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  • 2022.1
  • 12/20/2021
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SGELSD 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. * ******************************************************************************** */ /* SGELSD 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. ======================== SGELSD 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> /* SGELSD prototype */ extern void sgelsd( int* m, int* n, int* nrhs, float* a, int* lda, float* b, int* ldb, float* s, float* rcond, int* rank, float* work, int* lwork, int* iwork, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, float* a, int lda ); /* Parameters */ #define M 4 #define N 5 #define NRHS 3 #define LDA M #define LDB N /* Main program */ int main() { /* Locals */ int m = M, n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info, lwork, rank; /* Negative rcond means using default (machine precision) value */ float rcond = -1.0; float wkopt; float* work; /* Local arrays */ /* iwork dimension should be at least 3*min(m,n)*nlvl + 11*min(m,n), where nlvl = max( 0, int( log_2( min(m,n)/(smlsiz+1) ) )+1 ) and smlsiz = 25 */ int iwork[3*M*0+11*M]; float s[M]; float a[LDA*N] = { 0.12f, -6.91f, -3.33f, 3.97f, -8.19f, 2.22f, -8.94f, 3.33f, 7.69f, -5.12f, -6.72f, -2.74f, -2.26f, -9.08f, -4.40f, -7.92f, -4.71f, 9.96f, -9.98f, -3.20f }; float b[LDB*NRHS] = { 7.30f, 1.33f, 2.68f, -9.62f, 0.00f, 0.47f, 6.58f, -1.71f, -0.79f, 0.00f, -6.28f, -3.42f, 3.46f, 0.41f, 0.00f }; /* Executable statements */ printf( " SGELSD Example Program Results\n" ); /* Query and allocate the optimal workspace */ lwork = -1; sgelsd( &m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, &wkopt, &lwork, iwork, &info ); lwork = (int)wkopt; work = (float*)malloc( lwork*sizeof(float) ); /* Solve the equations A*X = B */ sgelsd( &m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, work, &lwork, iwork, &info ); /* 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 ); /* Free workspace */ free( (void*)work ); exit( 0 ); } /* End of SGELSD Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, int m, int n, float* 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" ); } }

Product and Performance Information

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