matrico

A flonum matrix module for CHICKEN Scheme.

matrico Function

matricoprocedure: returns void, prints help message for matrico function.

matrico symprocedure

returns any, depending on argument symbol sym:

'list - returns void, prints list of "mx" functions;
'about - returns void, prints summary about matrico;
'banner - returns void, prints the matrico banner;
'version - returns pair holding major and minor version numbers of matrico;
'citation - returns void, prints citation information for matrico;
'benchmark - returns fixnum, prints approximated million-instructions-per-second for current machine;
otherwise - returns boolean answering if argument is a symbol matching an existing function, starting with "mx", and prints its docstring.

Matrix Type

matrixtype: a list-of-f64vectors (flonum-)matrix type. This record type is not directly accessible, and can only be manipulated through "mx-" functions.

Matrix Generators

mx rows cols valprocedure: returns rows-by-cols matrix with all entries set to flonum val for positive fixnums rows and cols.

mx% lstprocedure: returns matrix from row-major list-of-lists-of-flonums lst.

mx-identity dimsprocedure: returns dims-by-dims identity matrix for a positive fixnum dims.

mx-exchange dimsprocedure: returns dims-by-dims exchange matrix for a positive fixnum dims.

mx-hilbert dimsprocedure: returns dims-by-dims Hilbert matrix for a positive fixnum dims.

mx-pascal dimsprocedure: returns dims-by-dims (lower triangular) Pascal matrix for a positive fixnum dims.

mx-lehmer rows colsprocedure: returns rows-by-cols Lehmer matrix for the positive fixnums rows and cols.

mx-random rows cols low uppprocedure: returns rows-by-cols uniformly distributed random matrix in the interval flonum low to flonum upp for the positive fixnums rows and cols.

mx-tridiag dims low mid uppprocedure: returns dims-by-dims matrix with lower, main, upper band entries given by the flonums low, mid, upp for a positive fixnum dims.

mx-unit rows numprocedure: returns dims-by-one column-matrix of zeros except the positive fixnum num-th entry set to one for a positive fixnum dims, aka canonical base vector.

mx-iota dimsprocedure: returns dims-by-one column-matrix with entries set to corresponding row index for a positive fixnum dims.

mx-linspace x y numprocedure: returns matrix of positive fixnum num row-wise linearly spaced entries with endpoints given by flonums or column-matrixes x and y.

mx-logspace x y numprocedure: returns matrix of positive fixnum num row-wise (base-10) logarithmic spaced entries with endpoints given by flonums or column matrixes x and y.

Matrix Dimensions

mx-cols matprocedure: returns fixnum number of columns of matrix mat.

mx-rows matprocedure: returns fixnum number of rows of matrix mat.

mx-numel matprocedure: returns fixnum number of entries of matrix mat.

mx-dims matprocedure: returns fixnum number of dimensions of matrix mat.

Matrix Predicates

mx? anyprocedure: returns boolean answering if any is a matrix.

mx-col? matprocedure: returns boolean answering if matrix mat has only a single column.

mx-row? matprocedure: returns boolean answering if matrix mat has only a single row.

mx-scalar? matprocedure: returns boolean answering if matrix mat has only a single row and single column.

mx-vector? matprocedure: returns boolean answering if matrix mat has only a single row or single column.

mx-square? matprocedure: returns boolean answering if matrix mat has the same number of rows and columns.

mx-samecols? x yprocedure: returns boolean answering if matrixes x and y have same number of columns.

mx-samerows? x yprocedure: returns boolean answering if matrixes x and y have same number of rows.

mx-samedim? x yprocedure: returns boolean answering if matrixes x and y have same number of columns and rows.

mx-any? pred matprocedure: returns boolean answering if any entry of matrix mat fulfills predicate procedure pred.

mx-all? pred matprocedure: returns boolean answering if all entries of matrix mat fulfills predicate procedure pred.

mx=? x y tolprocedure: returns boolean answering if all entry-wise distances between matrixes x and y are below tolerance flonum `tol`.

Matrix Accessors

mx-ref11 matprocedure: returns flonum being the entry in the first row and first column of matrix mat.

mx-ref mat row colprocedure: returns flonum being matrix mat entry in row and column specified by fixnums row, col.

mx-set mat row col valprocedure: returns matrix copy of matrix mat but with entry in row fixnum row and column fixnum col set to flonum or one-by-one matrix val.

mx-set! mat row col valprocedure: returns void, sets entry of matrix mat in row and column specified by fixnums row and col to flonum or one-by-one matrix val.

mx-col mat colprocedure: returns matrix being matrix mat's column specified by fixnum col.

mx-row mat rowprocedure: returns matrix being matrix mat's row specified by fixnum row.

mx-diag matprocedure: returns column-matrix holding square matrix mat's diagonal entries.

mx-submatrix mat row1 row2 col1 col2procedure: returns matrix holding entries of matrix mat in rows specified by fixnums row1 to row2 and columns specified by fixnums col1 to col2.

Matrix Expanders

mx+ x yprocedure: returns matrix of entry-wise addition of matrixes x and y.

mx* x yprocedure: returns matrix of entry-wise multiplication of matrixes x and y.

mx- x yprocedure: returns matrix of entry-wise subtraction of matrixes x and y.

mx/ x yprocedure: returns matrix of entry-wise division of matrixes x by y.

mx^ x yprocedure: returns matrix of entry-wise exponentiation of matrixes x to the y.

mx-where pred x yprocedure: returns matrix of entries of matrixes x or y based on predicate procedure pred.

Matrix Mappers

Entry-Wise Elementary Functions

mx- xprocedure: returns matrix of entry-wise negation of matrix x.

mx/ xprocedure: returns matrix of entry-wise reciprocal of matrix x.

mx*2 xprocedure: returns matrix of entry-wise doubling of matrix x.

mx^2 xprocedure: returns matrix of entry-wise squaring of matrix x.

Entry-Wise Rounding Functions

mx-round matprocedure: returns matrix with entries of matrix mat rounded to nearest integer.

mx-floor matprocedure: returns matrix with entries of matrix mat rounded to nearest upper integer.

mx-ceil matprocedure: returns matrix with entries of matrix mat rounded to nearest lower integer.

Entry-Wise Generalized Functions

mx-abs matprocedure: returns matrix with entry-wise absolute value of matrix mat.

mx-sign matprocedure: returns matrix with entry-wise sign of matrix mat.

mx-delta matprocedure: returns matrix with entry-wise Kronecker delta of matrix mat.

mx-heaviside matprocedure: returns matrix with entry-wise Heaviside step of matrix mat.

Entry-Wise Trigonometric Functions

mx-sin matprocedure: returns matrix with entry-wise sine of matrix mat.

mx-cos matprocedure: returns matrix with entry-wise cosine of matrix mat.

mx-tan matprocedure: returns matrix with entry-wise tangent of matrix mat.

Entry-Wise Inverse Trigonometric Functions

mx-asin matprocedure: returns matrix with entry-wise inverse sine of matrix mat, aka arcsine.

mx-acos matprocedure: returns matrix with entry-wise inverse cosine of matrix mat, aka arccosine.

mx-atan matprocedure: returns matrix with entry-wise inverse tangent of matrix mat, aka arctangent.

Entry-Wise Hyperbolic Functions

mx-sinh matprocedure: returns matrix with entry-wise hyperbolic sine of matrix mat.

mx-cosh matprocedure: returns matrix with entry-wise hyperbolic cosine of matrix mat.

mx-tanh matprocedure: returns matrix with entry-wise hyperbolic tangent of matrix mat.

Entry-Wise Inverse Hyperbolic Functions

mx-asinh matprocedure: returns matrix with entry-wise inverse hyperbolic sine of matrix mat, aka area hyperbolic sine.

mx-acosh matprocedure: returns matrix with entry-wise inverse hyperbolic cosine of matrix mat, aka area hyperbolic cosine.

mx-atanh matprocedure: returns matrix with entry-wise inverse hyperbolic tangent of matrix mat, aka area hyperbolic tangent.

Entry-Wise Haversed Trigonometric Functions

mx-hsin matprocedure: returns matrix with entry-wise haversed sine of matrix mat.

mx-hcos matprocedure: returns matrix with entry-wise haversed cosine of matrix mat.

Entry-Wise Logarithmic Hyperbolic Functions

mx-lnsinh matprocedure: returns matrix with entry-wise log-sinh of matrix mat.

mx-lncosh matprocedure: returns matrix with entry-wise log-cosh of matrix mat.

Entry-Wise Roots

mx-sqrt matprocedure: returns matrix with entry-wise square root of matrix mat.

mx-signsqrt matprocedure: returns matrix with entry-wise sign times square-root of absolute value of matrix mat.

Entry-Wise Logarithms

mx-ln matprocedure: returns matrix with entry-wise natural logarithm of matrix mat.

mx-lb matprocedure: returns matrix with entry-wise base-2 logarithm of matrix mat.

mx-lg matprocedure: returns matrix with entry-wise base-10 logarithm of matrix mat.

Entry-Wise Exponential

mx-exp matprocedure: returns matrix with entry-wise exponential of matrix mat.

mx-gauss matprocedure: returns matrix with entry-wise Gaussian of matrix mat.

Entry-Wise Special Functions

mx-sinc matprocedure: returns matrix with entry-wise cardinal sine of matrix mat.

mx-sigm matprocedure: returns matrix with entry-wise sigmoid of matrix mat.

mx-stirling matprocedure: returns matrix with entry-wise Stirling approximation of matrix mat.

Matrix Reducers

Sums

mx-rowsum matprocedure: returns column-matrix of summing row entries of matrix mat.

mx-colsum matprocedure: returns row-matrix of summing column entries of matrix mat.

mx-sum matprocedure: returns flonum of summing all entries of matrix mat.

Products

mx-rowprod matprocedure: returns column-matrix of multiplying row entries of matrix mat.

mx-colprod matprocedure: returns row-matrix of multiplying column entries of matrix mat.

mx-prod matprocedure: returns flonum of multiplying all entries of matrix mat.

Minima

mx-rowmin matprocedure: returns column-matrix of row-wise minima of matrix mat.

mx-colmin matprocedure: returns row-matrix of column-wise minima of matrix mat.

mx-min matprocedure: returns flonum minimum of all matrix mat entries.

Maxima

mx-rowmax matprocedure: returns column-matrix of row-wise maxima of matrix mat.

mx-colmax matprocedure: returns row-matrix of column-wise maxima of matrix mat.

mx-max matprocedure: returns flonum maximum of all matrix mat entries.

Midrange

mx-rowmidr matprocedure: returns column-matrix of row-wise midrange of matrix mat.

mx-colmidr matprocedure: returns row-matrix of column-wise midrange of matrix mat.

mx-midr matprocedure: returns flonum midrange of all matrix mat entries.

Means

mx-rowmean mat typprocedure: returns column-matrix of row-wise power means of matrix mat of type symbol typ, which can be -1, 0, 1, 2, or 'inf.

mx-colmean mat typprocedure: returns row-matrix of column-wise power means of matrix mat of type symbol typ, which can be -1, 0, 1, 2, or 'inf.

mx-mean mat typprocedure: returns flonum power mean of all matrix mat entries of type symbol typ, which can be -1, 0, 1, 2, or 'inf.

Norms

mx-rownorm mat typprocedure: returns column matrix of row-wise matrix norms of matrix mat of type symbol typ, which can be 1, 2, or 'inf.

mx-colnorm mat typprocedure: returns row matrix of column-wise matrix norms of matrix mat of type symbol typ, which can be 1, 2, or 'inf.

mx-norm mat typprocedure: returns flonum matrix norms of matrix mat of type symbol typ, which can be 1, 'inf, 'fro, or 'max.

Linear Algebra

mx-horcat x yprocedure: returns matrix of horizontally concatenated matrixes x and y.

mx-vercat x yprocedure: returns matrix of vertically concatenated matrixes x and y.

mx-vec matprocedure: returns matrix of vertically concatenated columns of matrix mat, aka vectorization.

mx-transpose matprocedure: returns matrix of entries of matrix mat with swapped row and column indices.

mx-axpy a x yprocedure: returns matrix of entry-wise generalized addition of flonum a times matrix x plus matrix y.

mx-sympart matprocedure: returns matrix being symmetric part of square matrix mat.

mx-skewpart matprocedure: returns matrix being skey-symmetric part of square matrix mat, aka anti-symmetric part.

mx-diagonal matprocedure: returns diagonal matrix from column matrix mat.

Linear Problems

mx-qr matprocedure: returns pair of orthogonal matrix (Q) and upper right triangular matrix (R) factoring full column rank matrix mat.

mx-solver matprocedure: returns function returning column-matrix solving the linear (least-squares) problem of matrix mat, given a column-matrix vec via QR decomposition.

mx-solve mat vecprocedure: returns column-matrix solving the linear problem of matrix mat and column-matrix vec via QR decomposition.

mx-orth matprocedure: returns matrix orthogonalizing matrix mat.

mx-absdet matprocedure: returns flonum being absolute value of the determinant of matrix mat.

mx-logdet matprocedure: returns flonum being the (natural) logarithm of the determinant of matrix mat.

Traces

mx-trace matprocedure: returns flonum being sum of square matrix mat's diagonal entries.

mx-multrace matprocedure: returns flonum being product of square matrix mat's diagonal entries.

mx-prodtrace* x ytprocedure: returns flonum being the trace of the matrix product of matrix x and transposed matrix yt.

mx-prodtrace x yprocedure: returns flonum being the trace of the matrix product of matrixes x and y.

Matrix Multiplication

mx-scalar xt yprocedure: returns flonum resulting from scalar product of column-matrixes xt and y.

mx-dyadic x yprocedure: returns flonum resulting from dyadic product of column-matrix x and row-matrix y.

mx-dot* xt yprocedure: returns matrix resulting from matrix multiplication of (transposed) matrix xt and matrix y.

mx-dot x yprocedure: returns matrix resulting from matrix multiplication of matrixes x and y.

mx-gram matprocedure: returns matrix resulting from matrix multiplication of transposed matrix mat with itself, aka Gram matrix.

mx-gram* matprocedure: returns matrix resulting from matrix multiplication of matrix mat with itself transposed.

mx-square matprocedure: returns matrix resulting from matrix multiplication of matrix mat with itself.

Multivariate Statistics

mx-xcov x yprocedure: returns matrix of cross-covariances of matrixes x and y, representing columns of observations.

mx-cov matprocedure: returns matrix of covariances of matrix mat, representing columns of observations.

mx-var matprocedure: returns column matrix of variances of matrix mat, representing columns of observations.

mx-std matprocedure: returns column matrix of standard deviations of matrix mat, representing columns of observations.

mx-xcor x yprocedure: returns matrix of cross-correlations of matrixes x and y, representing columns of observations.

mx-cor matprocedure: returns matrix of correlations of matrix mat, representing columns of observations.

mx-angle x yprocedure: returns matrix of angles between matrixes x and y, representing columns of observations.

mx-coher x yprocedure: returns flonum of distance coherence between matrixes x and y.

Analysis

mx-diff matprocedure: returns matrix of differences of consecutives columns of matrix mat.

mx-trapz matprocedure: returns column-matrix trapezoid approximate integral of matrix mat being columns data-points of rows-dimensional function.

mx-ode2-hyp num fun x0 dt tfprocedure: returns states-times-steps matrix trajectory solving an ordinary differential equation, by a 2nd order hyperbolic Runge-Kutta method of fixnum num stages, with vector field procedure fun, initial state column-matrix x0, time step flonum dt, and time horizon flonum tf.

mx-ode2-ssp num fun x0 dt tfprocedure: returns states-times-steps matrix trajectory solving an ordinary differential equation, by a 2nd order strong stability preserving Runge-Kutta method of fixnum num stages, with vector field procedure fun, initial state column-matrix x0, time step flonum dt, and time horizon flonum tf.

Matrix Utilities

mx-print matprocedure: returns void, prints matrix mat to terminal.

mx-export str matprocedure: returns void, writes matrix mat to new comma-separated-value (CSV) file with name string str.

mx-save str matprocedure: returns void, writes matrix mat to new Scheme (SCM) file with name string str.

mx-load strprocedure: returns matrix loaded from SCM file in relative path specified by string str.

Authors

Christian Himpe

Repository

https://git.io/matrico

License

Version History

0.1: Initial Release
0.2: Major Update
0.3: Major Update
0.4: Minor Update
0.5: Minor Update (details)

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