Artifact d9840874d331e6e4bf2a7a320d77d8ffc392ca6a818dd3fbbc81369d2e4ec567:
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r38/log/sparse.rlg
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2011-09-02 18:13:33
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Tue Apr 15 00:34:43 2008 run on win32 % Test file for Sparse Matrices and the Linear Algebra Package for % Sparse Matrices. % Author: Stephen Scowcroft. Date: June 1995. % Firstly, the matrices need to be created. % This is the standard way to create a sparse matrix. % Create a sparse matrix. sparse mat1(5,5); %Fill the sparse matrix with data mat1(1,1):=2; mat1(1,1) := 2 mat1(2,2):=4; mat1(2,2) := 4 mat1(3,3):=6; mat1(3,3) := 6 mat1(4,4):=8; mat1(4,4) := 8 mat1(5,5):=10; mat1(5,5) := 10 sparse mat4(5,5); mat4(1,1):=x; mat4(1,1) := x mat4(2,2):=x; mat4(2,2) := x mat4(3,3):=x; mat4(3,3) := x mat4(4,4):=x; mat4(4,4) := x mat4(5,5):=x; mat4(5,5) := x % A small function to automatically fill a sparse matrix with data. procedure makematsp(nam,row); begin; sparse nam(row,row); for i := 1:row do <<nam(i,i):=i>> end; makematsp clear mat2; makematsp(mat2,100); % Matrices created in the standard Matrix way. zz1:=mat((1,2),(3,4)); [1 2] zz1 := [ ] [3 4] zz2:=mat((x,x),(x,x)); [x x] zz2 := [ ] [x x] zz3:=mat((i+1,i+2,i+3),(4,5,2),(1,i,0)); [i + 1 i + 2 i + 3] [ ] zz3 := [ 4 5 2 ] [ ] [ 1 i 0 ] % I have taken advantage of the Linear Algebra Package (Matt Rebbeck) % in order to create some Sparse Matrices. mat3:=diagonal(zz1,zz1,zz1); [1 2 0 0 0 0] [ ] [3 4 0 0 0 0] [ ] [0 0 1 2 0 0] mat3 := [ ] [0 0 3 4 0 0] [ ] [0 0 0 0 1 2] [ ] [0 0 0 0 3 4] mat5:=band_matrix({1,3,1},100)$ mat6:=diagonal(zz3,zz3); [i + 1 i + 2 i + 3 0 0 0 ] [ ] [ 4 5 2 0 0 0 ] [ ] [ 1 i 0 0 0 0 ] mat6 := [ ] [ 0 0 0 i + 1 i + 2 i + 3] [ ] [ 0 0 0 4 5 2 ] [ ] [ 0 0 0 1 i 0 ] mat7:=band_matrix({a,b,c},4); [b c 0 0] [ ] [a b c 0] mat7 := [ ] [0 a b c] [ ] [0 0 a b] % These are then "translated" into the Sparse operator using the % function transmat. % This is a destructive function in the sense that the matrices are no % longer of type 'matrix but are now 'sparse. transmat mat3; transmat mat5; transmat mat6; transmat mat7; poly := x^7+x^5+4*x^4+5*x^3+12; 7 5 4 3 poly := x + x + 4*x + 5*x + 12 poly1 := x^2+x*y^3+x*y*z^3+y*x+2+y*3; 2 3 3 poly1 := x + x*y + x*y*z + x*y + 3*y + 2 % Firstly some basic matrix operations. % These are the same as the present matrix package mat1^-1; 1 spm(1,1) := ---$ 2 1 spm(2,2) := ---$ 4 1 spm(3,3) := ---$ 6 1 spm(4,4) := ---$ 8 1 spm(5,5) := ----$ 10 mat4^-1; 1 spm(1,1) := ---$ x 1 spm(2,2) := ---$ x 1 spm(3,3) := ---$ x 1 spm(4,4) := ---$ x 1 spm(5,5) := ---$ x mat2 + mat5$ mat2 - mat5$ mat1-mat1; "Empty Matrix" mat4 + mat1; spm(1,1) := x + 2$ spm(2,2) := x + 4$ spm(3,3) := x + 6$ spm(4,4) := x + 8$ spm(5,5) := x + 10$ mat4 * mat1; spm(1,1) := 2*x$ spm(2,2) := 4*x$ spm(3,3) := 6*x$ spm(4,4) := 8*x$ spm(5,5) := 10*x$ 2*mat1 + (3*mat4 + mat1); spm(1,1) := 3*(x + 2)$ spm(2,2) := 3*(x + 4)$ spm(3,3) := 3*(x + 6)$ spm(4,4) := 3*(x + 8)$ spm(5,5) := 3*(x + 10)$ % It is also possible to combine both 'matrix and 'sparse type matrices % in these operations. pp:=band_matrix({1,3,1},100)$ mat5*pp; spm(1,1) := 10$ spm(1,2) := 6$ spm(1,3) := 1$ spm(2,1) := 6$ spm(2,2) := 11$ spm(2,3) := 6$ spm(2,4) := 1$ spm(3,1) := 1$ spm(3,2) := 6$ spm(3,3) := 11$ spm(3,4) := 6$ spm(3,5) := 1$ spm(4,2) := 1$ spm(4,3) := 6$ spm(4,4) := 11$ spm(4,5) := 6$ spm(4,6) := 1$ spm(5,3) := 1$ spm(5,4) := 6$ spm(5,5) := 11$ spm(5,6) := 6$ spm(5,7) := 1$ spm(6,4) := 1$ spm(6,5) := 6$ spm(6,6) := 11$ spm(6,7) := 6$ spm(6,8) := 1$ spm(7,5) := 1$ spm(7,6) := 6$ spm(7,7) := 11$ spm(7,8) := 6$ spm(7,9) := 1$ spm(8,6) := 1$ spm(8,7) := 6$ spm(8,8) := 11$ spm(8,9) := 6$ spm(8,10) := 1$ spm(9,7) := 1$ spm(9,8) := 6$ spm(9,9) := 11$ spm(9,10) := 6$ spm(9,11) := 1$ spm(10,8) := 1$ spm(10,9) := 6$ spm(10,10) := 11$ spm(10,11) := 6$ spm(10,12) := 1$ spm(11,9) := 1$ spm(11,10) := 6$ spm(11,11) := 11$ spm(11,12) := 6$ spm(11,13) := 1$ spm(12,10) := 1$ spm(12,11) := 6$ spm(12,12) := 11$ spm(12,13) := 6$ spm(12,14) := 1$ spm(13,11) := 1$ spm(13,12) := 6$ spm(13,13) := 11$ spm(13,14) := 6$ spm(13,15) := 1$ spm(14,12) := 1$ spm(14,13) := 6$ spm(14,14) := 11$ spm(14,15) := 6$ spm(14,16) := 1$ spm(15,13) := 1$ spm(15,14) := 6$ spm(15,15) := 11$ spm(15,16) := 6$ spm(15,17) := 1$ spm(16,14) := 1$ spm(16,15) := 6$ spm(16,16) := 11$ spm(16,17) := 6$ spm(16,18) := 1$ spm(17,15) := 1$ spm(17,16) := 6$ spm(17,17) := 11$ spm(17,18) := 6$ spm(17,19) := 1$ spm(18,16) := 1$ spm(18,17) := 6$ spm(18,18) := 11$ spm(18,19) := 6$ spm(18,20) := 1$ spm(19,17) := 1$ spm(19,18) := 6$ spm(19,19) := 11$ spm(19,20) := 6$ spm(19,21) := 1$ spm(20,18) := 1$ spm(20,19) := 6$ spm(20,20) := 11$ spm(20,21) := 6$ spm(20,22) := 1$ spm(21,19) := 1$ spm(21,20) := 6$ spm(21,21) := 11$ spm(21,22) := 6$ spm(21,23) := 1$ spm(22,20) := 1$ spm(22,21) := 6$ spm(22,22) := 11$ spm(22,23) := 6$ spm(22,24) := 1$ spm(23,21) := 1$ spm(23,22) := 6$ spm(23,23) := 11$ spm(23,24) := 6$ spm(23,25) := 1$ spm(24,22) := 1$ spm(24,23) := 6$ spm(24,24) := 11$ spm(24,25) := 6$ spm(24,26) := 1$ spm(25,23) := 1$ spm(25,24) := 6$ spm(25,25) := 11$ spm(25,26) := 6$ spm(25,27) := 1$ spm(26,24) := 1$ spm(26,25) := 6$ spm(26,26) := 11$ spm(26,27) := 6$ spm(26,28) := 1$ spm(27,25) := 1$ spm(27,26) := 6$ spm(27,27) := 11$ spm(27,28) := 6$ spm(27,29) := 1$ spm(28,26) := 1$ spm(28,27) := 6$ spm(28,28) := 11$ spm(28,29) := 6$ spm(28,30) := 1$ spm(29,27) := 1$ spm(29,28) := 6$ spm(29,29) := 11$ spm(29,30) := 6$ spm(29,31) := 1$ spm(30,28) := 1$ spm(30,29) := 6$ spm(30,30) := 11$ spm(30,31) := 6$ spm(30,32) := 1$ spm(31,29) := 1$ spm(31,30) := 6$ spm(31,31) := 11$ spm(31,32) := 6$ spm(31,33) := 1$ spm(32,30) := 1$ spm(32,31) := 6$ spm(32,32) := 11$ spm(32,33) := 6$ spm(32,34) := 1$ spm(33,31) := 1$ spm(33,32) := 6$ spm(33,33) := 11$ spm(33,34) := 6$ spm(33,35) := 1$ spm(34,32) := 1$ spm(34,33) := 6$ spm(34,34) := 11$ spm(34,35) := 6$ spm(34,36) := 1$ spm(35,33) := 1$ spm(35,34) := 6$ spm(35,35) := 11$ spm(35,36) := 6$ spm(35,37) := 1$ spm(36,34) := 1$ spm(36,35) := 6$ spm(36,36) := 11$ spm(36,37) := 6$ spm(36,38) := 1$ spm(37,35) := 1$ spm(37,36) := 6$ spm(37,37) := 11$ spm(37,38) := 6$ spm(37,39) := 1$ spm(38,36) := 1$ spm(38,37) := 6$ spm(38,38) := 11$ spm(38,39) := 6$ spm(38,40) := 1$ spm(39,37) := 1$ spm(39,38) := 6$ spm(39,39) := 11$ spm(39,40) := 6$ spm(39,41) := 1$ spm(40,38) := 1$ spm(40,39) := 6$ spm(40,40) := 11$ spm(40,41) := 6$ spm(40,42) := 1$ spm(41,39) := 1$ spm(41,40) := 6$ spm(41,41) := 11$ spm(41,42) := 6$ spm(41,43) := 1$ spm(42,40) := 1$ spm(42,41) := 6$ spm(42,42) := 11$ spm(42,43) := 6$ spm(42,44) := 1$ spm(43,41) := 1$ spm(43,42) := 6$ spm(43,43) := 11$ spm(43,44) := 6$ spm(43,45) := 1$ spm(44,42) := 1$ spm(44,43) := 6$ spm(44,44) := 11$ spm(44,45) := 6$ spm(44,46) := 1$ spm(45,43) := 1$ spm(45,44) := 6$ spm(45,45) := 11$ spm(45,46) := 6$ spm(45,47) := 1$ spm(46,44) := 1$ spm(46,45) := 6$ spm(46,46) := 11$ spm(46,47) := 6$ spm(46,48) := 1$ spm(47,45) := 1$ spm(47,46) := 6$ spm(47,47) := 11$ spm(47,48) := 6$ spm(47,49) := 1$ spm(48,46) := 1$ spm(48,47) := 6$ spm(48,48) := 11$ spm(48,49) := 6$ spm(48,50) := 1$ spm(49,47) := 1$ spm(49,48) := 6$ spm(49,49) := 11$ spm(49,50) := 6$ spm(49,51) := 1$ spm(50,48) := 1$ spm(50,49) := 6$ spm(50,50) := 11$ spm(50,51) := 6$ spm(50,52) := 1$ spm(51,49) := 1$ spm(51,50) := 6$ spm(51,51) := 11$ spm(51,52) := 6$ spm(51,53) := 1$ spm(52,50) := 1$ spm(52,51) := 6$ spm(52,52) := 11$ spm(52,53) := 6$ spm(52,54) := 1$ spm(53,51) := 1$ spm(53,52) := 6$ spm(53,53) := 11$ spm(53,54) := 6$ spm(53,55) := 1$ spm(54,52) := 1$ spm(54,53) := 6$ spm(54,54) := 11$ spm(54,55) := 6$ spm(54,56) := 1$ spm(55,53) := 1$ spm(55,54) := 6$ spm(55,55) := 11$ spm(55,56) := 6$ spm(55,57) := 1$ spm(56,54) := 1$ spm(56,55) := 6$ spm(56,56) := 11$ spm(56,57) := 6$ spm(56,58) := 1$ spm(57,55) := 1$ spm(57,56) := 6$ spm(57,57) := 11$ spm(57,58) := 6$ spm(57,59) := 1$ spm(58,56) := 1$ spm(58,57) := 6$ spm(58,58) := 11$ spm(58,59) := 6$ spm(58,60) := 1$ spm(59,57) := 1$ spm(59,58) := 6$ spm(59,59) := 11$ spm(59,60) := 6$ spm(59,61) := 1$ spm(60,58) := 1$ spm(60,59) := 6$ spm(60,60) := 11$ spm(60,61) := 6$ spm(60,62) := 1$ spm(61,59) := 1$ spm(61,60) := 6$ spm(61,61) := 11$ spm(61,62) := 6$ spm(61,63) := 1$ spm(62,60) := 1$ spm(62,61) := 6$ spm(62,62) := 11$ spm(62,63) := 6$ spm(62,64) := 1$ spm(63,61) := 1$ spm(63,62) := 6$ spm(63,63) := 11$ spm(63,64) := 6$ spm(63,65) := 1$ spm(64,62) := 1$ spm(64,63) := 6$ spm(64,64) := 11$ spm(64,65) := 6$ spm(64,66) := 1$ spm(65,63) := 1$ spm(65,64) := 6$ spm(65,65) := 11$ spm(65,66) := 6$ spm(65,67) := 1$ spm(66,64) := 1$ spm(66,65) := 6$ spm(66,66) := 11$ spm(66,67) := 6$ spm(66,68) := 1$ spm(67,65) := 1$ spm(67,66) := 6$ spm(67,67) := 11$ spm(67,68) := 6$ spm(67,69) := 1$ spm(68,66) := 1$ spm(68,67) := 6$ spm(68,68) := 11$ spm(68,69) := 6$ spm(68,70) := 1$ spm(69,67) := 1$ spm(69,68) := 6$ spm(69,69) := 11$ spm(69,70) := 6$ spm(69,71) := 1$ spm(70,68) := 1$ spm(70,69) := 6$ spm(70,70) := 11$ spm(70,71) := 6$ spm(70,72) := 1$ spm(71,69) := 1$ spm(71,70) := 6$ spm(71,71) := 11$ spm(71,72) := 6$ spm(71,73) := 1$ spm(72,70) := 1$ spm(72,71) := 6$ spm(72,72) := 11$ spm(72,73) := 6$ spm(72,74) := 1$ spm(73,71) := 1$ spm(73,72) := 6$ spm(73,73) := 11$ spm(73,74) := 6$ spm(73,75) := 1$ spm(74,72) := 1$ spm(74,73) := 6$ spm(74,74) := 11$ spm(74,75) := 6$ spm(74,76) := 1$ spm(75,73) := 1$ spm(75,74) := 6$ spm(75,75) := 11$ spm(75,76) := 6$ spm(75,77) := 1$ spm(76,74) := 1$ spm(76,75) := 6$ spm(76,76) := 11$ spm(76,77) := 6$ spm(76,78) := 1$ spm(77,75) := 1$ spm(77,76) := 6$ spm(77,77) := 11$ spm(77,78) := 6$ spm(77,79) := 1$ spm(78,76) := 1$ spm(78,77) := 6$ spm(78,78) := 11$ spm(78,79) := 6$ spm(78,80) := 1$ spm(79,77) := 1$ spm(79,78) := 6$ spm(79,79) := 11$ spm(79,80) := 6$ spm(79,81) := 1$ spm(80,78) := 1$ spm(80,79) := 6$ spm(80,80) := 11$ spm(80,81) := 6$ spm(80,82) := 1$ spm(81,79) := 1$ spm(81,80) := 6$ spm(81,81) := 11$ spm(81,82) := 6$ spm(81,83) := 1$ spm(82,80) := 1$ spm(82,81) := 6$ spm(82,82) := 11$ spm(82,83) := 6$ spm(82,84) := 1$ spm(83,81) := 1$ spm(83,82) := 6$ spm(83,83) := 11$ spm(83,84) := 6$ spm(83,85) := 1$ spm(84,82) := 1$ spm(84,83) := 6$ spm(84,84) := 11$ spm(84,85) := 6$ spm(84,86) := 1$ spm(85,83) := 1$ spm(85,84) := 6$ spm(85,85) := 11$ spm(85,86) := 6$ spm(85,87) := 1$ spm(86,84) := 1$ spm(86,85) := 6$ spm(86,86) := 11$ spm(86,87) := 6$ spm(86,88) := 1$ spm(87,85) := 1$ spm(87,86) := 6$ spm(87,87) := 11$ spm(87,88) := 6$ spm(87,89) := 1$ spm(88,86) := 1$ spm(88,87) := 6$ spm(88,88) := 11$ spm(88,89) := 6$ spm(88,90) := 1$ spm(89,87) := 1$ spm(89,88) := 6$ spm(89,89) := 11$ spm(89,90) := 6$ spm(89,91) := 1$ spm(90,88) := 1$ spm(90,89) := 6$ spm(90,90) := 11$ spm(90,91) := 6$ spm(90,92) := 1$ spm(91,89) := 1$ spm(91,90) := 6$ spm(91,91) := 11$ spm(91,92) := 6$ spm(91,93) := 1$ spm(92,90) := 1$ spm(92,91) := 6$ spm(92,92) := 11$ spm(92,93) := 6$ spm(92,94) := 1$ spm(93,91) := 1$ spm(93,92) := 6$ spm(93,93) := 11$ spm(93,94) := 6$ spm(93,95) := 1$ spm(94,92) := 1$ spm(94,93) := 6$ spm(94,94) := 11$ spm(94,95) := 6$ spm(94,96) := 1$ spm(95,93) := 1$ spm(95,94) := 6$ spm(95,95) := 11$ spm(95,96) := 6$ spm(95,97) := 1$ spm(96,94) := 1$ spm(96,95) := 6$ spm(96,96) := 11$ spm(96,97) := 6$ spm(96,98) := 1$ spm(97,95) := 1$ spm(97,96) := 6$ spm(97,97) := 11$ spm(97,98) := 6$ spm(97,99) := 1$ spm(98,96) := 1$ spm(98,97) := 6$ spm(98,98) := 11$ spm(98,99) := 6$ spm(98,100) := 1$ spm(99,97) := 1$ spm(99,98) := 6$ spm(99,99) := 11$ spm(99,100) := 6$ spm(100,98) := 1$ spm(100,99) := 6$ spm(100,100) := 10$ mat5^2$ det(mat1); 3840 det(mat4); 5 x trace(mat1); 30 trace(mat4); 5*x rank(mat1); 5 rank mat5; 100 tp(mat3); spm(1,1) := 1$ spm(1,2) := 3$ spm(2,1) := 2$ spm(2,2) := 4$ spm(3,3) := 1$ spm(3,4) := 3$ spm(4,3) := 2$ spm(4,4) := 4$ spm(5,5) := 1$ spm(5,6) := 3$ spm(6,5) := 2$ spm(6,6) := 4$ spmateigen(mat3,eta); 2 {{eta - 5*eta - 2,3, 2*arbcomplex(1)*(eta + 1) spm(1,1) := ---------------------------$ 5*eta + 1 spm(2,1) := arbcomplex(1)$ 2*arbcomplex(2)*(eta + 1) spm(3,1) := ---------------------------$ 5*eta + 1 spm(4,1) := arbcomplex(2)$ 2*arbcomplex(3)*(eta + 1) spm(5,1) := ---------------------------$ 5*eta + 1 spm(6,1) := arbcomplex(3)$ }} % Next, tests for the Linear Algebra Package for Sparse Matrices. %Basic matrix manipulations. spadd_columns(mat1,1,2,5*y); spm(1,1) := 2$ spm(1,2) := 10*y$ spm(2,2) := 4$ spm(3,3) := 6$ spm(4,4) := 8$ spm(5,5) := 10$ spadd_rows(mat1,1,2,x); spm(1,1) := 2$ spm(2,1) := 2*x$ spm(2,2) := 4$ spm(3,3) := 6$ spm(4,4) := 8$ spm(5,5) := 10$ spadd_to_columns(mat1,3,1000); spm(1,1) := 2$ spm(1,3) := 1000$ spm(2,2) := 4$ spm(2,3) := 1000$ spm(3,3) := 1006$ spm(4,3) := 1000$ spm(4,4) := 8$ spm(5,3) := 1000$ spm(5,5) := 10$ spadd_to_columns(mat5,{1,2,3},y)$ spadd_to_rows(mat1,2,1000); spm(1,1) := 2$ spm(2,1) := 1000$ spm(2,2) := 1004$ spm(2,3) := 1000$ spm(2,4) := 1000$ spm(2,5) := 1000$ spm(3,3) := 6$ spm(4,4) := 8$ spm(5,5) := 10$ spadd_to_rows(mat5,{1,2,3},x)$ spaugment_columns(mat3,2); spm(1,1) := 2$ spm(2,1) := 4$ spaugment_columns(mat1,{1,2,5}); spm(1,1) := 2$ spm(2,2) := 4$ spm(5,3) := 10$ spstack_rows(mat1,3); spm(1,3) := 6$ spstack_rows(mat1,{1,3,5}); spm(1,1) := 2$ spm(2,3) := 6$ spm(3,5) := 10$ spchar_poly(mat1,x); 5 4 3 2 x - 30*x + 340*x - 1800*x + 4384*x - 3840 spcol_dim(mat2); 100 sprow_dim(mat1); 5 spcopy_into(mat7,mat1,2,2); spm(1,1) := 2$ spm(2,2) := b$ spm(2,3) := c$ spm(3,2) := a$ spm(3,3) := b$ spm(3,4) := c$ spm(4,3) := a$ spm(4,4) := b$ spm(4,5) := c$ spm(5,4) := a$ spm(5,5) := b$ spcopy_into(mat7,mat1,5,5); ***** Error in spcopy_into: the matrix spm(1,1) := b$ spm(1,2) := c$ spm(2,1) := a$ spm(2,2) := b$ spm(2,3) := c$ spm(3,2) := a$ spm(3,3) := b$ spm(3,4) := c$ spm(4,3) := a$ spm(4,4) := b$ does not fit into spm(1,1) := 2$ spm(2,2) := 4$ spm(3,3) := 6$ spm(4,4) := 8$ spm(5,5) := 10$ at position 5,5. spcopy_into(zz1,mat1,1,1); spm(1,1) := 1$ spm(1,2) := 2$ spm(2,1) := 3$ spm(2,2) := 4$ spm(3,3) := 6$ spm(4,4) := 8$ spm(5,5) := 10$ spdiagonal(3); spm(1,1) := 3$ % spdiagonal can take both a list of arguments or just the arguments. spdiagonal({mat2,mat5})$ spdiagonal(mat2,mat5)$ % spdiagonal can also take a mixture of 'sparse and 'matrix types. spdiagonal(zz1,mat4,zz1); spm(1,1) := 1$ spm(1,2) := 2$ spm(2,1) := 3$ spm(2,2) := 4$ spm(3,3) := x$ spm(4,4) := x$ spm(5,5) := x$ spm(6,6) := x$ spm(7,7) := x$ spm(8,8) := 1$ spm(8,9) := 2$ spm(9,8) := 3$ spm(9,9) := 4$ spextend(mat1,3,2,x); spm(1,1) := 2$ spm(2,2) := 4$ spm(3,3) := 6$ spm(4,4) := 8$ spm(5,5) := 10$ spm(6,6) := x$ spm(6,7) := x$ spm(7,6) := x$ spm(7,7) := x$ spm(8,6) := x$ spm(8,7) := x$ spfind_companion(mat5,x); 98 2 x *(x - 3*x - 1) spget_columns(mat1,1); { spm(1,1) := 2$ } spget_columns(mat1,{1,2}); { spm(1,1) := 2$ , spm(2,1) := 4$ } spget_rows(mat1,3); { spm(1,3) := 6$ } spget_rows(mat1,{1,3}); { spm(1,1) := 2$ , spm(1,3) := 6$ } sphermitian_tp(mat6); spm(1,1) := - i + 1$ spm(1,2) := 4$ spm(1,3) := 1$ spm(2,1) := - i + 2$ spm(2,2) := 5$ spm(2,3) := - i$ spm(3,1) := - i + 3$ spm(3,2) := 2$ spm(4,4) := - i + 1$ spm(4,5) := 4$ spm(4,6) := 1$ spm(5,4) := - i + 2$ spm(5,5) := 5$ spm(5,6) := - i$ spm(6,4) := - i + 3$ spm(6,5) := 2$ % matrix_augment and matrix_stack can take both a list of arguments % or just the arguments. spmatrix_augment({mat1,mat1}); spm(1,1) := 2$ spm(1,6) := 2$ spm(2,2) := 4$ spm(2,7) := 4$ spm(3,3) := 6$ spm(3,8) := 6$ spm(4,4) := 8$ spm(4,9) := 8$ spm(5,5) := 10$ spm(5,10) := 10$ spmatrix_augment(mat5,mat2,mat5)$ spmatrix_stack(mat2,mat2)$ spminor(mat1,2,3); spm(1,1) := 2$ spm(3,3) := 8$ spm(4,4) := 10$ spmult_columns(mat1,3,y); spm(1,1) := 2$ spm(2,2) := 4$ spm(3,3) := 6*y$ spm(4,4) := 8$ spm(5,5) := 10$ spmult_columns(mat2,{2,3,4},100)$ spmult_rows(mat2,2,x); spm(1,1) := 1$ spm(2,2) := 2*x$ spm(3,3) := 3$ spm(4,4) := 4$ spm(5,5) := 5$ spm(6,6) := 6$ spm(7,7) := 7$ spm(8,8) := 8$ spm(9,9) := 9$ spm(10,10) := 10$ spm(11,11) := 11$ spm(12,12) := 12$ spm(13,13) := 13$ spm(14,14) := 14$ spm(15,15) := 15$ spm(16,16) := 16$ spm(17,17) := 17$ spm(18,18) := 18$ spm(19,19) := 19$ spm(20,20) := 20$ spm(21,21) := 21$ spm(22,22) := 22$ spm(23,23) := 23$ spm(24,24) := 24$ spm(25,25) := 25$ spm(26,26) := 26$ spm(27,27) := 27$ spm(28,28) := 28$ spm(29,29) := 29$ spm(30,30) := 30$ spm(31,31) := 31$ spm(32,32) := 32$ spm(33,33) := 33$ spm(34,34) := 34$ spm(35,35) := 35$ spm(36,36) := 36$ spm(37,37) := 37$ spm(38,38) := 38$ spm(39,39) := 39$ spm(40,40) := 40$ spm(41,41) := 41$ spm(42,42) := 42$ spm(43,43) := 43$ spm(44,44) := 44$ spm(45,45) := 45$ spm(46,46) := 46$ spm(47,47) := 47$ spm(48,48) := 48$ spm(49,49) := 49$ spm(50,50) := 50$ spm(51,51) := 51$ spm(52,52) := 52$ spm(53,53) := 53$ spm(54,54) := 54$ spm(55,55) := 55$ spm(56,56) := 56$ spm(57,57) := 57$ spm(58,58) := 58$ spm(59,59) := 59$ spm(60,60) := 60$ spm(61,61) := 61$ spm(62,62) := 62$ spm(63,63) := 63$ spm(64,64) := 64$ spm(65,65) := 65$ spm(66,66) := 66$ spm(67,67) := 67$ spm(68,68) := 68$ spm(69,69) := 69$ spm(70,70) := 70$ spm(71,71) := 71$ spm(72,72) := 72$ spm(73,73) := 73$ spm(74,74) := 74$ spm(75,75) := 75$ spm(76,76) := 76$ spm(77,77) := 77$ spm(78,78) := 78$ spm(79,79) := 79$ spm(80,80) := 80$ spm(81,81) := 81$ spm(82,82) := 82$ spm(83,83) := 83$ spm(84,84) := 84$ spm(85,85) := 85$ spm(86,86) := 86$ spm(87,87) := 87$ spm(88,88) := 88$ spm(89,89) := 89$ spm(90,90) := 90$ spm(91,91) := 91$ spm(92,92) := 92$ spm(93,93) := 93$ spm(94,94) := 94$ spm(95,95) := 95$ spm(96,96) := 96$ spm(97,97) := 97$ spm(98,98) := 98$ spm(99,99) := 99$ spm(100,100) := 100$ spmult_rows(mat1,{1,3,5},10); spm(1,1) := 20$ spm(2,2) := 4$ spm(3,3) := 60$ spm(4,4) := 8$ spm(5,5) := 100$ sppivot(mat3,3,3); spm(1,1) := 1$ spm(1,2) := 2$ spm(2,1) := 3$ spm(2,2) := 4$ spm(3,3) := 1$ spm(3,4) := 2$ spm(4,4) := -2$ spm(5,5) := 1$ spm(5,6) := 2$ spm(6,5) := 3$ spm(6,6) := 4$ sprows_pivot(mat3,1,1,{2,4}); spm(1,1) := 1$ spm(1,2) := 2$ spm(2,2) := -2$ spm(3,3) := 1$ spm(3,4) := 2$ spm(4,3) := 3$ spm(4,4) := 4$ spm(5,5) := 1$ spm(5,6) := 2$ spm(6,5) := 3$ spm(6,6) := 4$ spremove_columns(mat1,3); spm(1,1) := 2$ spm(2,2) := 4$ spm(4,3) := 8$ spm(5,4) := 10$ spremove_columns(mat3,{2,3,4}); spm(1,1) := 1$ spm(2,1) := 3$ spm(5,2) := 1$ spm(5,3) := 2$ spm(6,2) := 3$ spm(6,3) := 4$ spremove_rows(mat1,2); spm(1,1) := 2$ spm(2,3) := 6$ spm(3,4) := 8$ spm(4,5) := 10$ spremove_rows(mat2,{1,3})$ spremove_rows(mat1,{1,2,3,4,5}); ***** Warning in spremove_rows: all the rows have been removed. Returning nil. spswap_cols(mat1,2,4); spm(1,1) := 2$ spm(2,4) := 4$ spm(3,3) := 6$ spm(4,2) := 8$ spm(5,5) := 10$ spswap_rows(mat5,1,2)$ spswap_entries(mat1,{1,1},{5,5}); spm(1,1) := 10$ spm(2,2) := 4$ spm(3,3) := 6$ spm(4,4) := 8$ spm(5,5) := 2$ % Constructors - functions that create matrices. spband_matrix(x,500)$ spband_matrix({x,y,z},6000)$ spblock_matrix(1,2,{mat1,mat1}); spm(1,1) := 2$ spm(1,6) := 2$ spm(2,2) := 4$ spm(2,7) := 4$ spm(3,3) := 6$ spm(3,8) := 6$ spm(4,4) := 8$ spm(4,9) := 8$ spm(5,5) := 10$ spm(5,10) := 10$ spblock_matrix(2,3,{mat3,mat6,mat3,mat6,mat3,mat6}); spm(1,1) := 1$ spm(1,2) := 2$ spm(1,7) := i + 1$ spm(1,8) := i + 2$ spm(1,9) := i + 3$ spm(1,13) := 1$ spm(1,14) := 2$ spm(2,1) := 3$ spm(2,2) := 4$ spm(2,7) := 4$ spm(2,8) := 5$ spm(2,9) := 2$ spm(2,13) := 3$ spm(2,14) := 4$ spm(3,3) := 1$ spm(3,4) := 2$ spm(3,7) := 1$ spm(3,8) := i$ spm(3,15) := 1$ spm(3,16) := 2$ spm(4,3) := 3$ spm(4,4) := 4$ spm(4,10) := i + 1$ spm(4,11) := i + 2$ spm(4,12) := i + 3$ spm(4,15) := 3$ spm(4,16) := 4$ spm(5,5) := 1$ spm(5,6) := 2$ spm(5,10) := 4$ spm(5,11) := 5$ spm(5,12) := 2$ spm(5,17) := 1$ spm(5,18) := 2$ spm(6,5) := 3$ spm(6,6) := 4$ spm(6,10) := 1$ spm(6,11) := i$ spm(6,17) := 3$ spm(6,18) := 4$ spm(7,1) := i + 1$ spm(7,2) := i + 2$ spm(7,3) := i + 3$ spm(7,7) := 1$ spm(7,8) := 2$ spm(7,13) := i + 1$ spm(7,14) := i + 2$ spm(7,15) := i + 3$ spm(8,1) := 4$ spm(8,2) := 5$ spm(8,3) := 2$ spm(8,7) := 3$ spm(8,8) := 4$ spm(8,13) := 4$ spm(8,14) := 5$ spm(8,15) := 2$ spm(9,1) := 1$ spm(9,2) := i$ spm(9,9) := 1$ spm(9,10) := 2$ spm(9,13) := 1$ spm(9,14) := i$ spm(10,4) := i + 1$ spm(10,5) := i + 2$ spm(10,6) := i + 3$ spm(10,9) := 3$ spm(10,10) := 4$ spm(10,16) := i + 1$ spm(10,17) := i + 2$ spm(10,18) := i + 3$ spm(11,4) := 4$ spm(11,5) := 5$ spm(11,6) := 2$ spm(11,11) := 1$ spm(11,12) := 2$ spm(11,16) := 4$ spm(11,17) := 5$ spm(11,18) := 2$ spm(12,4) := 1$ spm(12,5) := i$ spm(12,11) := 3$ spm(12,12) := 4$ spm(12,16) := 1$ spm(12,17) := i$ spchar_matrix(mat3,x); spm(1,1) := x - 1$ spm(1,2) := -2$ spm(2,1) := -3$ spm(2,2) := x - 4$ spm(3,3) := x - 1$ spm(3,4) := -2$ spm(4,3) := -3$ spm(4,4) := x - 4$ spm(5,5) := x - 1$ spm(5,6) := -2$ spm(6,5) := -3$ spm(6,6) := x - 4$ cfmat := spcoeff_matrix({y+4*+-5*w=10,y-z=20,y+4+3*z,w+x+50}); { spm(1,1) := 1$ spm(1,2) := -20$ spm(2,1) := 1$ spm(2,3) := -1$ spm(3,1) := 1$ spm(3,3) := 3$ spm(4,2) := 1$ spm(4,4) := 1$ , spm(1,1) := y$ spm(2,1) := w$ spm(3,1) := z$ spm(4,1) := x$ , spm(1,1) := 10$ spm(2,1) := 20$ spm(3,1) := -4$ spm(4,1) := -50$ cfmat := } first cfmat * second cfmat; spm(1,1) := - 20*w + y$ spm(2,1) := y - z$ spm(3,1) := y + 3*z$ spm(4,1) := w + x$ third cfmat; spm(1,1) := 10$ spm(2,1) := 20$ spm(3,1) := -4$ spm(4,1) := -50$ spcompanion(poly,x); spm(1,7) := -12$ spm(2,1) := 1$ spm(3,2) := 1$ spm(4,3) := 1$ spm(4,7) := -5$ spm(5,4) := 1$ spm(5,7) := -4$ spm(6,5) := 1$ spm(6,7) := -1$ spm(7,6) := 1$ sphessian(poly1,{w,x,y,z}); spm(2,2) := 2$ 2 3 spm(2,3) := 3*y + z + 1$ 2 spm(2,4) := 3*y*z $ 2 3 spm(3,2) := 3*y + z + 1$ spm(3,3) := 6*x*y$ 2 spm(3,4) := 3*x*z $ 2 spm(4,2) := 3*y*z $ 2 spm(4,3) := 3*x*z $ spm(4,4) := 6*x*y*z$ spjacobian({x^4,x*y^2,x*y*z^3},{w,x,y,z}); 3 spm(1,2) := 4*x $ 2 spm(2,2) := y $ spm(2,3) := 2*x*y$ 3 spm(3,2) := y*z $ 3 spm(3,3) := x*z $ 2 spm(3,4) := 3*x*y*z $ spjordan_block(x,500)$ spmake_identity(1000)$ on rounded; % makes output easier to read. ch := spcholesky(mat1); { spm(1,1) := 1.41421356237$ spm(2,2) := 2.0$ spm(3,3) := 2.44948974278$ spm(4,4) := 2.82842712475$ spm(5,5) := 3.16227766017$ , spm(1,1) := 1.41421356237$ spm(2,2) := 2.0$ spm(3,3) := 2.44948974278$ spm(4,4) := 2.82842712475$ spm(5,5) := 3.16227766017$ ch := } tp first ch - second ch; "Empty Matrix" tmp := first ch * second ch; spm(1,1) := 2.0$ spm(2,2) := 4.0$ spm(3,3) := 6.0$ spm(4,4) := 8.0$ spm(5,5) := 10.0$ tmp := tmp - mat1; "Empty Matrix" off rounded; % The gram schmidt functions takes a list of vectors. % These vectors are matrices of type 'sparse with column dimension 1. %Create the "vectors". sparse a(4,1); sparse b(4,1); sparse c(4,1); sparse d(4,1); %Fill the "vectors" with data. a(1,1):=1; a(1,1) := 1 b(1,1):=1; b(1,1) := 1 b(2,1):=1; b(2,1) := 1 c(1,1):=1; c(1,1) := 1 c(2,1):=1; c(2,1) := 1 c(3,1):=1; c(3,1) := 1 d(1,1):=1; d(1,1) := 1 d(2,1):=1; d(2,1) := 1 d(3,1):=1; d(3,1) := 1 d(4,1):=1; d(4,1) := 1 spgram_schmidt({{a},{b},{c},{d}}); { spm(1,1) := 1$ , spm(2,1) := 1$ , spm(3,1) := 1$ , spm(4,1) := 1$ } on rounded; % again, makes large quotients a bit more readable. % The algorithm used for splu_decom sometimes swaps the rows of the % input matrix so that (given matrix A, splu_decom(A) = {L,U,vec}), % we find L*U does not equal A but a row equivalent of it. The call % spconvert(A,vec) will return this row equivalent % (ie: L*U = convert(A,vec)). lu := splu_decom(mat5)$ tmp := first lu * second lu$ tmp1 := spconvert(mat5,third lu); spm(1,1) := 3$ spm(1,2) := 1$ spm(2,1) := 1$ spm(2,2) := 3$ spm(2,3) := 1$ spm(3,2) := 1$ spm(3,3) := 3$ spm(3,4) := 1$ spm(4,3) := 1$ spm(4,4) := 3$ spm(4,5) := 1$ spm(5,4) := 1$ spm(5,5) := 3$ spm(5,6) := 1$ spm(6,5) := 1$ spm(6,6) := 3$ spm(6,7) := 1$ spm(7,6) := 1$ spm(7,7) := 3$ spm(7,8) := 1$ spm(8,7) := 1$ spm(8,8) := 3$ spm(8,9) := 1$ spm(9,8) := 1$ spm(9,9) := 3$ spm(9,10) := 1$ spm(10,9) := 1$ spm(10,10) := 3$ spm(10,11) := 1$ spm(11,10) := 1$ spm(11,11) := 3$ spm(11,12) := 1$ spm(12,11) := 1$ spm(12,12) := 3$ spm(12,13) := 1$ spm(13,12) := 1$ spm(13,13) := 3$ spm(13,14) := 1$ spm(14,13) := 1$ spm(14,14) := 3$ spm(14,15) := 1$ spm(15,14) := 1$ spm(15,15) := 3$ spm(15,16) := 1$ spm(16,15) := 1$ spm(16,16) := 3$ spm(16,17) := 1$ spm(17,16) := 1$ spm(17,17) := 3$ spm(17,18) := 1$ spm(18,17) := 1$ spm(18,18) := 3$ spm(18,19) := 1$ spm(19,18) := 1$ spm(19,19) := 3$ spm(19,20) := 1$ spm(20,19) := 1$ spm(20,20) := 3$ spm(20,21) := 1$ spm(21,20) := 1$ spm(21,21) := 3$ spm(21,22) := 1$ spm(22,21) := 1$ spm(22,22) := 3$ spm(22,23) := 1$ spm(23,22) := 1$ spm(23,23) := 3$ spm(23,24) := 1$ spm(24,23) := 1$ spm(24,24) := 3$ spm(24,25) := 1$ spm(25,24) := 1$ spm(25,25) := 3$ spm(25,26) := 1$ spm(26,25) := 1$ spm(26,26) := 3$ spm(26,27) := 1$ spm(27,26) := 1$ spm(27,27) := 3$ spm(27,28) := 1$ spm(28,27) := 1$ spm(28,28) := 3$ spm(28,29) := 1$ spm(29,28) := 1$ spm(29,29) := 3$ spm(29,30) := 1$ spm(30,29) := 1$ spm(30,30) := 3$ spm(30,31) := 1$ spm(31,30) := 1$ spm(31,31) := 3$ spm(31,32) := 1$ spm(32,31) := 1$ spm(32,32) := 3$ spm(32,33) := 1$ spm(33,32) := 1$ spm(33,33) := 3$ spm(33,34) := 1$ spm(34,33) := 1$ spm(34,34) := 3$ spm(34,35) := 1$ spm(35,34) := 1$ spm(35,35) := 3$ spm(35,36) := 1$ spm(36,35) := 1$ spm(36,36) := 3$ spm(36,37) := 1$ spm(37,36) := 1$ spm(37,37) := 3$ spm(37,38) := 1$ spm(38,37) := 1$ spm(38,38) := 3$ spm(38,39) := 1$ spm(39,38) := 1$ spm(39,39) := 3$ spm(39,40) := 1$ spm(40,39) := 1$ spm(40,40) := 3$ spm(40,41) := 1$ spm(41,40) := 1$ spm(41,41) := 3$ spm(41,42) := 1$ spm(42,41) := 1$ spm(42,42) := 3$ spm(42,43) := 1$ spm(43,42) := 1$ spm(43,43) := 3$ spm(43,44) := 1$ spm(44,43) := 1$ spm(44,44) := 3$ spm(44,45) := 1$ spm(45,44) := 1$ spm(45,45) := 3$ spm(45,46) := 1$ spm(46,45) := 1$ spm(46,46) := 3$ spm(46,47) := 1$ spm(47,46) := 1$ spm(47,47) := 3$ spm(47,48) := 1$ spm(48,47) := 1$ spm(48,48) := 3$ spm(48,49) := 1$ spm(49,48) := 1$ spm(49,49) := 3$ spm(49,50) := 1$ spm(50,49) := 1$ spm(50,50) := 3$ spm(50,51) := 1$ spm(51,50) := 1$ spm(51,51) := 3$ spm(51,52) := 1$ spm(52,51) := 1$ spm(52,52) := 3$ spm(52,53) := 1$ spm(53,52) := 1$ spm(53,53) := 3$ spm(53,54) := 1$ spm(54,53) := 1$ spm(54,54) := 3$ spm(54,55) := 1$ spm(55,54) := 1$ spm(55,55) := 3$ spm(55,56) := 1$ spm(56,55) := 1$ spm(56,56) := 3$ spm(56,57) := 1$ spm(57,56) := 1$ spm(57,57) := 3$ spm(57,58) := 1$ spm(58,57) := 1$ spm(58,58) := 3$ spm(58,59) := 1$ spm(59,58) := 1$ spm(59,59) := 3$ spm(59,60) := 1$ spm(60,59) := 1$ spm(60,60) := 3$ spm(60,61) := 1$ spm(61,60) := 1$ spm(61,61) := 3$ spm(61,62) := 1$ spm(62,61) := 1$ spm(62,62) := 3$ spm(62,63) := 1$ spm(63,62) := 1$ spm(63,63) := 3$ spm(63,64) := 1$ spm(64,63) := 1$ spm(64,64) := 3$ spm(64,65) := 1$ spm(65,64) := 1$ spm(65,65) := 3$ spm(65,66) := 1$ spm(66,65) := 1$ spm(66,66) := 3$ spm(66,67) := 1$ spm(67,66) := 1$ spm(67,67) := 3$ spm(67,68) := 1$ spm(68,67) := 1$ spm(68,68) := 3$ spm(68,69) := 1$ spm(69,68) := 1$ spm(69,69) := 3$ spm(69,70) := 1$ spm(70,69) := 1$ spm(70,70) := 3$ spm(70,71) := 1$ spm(71,70) := 1$ spm(71,71) := 3$ spm(71,72) := 1$ spm(72,71) := 1$ spm(72,72) := 3$ spm(72,73) := 1$ spm(73,72) := 1$ spm(73,73) := 3$ spm(73,74) := 1$ spm(74,73) := 1$ spm(74,74) := 3$ spm(74,75) := 1$ spm(75,74) := 1$ spm(75,75) := 3$ spm(75,76) := 1$ spm(76,75) := 1$ spm(76,76) := 3$ spm(76,77) := 1$ spm(77,76) := 1$ spm(77,77) := 3$ spm(77,78) := 1$ spm(78,77) := 1$ spm(78,78) := 3$ spm(78,79) := 1$ spm(79,78) := 1$ spm(79,79) := 3$ spm(79,80) := 1$ spm(80,79) := 1$ spm(80,80) := 3$ spm(80,81) := 1$ spm(81,80) := 1$ spm(81,81) := 3$ spm(81,82) := 1$ spm(82,81) := 1$ spm(82,82) := 3$ spm(82,83) := 1$ spm(83,82) := 1$ spm(83,83) := 3$ spm(83,84) := 1$ spm(84,83) := 1$ spm(84,84) := 3$ spm(84,85) := 1$ spm(85,84) := 1$ spm(85,85) := 3$ spm(85,86) := 1$ spm(86,85) := 1$ spm(86,86) := 3$ spm(86,87) := 1$ spm(87,86) := 1$ spm(87,87) := 3$ spm(87,88) := 1$ spm(88,87) := 1$ spm(88,88) := 3$ spm(88,89) := 1$ spm(89,88) := 1$ spm(89,89) := 3$ spm(89,90) := 1$ spm(90,89) := 1$ spm(90,90) := 3$ spm(90,91) := 1$ spm(91,90) := 1$ spm(91,91) := 3$ spm(91,92) := 1$ spm(92,91) := 1$ spm(92,92) := 3$ spm(92,93) := 1$ spm(93,92) := 1$ spm(93,93) := 3$ spm(93,94) := 1$ spm(94,93) := 1$ spm(94,94) := 3$ spm(94,95) := 1$ spm(95,94) := 1$ spm(95,95) := 3$ spm(95,96) := 1$ spm(96,95) := 1$ spm(96,96) := 3$ spm(96,97) := 1$ spm(97,96) := 1$ spm(97,97) := 3$ spm(97,98) := 1$ spm(98,97) := 1$ spm(98,98) := 3$ spm(98,99) := 1$ spm(99,98) := 1$ spm(99,99) := 3$ spm(99,100) := 1$ spm(100,99) := 1$ spm(100,100) := 3$ tmp1 := tmp - tmp1; "Empty Matrix" % and the complex case.. on complex; *** Domain mode rounded changed to complex-rounded lu1 := splu_decom(mat6); { spm(1,1) := 1$ spm(2,1) := 4$ spm(2,2) := 5 - 4*i$ spm(3,1) := 1 + i$ spm(3,2) := 3$ spm(3,3) := 2.26829268293 + 0.414634146341*i$ spm(4,4) := 1$ spm(5,4) := 4$ spm(5,5) := 5 - 4*i$ spm(6,4) := 1 + i$ spm(6,5) := 3$ spm(6,6) := 2.26829268293 + 0.414634146341*i$ , spm(1,1) := 1$ spm(1,2) := i$ spm(2,2) := 1$ spm(2,3) := 0.243902439024 + 0.19512195122*i$ spm(3,3) := 1$ spm(4,4) := 1$ spm(4,5) := i$ spm(5,5) := 1$ spm(5,6) := 0.243902439024 + 0.19512195122*i$ spm(6,6) := 1$ lu1 := ,[3,2,3,6,5,6]} mat6; spm(1,1) := i + 1$ spm(1,2) := i + 2$ spm(1,3) := i + 3$ spm(2,1) := 4$ spm(2,2) := 5$ spm(2,3) := 2$ spm(3,1) := 1$ spm(3,2) := i$ spm(4,4) := i + 1$ spm(4,5) := i + 2$ spm(4,6) := i + 3$ spm(5,4) := 4$ spm(5,5) := 5$ spm(5,6) := 2$ spm(6,4) := 1$ spm(6,5) := i$ tmp := first lu1 * second lu1; spm(1,1) := 1$ spm(1,2) := i$ spm(2,1) := 4$ spm(2,2) := 5$ spm(2,3) := 2.0$ spm(3,1) := 1 + i$ spm(3,2) := 2 + i$ spm(3,3) := 3.0 + i$ spm(4,4) := 1$ spm(4,5) := i$ spm(5,4) := 4$ spm(5,5) := 5$ spm(5,6) := 2.0$ spm(6,4) := 1 + i$ spm(6,5) := 2 + i$ spm(6,6) := 3.0 + i$ tmp := tmp1 := spconvert(mat6,third lu1); spm(1,1) := 1$ spm(1,2) := i$ spm(2,1) := 4$ spm(2,2) := 5$ spm(2,3) := 2$ spm(3,1) := i + 1$ spm(3,2) := i + 2$ spm(3,3) := i + 3$ spm(4,4) := 1$ spm(4,5) := i$ spm(5,4) := 4$ spm(5,5) := 5$ spm(5,6) := 2$ spm(6,4) := i + 1$ spm(6,5) := i + 2$ spm(6,6) := i + 3$ tmp1 := tmp - tmp1; "Empty Matrix" off complex; *** Domain mode complex-rounded changed to rounded mat3inv := sppseudo_inverse(mat3); spm(1,1) := - 2.0$ spm(1,2) := 1$ spm(2,1) := 1.5$ spm(2,2) := - 0.5$ spm(3,3) := - 2.0$ spm(3,4) := 1$ spm(4,3) := 1.5$ spm(4,4) := - 0.5$ spm(5,5) := - 2.0$ spm(5,6) := 1$ spm(6,5) := 1.5$ spm(6,6) := - 0.5$ mat3inv := mat3 * mat3inv; spm(1,1) := 1$ spm(2,2) := 1$ spm(3,3) := 1$ spm(4,4) := 1$ spm(5,5) := 1$ spm(6,6) := 1$ % Predicates. matrixp(mat1); t matrixp(poly); squarep(mat2); t squarep(mat3); t symmetricp(mat1); t symmetricp(mat3); sparsematp(mat1); t sparsematp(poly); off rounded; end; Time for test: 427 ms, plus GC time: 26 ms