## Developer Reference

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

# LAPACKE_dgels Example Program in C for Row Major Data Layout

/******************************************************************************* * 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. * ******************************************************************************** */ /* LAPACKE_dgels Example. ====================== Program computes the least squares solution to the overdetermined linear system A*X = B with full rank matrix A using QR factorization, where A is the coefficient matrix: 1.44 -7.84 -4.39 4.53 -9.96 -0.28 -3.24 3.83 -7.55 3.24 6.27 -6.64 8.34 8.09 5.28 2.06 7.08 2.52 0.74 -2.47 -5.45 -5.70 -1.19 4.70 and B is the right-hand side matrix: 8.58 9.35 8.26 -4.43 8.48 -0.70 -5.28 -0.26 5.72 -7.36 8.93 -2.52 Description. ============ The routine solves overdetermined or underdetermined real 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. ======================== LAPACKE_dgels (row-major, high-level) Example Program Results Solution -0.45 0.25 -0.85 -0.90 0.71 0.63 0.13 0.14 Residual sum of squares for the solution 195.36 107.06 Details of QR factorization -17.54 -4.76 -1.96 0.42 -0.52 12.40 7.88 -5.84 -0.40 -0.14 -5.75 4.11 0.44 -0.66 -0.20 -7.78 0.37 -0.26 -0.17 -0.15 -0.29 0.46 0.41 0.24 */ #include <stdlib.h> #include <stdio.h> #include "mkl_lapacke.h" /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ); extern void print_vector_norm( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ); /* Parameters */ #define M 6 #define N 4 #define NRHS 2 #define LDA N #define LDB NRHS /* Main program */ int main() { /* Locals */ MKL_INT m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info; /* Local arrays */ double a[LDA*M] = { 1.44, -7.84, -4.39, 4.53, -9.96, -0.28, -3.24, 3.83, -7.55, 3.24, 6.27, -6.64, 8.34, 8.09, 5.28, 2.06, 7.08, 2.52, 0.74, -2.47, -5.45, -5.70, -1.19, 4.70 }; double b[LDB*M] = { 8.58, 9.35, 8.26, -4.43, 8.48, -0.70, -5.28, -0.26, 5.72, -7.36, 8.93, -2.52 }; /* Executable statements */ printf( "LAPACKE_dgels (row-major, high-level) Example Program Results\n" ); /* Solve the equations A*X = B */ info = LAPACKE_dgels( LAPACK_ROW_MAJOR, 'N', m, n, nrhs, a, lda, b, ldb ); /* 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 least squares solution could not be computed.\n" ); exit( 1 ); } /* Print least squares solution */ print_matrix( "Least squares solution", n, nrhs, b, ldb ); /* Print residual sum of squares for the solution */ print_vector_norm( "Residual sum of squares for the solution", m-n, nrhs, &b[n*ldb], ldb ); /* Print details of QR factorization */ print_matrix( "Details of QR factorization", m, n, a, lda ); exit( 0 ); } /* End of LAPACKE_dgels Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ) { MKL_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*lda+j] ); printf( "\n" ); } } /* Auxiliary routine: printing norms of matrix columns */ void print_vector_norm( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ) { MKL_INT i, j; double norm; printf( "\n %s\n", desc ); for( j = 0; j < n; j++ ) { norm = 0.0; for( i = 0; i < m; i++ ) norm += a[i*lda+j] * a[i*lda+j]; printf( " %6.2f", norm ); } printf( "\n" ); }

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