162 lines
6.5 KiB
C
162 lines
6.5 KiB
C
/*******************************************************************************
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* Copyright (C) 2009-2011 Intel Corporation. All Rights Reserved.
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* The information and material ("Material") provided below is owned by Intel
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* Corporation or its suppliers or licensors, and title to such Material remains
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* with Intel Corporation or its suppliers or licensors. The Material contains
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* proprietary information of Intel or its suppliers and licensors. The Material
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* is protected by worldwide copyright laws and treaty provisions. No part of
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* the Material may be copied, reproduced, published, uploaded, posted,
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* transmitted, or distributed in any way without Intel's prior express written
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* permission. No license under any patent, copyright or other intellectual
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* property rights in the Material is granted to or conferred upon you, either
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* expressly, by implication, inducement, estoppel or otherwise. Any license
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* under such intellectual property rights must be express and approved by Intel
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* in writing.
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*
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********************************************************************************
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*/
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/*
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LAPACKE_zgesv Example.
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======================
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The program computes the solution to the system of linear
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equations with a square matrix A and multiple
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right-hand sides B, where A is the coefficient matrix:
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( 1.23, -5.50) ( 7.91, -5.38) ( -9.80, -4.86) ( -7.32, 7.57)
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( -2.14, -1.12) ( -9.92, -0.79) ( -9.18, -1.12) ( 1.37, 0.43)
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( -4.30, -7.10) ( -6.47, 2.52) ( -6.51, -2.67) ( -5.86, 7.38)
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( 1.27, 7.29) ( 8.90, 6.92) ( -8.82, 1.25) ( 5.41, 5.37)
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and B is the right-hand side matrix:
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( 8.33, -7.32) ( -6.11, -3.81)
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( -6.18, -4.80) ( 0.14, -7.71)
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( -5.71, -2.80) ( 1.41, 3.40)
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( -1.60, 3.08) ( 8.54, -4.05)
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Description.
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============
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The routine solves for X the system of linear equations A*X = B,
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where A is an n-by-n matrix, the columns of matrix B are individual
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right-hand sides, and the columns of X are the corresponding
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solutions.
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The LU decomposition with partial pivoting and row interchanges is
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used to factor A as A = P*L*U, where P is a permutation matrix, L
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is unit lower triangular, and U is upper triangular. The factored
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form of A is then used to solve the system of equations A*X = B.
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Example Program Results.
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========================
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LAPACKE_zgesv (row-major, high-level) Example Program Results
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Solution
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( -1.09, -0.18) ( 1.28, 1.21)
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( 0.97, 0.52) ( -0.22, -0.97)
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( -0.20, 0.19) ( 0.53, 1.36)
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( -0.59, 0.92) ( 2.22, -1.00)
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Details of LU factorization
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( -4.30, -7.10) ( -6.47, 2.52) ( -6.51, -2.67) ( -5.86, 7.38)
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( 0.49, 0.47) ( 12.26, -3.57) ( -7.87, -0.49) ( -0.98, 6.71)
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( 0.25, -0.15) ( -0.60, -0.37) (-11.70, -4.64) ( -1.35, 1.38)
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( -0.83, -0.32) ( 0.05, 0.58) ( 0.93, -0.50) ( 2.66, 7.86)
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Pivot indices
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3 3 3 4
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*/
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#include <stdlib.h>
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#include <stdio.h>
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#include "lapacke.h"
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/* Auxiliary routines prototypes */
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extern void print_matrix( char* desc, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda );
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extern void print_int_vector( char* desc, lapack_int n, lapack_int* a );
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/* Parameters */
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#define N 4
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#define NRHS 2
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#define LDA N
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#define LDB NRHS
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/* Main program */
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int main() {
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/* Locals */
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lapack_int n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info;
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/* Local arrays */
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lapack_int ipiv[N];
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lapack_complex_double a[LDA*N];
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lapack_complex_double b[LDB*N];
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a[0] = lapack_make_complex_double( 1.23, -5.50);
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a[1] = lapack_make_complex_double( 7.91, -5.38);
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a[2] = lapack_make_complex_double(-9.80, -4.86);
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a[3] = lapack_make_complex_double(-7.32, 7.57);
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a[4] = lapack_make_complex_double(-2.14, -1.12);
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a[5] = lapack_make_complex_double(-9.92, -0.79);
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a[6] = lapack_make_complex_double(-9.18, -1.12);
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a[7] = lapack_make_complex_double( 1.37, 0.43);
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a[8] = lapack_make_complex_double(-4.30, -7.10);
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a[9] = lapack_make_complex_double(-6.47, 2.52);
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a[10] = lapack_make_complex_double(-6.51, -2.67);
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a[11] = lapack_make_complex_double(-5.86, 7.38);
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a[12] = lapack_make_complex_double( 1.27, 7.29);
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a[13] = lapack_make_complex_double( 8.90, 6.92);
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a[14] = lapack_make_complex_double(-8.82, 1.25);
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a[15] = lapack_make_complex_double( 5.41, 5.37);
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b[0] = lapack_make_complex_double( 8.33, -7.32);
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b[1] = lapack_make_complex_double(-6.11, -3.81);
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b[2] = lapack_make_complex_double(-6.18, -4.80);
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b[3] = lapack_make_complex_double( 0.14, -7.71);
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b[4] = lapack_make_complex_double(-5.71, -2.80);
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b[5] = lapack_make_complex_double( 1.41, 3.40);
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b[6] = lapack_make_complex_double(-1.60, 3.08);
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b[7] = lapack_make_complex_double( 8.54, -4.05);
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/* Print Entry Matrix */
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print_matrix( "Entry Matrix A", n, n, a, lda );
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/* Print Right Rand Side */
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print_matrix( "Right Rand Side", n, nrhs, b, ldb );
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printf( "\n" );
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/* Executable statements */
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printf( "LAPACKE_zgesv (row-major, high-level) Example Program Results\n" );
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/* Solve the equations A*X = B */
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info = LAPACKE_zgesv( LAPACK_ROW_MAJOR, n, nrhs, a, lda, ipiv, b, ldb );
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/* Check for the exact singularity */
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if( info > 0 ) {
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printf( "The diagonal element of the triangular factor of A,\n" );
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printf( "U(%i,%i) is zero, so that A is singular;\n", info, info );
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printf( "the solution could not be computed.\n" );
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exit( 1 );
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}
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/* Print solution */
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print_matrix( "Solution", n, nrhs, b, ldb );
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/* Print details of LU factorization */
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print_matrix( "Details of LU factorization", n, n, a, lda );
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/* Print pivot indices */
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print_int_vector( "Pivot indices", n, ipiv );
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exit( 0 );
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} /* End of LAPACKE_zgesv Example */
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/* Auxiliary routine: printing a matrix */
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void print_matrix( char* desc, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda ) {
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lapack_int i, j;
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printf( "\n %s\n", desc );
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for( i = 0; i < m; i++ ) {
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for( j = 0; j < n; j++ )
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printf( " (%6.2f,%6.2f)", lapack_complex_double_real(a[i*lda+j]), lapack_complex_double_imag(a[i*lda+j]) );
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printf( "\n" );
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}
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}
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/* Auxiliary routine: printing a vector of integers */
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void print_int_vector( char* desc, lapack_int n, lapack_int* a ) {
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lapack_int j;
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printf( "\n %s\n", desc );
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for( j = 0; j < n; j++ ) printf( " %6i", a[j] );
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printf( "\n" );
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}
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