## Developer Reference

• 2022.1
• 12/20/2021
• Public Content
Contents

# DGESV 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. * ******************************************************************************** */ /* DGESV 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: 6.80 -6.05 -0.45 8.32 -9.67 -2.11 -3.30 2.58 2.71 -5.14 5.66 5.36 -2.70 4.35 -7.26 5.97 -4.44 0.27 -7.17 6.08 8.23 1.08 9.04 2.14 -6.87 and B is the right-hand side matrix: 4.02 -1.56 9.81 6.19 4.00 -4.09 -8.22 -8.67 -4.57 -7.57 1.75 -8.61 -3.03 2.86 8.99 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. ======================== DGESV Example Program Results Solution -0.80 -0.39 0.96 -0.70 -0.55 0.22 0.59 0.84 1.90 1.32 -0.10 5.36 0.57 0.11 4.04 Details of LU factorization 8.23 1.08 9.04 2.14 -6.87 0.83 -6.94 -7.92 6.55 -3.99 0.69 -0.67 -14.18 7.24 -5.19 0.73 0.75 0.02 -13.82 14.19 -0.26 0.44 -0.59 -0.34 -3.43 Pivot indices 5 5 3 4 5 */ #include <stdlib.h> #include <stdio.h> /* DGESV prototype */ extern void dgesv( int* n, int* nrhs, double* a, int* lda, int* ipiv, double* b, int* ldb, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, double* a, int lda ); extern void print_int_vector( char* desc, int n, int* a ); /* Parameters */ #define N 5 #define NRHS 3 #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]; double a[LDA*N] = { 6.80, -2.11, 5.66, 5.97, 8.23, -6.05, -3.30, 5.36, -4.44, 1.08, -0.45, 2.58, -2.70, 0.27, 9.04, 8.32, 2.71, 4.35, -7.17, 2.14, -9.67, -5.14, -7.26, 6.08, -6.87 }; double b[LDB*NRHS] = { 4.02, 6.19, -8.22, -7.57, -3.03, -1.56, 4.00, -8.67, 1.75, 2.86, 9.81, -4.09, -4.57, -8.61, 8.99 }; /* Executable statements */ printf( " DGESV Example Program Results\n" ); /* Solve the equations A*X = B */ dgesv( &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 DGESV Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, int m, int n, double* 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", a[i+j*lda] ); 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" ); }

#### Product and Performance Information

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Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.