inversion with pivoting (more stable)

svn path=/trunk/externals/iem/iemmatrix/; revision=5815

2 files changed, 81 insertions, 0 deletions

diff --git a/abs/mtx_pinverse-help.pd b/abs/mtx_pinverse-help.pd
new file mode 100644
index 0000000..158e908
--- /dev/null
+++ b/abs/mtx_pinverse-help.pd
@@ -0,0 +1,51 @@
+#N canvas 366 49 705 646 10;
+#X text 347 472 updated for;
+#X obj 435 472 iemmatrix 0.2;
+#X obj 484 498 matrix;
+#X text 354 497 see also help for;
+#X text 243 142 singular;
+#X text 245 107 regular;
+#X text 246 158 regular;
+#X text 247 168 but badly conditioned;
+#X text 154 533 A*inv(A)=inv(A)*A=I;
+#X text 248 221 pseudoinverse: P1=inv(A'*A)*A';
+#X text 247 269 pseudoinverse: P2=A'*inv(A*A');
+#X text 245 553 P1*A=I;
+#X text 245 573 A*P2=I;
+#X obj 92 199 mtx 3;
+#X msg 112 164 1 2 3 2 4 4 3 4 5;
+#X msg 92 108 1 2 4 2 3 4 3 4 5;
+#X obj 92 472 mtx_print inverse;
+#X obj 92 300 t a a;
+#X obj 134 300 mtx_print original;
+#X obj 153 219 mtx_rand 4 3;
+#X msg 153 198 bang;
+#X msg 153 248 bang;
+#X obj 153 269 mtx_rand 3 4;
+#X obj 182 348 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
+-1;
+#X text 199 359 instability detected!;
+#X obj 92 348 mtx_pinverse;
+#X text 45 16 mtx_pinverse:: get the inverse of a matrix (with pivoting)
+;
+#X text 44 49 mtx_pinverse calculates the inverse of a square-matrix.
+For inverting rectangle matrices \, use [mtx_inverse] or [mtx_pseudoinverse]
+;
+#X msg 103 140 1 2 3 2 3 4 0 0 0;
+#X text 194 385 due to pivoting \, [mtx_pinverse] will handle badly
+conditioned matrices better than [mtx_inverse] \, however it will also
+detect less (real) instabilities than [mtx_inverse];
+#X obj 485 524 mtx_inverse;
+#X obj 485 548 mtx_pseudoinverse;
+#X connect 13 0 17 0;
+#X connect 14 0 13 0;
+#X connect 15 0 13 0;
+#X connect 17 0 25 0;
+#X connect 17 1 18 0;
+#X connect 19 0 17 0;
+#X connect 20 0 19 0;
+#X connect 21 0 22 0;
+#X connect 22 0 17 0;
+#X connect 25 0 16 0;
+#X connect 25 1 23 0;
+#X connect 28 0 13 0;
diff --git a/abs/mtx_pinverse.pd b/abs/mtx_pinverse.pd
new file mode 100644
index 0000000..810e865
--- /dev/null
+++ b/abs/mtx_pinverse.pd
@@ -0,0 +1,30 @@
+#N canvas 0 0 630 350 10;
+#X obj 44 102 inlet;
+#X obj 44 132 mtx_pivot;
+#X obj 44 154 mtx_inverse;
+#X obj 74 200 mtx_*;
+#X obj 44 221 mtx_*;
+#X obj 44 198 mtx;
+#X obj 44 176 t b a;
+#X obj 44 264 outlet;
+#X obj 116 264 outlet;
+#X text 109 22 matrix inversion with pivoting;
+#X text 107 56 pivoting makes the inversion of badly conditioned matrices
+more stable.;
+#X text 158 105 it also stabilizes the inversion of singular matrices
+(not so good) and is more expensive;
+#X text 188 202 for license-details see LICENSE.txt that must come
+with iemmatrix.;
+#X text 188 181 (c) 2006 by IOhannes m zmoelnig \, IEM KUG \, graz
+austria;
+#X connect 0 0 1 0;
+#X connect 1 0 2 0;
+#X connect 1 1 3 1;
+#X connect 1 2 5 1;
+#X connect 2 0 6 0;
+#X connect 2 1 8 0;
+#X connect 3 0 4 1;
+#X connect 4 0 7 0;
+#X connect 5 0 4 0;
+#X connect 6 0 5 0;
+#X connect 6 1 3 0;