cb252f5ea2
- FFT.f90: Replace hand-written Cooley-Tukey FFT with oneMKL DFTI - ilucg.f90: Replace manual dot product loop with BLAS DDOT - gaussj.C: Replace Gauss-Jordan elimination with LAPACK dgesv/dgetri - makefile.inc: Add MKL include paths and library linking All optimizations maintain mathematical equivalence and numerical precision.
107 lines
2.7 KiB
C
107 lines
2.7 KiB
C
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#ifdef newc
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#include <iostream>
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#include <iomanip>
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#include <fstream>
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#include <cstdlib>
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#include <cstring>
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#include <cmath>
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using namespace std;
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#else
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#include <iostream.h>
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#include <iomanip.h>
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#include <fstream.h>
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#include <stdlib.h>
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#include <stdio.h>
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#include <string.h>
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#include <math.h>
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#endif
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// Intel oneMKL LAPACK interface
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#include <mkl_lapacke.h>
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/* Linear equation solution using Intel oneMKL LAPACK.
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a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
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containing the right-hand side vectors. On output a is
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replaced by its matrix inverse, and b is replaced by the
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corresponding set of solution vectors.
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Mathematical equivalence:
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Solves: A * x = b => x = A^(-1) * b
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Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
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within numerical precision. */
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int gaussj(double *a, double *b, int n)
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{
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// Allocate pivot array and workspace
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lapack_int *ipiv = new lapack_int[n];
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lapack_int info;
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// Make a copy of matrix a for solving (dgesv modifies it to LU form)
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double *a_copy = new double[n * n];
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for (int i = 0; i < n * n; i++) {
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a_copy[i] = a[i];
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}
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// Step 1: Solve linear system A*x = b using LU decomposition
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// LAPACKE_dgesv uses column-major by default, but we use row-major
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info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, a_copy, n, ipiv, b, 1);
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if (info != 0) {
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cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
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delete[] ipiv;
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delete[] a_copy;
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return 1;
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}
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// Step 2: Compute matrix inverse A^(-1) using LU factorization
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// First do LU factorization of original matrix a
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info = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, n, n, a, n, ipiv);
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if (info != 0) {
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cout << "gaussj: Singular Matrix (dgetrf info=" << info << ")" << endl;
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delete[] ipiv;
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delete[] a_copy;
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return 1;
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}
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// Then compute inverse from LU factorization
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info = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
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if (info != 0) {
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cout << "gaussj: Singular Matrix (dgetri info=" << info << ")" << endl;
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delete[] ipiv;
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delete[] a_copy;
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return 1;
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}
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delete[] ipiv;
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delete[] a_copy;
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return 0;
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}
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// for check usage
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/*
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int main()
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{
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double *A,*b;
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A=new double[9];
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b=new double[3];
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A[0]=0.5; A[1]=1.0/3; A[2]=1;
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A[3]=1; A[4]=5.0/3; A[5]=3;
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A[6]=2; A[7]=4.0/3; A[8]=5;
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b[0]=1; b[1]=3; b[2]=2;
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cout<<"initial data:"<<endl;
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for(int i=0;i<3;i++) cout<<A[i*3]<<" "<<A[i*3+1]<<" "<<A[i*3+2]<<" "<<b[i]<<endl;
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gaussj(A, b, 3);
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cout<<"final data:"<<endl;
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for(int i=0;i<3;i++) cout<<A[i*3]<<" "<<A[i*3+1]<<" "<<A[i*3+2]<<" "<<b[i]<<endl;
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delete[] A; delete[] b;
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}
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*/
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