(42S; DM 42) Eigenvalues and eigenvectors of symmetric matrices
06-15-2023, 02:51 PM (This post was last modified: 07-02-2023 02:32 PM by rawi.)
Post: #1
 rawi Member Posts: 171 Joined: Nov 2019
(42S; DM 42) Eigenvalues and eigenvectors of symmetric matrices
User Instructions:
(Optional: Put the starting number of the random number generator in SEED)
Put symmetric matrix in M1.
Run program. The vector of eigenvalues is in M2, matrix of standardized eigenvectors is in M3.

Example:
Matrix:
1.00 -0.36 0.12
-0.36 1.00 0.09
0.12 0.09 1.00
Store matrix in M1 - PI SEED - XEQ EVV
Result:
Eigenvalues:
RCL “M2” -> 1.3613; 1.0521; 0.5866
Eigenvalues are sorted according to absolute size.
Eigenvectors:
RCL “M3” -> eigenvectors are in corresponding columns:
-0.7149 0.1937 0.6719
0.6963 0.2848 0.6587
-0.0638 0.9388 -0.3386

Code:
00 { 186-Byte Prgm } 01 LBL “EVV” 02 RCL “M1” 03 STO “M4” 04 STO “M3” 05 DIM? 06 1E-3 07 / 08 1 09 + 10 STO 01 11 STO 02 12 NEWMAT 13 STO “M2” 14 STO “M5” 15 LBL 00 16 INDEX “M5” 17 RAN 18 STOEL 19 I+ 20 ISG 01 21 GTO 00 22 RCL “M5” 23 FNRM 24 STO/ ”M5” 25 LBL 01 26 CF 00 27 RCL “M4” 28 RCL “M5” 29 x 30 STO “M6” 31 RCL “M5” 32 DOT 33 X<0? 34 SF 00 35 RCL “M6” 36 FNRM 37 STO/ ”M6” 38 RCL “M6” 39 STO “M5” 40 R↓ 41 RCL 00 42 X<>Y 43 FS? 00 44 +/- 45 STO 00 46 - 47 ABS 48 1E-8 49 X<Y? 50 GTO 01 51 RCL “M5” 52 ENTER 53 TRANS 54 x 55 RCLx 00 56 STO- “M4” 57 RCL 02 58 1 59 INDEX “M2” 60 STOIJ 61 RCL 00 62 STOEL 63 INDEX “M3” 64 R↓ 65 X<>Y 66 STOIJ 67 RCL “M5” 68 PUTM 69 ISG 02 70 GTO 00 71 CLST 72 CF 00 73 CLV “M4” 74 CLV “M5” 75 CLV “M6” 76 END

Edit: Slightly shorter version of program
 « Next Oldest | Next Newest »