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  • 2022.1
  • 12/20/2021
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DPOSV 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. * ******************************************************************************** */ /* DPOSV Example. ============== The program computes the solution to the system of linear equations with a symmetric positive-definite matrix A and multiple right-hand sides B, where A is the coefficient matrix: 3.14 0.17 -0.90 1.65 -0.72 0.17 0.79 0.83 -0.65 0.28 -0.90 0.83 4.53 -3.70 1.60 1.65 -0.65 -3.70 5.32 -1.37 -0.72 0.28 1.60 -1.37 1.98 and B is the right-hand side matrix: -7.29 6.11 0.59 9.25 2.90 8.88 5.99 -5.05 7.57 -1.94 -3.80 5.57 -8.30 9.66 -1.67 Description. ============ The routine solves for X the real system of linear equations A*X = B, where A is an n-by-n symmetric positive-definite matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The Cholesky decomposition is used to factor A as A = UT*U, if uplo = 'U' or A = L*LT, if uplo = 'L', where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A*X = B. Example Program Results. ======================== DPOSV Example Program Results Solution -6.02 3.95 -3.14 15.62 4.32 13.05 3.02 -8.25 4.91 3.25 -4.83 6.11 -8.78 9.04 -3.57 Details of Cholesky factorization 1.77 0.10 -0.51 0.93 -0.41 0.00 0.88 0.99 -0.84 0.36 0.00 0.00 1.81 -1.32 0.57 0.00 0.00 0.00 1.42 0.05 0.00 0.00 0.00 0.00 1.16 */ #include <stdlib.h> #include <stdio.h> /* DPOSV prototype */ extern void dposv( char* uplo, int* n, int* nrhs, double* a, int* lda, double* b, int* ldb, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, double* a, int lda ); /* 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 */ double a[LDA*N] = { 3.14, 0.00, 0.00, 0.00, 0.00, 0.17, 0.79, 0.00, 0.00, 0.00, -0.90, 0.83, 4.53, 0.00, 0.00, 1.65, -0.65, -3.70, 5.32, 0.00, -0.72, 0.28, 1.60, -1.37, 1.98 }; double b[LDB*NRHS] = { -7.29, 9.25, 5.99, -1.94, -8.30, 6.11, 2.90, -5.05, -3.80, 9.66, 0.59, 8.88, 7.57, 5.57, -1.67 }; /* Executable statements */ printf( " DPOSV Example Program Results\n" ); /* Solve the equations A*X = B */ dposv( "Upper", &n, &nrhs, a, &lda, b, &ldb, &info ); /* Check for the positive definiteness */ if( info > 0 ) { printf( "The leading minor of order %i is not positive ", info ); printf( "definite;\nthe solution could not be computed.\n" ); exit( 1 ); } /* Print solution */ print_matrix( "Solution", n, nrhs, b, ldb ); /* Print details of Cholesky factorization */ print_matrix( "Details of Cholesky factorization", n, n, a, lda ); exit( 0 ); } /* End of DPOSV 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" ); } }

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