matrix_review.txt

matrix相关函数及处理方法

MATRIX and LINEAR ALGEBRA Package For EXCEL

History review

MATRIX.XLA - Ver. 2.3.2 -  March 2007
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Only minor changes and fixes.
routine Block_Matrix_Reduction improved

MATRIX.XLA - Ver. 2.3.1 -  Jan 2007
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Only minor changes and fixes.
Function MNormalize added type=4: dividing each column-vector for the absolute values mean.
(suggested by Laurent N.) 
Bug 2.1.2007 Jacobi algorithm returned #VALUE for diagonal or near-diagonal matrices (thanks to David Schwartz) 

MATRIX.XLA - Ver. 2.3 -  Dic 2006
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Function MCond  - matrix condition number
Function MpCond - log10 of matrix condition number
The Matrix function names have been totally revised. the multitude of matrix specifiers 
(M as in MT, M_ as in M_Abs, Mat as in MatChar, or Mat_ as in Mat_Block, etc.) have been replaced by their common denominator, the uniform prefix M (MT, MAbs, MChar, MBlock, etc.). Backward compatibility is guaranteed.
Tutorial and help-on-line revised
Bug 9.11.06 macro Mat_Block_transform broken link (thanks to Robert de Levie)

MATRIX.XLA - Ver. 2.2.2 -  Nov 2006
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Bug 8.11.06: Macro multiplication error for (1 x 1) matrix result(thanks to Darrik V. Heyd)
Document correction for MatEigenvector_Pow (thanks to Hood, Bill  20.9.06)
Bug 24.10.06: SVD raises error for (n x 2n) matrices (thanks to Bruce MacWilliams)

MATRIX.XLA - Ver. 2.2.2 -  Nov 2006
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Bug 8.11.06: Macro multiplication error for (1 x 1) matrix result(thanks to Darrik V. Heyd)
Document correction for MatEigenvector_Pow (thanks to Hood, Bill  20.9.06)
Bug 24.10.06: SVD raises error for (n x 2n) matrices (thanks to Bruce MacWilliams)
Document correction for MatEigenvector_Pow (thanks to Hood, Bill  20.9.06)

MATRIX.XLA - Ver. 2.2 -  Ago 2006
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Function M_POW_C - Complex matrix power (proposed by Raj Sinha 14.4.2006)
Function REGRCIR   - circular regression
Function REGRL	   - can also return the standard deviations
Function REGRP	   - can also return the standard deviations
Tutorial and help-on-line revision (thanks to Robert de Levie and David Forfar)

MATRIX.XLA - Ver. 2.1 -  March 2006
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Macros for sparse linear systems
Function M_DETPAR - Parameteric determinant
Function SYSLIN_ITER_G - Relaxation parameter added
Bug 05.02.06: Macro Gauss-Step-ByR did not return last matrix if it is singular
Bug 28.01.06: function SYSLIN3 determinant overflow for large matrices

MATRIX.XLA - Ver. 2.0.1 -  Jan 2006
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only minor bugs fixed

MATRIX.XLA - Ver. 2.0 -  Jan 2006
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function MAT_QH - factorization QH by Arnoldi-Lanczos algorithm 
Poly_Root: now it uses the Siliak + Ruffini algorithm
function MatOrthoGS - orthogonalization with modified Gram-Schmidt algorithm 
Bug 13.07.05: Macro QR did not accept a rectangular matrix
Bug 02.11.05: HQR routine incorrect results for large unbalanced matrices

MATRIX.XLA - Ver. 1.9 -  July 2005
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Function MatCplx    - converts 2 real matrices into a complex matrix
Function JoinCol    - Build a matrix with separate columns
Function JoinRow    - Build a matrix with separate rows
Function MatChar    - Characteristic matrix A-xI
Function MatChar_C  - Complex Characteristic matrix A-zI
Function M_ABS_C    - Complex vector or matrix norm
Function M_ADD_C    - Complex matrix addition A+B
Function M_SUB_C    - Complex matrix subtraction A-B
Function M_PRODS_C  - Complex matrix-scalar multiplication A*B
Function MTC 	    - Transpose of complex matrix
Function MTH        - Transpose-conjugate of complex matrix
Function M_INV 	    - Improved accuracy for Tartaglia's integer matrices
Function Mat_Pseudoinv 	 - Moore-Penrose Pseudoinverse A^+
Function VectAngle	 - Angle of two vectors
Function MatCharPoly_C 	 - Characteristic polynomial of complex matrix
Function Poly_Roots_QRC  - Roots of complex polynomial with QR method
Function MatNormalize_C	 - Complex normalization
Function Mat_Hilbert_inv      - Inverse of Hilbert's matrix
Function MatEigenvalue_QRC    - Eigenvalues of complex matrix
Function MatEigenvector_C     - now works also for complex matrix 
Function MatEigenvectorInv_C  - Eigenvectors of complex matrix
Function MatEigenSort_Jacobi  - Sort the eigenvectors in descending order (thanks to Carlos Aya)

Bug fix 06.06.05 - MatNromalize returned #Value for null vectors
Bug fix 29.03.05 - pivot strategy in routine GJC  (thanks to Jim Lux)
Bug fix 10.01.05 - macro Gauss step-by step: too high coefficients for decimal numbers
Fixed installation problems (thanks to Vladimir Zakharov)
Substituted the static toolbar with a dynamic toolbar to avoid problems following to the Excel crashes

MATRIX.XLA - Ver. 1.8.1 -  July 2004
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Macro Random Toeplitz generator 
Function SYSLIN_TPZ   - Solves Toeplitz Linear system
Function M_MULT_TPZ   - Multiplies a Toeplitz matrix for a vector
Function M_TPZ_ERR    - Check if a matrix is a Toeplitz form

Bug fix 23.07.04 - MatEigenvalue_QR and Mat_hessemberg return incorrect values
 (thanks to Levent Kayili)

MATRIX.XLA - Ver. 1.6 -  May 2004
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Macro Gauss_Step  - Didactic macro for reducing to the diagonal or triangular form 
		    with the Gauss-Jordan algorithm
Macro Shortest_Path - Generates the shortest path matrix (up to 255 x 255) from its distance matrix
Macro Graph drawing - Draws a graph from its adjacent matrix 
Macro Block reduction - transforms a matrix into a block-partioned form
Macro Matrix Operations - Several common tasks: multiplication, inversion, addition, etc.
Macro Matrix methods for round-off clean-up and decimal rounding.
Function Mat_Block    - returns the block-partioned form of a given matrix
Function Mat_Block_Perm - returns the permutation matrix for the block reduction

Bug fix 1.02.04 - ProdScal_C returns incorrect value 

MATRIX.XLA - Ver. 1.5 -  Jan 2004
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Finally all the functions will appear in the category "Matrix" of the function wizard,
thanks to the FunCustomize.dll of Laurent Longre  (http://longre.free.fr)

The following new functions are added:
Interpolate	Pieces polynomial interpolation
Mat_Adm		Admittance matrix of a Linear Network Graph
Mat_Leontief   	Leontief matrix for IO-Analysis
M_DET_C		Determinant for complex matrix

All complex functions now accept the parameter "CFormat" to set one of the following formats:
- splitted matrix format
- interlaced matrix format
- string matrix format

The following functions are modified:
M_MULT_C	Complex matrices multiplication  with CFormat
M_INV_C		Complex matrix inversion  with CFormat 
SYSLIN_C	Complex linear system  with CFormat 
ProdScal_C	Complex vectors scalar product  with CFormat
REGRP 		Polynomila regression. Parameter "Degree" added
MatNormalize	The normalize number has changed. New parameter Tiny has added

The following bugs are fixed:
Bug 25.11.03  	Varimax gives the wrong sign   (thanks to Steve Futch)
Bug 20.12.03	MatEigenvector_inv. Iteration limit could fail under certain condition
Bug 09.11.03	Switch off/on the determinat computing in the GJ() Gauss-Jordan routine
This avoid the determinant overflow error during the matrix inverse computing

Now also this addin has a little menu bar "Matrix Tool" performing useful matrix operations:  selecting, coping piece of matrix, and running macros. And of course for calling Matrix help.

The following new macros are added:
Matrix Selector - Selects special matrix format: triangular, diagonal, tridiagonal
Matrix Scarp Paster - Pastes matrix pieces in the worksheet
Matrix Generator - Generates several kind of matrices: random, tartaglia, hilbert, etc.

MATRIX.XLA- Ver. 1.4 -  Sept 2003
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The following new functions are added:
MatEigenvalue_QL	Real eigenvalues for tridiagonal matrices with QL algorithm
MatEigenvalue_TridUni	Eigenvalues of tridiagonal uniform matrices
Mat_Hessemberg		Returns the Hessemberg form of a matrix
Poly_Roots_QR		Polynomial rootfinder with QR method
MatEigenvector3		Eigenvalues of tridiagonal matrices
Mat_QR_iter		Performs the diagonalization with the QR iterative method

The following functions are modified:
MatEigenvalue_QR  	Now returns real and complex eigenvalues of any real matrix 
SYSLIN3			Partial pivot strategy for tridiagonal matrices reduction

The following bugs are fixed:
Mat_QR			return #VALUE for rectangular matrices 
 (many thanks to Bob Chesebrough, Bob Foulser, Tom Lasinski)
SYSLIN3			incorrect return "?" if b1=0

MATRIX.XLA - Ver. 1.3 -  May 2003
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The following new functions are added:
REGRP		polynomial regression
M_T		new function name for transpose matrix (the old was too verbose)
M_DET3		determinant for tridiagonal matrix
M_MULT3		multiply tridiagonal matrix
SYSLIN3		tridiagonal linear system
SYSLIN_T	triangular linear system with back/forward algorithms
RRMS		residuals root mean squares  
MatPerm		permutation matrix
M_TRIA_ERR	return the average error for a tringular matrix
MatNorm		norm of a matrix/vectors (norm 0, 1, 2, 3)

Matrix Icon added

REGRL bug fixed: #VALUE returned for one column parameter x
REGRL accuracy improved.
MAT_LU was modified. Now return also the permuation matrix P, being A = PLU
MatNormalize bug fixed: uncorrected value returned
M_DET	accuracy improved for integer matrices
M_INV   accuracy improved for integer matrices
SYSLIN  accuracy improved for integer matrices
M_EXP	efficence improved with the Pad