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grsp3.scm
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;; =========================================================================
;;
;; grsp3.scm
;;
;; Relational vectors, matrices, files and databases. In general, these
;; functions constitute the basis for other functions found in the grspX.scm
;; files, where X > 3.
;;
;; =========================================================================
;;
;; Copyright (C) 2020 - 2024 Pablo Edronkin (pablo.edronkin at yahoo.com)
;;
;; This program is free software: you can redistribute it and/or modify
;; it under the terms of the GNU Lesser 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 Lesser General Public License for more details.
;;
;; You should have received a copy of the GNU Lesser General Public
;; License along with this program. If not, see
;; <https://www.gnu.org/licenses/>.
;;
;; =========================================================================
;;;; General notes:
;;
;; - Read sources for limitations on function parameters.
;; - grsp3 provides some level of matrix algebra functionality for Guile,
;; but in its current version it is not intended to be particulary fast.
;; It does not make use of any additional non-Scheme library like BLAS
;; or Lapack.
;; - As a convention here, m represents rows, n represents columns;
;; variations in this theme include:
;;
;; - lm: lowest row number.
;; - hm: highest row number.
;; - ln: lowest col number.
;; - hn: highest col number.
;; - tm: total number of rows.
;; - tn: total number of columns.
;;
;; - All matrices referred in this file are numeric except wherever
;; specifically stated.
;;
;; Sources:
;;
;; See code of functions used and their respective source files for more
;; credits and references.
;;
;; - [1] Hep.by. (2020). Array Procedures - Guile Reference Manual. [online]
;; Available at:
;; http://www.hep.by/gnu/guile/Array-Procedures.html#Array-Procedures
;; [Accessed 28 Jan. 2020].
;; - [2] En.wikipedia.org. (2020). Numerical linear algebra. [online]
;; Available at: https://en.wikipedia.org/wiki/Numerical_linear_algebra
;; [Accessed 28 Jan. 2020].
;; - [3] En.wikipedia.org. (2020). Matrix theory. [online] Available at:
;; https://en.wikipedia.org/wiki/Category:Matrix_theory
;; [Accessed 28 Jan. 2020].
;; - [4] En.wikipedia.org. (2020). List of matrices. [online] Available at:
;; https://en.wikipedia.org/wiki/List_of_matrices [Accessed 8 Mar. 2020].
;; - [5] Gnu.org. (2020). Random (Guile Reference Manual). [online]
;; Available at:
;; https://www.gnu.org/software/guile/manual/html_node/Random.html
;; [Accessed 26 Jan. 2020].
;; - [6] Es.wikipedia.org. (2020). Factorización LU. [online] Available at:
;; https://es.wikipedia.org/wiki/Factorizaci%C3%B3n_LU
;; [Accessed 28 Jan. 2020].
;; - [7] Gnu.org. (2020). Guile Reference Manual. [online] Available at:
;; https://www.gnu.org/software/guile/manual/guile.html#Arithmetic
;; [Accessed 6 Feb. 2020].
;; - [8] En.wikipedia.org. (2020). Elementary matrix. [online] Available at:
;; https://en.wikipedia.org/wiki/Elementary_matrix#Operations
;; [Accessed 24 Feb. 2020].
;; - [9] En.wikipedia.org. 2020. Determinant. [online] Available at:
;; https://en.wikipedia.org/wiki/Determinant [Accessed 2 August 2020].
;; - [10] En.wikipedia.org. 2020. Leibniz Formula For Determinants.
;; [online]
;; Available at:
;; https://en.wikipedia.org/wiki/Leibniz_formula_for_determinants
;; [Accessed 4 August 2020].
;; - [11] En.wikipedia.org. 2020. Invertible Matrix. [online] Available at:
;; https://en.wikipedia.org/wiki/Invertible_matrix [Accessed 5 August
;; 2020].
;; - [12] En.wikipedia.org. 2020. Permanent (Mathematics). [online]
;; Available at: https://en.wikipedia.org/wiki/Permanent_(mathematics)
;; [Accessed 7 August 2020].
;; - [13] En.wikipedia.org. 2020. Immanant. [online] Available at:
;; https://en.wikipedia.org/wiki/Immanant [Accessed 14 August 2020].
;; - [14] En.wikipedia.org. 2020. Eigendecomposition Of A Matrix. [online]
;; Available at:
;; https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix
;; - [15] En.wikipedia.org. 2020. Eigenvalue Algorithm. [online]
;; Available at: https://en.wikipedia.org/wiki/Eigenvalue_algorithm
;; [Accessed 12 August 2020].
;; - [16] En.wikipedia.org. 2021. Relational algebra. [online] Available
;; at: https://en.wikipedia.org/wiki/Relational_algebra [Accessed 16
;; March 2021].
;; - [17] En.wikipedia.org. 2021. Support (mathematics). [online]
;; Available at:
;; https://en.wikipedia.org/wiki/Support_(mathematics)> [Accessed 27
;; March 2021].
;; - [18] Mathispower4u. (2020). LU Decomposition. [online] Available at:
;; https://www.youtube.com/watch?v=UlWcofkUDDU [Accessed 5 Mar. 2020].
;; - [19] En.wikipedia.org. 2021. Genetic algorithm - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Genetic_algorithm
;; [Accessed 13 May 2021].
;; - [20] En.wikipedia.org. 2021. Crossover (genetic algorithm) -
;; Wikipedia. [online] Available at:
;; https://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)
;; [Accessed 13 May 2021].
;; - [21] En.wikipedia.org. 2021. Mutation (genetic algorithm) - Wikipedia.
;; [online] Available at:
;; https://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)
;; [Accessed 13 May 2021].
;; - [22] En.wikipedia.org. 2021. Selection (genetic algorithm) -
;; Wikipedia. [online] Available at:
;; https://en.wikipedia.org/wiki/Selection_(genetic_algorithm)
;; [Accessed 13 May 2021].
;; - [23] fitness, A., 2015. Accumulated normalized fitness. [online] Stack
;; Overflow. Available at:
;; https://stackoverflow.com/questions/27524241/accumulated-normalized-fitness
;; [Accessed 13 May 2021].
;; - [24] En.wikipedia.org. 2021. Multiset - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Multiset [Accessed 17
;; September 2021].
;; - [25] Gnuplotting.org. 2021. Plotting data « Gnuplotting. [online]
;; Available at: http://www.gnuplotting.org/plotting-data/
;; [Accessed 21 November 2021].
;; - [26] Gnu.org. 2022. Scheduling (Guile Reference Manual). [online]
;; Available at:
;; https://www.gnu.org/software/guile/manual/html_node/Scheduling.html
;; [Accessed 16 May 2022].
;; - [27] En.wikipedia.org. 2022. Pauli matrices - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Pauli_matrices
;; [Accessed 16 May 2022].
;; - [28] En.wikipedia.org. 2022. Gamma matrices - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Gamma_matrices#Dirac_basis
;; [Accessed 16 May 2022].
;; - [29] En.wikipedia.org. 2022. Higher-dimensional gamma matrices -
;; Wikipedia. [online] Available at:
;; https://en.wikipedia.org/wiki/Higher-dimensional_gamma_matrices
;; [Accessed 16 May 2022].
;; - [30] En.wikipedia.org. 2022. Gell-Mann matrices - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Gell-Mann_matrices
;; [Accessed 19 May 2022].
;; - [31] En.wikipedia.org. 2022. Quantum logic gate - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Quantum_logic_gate
;; [Accessed 31 May 2022].
;; - [32] En.wikipedia.org. 2022. Quantum circuit - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Quantum_circuit
;; [Accessed 31 May 2022].
;; - [33] En.wikipedia.org. 2022. Penrose graphical notation - Wikipedia.
;; [online] Available at:
;; https://en.wikipedia.org/wiki/Penrose_graphical_notation
;; [Accessed 31 May 2022].
;; - [34] En.wikipedia.org. 2022. Categorical quantum mechanics -
;; Wikipedia. [online] Available at:
;; https://en.wikipedia.org/wiki/Categorical_quantum_mechanics
;; [Accessed 31 May 2022].
;; - [35] En.wikipedia.org. 2022. Qutrit - Wikipedia. [online] Available
;; at: https://en.wikipedia.org/wiki/Qutrit#Qutrit_quantum_gates
;; [Accessed 31 May 2022].
;; - [36] En.wikipedia.org. 2022. Tensor product - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Tensor_product
;; [Accessed 31 May 2022].
;; - [37] En.wikipedia.org. 2022. Kronecker product - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Kronecker_product
;; [Accessed 31 May 2022].
;; - [38] Product, T., Borah, M. and Orrick, W., 2022. Tensor product and
;; Kronecker Product. [online] Mathematics Stack Exchange. Available at:
;; https://math.stackexchange.com/questions/203947/tensor-product-and-kronecker-product
;; [Accessed 1 June 2022].
;; - [39] En.wikipedia.org. 2022. List of named matrices - Wikipedia.
;; [online] Available at:
;; https://en.wikipedia.org/wiki/List_of_named_matrices [Accessed 6
;; June 2022].
;; - [40] En.wikipedia.org. 2022. Hermitian adjoint - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Hermitian_adjoint
;; [Accessed 9 June 2022].
;; - [41] En.wikipedia.org. 2022. Conjugate transpose - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Conjugate_transpose
;; [Accessed 9 June 2022].
;; - [42] En.wikipedia.org. 2022. Minor (linear algebra) - Wikipedia.
;; [online] Available at:
;; https://en.wikipedia.org/wiki/Minor_(linear_algebra)
;; [Accessed 9 June 2022].
;; - [43] GeeksforGeeks. 2022. Doolittle Algorithm : LU Decomposition -
;; GeeksforGeeks. [online] Available at:
;; https://www.geeksforgeeks.org/doolittle-algorithm-lu-decomposition/
;; [Accessed 27 June 2022].
;; - [44] En.wikipedia.org. 2022. Crout matrix decomposition - Wikipedia.
;; [online] Available at:
;; https://en.wikipedia.org/wiki/Crout_matrix_decomposition
;; [Accessed 27 June 2022].
;; - [45] En.wikipedia.org. 2022. Unit vector - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Unit_vector
;; [Accessed 27 June 2022].
;; - [46] En.wikipedia.org. 2022. Dot product - Wikipedia. [online]
;; Available at:
;; https://en.wikipedia.org/wiki/Dot_product [Accessed 27 June 2022].
;; - [47] En.wikipedia.org. 2022. Inner product space - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Inner_product_space
;; [Accessed 27 June 2022].
;; - [48] En.wikipedia.org. 2022. Gram–Schmidt process - Wikipedia.
;; [online] Available at:
;; https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
;; [Accessed 27 June 2022].
;; - [49] 1980. Algorithms for the QR-Decomposition. [ebook] Zuerich.
;; Gander. Available at:
;; https://people.inf.ethz.ch/gander/papers/qrneu.pdf [Accessed 6 July
;; 2022].
;; - [50] Bindel, 2017. Householder QR. [ebook] Available at:
;; https://www.cs.cornell.edu/~bindel/class/cs6210-f09/lec18.pdf
;; [Accessed 6 July 2022].
;; - [51] People.math.wisc.edu. 2022. qr-4-ls-by-qr. [online] Available at:
;; https://people.math.wisc.edu/~roch/mmids/qr-4-ls-by-qr.html
;; [Accessed 6 July 2022].
;; - [52] En.wikipedia.org. 2022. Wilson matrix - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Wilson_matrix [Accessed
;; 7 July 2022].
;; - [53] En.wikipedia.org. 2022. Cholesky decomposition - Wikipedia.
;; [online] Available at:
;; https://en.wikipedia.org/wiki/Cholesky_decomposition [Accessed 7
;; July 2022].
;; - [54] Es.wikipedia.org. 2022. Norma matricial - Wikipedia, la
;; enciclopedia libre. [online] Available at:
;; https://es.wikipedia.org/wiki/Norma_matricial [Accessed 10 July 2022].
;; - [55] En.wikipedia.org. 2022. QR algorithm - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/QR_algorithm [Accessed
;; 18 July 2022].
;; - [56] En.wikipedia.org. 2022. List of numerical analysis topics -
;; Wikipedia. [online] Available at:
;; https://en.wikipedia.org/wiki/List_of_numerical_analysis_topics
;; [Accessed 18 July 2022].
;; - [57] En.wikipedia.org. 2022. Matrix splitting - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Matrix_splitting
;; [Accessed 21 July 2022].
;; - [58] En.wikipedia.org. 2022. Gauss–Seidel method - Wikipedia. [online]
;; Available at:
;; https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method [Accessed
;; 21 July 2022].
;; - [59] En.wikipedia.org. 2022. Jacobi method - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Jacobi_method [Accessed
;; 21 July 2022].
;; - [60] En.wikipedia.org. 2022. Spectral radius - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Spectral_radius
;; [Accessed 22 July 2022].
;; - [61] En.wikipedia.org. 2022. Rotation matrix - Wikipedia. [online]
;; Available at: https://en.wikipedia.org/wiki/Rotation_matrix
;; [Accessed 5 October 2022].
;; - [62] Eigenvector and eigenvalue (no date) Math is Fun Advanced.
;; Available at: https://www.mathsisfun.com/algebra/eigenvalue.html
;; (Accessed: January 26, 2023).
;; - [63] Ciobanu, A. (2021) Writing your own Linear Algebra Matrix
;; Library in C, andreinc. Available at:
;; https://www.andreinc.net/2021/01/20/writing-your-own-linear-algebra-matrix-library-in-c#solving-linear-systems-of-equations
;; (Accessed: January 26, 2023).
;; - [64] Forward substitution (no date) Algowiki. Available at:
;; https://algowiki-project.org/en/Forward_substitution
;; (Accessed: January 26, 2023).
;; - [65] Backward substitution (no date) Algowiki. Available at:
;; https://algowiki-project.org/en/Backward_substitution
;; (Accessed: January 26, 2023).
;; - [66] Singular Value Decomposition (SVD) tutorial BE.400 / 7.548
;; (no date) Singular value decomposition (SVD) tutorial. Available at:
;; https://web.mit.edu/be.400/www/SVD/Singular_Value_Decomposition.htm
;; (Accessed: March 13, 2023).
;; - [67] Singular value decomposition (2023) Wikipedia. Wikimedia
;; Foundation. Available at:
;; https://en.wikipedia.org/wiki/Singular_value_decomposition
;; (Accessed: March 16, 2023).
;; - [68] Frobenius inner product (2022) Wikipedia. Wikimedia Foundation.
;; Available at: https://en.wikipedia.org/wiki/Frobenius_inner_product
;; (Accessed: March 16, 2023).
;; - [69] Khatri–rao product (2023) Wikipedia. Wikimedia Foundation.
;; Available at: https://en.wikipedia.org/wiki/Khatri%E2%80%93Rao_product
;; (Accessed: March 17, 2023).
;; - [70] Block matrix (2023) Wikipedia. Wikimedia Foundation. Available
;; at: https://en.wikipedia.org/wiki/Block_matrix (Accessed: March 28,
;; 2023).
;; - [71] https://www.gnu.org/software/guile/manual/html_node/Futures.html
(define-module (grsp grsp3)
#:use-module (grsp grsp0)
#:use-module (grsp grsp1)
#:use-module (grsp grsp2)
#:use-module (grsp grsp4)
#:use-module (grsp grsp11)
#:use-module (ice-9 threads)
#:use-module (ice-9 futures)
#:use-module (ice-9 string-fun)
#:export (grsp-lm
grsp-hm
grsp-ln
grsp-hn
grsp-tm
grsp-tn
grsp-matrix-order
grsp-matrix-esi
grsp-matrix-create
grsp-matrix-create-set
grsp-matrix-create-fix
grsp-matrix-create-dim
grsp-matrix-change
grsp-matrix-find
grsp-matrix-transpose
grsp-matrix-transposer
grsp-matrix-conjugate
grsp-matrix-conjugate-transpose
grsp-matrix-opio
grsp-matrix-opsc
grsp-matrix-opew
grsp-matrix-opewl
grsp-matrix-opfn
grsp-matrix-opmm
grsp-matrix-opmml
grsp-matrix-opmsc
grsp-matrix-cpy
grsp-matrix-subcpy
grsp-matrix-subrep
grsp-matrix-subdcn
grsp-matrix-subdel
grsp-matrix-subexp
grsp-matrix-is-equal
grsp-matrix-is-square
grsp-matrix-is-symmetric
grsp-matrix-is-diagonal
grsp-matrix-is-hermitian
grsp-matrix-is-binary
grsp-matrix-is-nonnegative
grsp-matrix-is-positive
grsp-matrix-row-opar
grsp-matrix-row-opmm
grsp-matrix-row-opsc
grsp-matrix-row-opsw
grsp-matrix-decompose
grsp-matrix-density
grsp-matrix-is-sparse
grsp-matrix-is-symmetric-md
grsp-matrix-total-elements
grsp-matrix-total-element
grsp-matrix-is-hadamard
grsp-matrix-is-markov
grsp-matrix-is-signature
grsp-matrix-is-single-entry
grsp-matrix-identify
grsp-matrix-is-metzler
grsp-l2m
grsp-m2l
grsp-m2v
grsp-dbc2mc
grsp-dbc2mc-csv
grsp-mc2dbc
grsp-mc2dbc-sqlite3
grsp-mc2dbc-hdf5
grsp-mc2dbc-csv
grsp-mc2dbc-gnuplot1
grsp-mc2dbc-gnuplot2
grsp-matrix-interval-mean
grsp-matrix-determinant-lu
grsp-matrix-determinant-qr
grsp-matrix-is-invertible
grsp-eigenval-opio
grsp-matrix-sort
grsp-matrix-minmax
grsp-matrix-trim
grsp-matrix-select
grsp-matrix-row-minmax
grsp-matrix-row-select
grsp-matrix-row-delete
grsp-matrix-row-sort
grsp-matrix-row-invert
grsp-matrix-commit
grsp-matrix-row-selectn
grsp-matrix-col-selectn
grsp-matrix-col-select
grsp-matrix-njoin
grsp-matrix-sjoin
grsp-matrix-ajoin
grsp-matrix-supp
grsp-matrix-row-div
grsp-matrix-row-update
grsp-matrix-te1
grsp-matrix-te2
grsp-matrix-row-append
grsp-matrix-lojoin
grsp-matrix-subrepv
grsp-matrix-subswp
grsp-matrix-col-total-element
grsp-matrix-row-deletev
grsp-matrix-clear
grsp-matrix-clearni
grsp-matrix-row-cartesian
grsp-matrix-col-append
grsp-matrix-col-find-nth
grsp-mn2ll
grsp-matrix-mutation
grsp-matrix-col-mutation
grsp-matrix-col-lmutation
grsp-matrix-crossover
grsp-matrix-crossover-rprnd
grsp-matrix-same-dims
grsp-matrix-fitness-rprnd
grsp-matrix-selectg
grsp-matrix-keyon
grsp-matrix-col-aupdate
grsp-matrix-row-selectc
grsp-matrix-is-empty
grsp-matrix-is-multiset
grsp-matrix-argtype
grsp-matrix-argstru
grsp-matrix-row-subrepal
grsp-matrix-subdell
grsp-matrix-is-samedim
grsp-matrix-is-samediml
grsp-matrix-fill
grsp-matrix-fdif
grsp-matrix-opewc
grsp-matrix-row-opew-mth
grsp-matrix-opew-mth
grsp-mr2l
grsp-l2mr
grsp-matrix-is-traceless
grsp-matrix-movemm
grsp-matrix-movsmm
grsp-matrix-movcrm
grsp-matrix-movtrm
grsp-matrix-ldiagonal
grsp-matrix-minor
grsp-matrix-minor-cofactor
grsp-matrix-cofactor
grsp-matrix-inverse
grsp-matrix-adjugate
grsp-mn2ms
grsp-matrix-spjustify
grsp-matrix-slongest
grsp-ms2s
grsp-matrix-display
grsp-ms2mn
grsp-matrix-tio
grsp-matrix-diagonal-update
grsp-matrix-diagonal-vector
grsp-matrix-row-proj
grsp-matrix-normp
grsp-matrix-normf
grsp-matrix-normm
grsp-eigenval-qr
grsp-eigenvec
grsp-matrix-is-srddominant
grsp-matrix-jacobim
grsp-matrix-sradius
grsp-ms2ts
grsp-mr2ls
grsp-dbc2lls
grsp-matrix-row-prkey
grsp-matrix-strot
grsp-matrix-row-corr
grsp-matrix-correwl
grsp-matrix-wlongest
grsp-matrix-mmt
grsp-matrix-mtm
grsp-matrix-fsubst
grsp-matrix-bsubst
grsp-matrix-compatibility
grsp-matrix-part-create
grsp-matrix-is-filled-with
grsp-matrix-row-selectrn
grsp-matrix-col-selectcn
grsp-matrix-row-subrepf
grsp-matrix-row-subreps
grsp-matrix-ldvl
grsp-matrix-blur
grsp-matrix-col-replacev
grsp-matrix-selectmb
grsp-matrix-row-opscr
grsp-ms2dbc
grsp-dbc2ms
grsp-matrix-split
grsp-matrix-inputev
grsp-matrix-row-inputev
grsp-matrix-rows-inputev
grsp-matrix-rows-addev
grsp-matrix-rows-filled-with
grsp-matrix-displayts
grsp-matrix-subadd
grsp-matrix-displaytn
grsp-matrix-edit
grsp-my2ms
grsp-matrix-displaytm
grsp-matrix-editu
grsp-my2code
grsp-ms2my
grsp-cy2cy
grsp-ms2mb
grsp-matrix-row-select-like
grsp-matrix-sincostan-mth
grsp-matrix-row-number
grsp-matrix-keygen
grsp-matrix-keyapl
grsp-matrix-subdelr
grsp-matrix-row-vol
grsp-ms-get-longest-element
grsp-ms-create-col-headers
grsp-ms-create-row-headers
grsp-ms-pad-elements
grsp-matrix-displaytms
grsp-matrix-row-subrepk
grsp-matrix-row-numk
grsp-matrix-subrepk
grsp-matrix-row-subrepkl
grsp-matrix-row-col-setk
grsp-matrix-find-if-prkey-exists
grsp-matrix-row-subexpk
grsp-matrix-row-insert
grsp-matrix-tf-idf
grsp-matrix-row-insert-ioe
grsp-2l2cm
grsp-l2cm))
;;;; grsp-lm - Short form of (grsp-matrix-esi 1 p_a1).
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices, properties, dimensions, size
;;
;; Parameters:
;;
;; - p_a1: matrix.
;;
;; Notes:
;;
;; - See grsp-matrix-esi.
;;
;; Output:
;;
;; - Numeric, lm value.
;;
(define (grsp-lm p_a1)
(let ((res1 0))
(set! res1 (grsp-matrix-esi 1 p_a1))
res1))
;;;; grsp-hm - Short form of (grsp-matrix-esi 2 p_a1).
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices
;;
;; Parameters:
;;
;; - p_a1: matrix.
;;
;; Notes:
;;
;; - See grsp-matrix-esi.
;;
;; Output:
;;
;; - Numeric, hm value.
;;
(define (grsp-hm p_a1)
(let ((res1 0))
(set! res1 (grsp-matrix-esi 2 p_a1))
res1))
;;;; grsp-ln - Short form of (grsp-matrix-esi 3 p_a1).
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices
;;
;; Parameters:
;;
;; - p_a1: matrix.
;;
;; Notes:
;;
;; - See grsp-matrix-esi.
;;
;; Output:
;;
;; - Numeric, ln value.
;;
(define (grsp-ln p_a1)
(let ((res1 0))
(set! res1 (grsp-matrix-esi 3 p_a1))
res1))
;;;; grsp-hn - Short form of (grsp-matrix-esi 4 p_a1).
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices
;;
;; Parameters:
;;
;; - p_a1: matrix.
;;
;; Notes:
;;
;; - See grsp-matrix-esi.
;;
;; Output:
;;
;; - Numeric, hn value.
;;
(define (grsp-hn p_a1)
(let ((res1 0))
(set! res1 (grsp-matrix-esi 4 p_a1))
res1))
;;;; grsp-tm - Convenience function that returns the total number of rows
;; in p_a1.
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices
;;
;; Parameters:
;;
;; - p_a1: matrix.
;;
;; Notes:
;;
;; - See grsp-matrix-te2.
;;
;; Output:
;;
;; - Numeric, (+ (- hm lm)) value.
;;
(define (grsp-tm p_a1)
(let ((res1 0)
(res2 0))
(set! res2 (grsp-matrix-te2 p_a1))
(set! res1 (array-ref res2 0 0))
res1))
;;;; grsp-tn - Convenience function that returns the total number of cols
;; in p_a1.
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices
;;
;; Parameters:
;;
;; - p_a1: matrix.
;;
;; Notes:
;;
;; - See grsp-matrix-te2.
;;
;; Output:
;;
;; - Numeric, (+ (- hn ln)) value.
;;
(define (grsp-tn p_a1)
(let ((res1 0)
(res2 0))
(set! res2 (grsp-matrix-te2 p_a1))
(set! res1 (array-ref res2 0 1))
res1))
;;;; grsp-matrix-order - Returns the order (* tm tn) of a matrix.
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices, vectors
;;
;; Parameters:
;;
;; - p_a1: matrix.
;;
;; Output:
;;
;; - Numeric.
;;
(define (grsp-matrix-order p_a1)
(let ((res1 (* (grsp-tm p_a1) (grsp-tn p_a1))))
res1))
;;;; grsp-matrix-esi - Extracts shape information from an m x n matrix.
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices, vectors
;;
;; Parameters:
;;
;; - p_e1: number indicating the element value desired.
;;
;; - 1: lm. low boundary for m (rows).
;; - 2: hm. high boundary for m (rows).
;; - 3: ln. low boundary for n (cols).
;; - 4: hn. high boundary for n (cols).
;;
;; - p_m1: m.
;;
;; Sources:
;;
;; - [1][2][3][4].
;;
;; Output:
;;
;; - A number corresponding to the shape element value desired. Returns
;; zero if p_e1 is incorrect.
;;
(define (grsp-matrix-esi p_e1 p_m1)
(let ((res1 0)
(s1 0))
(set! s1 (array-shape p_m1))
(cond ((equal? p_e1 1)
(set! res1 (car (car s1))))
((equal? p_e1 2)
(set! res1 (car (cdr (car s1)))))
((equal? p_e1 3)
(set! res1 (car (car (cdr s1)))))
((equal? p_e1 4)
(set! res1 (car (cdr (car (cdr s1)))))))
res1))
;;;; grsp-matrix-create - Creates an p_m1 x p_n1 matrix and fills it with
;; element value p_s1.
;;
;; Keywords:
;;
;; - functions, algebra, matrix, matrices, vectors
;;
;; Parameters:
;;
;; - p_s1: matrix type.
;;
;; - "#I": Identity matrix.
;; - "#AI": Anti Identity matrix (anti diagonal).
;; - "#Q": Quincunx matrix.
;; - "#Test1": Test matrix 1 (LU decomposable)[1].
;; - "#Test2": Test matrix 2 (LU decomposable)[2].
;; - "#Ladder": Ladder matrix.
;; - "#Arrow": Arrowhead matrix.
;; - "#Hilbert": Hilbert matrix.
;; - "#Lehmer": Lehmer matrix.
;; - "#Pascal": Pascal matrix.
;; - "#Ex2SVD": 4 x 2 matrix example for SVD, see [66].
;; - "#Ex1SVD": 4 X 5 matrix example for SVD, see [67].
;; - "#CH": 0-1 checkerboard pattern matrix.
;; - "#CHR": 0-1 checkerboard pattern matrix, randomized.
;; - "#+IJ": matrix containing the sum of i and j values.
;; - "#-IJ": matrix containing the substraction of i and j values.
;; - "#+IJ": matrix containing the product of i and j values.
;; - "#-IJ": matrix containing the quotient of i and j values.
;; - "#US": upper shift matrix.
;; - "#LS": lower shift matrix.
;; - "#UT": upper triangular matrix, with value 1 in non-zero elements.
;; - "#LT": lower triangular matrix, with value 1 in non-zero elements.
;; - "#rprnd": pseduo random values, normal distribution, sd = 0.15.
;; - "#zrow": zebra row.
;; - "#zcol": zebra col.
;; - "#n0[-m:+m]": matrix of (2m +1 ) rows and n cols, with first column
;; element -m and last row, first col element reaching m.
;;
;; - p_m1: rows, positive integer.
;; - p_n1: cols, positive integer.
;;
;; Examples:
;;
;; - example3.scm, example5.scm.
;;
;; Notes:
;;
;; - See grsp0.grsp-s2dbc, grsp0.grsp-dbc2s, grsp0.grsp-random-state-set.
;;
;; Output:
;;
;; - Matrix.
;;
;; Sources:
;;
;; - [1][2][18][31].
;;
(define (grsp-matrix-create p_s1 p_m1 p_n1)
(let ((res1 0)
(t1 "n")
(s1 0)
(i1 0)
(j1 0)
(m1 p_m1)
(m3 p_m1)
(n1 p_n1)
(p0 0)
(p1 0)
(p2 0)
(p3 0))
(cond ((eq? (grsp-eiget m1 0) #t)
(cond ((eq? (grsp-eiget n1 0) #t)
;; For an identity matrix, first set all elements to 0.
(cond ((equal? p_s1 "#I")
(set! s1 0))
((equal? p_s1 "#AI")
(set! s1 0))
((equal? p_s1 "#Q")
(set! s1 1)
(set! m1 2)
(set! n1 2))
((equal? p_s1 "#Test1")
(set! s1 0)
(set! m1 3)
(set! n1 3))
((equal? p_s1 "#Test2")
(set! s1 0)
(set! m1 3)
(set! n1 3))
((equal? p_s1 "#Ladder")
(set! s1 1))
((equal? p_s1 "#Arrow")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#Hilbert")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#Lehmer")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#Pascal")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#Ex2SVD")
(set! s1 0))
((equal? p_s1 "#Ex1SVD")
(set! s1 0))
((equal? p_s1 "#Fibonacci")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#CH")
(set! s1 0))
((equal? p_s1 "#CHR")
(set! s1 0))
((equal? p_s1 "#+IJ")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#-IJ")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#*IJ")
(set! s1 1)
(set! n1 m1))
((equal? p_s1 "#/IJ")
(set! s1 1)
(set! n1 m1))
((equal? p_s1 "#US")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#LS")
(set! s1 0)
(set! n1 m1))
((equal? p_s1 "#rprnd")
(set! s1 0))
((equal? p_s1 "#zrow")
(set! s1 0))
((equal? p_s1 "#zcol")
(set! s1 0))
((equal? p_s1 "#n0[-m:+m]")
(set! s1 0)
(set! m1 (+ 1 (* m1 2))))
(else (set! s1 p_s1)))
;; Build the matrix.
(set! res1 (make-array s1 m1 n1))
;; Once the matrix has been created, depending on the
;; type of matrix, modify its values.
(cond ((equal? p_s1 "#I")
(while (< i1 m1)
(set! j1 0)
(while (< j1 n1)
(cond ((eq? i1 j1)
(array-set! res1 1 i1 j1)))
(set! j1 (+ j1 1)))
(set! i1 (+ i1 1))))
((equal? p_s1 "#Test1")
(set! res1 (grsp-l2mr res1 (list 1 4 -3) 0 0))
(set! res1 (grsp-l2mr res1 (list -2 8 5) 1 0))
(set! res1 (grsp-l2mr res1 (list 3 4 7) 2 0)))
((equal? p_s1 "#Test2")
(set! res1 (grsp-l2mr res1 (list 2 4 -4) 0 0))
(set! res1 (grsp-l2mr res1 (list 1 -4 3) 1 0))
(set! res1 (grsp-l2mr res1 (list -6 -9 5) 2 0)))
((equal? p_s1 "#Ladder")
(while (< i1 m1)
(set! j1 0)
(while (< j1 n1)
(array-set! res1 s1 i1 j1)
(set! s1 (+ s1 1))
(set! j1 (+ j1 1)))
(set! i1 (+ i1 1))))
((equal? p_s1 "#Arrow")
(set! res1 (grsp-matrix-create "#I" m1 n1))
(grsp-matrix-row-opsc "#+" res1 0 1)
(set! res1 (grsp-matrix-transpose res1))
(grsp-matrix-row-opsc "#+" res1 0 1)
(set! res1 (grsp-matrix-transpose res1))
(set! res1 (grsp-matrix-transpose res1))
(array-set! res1 1 0 0))
((equal? p_s1 "#AI")
(set! i1 (- m1 1))
(while (>= i1 0)
(set! j1 (- n1 1))
(while (>= j1 0)
(cond ((equal? (+ i1 j1) (- m1 1))
(array-set! res1 1 i1 j1)))
(set! j1 (- j1 1)))
(set! i1 (- i1 1))))
((equal? p_s1 "#Hilbert")
(while (< i1 m1)
(set! j1 0)
(while (< j1 n1)
(array-set! res1
(/ 1
(- (+ (+ i1 1) (+ j1 1))
1))
i1
j1)
(set! j1 (+ j1 1)))
(set! i1 (+ i1 1))))
((equal? p_s1 "#Lehmer")
(while (< i1 m1)
(set! j1 0)
(while (< j1 n1)
(array-set! res1 (/ (min (+ i1 1)
(+ j1 1))
(max (+ i1 1)
(+ j1 1)))
i1 j1)
(set! j1 (+ j1 1)))
(set! i1 (+ i1 1))))
((equal? p_s1 "#Pascal")
(while (< i1 m1)
(set! j1 0)
(while (< j1 n1)
(array-set! res1
(grsp-biconr (+ i1 j1)