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  • 12/20/2021
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CGESV Example Program in C

/******************************************************************************* * Copyright (C) 2009-2015 Intel Corporation. All Rights Reserved. * The information and material ("Material") provided below is owned by Intel * Corporation or its suppliers or licensors, and title to such Material remains * with Intel Corporation or its suppliers or licensors. The Material contains * proprietary information of Intel or its suppliers and licensors. The Material * is protected by worldwide copyright laws and treaty provisions. No part of * the Material may be copied, reproduced, published, uploaded, posted, * transmitted, or distributed in any way without Intel's prior express written * permission. No license under any patent, copyright or other intellectual * property rights in the Material is granted to or conferred upon you, either * expressly, by implication, inducement, estoppel or otherwise. Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ******************************************************************************** */ /* CGESV Example. ============== The program computes the solution to the system of linear equations with a square matrix A and multiple right-hand sides B, where A is the coefficient matrix: ( 1.23, -5.50) ( 7.91, -5.38) ( -9.80, -4.86) ( -7.32, 7.57) ( -2.14, -1.12) ( -9.92, -0.79) ( -9.18, -1.12) ( 1.37, 0.43) ( -4.30, -7.10) ( -6.47, 2.52) ( -6.51, -2.67) ( -5.86, 7.38) ( 1.27, 7.29) ( 8.90, 6.92) ( -8.82, 1.25) ( 5.41, 5.37) and B is the right-hand side matrix: ( 8.33, -7.32) ( -6.11, -3.81) ( -6.18, -4.80) ( 0.14, -7.71) ( -5.71, -2.80) ( 1.41, 3.40) ( -1.60, 3.08) ( 8.54, -4.05) Description. ============ The routine solves for X the system of linear equations A*X = B, where A is an n-by-n matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P*L*U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A*X = B. Example Program Results. ======================== CGESV Example Program Results Solution ( -1.09, -0.18) ( 1.28, 1.21) ( 0.97, 0.52) ( -0.22, -0.97) ( -0.20, 0.19) ( 0.53, 1.36) ( -0.59, 0.92) ( 2.22, -1.00) Details of LU factorization ( -4.30, -7.10) ( -6.47, 2.52) ( -6.51, -2.67) ( -5.86, 7.38) ( 0.49, 0.47) ( 12.26, -3.57) ( -7.87, -0.49) ( -0.98, 6.71) ( 0.25, -0.15) ( -0.60, -0.37) (-11.70, -4.64) ( -1.35, 1.38) ( -0.83, -0.32) ( 0.05, 0.58) ( 0.93, -0.50) ( 2.66, 7.86) Pivot indices 3 3 3 4 */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _fcomplex { float re, im; }; typedef struct _fcomplex fcomplex; /* CGESV prototype */ extern void cgesv( int* n, int* nrhs, fcomplex* a, int* lda, int* ipiv, fcomplex* b, int* ldb, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, fcomplex* a, int lda ); extern void print_int_vector( char* desc, int n, int* a ); /* Parameters */ #define N 4 #define NRHS 2 #define LDA N #define LDB N /* Main program */ int main() { /* Locals */ int n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info; /* Local arrays */ int ipiv[N]; fcomplex a[LDA*N] = { { 1.23f, -5.50f}, {-2.14f, -1.12f}, {-4.30f, -7.10f}, { 1.27f, 7.29f}, { 7.91f, -5.38f}, {-9.92f, -0.79f}, {-6.47f, 2.52f}, { 8.90f, 6.92f}, {-9.80f, -4.86f}, {-9.18f, -1.12f}, {-6.51f, -2.67f}, {-8.82f, 1.25f}, {-7.32f, 7.57f}, { 1.37f, 0.43f}, {-5.86f, 7.38f}, { 5.41f, 5.37f} }; fcomplex b[LDB*NRHS] = { { 8.33f, -7.32f}, {-6.18f, -4.80f}, {-5.71f, -2.80f}, {-1.60f, 3.08f}, {-6.11f, -3.81f}, { 0.14f, -7.71f}, { 1.41f, 3.40f}, { 8.54f, -4.05f} }; /* Executable statements */ printf( " CGESV Example Program Results\n" ); /* Solve the equations A*X = B */ cgesv( &n, &nrhs, a, &lda, ipiv, b, &ldb, &info ); /* Check for the exact singularity */ if( info > 0 ) { printf( "The diagonal element of the triangular factor of A,\n" ); printf( "U(%i,%i) is zero, so that A is singular;\n", info, info ); printf( "the solution could not be computed.\n" ); exit( 1 ); } /* Print solution */ print_matrix( "Solution", n, nrhs, b, ldb ); /* Print details of LU factorization */ print_matrix( "Details of LU factorization", n, n, a, lda ); /* Print pivot indices */ print_int_vector( "Pivot indices", n, ipiv ); exit( 0 ); } /* End of CGESV Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, int m, int n, fcomplex* a, int lda ) { int i, j; printf( "\n %s\n", desc ); for( i = 0; i < m; i++ ) { for( j = 0; j < n; j++ ) printf( " (%6.2f,%6.2f)", a[i+j*lda].re, a[i+j*lda].im ); printf( "\n" ); } } /* Auxiliary routine: printing a vector of integers */ void print_int_vector( char* desc, int n, int* a ) { int j; printf( "\n %s\n", desc ); for( j = 0; j < n; j++ ) printf( " %6i", a[j] ); printf( "\n" ); }

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