From d6f2a2564f7d563ab84e27f9e4a912fef88428dd Mon Sep 17 00:00:00 2001 From: Armando Luiz Nicolini Delgado <nicolui@inf.ufpr.br> Date: Wed, 4 Oct 2023 10:41:37 -0300 Subject: [PATCH] =?UTF-8?q?/*=20-=20Criado=20diret=C3=B3rio=20com=20fun?= =?UTF-8?q?=C3=A7=C3=B5es=20de=20manipula=C3=A7=C3=A3o=20de=20matrizes=20e?= =?UTF-8?q?=20sistemas=20lineares.=20=20=20=20-=20Atualizados=20README.md?= =?UTF-8?q?=20e=20gnuplor.pdf=20=20*/?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 5 ++ gnuplot/gnuplot.pdf | Bin 1735265 -> 2209518 bytes sislin/matrix.c | 117 ++++++++++++++++++++++++++++ sislin/matrix.h | 20 +++++ sislin/sislin.c | 186 ++++++++++++++++++++++++++++++++++++++++++++ sislin/sislin.h | 43 ++++++++++ 6 files changed, 371 insertions(+) create mode 100644 sislin/matrix.c create mode 100644 sislin/matrix.h create mode 100644 sislin/sislin.c create mode 100644 sislin/sislin.h diff --git a/README.md b/README.md index b60d30f..6c54f86 100644 --- a/README.md +++ b/README.md @@ -2,3 +2,8 @@ Funções e bibliotecas de uso genérico para a disciplina CI1164 (DINF/UFPR) +* gnuplot: documentação e modelos de scripts para uso de gnuplot. +* sislin: funções básicas de manipulação de matrizes e Sistemas Lineares +* utils: funções utilitárias diversas: timestamp, geradores de + números pseudo-aleatórios, etc. + diff --git a/gnuplot/gnuplot.pdf b/gnuplot/gnuplot.pdf index 3ff8881440946a4c547aa774e198174262999f94..8d7e815c5a47c090bc9911c7c9a41f4c7742cfdf 100644 GIT binary patch delta 2126021 zcmaF(CG*|eHpU5Jj9ili)#dpt3{1K7eNyw%OEMG;4W}#a5!J2_JKcBNO<>P!Z7I8( zj8C50oMhyY-?ZDTsIxamE?v)b(u@zHMO&tQ`npohJxuPz8Ug8uwQecprQzXcCo~xu zsT6NoB4c^VSV&TIQj5|-d0!_nl_H^I6A!F9;lcH%bLte8rK+7ZlZDsMIo2++Zbi?O zqtlsm7MNxpST$#h*b=Twmi5z`e4d3xO}f~%MRBt9rD-}!Ta{0n8*SRDyjVlL<JuJM zm@}H&XZbi*HX1bM9X;ixHKAdW>$;OsT3j`a6E~bWY1pC^E^#P#Vk4uKfMh(|@--(` z3MlB@>DtNNEh$lBeIUxmA<Icuu~)U7(^LIKqJ<ZeaD~_NCk@LltYMz#7CNz>G2nGl 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Cria com calloc() matriz 'n x m' */ +double **criaMatriz (int n, int m) +{ + double **C; + int i, j; + + C = (double **) calloc(n,sizeof(double *)); + C[0] = (double *) calloc(n*m,sizeof(double)); + for (i=1; i < n; ++i) + C[i] = C[i-1] + m; + + return C; +} + +/* Retorna ponteiro para matriz inversa de matriz 'A'. + Matriz inversa é alocada com 'criaMatriz()' +*/ +// Adaptação de https://www.programming-techniques.com/2011/09/numerical-methods-inverse-of-nxn-matrix.html +double **invMatriz (double **A, int n) +{ + double ratio,a, **aux, **IA; + int i, j, k; + + aux = criaMatriz(n, 2*n); + IA = criaMatriz(n,n); + + for(i = 0; i < n; i++) { + for(j = 0; j < 2*n; j++) { + if (j < n) + aux[i][j] = A[i][j]; + else if(i==(j-n)) + aux[i][j] = 1.0; + else + aux[i][j] = 0.0; + } + } + + for(i = 0; i < n; i++){ + for(j = 0; j < n; j++){ + if(i!=j){ + ratio = aux[j][i]/aux[i][i]; + for(k = 0; k < 2*n; k++){ + aux[j][k] -= ratio * aux[i][k]; + } + } + } + } + + for(i = 0; i < n; i++){ + a = aux[i][i]; + for(j = n; j < 2*n; j++){ + IA[i][j-n] = aux[i][j] / a; + } + } + + freeMatriz(aux, n); + + return IA; + +} + +/* Libera matriz com 'n' linhas, alocada com 'criaMatriz()' */ +void freeMatriz (double **A, int n) +{ + int i; + + free(A[0]); + free(A); +} + +/* Multiplica matrizes 'A' e 'B', ambas 'n x n' */ +double **multMatriz (double **A, double **B, int n) +{ + double **C; + int i, j,k; + + C = (double **) malloc(n*sizeof(double *)); + for (i=0; i < n; ++i) { + C[i] = (double *) calloc(n,sizeof(double)); + for (j=0; j < n; ++j) + for (k=0; k < n; ++k) + C[i][j] += A[i][k] * B[k][j]; + } + + return C; +} + +/* Mostra na tela matriz 'n x n' alocada com 'criaMatriz()' */ +void prnMatriz (double **A, int n) +{ + int i, j; + + for(i = 0; i < n; i++){ + for(j = 0; j < n; j++){ + printf("%15.5lg", A[i][j]); + } + printf("\n"); + } +} + +/* Preenche matriz 'n x n' alocada com 'criaMatriz()' */ +void lerMatriz (double **A, int n) +{ + int i, j; + + for(i = 0; i < n; i++){ + for(j = 0; j < n; j++){ + scanf("%lg", A[i]+j); + } + } +} + diff --git a/sislin/matrix.h b/sislin/matrix.h new file mode 100644 index 0000000..53a7bbb --- /dev/null +++ b/sislin/matrix.h @@ -0,0 +1,20 @@ +/* Cria com calloc() matriz 'n x m' */ +double **criaMatriz (int n, int m); + +/* Retorna ponteiro para matriz inversa de matriz 'A'. + Matriz inversa é alocada com 'criaMatriz()' +*/ +double **invMatriz (double **A, int n); + +/* Libera matriz com 'n' linhas, alocada com 'criaMatriz()' */ +void freeMatriz (double **A, int n); + +/* Multiplica matrizes 'A' e 'B', ambas 'n x n' */ +double **multMatriz (double **A, double **B, int n); + +/* Mostra na tela matriz 'n x n' alocada com 'criaMatriz()' */ +void prnMatriz (double **A, int n); + +/* Preenche matriz 'n x n' alocada com 'criaMatriz()' */ +void lerMatriz (double **A, int n); + diff --git a/sislin/sislin.c b/sislin/sislin.c new file mode 100644 index 0000000..75f649b --- /dev/null +++ b/sislin/sislin.c @@ -0,0 +1,186 @@ +#include <stdio.h> +#include <math.h> +#include <stdlib.h> + +#include "utils.h" +#include "sislin.h" + +// Alocaçao de matriz em memória. +SistLinear_t* alocaSisLin (unsigned int n, tipoAloc_t tipo) +{ + SistLinear_t *SL = (SistLinear_t *) malloc(sizeof(SistLinear_t)); + + if ( SL ) { + + SL->n = n; + SL->tipoAloc_A = tipo; + SL->A = (real_t **) malloc(n * sizeof(real_t *)); + SL->b = (real_t *) malloc(n * sizeof(real_t)); + + if (!(SL->A) || !(SL->b)) { + liberaSisLin(SL); + return NULL; + } + + // Matriz como vetor de N ponteiros para um único vetor com N*N elementos + if (tipo == pontVet) { + SL->A[0] = (real_t *) malloc(n * n * sizeof(real_t)); + if (!(SL->A[0])) { + liberaSisLin(SL); + return NULL; + } + + for (int i=1; i < n; ++i) { + SL->A[i] = SL->A[i-1]+n; + } + } + else if (tipo == pontPont) { // Matriz como vetor de N ponteiros + // para N vetores de N elementos cada + + for (int i=0; i < n; ++i) + SL->A[i] = (real_t *) malloc(n * sizeof(real_t)); + } + } + + return (SL); +} + +// Liberacao de memória +void liberaSisLin (SistLinear_t *SL) +{ + if (SL) { + if (SL->A) { + if (SL->tipoAloc_A == pontVet) { + if (SL->A[0]) free (SL->A[0]); + } + else if (SL->tipoAloc_A == pontPont) { + for (int i=0; i < SL->n; ++i) + free (SL->A[i]); + } + + free(SL->A); + } + if (SL->b) free(SL->b); + free(SL); + } +} + + +/*! + \brief Cria coeficientes e termos independentes do SL + * + \param SL Ponteiro para o sistema linear + \param tipo Tipo de sistema linear a ser criado. Pode ser: + comSolucao, eqNula, eqProporcional, eqCombLinear, hilbert + \param coef_max Maior valor para coeficientes e termos independentes +*/ +void iniSisLin (SistLinear_t *SL, tipoSistLinear_t tipo, real_t coef_max) +{ + unsigned int n = SL->n; + // para gerar valores no intervalo [0,coef_max] + real_t invRandMax = ((real_t)coef_max / (real_t)RAND_MAX); + + // inicializa vetor b + for (unsigned int i=0; i<n; ++i) { + SL->b[i] = (real_t)rand() * invRandMax; + } + + if (tipo == hilbert) { + for (unsigned int i=0; i<n; ++i) { + for (unsigned int j=0; j<n; ++j) { + SL->A[i][j] = 1.0 / (real_t)(i+j+1); + } + } + } + else { // inicializa sistema normal e depois altera + // inicializa a matriz A + for (unsigned int i=0; i<n; ++i) { + for (unsigned int j=0; j<n; ++j) { + SL->A[i][j] = (real_t)rand() * invRandMax; + } + } + if (tipo == eqNula) { + // sorteia eq a ser "nula" + unsigned int nula = rand() % n; + for (unsigned int j=0; j<n; ++j) { + SL->A[nula][j] = 0.0; + } + SL->b[nula] = 0.0; + } + else if (tipo == eqProporcional) { + // sorteia eq a ser "proporcional" e valor + unsigned int propDst = rand() % n; + unsigned int propSrc = (propDst + 1) % n; + real_t mult = (real_t)rand() * invRandMax; + for (unsigned int j=0; j<n; ++j) { + SL->A[propDst][j] = SL->A[propSrc][j] * mult; + } + SL->b[propDst] = SL->b[propSrc] * mult; + } + else if (tipo == eqCombLinear) { + // sorteia eq a ser "combLinear" + unsigned int combDst = rand() % n; + unsigned int combSrc1 = (combDst + 1) % n; + unsigned int combSrc2 = (combDst + 2) % n; + for (unsigned int j=0; j<n; ++j) { + SL->A[combDst][j] = SL->A[combSrc1][j] + SL->A[combSrc2][j]; + } + SL->b[combDst] = SL->b[combSrc1] + SL->b[combSrc2]; + } + else if (tipo == diagDominante) { + // aumenta o valor dos termos da diagonal principal + for (unsigned int i=0; i<n; ++i) { + real_t soma = 0.0; + for (unsigned int j=0; j < i; ++j) soma += SL->A[i][j]; + for (unsigned int j=i+1; j < n; ++j) soma += SL->A[i][j]; + SL->A[i][i] += soma; + } + } + } +} + + +SistLinear_t *lerSisLin (tipoAloc_t tipo) +{ + unsigned int n; + SistLinear_t *SL; + + scanf("%d",&n); + + SL = alocaSisLin (n, tipo); + + for(int i=0; i < n; ++i) + for(int j=0; j < n; ++j) + scanf ("%lg", &SL->A[i][j]); + + for(int i=0; i < n; ++i) + scanf ("%lg", &SL->b[i]); + + return SL; +} + + +void prnSisLin (SistLinear_t *SL) +{ + int n=SL->n; + + for(int i=0; i < n; ++i) { + printf("\n "); + for(int j=0; j < n; ++j) + printf ("%10g", SL->A[i][j]); + printf (" | %g", SL->b[i]); + } + printf("\n\n"); +} + +void prnVetor (real_t *v, unsigned int n) +{ + int i; + + printf ("\n"); + for(i=0; i < n; ++i) + printf ("%10g ", v[i]); + printf ("\n\n"); + +} + diff --git a/sislin/sislin.h b/sislin/sislin.h new file mode 100644 index 0000000..e861bee --- /dev/null +++ b/sislin/sislin.h @@ -0,0 +1,43 @@ +#ifndef __SISLIN_H__ +#define __SISLIN_H__ + +#define COEF_MAX 32.0 // Valor máximo usado para gerar valores aleatórios de + // coeficientes nos sistemas lineares. + +// Tipo de alocação para matrizes +typedef enum { + pontPont=0, // Matriz como vetor de N ponteiros para vetores de tamanho N + pontVet // Matriz como vetor de N ponteiros para um único vetor de tamanho N*N +} tipoAloc_t; + +// Estrutura para definiçao de um sistema linear qualquer +typedef struct { + real_t **A; // coeficientes + real_t *b; // termos independentes + unsigned int n; // tamanho do SL + tipoAloc_t tipoAloc_A; // tipo de alocação usada na matriz de coeficientes +} SistLinear_t; + +// Tipos de matrizes de coeficientes usados pela função 'inicializaSistLinear()' +typedef enum { + generico = 0, + hilbert, + diagDominante, + eqNula, + eqProporcional, + eqCombLinear +} tipoSistLinear_t; + + +// Alocaçao e desalocação de matrizes +SistLinear_t* alocaSisLin (unsigned int n, tipoAloc_t tipo); +void liberaSisLin (SistLinear_t *SL); +void iniSisLin (SistLinear_t *SL, tipoSistLinear_t tipo, real_t coef_max); + +// Leitura e impressão de sistemas lineares +SistLinear_t *lerSisLin (); +void prnSisLin (SistLinear_t *SL); +void prnVetor (real_t *vet, unsigned int n); + +#endif // __SISLIN_H__ + -- GitLab