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 fulfill 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 sys tim x0procedure: 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 or pair of vector field and output procedures sys, time step flonum and time horizon flonum in pair tim, initial state column-matrix x0.

mx-ode2-ssp num sys tim x0procedure: 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 or pair of vector field and output procedures sys, time step flonum and time horizon flonum in pair tim, initial state column-matrix x0.

Matrix Utilities

mx->list matprocedure: returns list of entries of one-dimensional matrix mat.

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

mx-export str mat #!rest sepprocedure: returns void, writes matrix mat to new character sep-separated-value file in relative path string str, by default sep is , resulting in CSV.

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.

Additional Flonum Operations

The matrico module implicitly exports the (chicken flonum) module, as well as the following additional flonum operations:

fpprocedure: is an alias for exact->inexact.

fp% n dprocedure: returns flonum fraction with numerator fixnum n and denominator fixnum d.

fpzero?? xprocedure: returns boolean answering if flonum x is exactly zero.

fpzero? x tolprocedure: returns boolean answering if absolute value of flonum x is less than flonum tol.

fp*2 xprocedure: returns flonum double of flonum x.

fp^2 xprocedure: returns flonum square of flonum x.

fprec xprocedure: returns flonum reciprocal of flonum x.

fptauprocedure: returns flonum circle constant Tau via fraction.

fpeulprocedure: returns flonum Euler's number via fraction.

fpphiprocedure: returns flonum golden ratio via fraction of consecutive Fibonacci numbers.

fpdelta xprocedure: returns flonum Kronecker delta of flonum x.

fpheaviside xprocedure: returns flonum Heaviside step function of flonum x.

fpsign xprocedure: returns flonum sign of flonum x.

fpln xprocedure: returns flonum natural logarithm of flonum x.

fplb xprocedure: returns flonum base-2 logarithm of flonum x.

fplg xprocedure: returns flonum base-10 logarithm of flonum x.

fphsin xprocedure: returns flonum haversed sine of flonum x.

fphcos xprocedure: returns flonum haversed cosine of flonum x.

fplnsinh xprocedure: returns flonum log-of-sinh of flonum x.

fplncosh xprocedure: returns flonum log-of-cosh of flonum x.

fpsignsqrt xprocedure: returns flonum sign times square root of absolute value of flonum x.

fpsinc xprocedure: returns flonum cardinal sine function with removed singularity of flonum x.

fpsigm xprocedure: returns flonum standard logistic function of flonum x, aka sigmoid.

fpgauss xprocedure: returns flonum Gauss bell curve function evaluation of flonum x.

fpstirling xprocedure: returns flonum Stirling approximation of factorial of flonum x.

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
0.6: Major Update (details)

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