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  • 12/20/2021
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LAPACKE_zhesv Example Program in C for Column 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_zhesv Example. ====================== The program computes the solution to the system of linear equations with a Hermitian matrix A and multiple right-hand sides B, where A is the coefficient matrix: ( -2.90, 0.00) ( 0.31, 4.46) ( 9.66, -5.66) ( -2.28, 2.14) ( 0.31, -4.46) ( -7.93, 0.00) ( 9.55, -4.62) ( -3.51, 3.11) ( 9.66, 5.66) ( 9.55, 4.62) ( 0.30, 0.00) ( 9.33, -9.66) ( -2.28, -2.14) ( -3.51, -3.11) ( 9.33, 9.66) ( 2.40, 0.00) and B is the right-hand side matrix: ( -5.69, -8.21) ( -2.83, 6.46) ( -3.57, 1.99) ( -7.64, 1.10) ( 8.42, -9.83) ( -2.33, -4.23) ( -5.00, 3.85) ( 6.48, -3.81) Description. ============ The routine solves for X the complex system of linear equations A*X = B, where A is an n-by-n Hermitian matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The diagonal pivoting method is used to factor A as A = U*D*UH or A = L*D*LH, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A*X = B. Example Program Results. ======================== LAPACKE_zhesv (column-major, high-level) Example Program Results Solution ( 0.22, -0.95) ( -1.13, 0.18) ( -1.42, -1.30) ( 0.70, 1.13) ( -0.65, -0.40) ( 0.04, 0.07) ( -0.48, 1.35) ( 1.15, -0.27) Details of factorization ( 3.17, 0.00) ( 7.32, 3.28) ( -0.36, 0.06) ( 0.20, -0.82) ( 0.00, 0.00) ( 0.03, 0.00) ( -0.48, 0.03) ( 0.25, -0.76) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.30, 0.00) ( 9.33, -9.66) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 2.40, 0.00) Pivot indices -1 -1 -3 -3 */ #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, MKL_Complex16* a, MKL_INT lda ); extern void print_int_vector( char* desc, MKL_INT n, MKL_INT* a ); /* Parameters */ #define N 4 #define NRHS 2 #define LDA N #define LDB N /* Main program */ int main() { /* Locals */ MKL_INT n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info; /* Local arrays */ MKL_INT ipiv[N]; MKL_Complex16 a[LDA*N] = { {-2.90, 0.00}, { 0.00, 0.00}, { 0.00, 0.00}, { 0.00, 0.00}, { 0.31, 4.46}, {-7.93, 0.00}, { 0.00, 0.00}, { 0.00, 0.00}, { 9.66, -5.66}, { 9.55, -4.62}, { 0.30, 0.00}, { 0.00, 0.00}, {-2.28, 2.14}, {-3.51, 3.11}, { 9.33, -9.66}, { 2.40, 0.00} }; MKL_Complex16 b[LDB*NRHS] = { {-5.69, -8.21}, {-3.57, 1.99}, { 8.42, -9.83}, {-5.00, 3.85}, {-2.83, 6.46}, {-7.64, 1.10}, {-2.33, -4.23}, { 6.48, -3.81} }; /* Executable statements */ printf( "LAPACKE_zhesv (column-major, high-level) Example Program Results\n" ); /* Solve the equations A*X = B */ info = LAPACKE_zhesv( LAPACK_COL_MAJOR, 'U', n, nrhs, a, lda, ipiv, b, ldb ); /* Check for the exact singularity */ if( info > 0 ) { printf( "The element of the diagonal factor " ); printf( "D(%i,%i) is zero, so that D is singular;\n", info, info ); printf( "the solution could not be computed.\n" ); exit( 1 ); } /* Print solution */ print_matrix( "Solution", n, nrhs, b, ldb ); /* Print details of factorization */ print_matrix( "Details of factorization", n, n, a, lda ); /* Print pivot indices */ print_int_vector( "Pivot indices", n, ipiv ); exit( 0 ); } /* End of LAPACKE_zhesv Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex16* 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,%6.2f)", a[i+j*lda].real, a[i+j*lda].imag ); printf( "\n" ); } } /* Auxiliary routine: printing a vector of integers */ void print_int_vector( char* desc, MKL_INT n, MKL_INT* a ) { MKL_INT j; printf( "\n %s\n", desc ); for( j = 0; j < n; j++ ) printf( " %6i", a[j] ); printf( "\n" ); }

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