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Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ******************************************************************************** */ /* LAPACKE_zgesv Example. ====================== The program computes the solution to the system of linear equations with a square matrix A and multiple right-hand sides B, where A is the coefficient matrix: ( 1.23, -5.50) ( 7.91, -5.38) ( -9.80, -4.86) ( -7.32, 7.57) ( -2.14, -1.12) ( -9.92, -0.79) ( -9.18, -1.12) ( 1.37, 0.43) ( -4.30, -7.10) ( -6.47, 2.52) ( -6.51, -2.67) ( -5.86, 7.38) ( 1.27, 7.29) ( 8.90, 6.92) ( -8.82, 1.25) ( 5.41, 5.37) and B is the right-hand side matrix: ( 8.33, -7.32) ( -6.11, -3.81) ( -6.18, -4.80) ( 0.14, -7.71) ( -5.71, -2.80) ( 1.41, 3.40) ( -1.60, 3.08) ( 8.54, -4.05) Description. ============ The routine solves for X the system of linear equations A*X = B, where A is an n-by-n matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P*L*U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A*X = B. Example Program Results. ======================== LAPACKE_zgesv (row-major, high-level) Example Program Results Solution ( -1.09, -0.18) ( 1.28, 1.21) ( 0.97, 0.52) ( -0.22, -0.97) ( -0.20, 0.19) ( 0.53, 1.36) ( -0.59, 0.92) ( 2.22, -1.00) Details of LU factorization ( -4.30, -7.10) ( -6.47, 2.52) ( -6.51, -2.67) ( -5.86, 7.38) ( 0.49, 0.47) ( 12.26, -3.57) ( -7.87, -0.49) ( -0.98, 6.71) ( 0.25, -0.15) ( -0.60, -0.37) (-11.70, -4.64) ( -1.35, 1.38) ( -0.83, -0.32) ( 0.05, 0.58) ( 0.93, -0.50) ( 2.66, 7.86) Pivot indices 3 3 3 4 */ #include #include #include "lapacke.h" /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda ); extern void print_int_vector( char* desc, lapack_int n, lapack_int* a ); /* Parameters */ #define N 4 #define NRHS 2 #define LDA N #define LDB NRHS /* Main program */ int main() { /* Locals */ lapack_int n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info; /* Local arrays */ lapack_int ipiv[N]; lapack_complex_double a[LDA*N]; lapack_complex_double b[LDB*N]; a[0] = lapack_make_complex_double( 1.23, -5.50); a[1] = lapack_make_complex_double( 7.91, -5.38); a[2] = lapack_make_complex_double(-9.80, -4.86); a[3] = lapack_make_complex_double(-7.32, 7.57); a[4] = lapack_make_complex_double(-2.14, -1.12); a[5] = lapack_make_complex_double(-9.92, -0.79); a[6] = lapack_make_complex_double(-9.18, -1.12); a[7] = lapack_make_complex_double( 1.37, 0.43); a[8] = lapack_make_complex_double(-4.30, -7.10); a[9] = lapack_make_complex_double(-6.47, 2.52); a[10] = lapack_make_complex_double(-6.51, -2.67); a[11] = lapack_make_complex_double(-5.86, 7.38); a[12] = lapack_make_complex_double( 1.27, 7.29); a[13] = lapack_make_complex_double( 8.90, 6.92); a[14] = lapack_make_complex_double(-8.82, 1.25); a[15] = lapack_make_complex_double( 5.41, 5.37); b[0] = lapack_make_complex_double( 8.33, -7.32); b[1] = lapack_make_complex_double(-6.11, -3.81); b[2] = lapack_make_complex_double(-6.18, -4.80); b[3] = lapack_make_complex_double( 0.14, -7.71); b[4] = lapack_make_complex_double(-5.71, -2.80); b[5] = lapack_make_complex_double( 1.41, 3.40); b[6] = lapack_make_complex_double(-1.60, 3.08); b[7] = lapack_make_complex_double( 8.54, -4.05); /* Print Entry Matrix */ print_matrix( "Entry Matrix A", n, n, a, lda ); /* Print Right Rand Side */ print_matrix( "Right Rand Side", n, nrhs, b, ldb ); printf( "\n" ); /* Executable statements */ printf( "LAPACKE_zgesv (row-major, high-level) Example Program Results\n" ); /* Solve the equations A*X = B */ info = LAPACKE_zgesv( LAPACK_ROW_MAJOR, n, nrhs, a, lda, ipiv, b, ldb ); /* Check for the exact singularity */ if( info > 0 ) { printf( "The diagonal element of the triangular factor of A,\n" ); printf( "U(%i,%i) is zero, so that A 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 LU factorization */ print_matrix( "Details of LU factorization", n, n, a, lda ); /* Print pivot indices */ print_int_vector( "Pivot indices", n, ipiv ); exit( 0 ); } /* End of LAPACKE_zgesv Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda ) { lapack_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)", lapack_complex_double_real(a[i*lda+j]), lapack_complex_double_imag(a[i*lda+j]) ); printf( "\n" ); } } /* Auxiliary routine: printing a vector of integers */ void print_int_vector( char* desc, lapack_int n, lapack_int* a ) { lapack_int j; printf( "\n %s\n", desc ); for( j = 0; j < n; j++ ) printf( " %6i", a[j] ); printf( "\n" ); }