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Article contents:== Outdated egg! This is an egg for CHICKEN 4, the unsupported old release. You're almost certainly looking for [[/eggref/5/matrix-utils|the CHICKEN 5 version of this egg]], if it exists. If it does not exist, there may be equivalent functionality provided by another egg; have a look at the [[https://wiki.call-cc.org/chicken-projects/egg-index-5.html|egg index]]. Otherwise, please consider porting this egg to the current version of CHICKEN. [[tags:egg]] == matrix-utils Generation of special utility matrices that are represented as SRFI-4 vectors. [[toc:]] == Usage (require-extension matrix-utils) == Documentation {{matrix-utils}} contains a set of procedures that allow the convenient creation of utility matrices, such as identity matrices, diagonal matrices, zero matrices, and so on. It uses a representation of matrices as [[http://srfi.schemers.org/srfi-4/srfi-4.html|SRFI-4]] vectors, where the matrix can be in row-major or column-major layout. {{matrix-utils}} defines a procedure {{(MAKE-FILL-MATRIX)}} which takes as an argument an SRFI-4 vector setter and returns a {{FILL-MATRIX!}} procedure, which fills a given matrix with the values returned by applying a user-specified procedure to every pair of indices in the matrix, in a manner similar to fold. All other procedures in the library use the {{FILL-MATRIX!}} abstraction, and are constructed in a similar way, with SRFI-4 procedures and {{FILL-MATRIX!}} as parameters. === Procedures <procedure>make-matrix-map:: VECTOR-REF * VECTOR-SET! -> (ORDER * M * N * A * F * [IX * IY * EX * EY] -> A)</procedure> Given procedures {{VECTOR-REF}} and {{FILL-MATRIX!}}, returns a procedure {{MATRIX-MAP}} of the form {{MATRIX-MAP:: M * N * A * F * [IX * IY * EX * EY] -> B}} Where procedure {{MATRIX-MAP}} applies the map operation on a matrix {{A}} of size {{M x N}} with the values returned by applying procedure {{F}} to each pair of indices and the corresponding value at that position in the matrix. Procedure {{F}} is of the form {{LAMBDA I J V -> U}}, where {{V}} is a matrix element at position {{(I,J)}} and {{U}} is corresponding element in the return matrix. Optional arguments {{IX IY EX EY}} may specify a sub-matrix in matrix {{A}}. {{VECTOR-REF}} is one of the homogeneous vector accessor procedures from SRFI-4. <procedure>make-matrix-fold:: VECTOR-REF -> (ORDER * M * N * A * F * X0 * [IX * IY * EX * EY] -> A)</procedure> Given a procedure {{VECTOR-REF}}, returns a procedure {{MATRIX-FOLD}} of the form {{MATRIX-FOLD:: M * N * A * F * X0 * [IX * IY * EX * EY] -> XN}} Where procedure {{MATRIX-FOLD}} applies the fold operation on a matrix {{A}} of size {{M x N}} with the values returned by applying procedure {{F}} to each pair of indices and the corresponding value at that position in the matrix. Procedure {{F}} is of the form {{LAMBDA I J V AX -> AX1}}, where {{V}} is a matrix element at position {{(I,J)}} and {{AX}} is accumulator value. The initial value of {{AX}} is given by {{X0}}. Procedure {{F}} is expected to return the new accumulator value. Optional arguments {{IX IY EX EY}} may specify a sub-matrix in matrix {{A}}. {{VECTOR-REF}} is one of the homogeneous vector accessor procedures from SRFI-4. <procedure>make-matrix-fold-partial:: VECTOR-REF -> (ORDER * M * N * A * F * P * X0 * [IX * IY * EX * EY] -> A)</procedure> Given a procedure {{VECTOR-REF}}, returns a procedure {{MATRIX-FOLD-PARTIAL}} of the form {{MATRIX-FOLD-PARTIAL:: M * N * A * F * P * X0 * [IX * IY * EX * EY] -> XN}} Where procedure {{MATRIX-FOLD-PARTIAL}} applies the fold operation on a matrix {{A}} of size {{M x N}} with the values returned by applying procedure {{F}} to each pair of indices and the corresponding value at that position in the matrix. {{MATRIX-FOLD-PARTIAL}} first applies the predicate {{P}} to the current pair of indices, and if the result is true, then {{F}} is applied. Procedure {{F}} is of the form {{LAMBDA V AX -> AX1}}, where {{V}} is a matrix element at position {{(I,J)}} and {{AX}} is accumulator value. The initial value of {{AX}} is given by {{X0}}. Procedure {{F}} is expected to return the new accumulator value. Procedure {{P}} is of the form {{LAMBDA I J -> boolean}}, where {{I,J}} are matrix indices. Optional arguments {{IX IY EX EY}} may specify a sub-matrix in matrix {{A}}. {{VECTOR-REF}} is one of the homogeneous vector accessor procedures from SRFI-4. <procedure>make-fill-matrix:: VECTOR-SET! -> (ORDER * M * N * A * F * F0 * [IX * IY * EX * EY] -> A)</procedure> Given a procedure {{VECTOR-SET!}}, returns a procedure {{FILL-MATRIX!}} of the form {{FILL-MATRIX!:: M * N * A * F * F0 * [IX * IY * EX * EY] -> A}} Where procedure {{FILL-MATRIX!}} fills matrix {{A}} of size {{M x N}} with the values returned by applying procedure {{F}} to each pair of indices in the matrix. Procedure {{F}} is of the form {{LAMBDA I J AX -> VAL * AX1}}, where {{I, J}} are matrix indices, and {{AX}} is accumulator value (like in fold). The initial value of {{AX}} is given by {{F0}}. Procedure {{F}} is expected to return two values: the value to be placed in matrix {{A}} at position {{[I,J]}}, and the new accumulator value (or {{#f}}). Optional arguments {{IX IY EX EY}} may specify a sub-matrix in matrix {{A}} to be filled. These arguments are checked to make sure they specify a valid sub-matrix. {{VECTOR-SET!}} is one of the homogeneous vector setting procedures from SRFI-4. Procedure {{F}} must ensure that it returns values that are within the range of the SRFI-4 type used. <procedure>make-matrix-ones:: MAKE-VECTOR * FILL-MATRIX! -> (M * N [* ORDER] -> A)</procedure> Given procedures {{MAKE-VECTOR}} and {{FILL-MATRIX!}}, returns a procedure {{ONES}} of the form {{ONES:: M * N [* ORDER] -> A}} Where procedure {{ONES}} returns a matrix {{A}} of size {{M x N}}, in which all elements are 1. Optional argument {{ORDER}} specifies the matrix layout: {{ColMajor}} or {{RowMajor}}, default is {{RowMajor}}. {{MAKE-VECTOR}} is one of the homogeneous vector creation procedures from SRFI-4, and {{FILL-MATRIX!}} is a procedure created by {{MAKE-FILL-MATRIX}}, above. {{FILL-MATRIX!}} must operate on the same type of vector as {{MAKE-VECTOR}}. <procedure>make-matrix-zeros:: MAKE-VECTOR * FILL-MATRIX! -> (M * N [* ORDER] -> A)</procedure> Given procedures {{MAKE-VECTOR}} and {{FILL-MATRIX!}}, returns a procedure {{ZEROS}} of the form {{ZEROS:: M * N [* ORDER] -> A}} Where procedure {{ZEROS}} returns a matrix {{A}} of size {{M x N}}, in which all elements are 0. Optional argument {{ORDER}} specifies the matrix layout: {{ColMajor}} or {{RowMajor}}, default is {{RowMajor}}. {{MAKE-VECTOR}} is one of the homogeneous vector creation procedures from SRFI-4, and {{FILL-MATRIX!}} is a procedure created by {{MAKE-FILL-MATRIX}}, above. {{FILL-MATRIX!}} must operate on the same type of vector as {{MAKE-VECTOR}}. <procedure>make-matrix-eye:: MAKE-VECTOR * FILL-MATRIX! -> (M * N [* ORDER] -> I)</procedure> Given procedures {{MAKE-VECTOR}} and {{FILL-MATRIX!}}, returns a procedure {{EYE}} of the form {{EYE:: M * N [* ORDER] -> I}} Where procedure {{EYE}} returns an identity matrix of size {{M x N}}. Optional argument {{ORDER}} specifies the matrix layout: {{ColMajor}} or {{RowMajor}}, default is {{RowMajor}}. {{MAKE-VECTOR}} is one of the homogeneous vector creation procedures from SRFI-4, and {{FILL-MATRIX!}} is a procedure created by {{MAKE-FILL-MATRIX}}, above. {{FILL-MATRIX!}} must operate on the same type of vector as {{MAKE-VECTOR}}. <procedure>make-matrix-diag:: VECTOR-REF * MAKE-VECTOR * FILL-MATRIX! -> (M * N * V [K * ORDER] -> D)</procedure> Given procedures {{VECTOR-REF}}, {{MAKE-VECTOR}} and {{FILL-MATRIX!}}, returns a procedure {{DIAG}} of the form {{DIAG:: M * N * V [K * ORDER] -> D}} Where procedure {{DIAG}} returns a diagonal matrix {{D}} of size {{M x N}}, with vector {{V}} on diagonal {{K}}. Argument {{K}} is optional. If it is positive, the vector is placed on the {{K}}-th super-diagonal of matrix {{D}}. If it is negative, it is placed on the -{{K}}-th sub-diagonal of matrix {{D}}. The default value of {{K}} is 0, and the vector is placed on the main diagonal of matrix {{D}}. Optional argument {{ORDER}} specifies the matrix layout: {{ColMajor}} or {{RowMajor}}, default is {{RowMajor}}. Vector {{V}} is always assumed to be a row vector. {{VECTOR-REF}} and {{MAKE-VECTOR}} are two of the homogeneous vector procedures from SRFI-4, and {{FILL-MATRIX!}} is a procedure created by {{MAKE-FILL-MATRIX}}, above. {{FILL-MATRIX!}} must operate on the same type of vector as {{VECTOR-REF}} and {{MAKE-VECTOR}}. <procedure>make-linspace:: MAKE-VECTOR * FILL-MATRIX! -> (N * BASE * LIMIT -> V)</procedure> Given procedures {{MAKE-VECTOR}} and {{FILL-MATRIX!}}, returns a procedure {{LINSPACE}} of the form {{LINSPACE:: N * BASE * LIMIT -> V}} Where {{LINSPACE}} returns a row vector with {{N}} linearly spaced elements between {{BASE}} and {{LIMIT}}. The number of elements, {{N}}, must be greater than 1. The {{BASE}} and {{LIMIT}} are always included in the range. If {{BASE}} is greater than {{LIMIT}}, the elements are stored in decreasing order. {{MAKE-VECTOR}} is one of the homogeneous vector creation procedures from SRFI-4, and {{FILL-MATRIX!}} is a procedure created by {{MAKE-FILL-MATRIX}}, above. {{FILL-MATRIX!}} must operate on the same type of vector as {{MAKE-VECTOR}}. <procedure>make-logspace:: VECTOR-REF * MAKE-VECTOR * FILL-MATRIX! -> (N * BASE * LIMIT -> V)</procedure> Given procedures {{VECTOR-REF}}, {{MAKE-VECTOR}} and {{FILL-MATRIX!}}, returns a procedure {{LOGSPACE}} of the form {{LOGSPACE:: N * BASE * LIMIT -> V}} Where {{LOGSPACE}} returns a row vector with {{N}} logarithmically spaced elements between {{10^BASE}} and {{10^LIMIT}}. The number of elements, {{N}}, must be greater than 1. The {{BASE}} and {{LIMIT}} are always included in the range. If {{BASE}} is greater than {{LIMIT}}, the elements are stored in decreasing order. {{VECTOR-REF}} and {{MAKE-VECTOR}} are two of the homogeneous vector procedures from SRFI-4, and {{FILL-MATRIX!}} is a procedure created by {{MAKE-FILL-MATRIX}}, above. {{FILL-MATRIX!}} must operate on the same type of vector as {{VECTOR-REF}} and {{MAKE-VECTOR}}. <procedure>f64vector-repmat:: SRC * DIMS * REPS -> A</procedure> Constructs a block matrix of size {{DIMS}}, with a copy of matrix {{SRC}} as each element. <procedure>f64vector-meshgrid:: X * Y [* Z] -> XX * YY [* ZZ]</procedure> Given {{f64vector}} objects of X, Y, and Z coordinates, constructs matrices XX, YY, ZZ corresponding to a full 3-D grid. If optional argument Z is not given, then matrices XX and YY corresponding to a 2-D grid are constructed. === Macros <macro>(define-utility-matrices type)</macro> Creates utility matrix procedures that create matrices of the specified type. {{TYPE}} is one of the following: <table class="symbol-table"><tr><td>f64</td><td>Double precision IEEE floating point</td></tr> <tr><td>f32</td><td>Single precision IEEE floating point</td></tr> <tr><td>s32</td><td>Signed 32-bit integer</td></tr> <tr><td>u32</td><td>Unsigned 32-bit integer</td></tr> <tr><td>alist</td><td>An association list of the form {{((vector-ref . proc) (make-vector . proc) (vector-set! . proc))}}</td></tr> </table> The following procedures are created: <table class="symbol-table"><tr><td>fill-matrix!</td><td></td></tr> <tr><td>ones</td><td></td></tr> <tr><td>zeros</td><td></td></tr> <tr><td>eye</td><td></td></tr> <tr><td>diag</td><td></td></tr> <tr><td>linspace</td><td></td></tr> <tr><td>logspace</td><td></td></tr> </table> <macro>(with-utility-matrices type expr)</macro> As the above macro, except that it creates local bindings for the utility matrix procedures, and evaluates {{EXPR}} with those bindings. <macro>(define-matrix-map type)</macro> Creates procedure {{MATRIX-MAP:: F * M -> A}} that, given an input matrix {{M}} and procedure {{F}}, returns a new matrix {{A}} such that {{A(i,j) = F(M(i,j))}}. {{TYPE}} is one of the following: ; f64 : Double precision IEEE floating point ; f32 : Single precision IEEE floating point ; s32 : Signed 32-bit integer ; u32 : Unsigned 32-bit integer == Examples == About this egg === Author [[/users/ivan-raikov|Ivan Raikov]] === Version history ; 1.14-1.15 : Added repmat and meshgrid ; 1.12 : Updated use of blas ; 1.11 : Documentation converted to wiki format ; 1.10 : Ported to Chicken 4 ; 1.9 : Build script updated for better cross-platform compatibility ; 1.8 : Added procedure make-matrix-map ; 1.7 : Added procedure make-matrix-fold ; 1.6 : Added procedure make-matrix-fold-partial ; 1.5 : Migrated matrix-fold/map to srfi-4-utils ; 1.4 : Added define-matrix-fold ; 1.3 : Added define-matrix-map ; 1.2 : Bug fix in the definition of make-matrix-zeros ; 1.1 : Fixes in the setup file ; 1.0 : Initial release === License Copyright 2007-2014 Ivan Raikov and the Okinawa Institute of Science and Technology. This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. A full copy of the GPL license can be found at <http://www.gnu.org/licenses/>. Description of your changes:

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