MATRIX.MAC

DIMENSIONS

 

MINDIM returns minimum of number of rows and columns

MAXDIM returns maximum of number of rows and columns

 

ELEMENTARY STATISTICS

 

COLTOTAL returns sum of each column of matrix

ROWMAX returns maximum of each row of matrix

ROWMEAN returns mean of each row of matrix

ROWMEDIAN returns median of each row of matrix

ROWMIN returns minimum of each row of matrix

ROWSTDEV returns standard deviation of each row of matrix

ROWTOTAL returns sum of each row of matrix

 

MATRIX GENERATORS

 

GMCOLNOS generates matrix of column numbers

GMCONST generates constant matrix

GMIDENT generates identity matrix

GMONES  generates matrix of all ones

GMROWNOS generates matrix of row numbers

GMZEROS generates zero matrix

 

OVERALL MATRIX STATISTICS

 

GRANDCOUNT returns number of entries in matrix

GRANDMAX returns maximum of all entries of matrix

GRANDMEAN returns mean of all entries of matrix

GRANDMIN returns minimum of all entries of matrix

GRANDSTDEV returns standard deviation of all entries of matrix

GRANDTOTAL returns sum of all entries of matrix

 

POINT CHANGE

 

SETPM replaces entry of current matrix with scalar

SETPMS replaces entry of any matrix with scalar

 

REGION PROCESSING

 

ADDROW appends series as row to matrix

ADDCOL appends series as column to matrix

ADDZEROROW appends zero row to matrix

ADDZEROCOL appends zero column to matrix

DROPROW removes last row from matrix

DROPCOL removes last column from matrix

DELETEROW removes n-th row from matrix

DELETECOL removes n-th column from a matrix

SUBSTROW substitutes series into n-th row of matrix

SUBSTCOL substitutes series into n-th column of matrix

 

ROTATE AND SHIFT

 

ROTATEL rotates matrix to the left

ROTATER rotates matrix to the right

SHIFTL shifts matrix to the left

SHIFTR shifts matrix to the right

 

REGION PROCESSING

 

FLIPCOL reverses positions of columns of matrix

FLIPROW reverses positions of rows of matrix

LOWERTRI returns lower triangle including diagnonal

LOWERTRIX returns lower triangle excluding diagnonal

RESHAPEM changes number of rows and columns in matrix

TRSEC transposes matrix about secondary diagonal

UPPERTRI returns upper triangle including diagonal

UPPERTRIX returns upper triangle excluding diagnonal

 

ROW AND COLUMN NUMBERS

 

COLNOS matrix of column numbers

NUMROWS number of rows in matrix

ROWNOS matrix of row numbers

 

SINGULAR VALUE DECOMPOSITION

 

SVDDIV performs matrix division using SVD

SVDCOND returns the condition number of a matrix

USVD returns the left side of a pre-calculated SVD matrix

VSVD returns the right side of a pre-calculated SVD matrix

WSVD returns the diagonal of a pre-calculated SVD matrix

IWSVD returns the inverse diagonal of a pre-calculated SVD matrix

SVDSIZE returns the number of rows/columns of left/right SVD matrix

 

TOEPLITZ MATRICES

 

TOEPLITZ creates Toeplitz matrix from vector

 

VANDERMONDE MATRICES

 

VANDERMONDE computes Vandermonde matrix from vector

 

VECTOR GENERATORS

 

GVCONST generates constant column vector

GVINDEX generates column vector of row numbers

GVONES generates column vector of ones

GVTRI generates triangular vector

GVZEROS generates column vector of zeros