ls=single(1+rand()) ls = 1.9133759 rs=ls+eps(single(ls)) rs = 1.9133760 ld=double(ls) ld = 1.913375854492188 rd=double(rs) rd = 1.913375973701477 cnt=0; mark=ld; while( mark <= rd ) cnt=cnt+1; mark=mark+eps(mark); end cnt cnt = 536870913 cnt=cnt-2 cnt = 536870911 2^29-1 ans = 536870911 pwd ans = /Users/pauldj/works/courses/LSC/LSC-15 ls ls = 1.9133759 lu(rand(3)) ans = 0.632359246225410 0.546881519204984 0.157613081677548 0.154248404813615 0.873151233474882 0.946281215334096 0.440411396732824 0.829221392263737 0.103075723945612 lu = 4 lu = 4 lu(rand(3)) {Subscript indices must either be real positive integers or logicals. } clear('lu') C=reshape(36,6,6) {Error using reshape To RESHAPE the number of elements must not change. } C=reshape(1:36,6,6) C = 1 7 13 19 25 31 2 8 14 20 26 32 3 9 15 21 27 33 4 10 16 22 28 34 5 11 17 23 29 35 6 12 18 24 30 36 C( 2:3, 2:3 ) = eye(2) C = 1 7 13 19 25 31 2 1 0 20 26 32 3 0 1 21 27 33 4 10 16 22 28 34 5 11 17 23 29 35 6 12 18 24 30 36 C( [2 3 6], [2 3] ) = rand(3,2) C = Columns 1 through 3 1.000000000000000 7.000000000000000 13.000000000000000 2.000000000000000 0.849129305868777 0.757740130578333 3.000000000000000 0.933993247757551 0.743132468124916 4.000000000000000 10.000000000000000 16.000000000000000 5.000000000000000 11.000000000000000 17.000000000000000 6.000000000000000 0.678735154857773 0.392227019534168 Columns 4 through 6 19.000000000000000 25.000000000000000 31.000000000000000 20.000000000000000 26.000000000000000 32.000000000000000 21.000000000000000 27.000000000000000 33.000000000000000 22.000000000000000 28.000000000000000 34.000000000000000 23.000000000000000 29.000000000000000 35.000000000000000 24.000000000000000 30.000000000000000 36.000000000000000 format short C C = 1.0000 7.0000 13.0000 19.0000 25.0000 31.0000 2.0000 0.8491 0.7577 20.0000 26.0000 32.0000 3.0000 0.9340 0.7431 21.0000 27.0000 33.0000 4.0000 10.0000 16.0000 22.0000 28.0000 34.0000 5.0000 11.0000 17.0000 23.0000 29.0000 35.0000 6.0000 0.6787 0.3922 24.0000 30.0000 36.0000 C( [2 3 6], [2 3] ) = -1 C = 1 7 13 19 25 31 2 -1 -1 20 26 32 3 -1 -1 21 27 33 4 10 16 22 28 34 5 11 17 23 29 35 6 -1 -1 24 30 36 C( 3, : ) = [ 1 2 3 4 5 6 ] C = 1 7 13 19 25 31 2 -1 -1 20 26 32 1 2 3 4 5 6 4 10 16 22 28 34 5 11 17 23 29 35 6 -1 -1 24 30 36 C( :, 3 ) = [] C = 1 7 19 25 31 2 -1 20 26 32 1 2 4 5 6 4 10 22 28 34 5 11 23 29 35 6 -1 24 30 36 C( end:-3:2, 2:3:end ) = 0 C = 1 7 19 25 31 2 -1 20 26 32 1 0 4 5 0 4 10 22 28 34 5 11 23 29 35 6 0 24 30 0 C( end:-3:2, 2:3:end ) = [1000 1001; 1002 1003] C = 1 7 19 25 31 2 -1 20 26 32 1 1002 4 5 1003 4 10 22 28 34 5 11 23 29 35 6 1000 24 30 1001 C( end:-3:2, 2:3:end ) = [1000 1001] {Subscripted assignment dimension mismatch. } C( end:-3:2, 2:3:end ) = [1000 1001 1002 1004] {Subscripted assignment dimension mismatch. } C C = 1 7 19 25 31 2 -1 20 26 32 1 1002 4 5 1003 4 10 22 28 34 5 11 23 29 35 6 1000 24 30 1001 [m,n]=size(C) m = 6 n = 5 edit pwd ans = /Users/pauldj/works/courses/LSC/LSC-15 script ans = 1 ans = 7 ans = 19 ans = 25 ans = 31 {Index exceeds matrix dimensions. Error in script (line 3) C(i,j) } script {Error: File: script.m Line: 3 Column: 10 Unbalanced or unexpected parenthesis or bracket. } script ans = 1 ans = 7 ans = 19 ans = 25 ans = 31 ans = 2 ans = -1 ans = 20 ans = 26 ans = 32 ans = 1 ans = 1002 ans = 4 ans = 5 ans = 1003 ans = 4 ans = 10 ans = 22 ans = 28 ans = 34 ans = 5 ans = 11 ans = 23 ans = 29 ans = 35 ans = 6 ans = 1000 ans = 24 ans = 30 ans = 1001 C=reshape(1:36,6,6) C = 1 7 13 19 25 31 2 8 14 20 26 32 3 9 15 21 27 33 4 10 16 22 28 34 5 11 17 23 29 35 6 12 18 24 30 36 script ans = 1 7 2 8 ans = 13 19 14 20 ans = 25 31 26 32 ans = 3 9 4 10 ans = 15 21 16 22 ans = 27 33 28 34 ans = 5 11 6 12 ans = 17 23 18 24 ans = 29 35 30 36 script ans = 1 7 13 2 8 14 3 9 15 ans = 19 25 31 20 26 32 21 27 33 ans = 4 10 16 5 11 17 6 12 18 ans = 22 28 34 23 29 35 24 30 36 script ans = 1 7 13 19 2 8 14 20 3 9 15 21 4 10 16 22 {Index exceeds matrix dimensions. Error in script (line 5) C(i:i+b-1,j:j+b-1) } C C = 1 7 13 19 25 31 2 8 14 20 26 32 3 9 15 21 27 33 4 10 16 22 28 34 5 11 17 23 29 35 6 12 18 24 30 36 script ans = 1 7 13 19 2 8 14 20 3 9 15 21 4 10 16 22 ans = 25 31 26 32 27 33 28 34 ans = 5 11 17 23 6 12 18 24 ans = 29 35 30 36 script ans = 1 7 13 19 25 2 8 14 20 26 3 9 15 21 27 4 10 16 22 28 ans = 5 11 17 23 29 6 12 18 24 30 C C = 1 7 13 19 25 31 2 8 14 20 26 32 3 9 15 21 27 33 4 10 16 22 28 34 5 11 17 23 29 35 6 12 18 24 30 36 m m = 6 n n = 5 [m,n]=size(C) m = 6 n = 6 script ans = 1 7 13 19 25 2 8 14 20 26 3 9 15 21 27 4 10 16 22 28 ans = 31 32 33 34 ans = 5 11 17 23 29 6 12 18 24 30 ans = 35 36 C C = 1 7 13 19 25 31 2 8 14 20 26 32 3 9 15 21 27 33 4 10 16 22 28 34 5 11 17 23 29 35 6 12 18 24 30 36 size(C(3:2, 1:3)) ans = 0 3 C(3:2, 1:3) ans = Empty matrix: 0-by-3 C(3:2, :) ans = Empty matrix: 0-by-6 C(3:2, :) * rand(6,3) ans = Empty matrix: 0-by-3 C(3:2, :)' ans = Empty matrix: 6-by-0 C(3:2, :)'*C(3:2, :) ans = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C(3:2, :)*C(3:2, :)' ans = [] [C(3:2, :); eye(6)] ans = 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 edit MatVec [W,V]=eig(rand(4)) W = 0.2743 0.5692 -0.4828 -0.0490 0.4924 -0.3102 0.5389 -0.7973 0.7611 0.2512 0.5708 0.5329 0.3211 -0.7188 -0.3882 0.2792 V = 1.9561 0 0 0 0 -0.3914 0 0 0 0 0.4674 0 0 0 0 0.3080 MatVec( eye(5), 1:5 ) {Error: File: MatVec.m Line: 5 Column: 4 This statement is not inside any function. (It follows the END that terminates the definition of the function "MatVec".) } MatVec( eye(5), 1:5 ) {Error using * Inner matrix dimensions must agree. Error in MatVec (line 4) y = M*v; } 1:5 ans = 1 2 3 4 5 1:5' ans = 1 2 3 4 5 (1:5)' ans = 1 2 3 4 5 MatVec( eye(5), (1:5)' ) ans = 1 2 3 4 5 [output1, output2]=MatVec( eye(5), (1:5)' ) output1 = 1 2 3 4 5 output2 = 5 1 [~, output2]=MatVec( eye(5), (1:5)' ) output2 = 5 1 matrix(4) M = 0 0 1 1 0 0 1 1 2 3 3 4 2 3 3 4 ans = 0 0 1 1 0 0 1 1 2 3 3 4 2 3 3 4 matrix(8) M = 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 2 2 3 3 3 3 4 4 2 2 3 3 3 3 4 4 2 2 3 3 3 3 4 4 2 2 3 3 3 3 4 4 ans = 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 2 2 3 3 3 3 4 4 2 2 3 3 3 3 4 4 2 2 3 3 3 3 4 4 2 2 3 3 3 3 4 4 matrix(12) M = 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 ans = 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 matrixV(12,rand(12,1)) M = 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 x = 2.5596 2.5596 2.5596 2.5596 2.5596 2.5596 18.1182 18.1182 18.1182 18.1182 18.1182 18.1182 ans = 2.5596 2.5596 2.5596 2.5596 2.5596 2.5596 18.1182 18.1182 18.1182 18.1182 18.1182 18.1182 y=rand(12,1) y = 0.9293 0.3500 0.1966 0.2511 0.6160 0.4733 0.3517 0.8308 0.5853 0.5497 0.9172 0.2858 matrixV(12,y) M = 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 x = 3.5205 3.5205 3.5205 3.5205 3.5205 3.5205 19.2872 19.2872 19.2872 19.2872 19.2872 19.2872 ans = 3.5205 3.5205 3.5205 3.5205 3.5205 3.5205 19.2872 19.2872 19.2872 19.2872 19.2872 19.2872 sum(y(7:12)) ans = 3.5205 matrixV(12,y) x = 3.5205 19.2872 ans = 3.5205 19.2872 matrixV(12,y) x = 3.5205 3.5205 3.5205 3.5205 3.5205 3.5205 19.2872 19.2872 19.2872 19.2872 19.2872 19.2872 ans = 3.5205 3.5205 3.5205 3.5205 3.5205 3.5205 19.2872 19.2872 19.2872 19.2872 19.2872 19.2872 matrixV(12,y) {Undefined function or variable 'xT'. Error in matrixV (line 12) x = [xT * ones(h,1) ; } matrixV(12,y) x = 3.5205 3.5205 3.5205 3.5205 3.5205 3.5205 19.2872 19.2872 19.2872 19.2872 19.2872 19.2872 ans = 3.5205 3.5205 3.5205 3.5205 3.5205 3.5205 19.2872 19.2872 19.2872 19.2872 19.2872 19.2872 matrixV0(12,y) M = 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 2 2 2 3 3 3 3 3 3 4 4 4 ans = 3.5205 3.5205 3.5205 3.5205 3.5205 3.5205 19.2872 19.2872 19.2872 19.2872 19.2872 19.2872 matrixV0(12,y) ans = 3.5205 3.5205 3.5205 3.5205 3.5205 3.5205 19.2872 19.2872 19.2872 19.2872 19.2872 19.2872 n=6000; y=rand(n,1); tic; matrixV0(n,y); toc Elapsed time is 0.455725 seconds. clc clc n=6000; y=rand(n,1); tic; matrixV0(n,y); toc Elapsed time is 0.425470 seconds. n=6000; y=rand(n,1); tic; matrixV0(n,y); toc Elapsed time is 0.418413 seconds. n=6000; y=rand(n,1); tic; matrixV0(n,y); toc Elapsed time is 0.420060 seconds. n=6000; y=rand(n,1); tic; matrixV(n,y); toc Elapsed time is 0.000978 seconds. n=6000; y=rand(n,1); tic; matrixV(n,y); toc Elapsed time is 0.000230 seconds. n=6000; y=rand(n,1); tic; matrixV(n,y); toc Elapsed time is 0.000166 seconds. n=6000; y=rand(n,1); tic; matrixV(n,y); toc Elapsed time is 0.000212 seconds. diary