Mon Jan 4 00:05:34 MET 1999
REDUCE 3.7, 15-Jan-99 ...
1: 1:
2: 2: 2: 2: 2: 2: 2: 2: 2:
3: 3: % 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;
4: 4: 4: 4: 4: 4: 4: 4: 4:
Time for test: 2770 ms, plus GC time: 200 ms
5: 5:
Quitting
Mon Jan 4 00:05:46 MET 1999