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  • 2022.1
  • 12/20/2021
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CGELS 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. * ******************************************************************************** */ /* CGELS Example. ============== Program computes the minimum norm solution to the underdetermined linear system A*X = B with full rank matrix A using LQ factorization, where A is the coefficient matrix: ( -4.20, -3.44) ( -3.35, 1.52) ( 1.73, 8.85) ( 2.35, 0.34) ( -5.43, -8.81) ( -4.53, -8.47) ( 5.93, 3.75) ( -3.75, -5.66) ( -5.56, 3.39) ( 2.90, -9.22) ( 8.03, 9.37) ( 5.69, -0.47) and B is the right-hand side matrix: ( -7.02, 4.80) ( 3.88, -2.59) ( 0.62, -2.40) ( 1.57, 3.24) ( 3.10, -2.19) ( -6.93, -5.99) Description. ============ The routine solves overdetermined or underdetermined complex linear systems involving an m-by-n matrix A, or its transpose, using a QR or LQ factorization of A. It is assumed that A has full rank. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the m-by-nrhs right hand side matrix B and the n-by-nrhs solution matrix X. Example Program Results. ======================== CGELS Example Program Results Minimum norm solution ( -0.25, -0.04) ( -0.21, 0.42) ( 0.99, 0.27) ( -0.21, -0.43) ( 0.25, 0.43) ( -0.24, -0.13) ( -0.32, 0.14) ( -0.23, -0.09) Details of LQ factorization ( 11.40, 0.00) ( 0.18, -0.14) ( -0.23, -0.52) ( -0.15, 0.01) ( 7.73, -0.39) ( 15.32, 0.00) ( -0.22, 0.42) ( 0.45, 0.17) ( 8.60, -5.68) ( 3.96, 6.46) ( 12.54, 0.00) ( -0.02, -0.47) */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _fcomplex { float re, im; }; typedef struct _fcomplex fcomplex; /* CGELS prototype */ extern void cgels( char* trans, int* m, int* n, int* nrhs, fcomplex* a, int* lda, fcomplex* b, int* ldb, fcomplex* work, int* lwork, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, fcomplex* a, int lda ); /* Parameters */ #define M 3 #define N 4 #define NRHS 2 #define LDA M #define LDB N /* Main program */ int main() { /* Locals */ int m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, lwork; fcomplex wkopt; fcomplex* work; /* Local arrays */ fcomplex a[LDA*N] = { {-4.20f, -3.44f}, {-5.43f, -8.81f}, {-5.56f, 3.39f}, {-3.35f, 1.52f}, {-4.53f, -8.47f}, { 2.90f, -9.22f}, { 1.73f, 8.85f}, { 5.93f, 3.75f}, { 8.03f, 9.37f}, { 2.35f, 0.34f}, {-3.75f, -5.66f}, { 5.69f, -0.47f} }; fcomplex b[LDB*NRHS] = { {-7.02f, 4.80f}, { 0.62f, -2.40f}, { 3.10f, -2.19f}, { 0.00f, 0.00f}, { 3.88f, -2.59f}, { 1.57f, 3.24f}, {-6.93f, -5.99f}, { 0.00f, 0.00f} }; /* Executable statements */ printf( " CGELS Example Program Results\n" ); /* Query and allocate the optimal workspace */ lwork = -1; cgels( "No transpose", &m, &n, &nrhs, a, &lda, b, &ldb, &wkopt, &lwork, &info ); lwork = (int)wkopt.re; work = (fcomplex*)malloc( lwork*sizeof(fcomplex) ); /* Solve the equations A*X = B */ cgels( "No transpose", &m, &n, &nrhs, a, &lda, b, &ldb, work, &lwork, &info ); /* Check for the full rank */ if( info > 0 ) { printf( "The diagonal element %i of the triangular factor ", info ); printf( "of A is zero, so that A does not have full rank;\n" ); printf( "the minimum norm solution could not be computed.\n" ); exit( 1 ); } /* Print minimum norm solution */ print_matrix( "Minimum norm solution", n, nrhs, b, ldb ); /* Print details of LQ factorization */ print_matrix( "Details of LQ factorization", m, n, a, lda ); /* Free workspace */ free( (void*)work ); exit( 0 ); } /* End of CGELS 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" ); } }

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