LinearSystem: CEDAR DEFINITIONS = BEGIN Real0: TYPE = REAL _ 0; VecSeq: TYPE = RECORD[SEQUENCE ncols: INTEGER OF Real0]; RowN: TYPE = REF VecSeq; MatrixSeq: TYPE = RECORD[SEQUENCE nrows: INTEGER OF RowN]; MatrixN: TYPE = REF MatrixSeq; ColumnN: TYPE = REF VecSeq; SolveN: PROCEDURE [A:MatrixN, b:ColumnN, n: INTEGER] RETURNS [x:ColumnN] ; -- solves Ax=b Invert: PROCEDURE [a: MatrixN] RETURNS [ai: MatrixN]; Determinant: PROC[a: MatrixN] RETURNS [det: REAL]; Transpose: PROCEDURE [a: MatrixN] RETURNS [transpose: MatrixN]; Multiply: PROCEDURE [a: MatrixN, b: MatrixN] RETURNS [c: MatrixN]; MultiplyVec: PROC[a: MatrixN, v: ColumnN] RETURNS [c: RowN]; Create: PROC [nrows, ncols: INTEGER] RETURNS [a: MatrixN]; Copy: PROC [a: MatrixN] RETURNS[MatrixN]; Matrix2: TYPE = ARRAY [1..2] OF Row2; Row2: TYPE = ARRAY [1..2] OF REAL; Column2: TYPE = ARRAY [1..2] OF Real0; Solve2: PROCEDURE [A:Matrix2, b:Column2] RETURNS [x:Column2] ; -- solves Ax=b Matrix3: TYPE = ARRAY [1..3] OF Row3; Row3: TYPE = ARRAY [1..3] OF REAL; Column3: TYPE = ARRAY [1..3] OF Real0; Solve3: PROCEDURE [A:Matrix3, b:Column3] RETURNS [x:Column3] ; -- solves Ax=b Matrix4: TYPE = ARRAY [1..4] OF Row4; Row4: TYPE = ARRAY [1..4] OF REAL; Column4: TYPE = ARRAY [1..4] OF Real0; Solve4: PROCEDURE [A:Matrix4, b:Column4] RETURNS [x:Column4] ; -- solves Ax=b Matrix5: TYPE = ARRAY [1..5] OF Row5; Row5: TYPE = ARRAY [1..5] OF REAL; Column5: TYPE = ARRAY [1..5] OF Real0; Solve5: PROCEDURE [A:Matrix5, b:Column5] RETURNS [x:Column5] ; -- solves Ax=b Matrix6: TYPE = ARRAY [1..6] OF Row6; Row6: TYPE = ARRAY [1..6] OF REAL; Column6: TYPE = ARRAY [1..6] OF Real0; Solve6: PROCEDURE [A:Matrix6, b:Column6] RETURNS [x:Column6] ; -- solves Ax=b END. dLinearSystem.mesa Copyright c 1985 by Xerox Corporation. All rights reserved. Last edited by Maureen Stone 19-Oct-81 16:42:28 Written by Michael Plass, 8-Oct-81 Tim Diebert May 21, 1985 5:50:50 pm PDT Stone, October 16, 1985 10:35:34 am PDT Catch the signal Real.RealException to detect singular or unstable systems, e.g., singular:BOOLEAN _ FALSE; x _ LinearSystem.Solve3[A,b! Real.RealException => {singular_TRUE;CONTINUE}]; IF NOT singular THEN ... SolveN destroys A. Use SolveN[Copy[A],b,n] if this is a problem; Invert and Determinant are very simple-minded. Not recommended for large matrices. ΚK˜šœ™Icodešœ Οmœ1™