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  • 2022.1
  • 12/20/2021
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ZPOSV 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. * ******************************************************************************** */ /* ZPOSV Example. ============== The program computes the solution to the system of linear equations with a Hermitian positive-definite matrix A and multiple right-hand sides B, where A is the coefficient matrix: ( 5.96, 0.00) ( 0.40, -1.19) ( -0.83, -0.48) ( -0.57, 0.40) ( 0.40, 1.19) ( 7.95, 0.00) ( 0.33, 0.09) ( 0.22, 0.74) ( -0.83, 0.48) ( 0.33, -0.09) ( 4.43, 0.00) ( -1.09, 0.32) ( -0.57, -0.40) ( 0.22, -0.74) ( -1.09, -0.32) ( 3.46, 0.00) and B is the right-hand side matrix: ( -2.94, 5.79) ( 8.44, 3.07) ( 8.12, -9.12) ( 1.00, -4.62) ( 9.09, -5.03) ( 3.64, -2.33) ( 7.36, 6.77) ( 8.04, 2.87) Description. ============ The routine solves for X the complex system of linear equations A*X = B, where A is an n-by-n Hermitian 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 = UH*U, if uplo = 'U' or A = L*LH, 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. ======================== ZPOSV Example Program Results Solution ( 0.80, 1.62) ( 2.52, 0.61) ( 1.26, -1.78) ( 0.01, -1.38) ( 3.38, -0.29) ( 2.42, -0.52) ( 3.46, 2.92) ( 3.77, 1.37) Details of Cholesky factorization ( 2.44, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.16, 0.49) ( 2.77, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( -0.34, 0.20) ( 0.10, -0.10) ( 2.06, 0.00) ( 0.00, 0.00) ( -0.23, -0.16) ( 0.12, -0.30) ( -0.57, -0.20) ( 1.71, 0.00) */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _dcomplex { double re, im; }; typedef struct _dcomplex dcomplex; /* ZPOSV prototype */ extern void zposv( char* uplo, int* n, int* nrhs, dcomplex* a, int* lda, dcomplex* b, int* ldb, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, dcomplex* a, int lda ); /* 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 */ dcomplex a[LDA*N] = { { 5.96, 0.00}, { 0.40, 1.19}, {-0.83, 0.48}, {-0.57, -0.40}, { 0.00, 0.00}, { 7.95, 0.00}, { 0.33, -0.09}, { 0.22, -0.74}, { 0.00, 0.00}, { 0.00, 0.00}, { 4.43, 0.00}, {-1.09, -0.32}, { 0.00, 0.00}, { 0.00, 0.00}, { 0.00, 0.00}, { 3.46, 0.00} }; dcomplex b[LDB*NRHS] = { {-2.94, 5.79}, { 8.12, -9.12}, { 9.09, -5.03}, { 7.36, 6.77}, { 8.44, 3.07}, { 1.00, -4.62}, { 3.64, -2.33}, { 8.04, 2.87} }; /* Executable statements */ printf( " ZPOSV Example Program Results\n" ); /* Solve the equations A*X = B */ zposv( "Lower", &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 ZPOSV Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, int m, int n, dcomplex* 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" ); } }

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