1700
1.4000 2.1000 2.7300 1.4000 2.1000 2.7300 1.4000 2.1000 2.7300
1.8000 2.7000 3.5100 1.8000 2.7000 3.5100 1.8000 2.7000 3.5100
1.9980 2.9970 3.8961 1.9980 2.9970 3.8961 1.9980 2.9970 3.8961
mt_a = repmat(mt_a, [1, length(ar_coh_bridge_perc)])
mt_a = 6x9
-2.0020 -1.0030 -0.1039 -2.0020 -1.0030 -0.1039 -2.0020 -1.0030 -0.1039
-2.2000 -1.3000 -0.4900 -2.2000 -1.3000 -0.4900 -2.2000 -1.3000 -0.4900
-2.6000 -1.9000 -1.2700 -2.6000 -1.9000 -1.2700 -2.6000 -1.9000 -1.2700
-3.4000 -3.1000 -2.8300 -3.4000 -3.1000 -2.8300 -3.4000 -3.1000 -2.8300
-3.8000 -3.7000 -3.6100 -3.8000 -3.7000 -3.6100 -3.8000 -3.7000 -3.6100
-3.9980 -3.9970 -3.9961 -3.9980 -3.9970 -3.9961 -3.9980 -3.9970 -3.9961
mt_a = mt_a
mt_a = 6x9
-2.0020 -1.0030 -0.1039 -2.0020 -1.0030 -0.1039 -2.0020 -1.0030 -0.1039
-2.2000 -1.3000 -0.4900 -2.2000 -1.3000 -0.4900 -2.2000 -1.3000 -0.4900
-2.6000 -1.9000 -1.2700 -2.6000 -1.9000 -1.2700 -2.6000 -1.9000 -1.2700
-3.4000 -3.1000 -2.8300 -3.4000 -3.1000 -2.8300 -3.4000 -3.1000 -2.8300
-3.8000 -3.7000 -3.6100 -3.8000 -3.7000 -3.6100 -3.8000 -3.7000 -3.6100
-3.9980 -3.9970 -3.9961 -3.9980 -3.9970 -3.9961 -3.9980 -3.9970 -3.9961
% bridge loan component of borrowing
ar_brdige_a = (ar_coh_bridge_perc'*ar_w_level)'
ar_brdige_a = 3x3
0 -1.0000 -1.9980
0 -0.5000 -0.9990
0 -0.0500 -0.0999
ar_brdige_a = ar_brdige_a(:)'
ar_brdige_a = 1x9
0 0 0 -1.0000 -0.5000 -0.0500 -1.9980 -0.9990 -0.0999
% borrowing choices excluding bridge loan
mt_a_nobridge = mt_a - ar_brdige_a
mt_a_nobridge = 6x9
-2.0020 -1.0030 -0.1039 -1.0020 -0.5030 -0.0539 -0.0040 -0.0040 -0.0040
-2.2000 -1.3000 -0.4900 -1.2000 -0.8000 -0.4400 -0.2020 -0.3010 -0.3901
-2.6000 -1.9000 -1.2700 -1.6000 -1.4000 -1.2200 -0.6020 -0.9010 -1.1701
-3.4000 -3.1000 -2.8300 -2.4000 -2.6000 -2.7800 -1.4020 -2.1010 -2.7301
-3.8000 -3.7000 -3.6100 -2.8000 -3.2000 -3.5600 -1.8020 -2.7010 -3.5101
-3.9980 -3.9970 -3.9961 -2.9980 -3.4970 -3.9461 -2.0000 -2.9980 -3.8962