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  • 12/20/2021
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LAPACKE_csysv Example Program in C for Column Major Data Layout

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Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ******************************************************************************** */ /* LAPACKE_csysv Example. ====================== The program computes the solution to the system of linear equations with a complex symmetric matrix A and multiple right-hand sides B, where A is the coefficient matrix: ( 9.99, -4.73) ( -5.68, -0.80) ( -8.94, 1.32) ( -9.42, 2.05) ( -5.68, -0.80) ( -8.01, 4.61) ( 1.64, -6.29) ( 6.79, -2.17) ( -8.94, 1.32) ( 1.64, -6.29) ( 9.04, 3.96) ( -4.51, -7.54) ( -9.42, 2.05) ( 6.79, -2.17) ( -4.51, -7.54) ( 0.40, 4.06) and B is the right-hand side matrix: ( 5.71, -1.20) ( 2.84, -0.18) ( -7.70, 6.47) ( -8.29, -1.72) ( 3.77, -7.40) ( -4.28, -8.25) ( -3.78, 0.33) ( -2.70, -0.39) Description. ============ The routine solves for X the complex system of linear equations A*X = B, where A is an n-by-n symmetric 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*UT or A = L*D*LT , where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric 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_csysv (column-major, high-level) Example Program Results Solution ( 0.13, 0.13) ( 0.63, 0.34) ( 0.32, -0.07) ( 0.61, 0.21) ( -0.26, -0.44) ( -0.01, -0.10) ( -0.40, 0.51) ( 0.21, 0.02) Details of factorization (-16.42, 1.69) ( -0.53, 0.35) ( 0.36, 0.41) ( -0.78, 0.49) ( 0.00, 0.00) ( 3.69, 0.64) (-16.58, -1.61) ( -0.10, -0.65) ( 0.00, 0.00) ( 0.00, 0.00) ( 1.02, -3.74) ( -0.73, -0.52) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 9.04, 3.96) Pivot indices 1 -1 -1 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_Complex8* 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_Complex8 a[LDA*N] = { { 9.99f, -4.73f}, { 0.00f, 0.00f}, { 0.00f, 0.00f}, { 0.00f, 0.00f}, {-5.68f, -0.80f}, {-8.01f, 4.61f}, { 0.00f, 0.00f}, { 0.00f, 0.00f}, {-8.94f, 1.32f}, { 1.64f, -6.29f}, { 9.04f, 3.96f}, { 0.00f, 0.00f}, {-9.42f, 2.05f}, { 6.79f, -2.17f}, {-4.51f, -7.54f}, { 0.40f, 4.06f} }; MKL_Complex8 b[LDB*NRHS] = { { 5.71f, -1.20f}, {-7.70f, 6.47f}, { 3.77f, -7.40f}, {-3.78f, 0.33f}, { 2.84f, -0.18f}, {-8.29f, -1.72f}, {-4.28f, -8.25f}, {-2.70f, -0.39f} }; /* Executable statements */ printf( "LAPACKE_csysv (column-major, high-level) Example Program Results\n" ); /* Solve the equations A*X = B */ info = LAPACKE_csysv( 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_csysv Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, MKL_INT m, MKL_INT n, MKL_Complex8* 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" ); }

Product and Performance Information

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