Developer Reference

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

LAPACKE_dgelsd 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_dgelsd Example. ======================= Program computes the minimum norm-solution to a real linear least squares problem using the singular value decomposition of A, where A is the coefficient matrix: 0.12 -8.19 7.69 -2.26 -4.71 -6.91 2.22 -5.12 -9.08 9.96 -3.33 -8.94 -6.72 -4.40 -9.98 3.97 3.33 -2.74 -7.92 -3.20 and B is the right-hand side matrix: 7.30 0.47 -6.28 1.33 6.58 -3.42 2.68 -1.71 3.46 -9.62 -0.79 0.41 Description. ============ The routine computes the minimum-norm solution to a real linear least squares problem: minimize ||b - A*x|| using the singular value decomposition (SVD) of A. A is an m-by-n matrix which may be rank-deficient. 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. The effective rank of A is determined by treating as zero those singular values which are less than rcond times the largest singular value. Example Program Results. ======================== LAPACKE_dgelsd (row-major, high-level) Example Program Results Minimum norm solution -0.69 -0.24 0.06 -0.80 -0.08 0.21 0.38 0.12 -0.65 0.29 -0.24 0.42 0.29 0.35 -0.30 Effective rank = 4 Singular values 18.66 15.99 10.01 8.51 */ #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 ); /* Parameters */ #define M 4 #define N 5 #define NRHS 3 #define LDA N #define LDB NRHS /* Main program */ int main() { /* Locals */ MKL_INT m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, rank; /* Negative rcond means using default (machine precision) value */ double rcond = -1.0; /* Local arrays */ double s[M]; double a[LDA*M] = { 0.12, -8.19, 7.69, -2.26, -4.71, -6.91, 2.22, -5.12, -9.08, 9.96, -3.33, -8.94, -6.72, -4.40, -9.98, 3.97, 3.33, -2.74, -7.92, -3.20 }; double b[LDB*N] = { 7.30, 0.47, -6.28, 1.33, 6.58, -3.42, 2.68, -1.71, 3.46, -9.62, -0.79, 0.41, 0.00, 0.00, 0.00 }; /* Executable statements */ printf( "LAPACKE_dgelsd (row-major, high-level) Example Program Results\n" ); /* Solve the equations A*X = B */ info = LAPACKE_dgelsd( LAPACK_ROW_MAJOR, m, n, nrhs, a, lda, b, ldb, s, rcond, &rank ); /* Check for convergence */ if( info > 0 ) { printf( "The algorithm computing SVD failed to converge;\n" ); printf( "the least squares solution could not be computed.\n" ); exit( 1 ); } /* Print minimum norm solution */ print_matrix( "Minimum norm solution", n, nrhs, b, ldb ); /* Print effective rank */ printf( "\n Effective rank = %6i\n", rank ); /* Print singular values */ print_matrix( "Singular values", 1, m, s, 1 ); exit( 0 ); } /* End of LAPACKE_dgelsd 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" ); } }

Product and Performance Information

1

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