ここでは、LAPACKE の関数 LAPACKE_zheevx() を使用しているときに遭遇した奇妙なバグについて説明します。4 つの固有値/ベクトルのうち 3 つを計算する単純なテスト コード (Intel の Web サイトの例) はうまく機能し、正しい出力が得られます。ただし、ソース コードに任意の文字列の宣言を導入すると (例: std::string OutputFIlename;)、コンパイルはうまくいきますが、実行時にセグメンテーション エラー SIGSEGV が発生します !!!
まず、機能するコードをリストします。
//===========================
#include <iostream>
#include <string>
#include <fstream>
#include <cassert>
#include <stdlib.h>
#include <stdio.h>
#include <complex>
#include <math.h>
#include "Headers_LAPACKE\lapacke.h"
#include "Headers_LAPACKE\lapacke_config.h"
#include "Headers_LAPACKE\lapacke_mangling.h"
#include "Headers_LAPACKE\lapacke_utils.h"
void print_matrix( char* desc, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda );
int main()
{
std::cout << "Start..." << std::endl;
//std::string fn_VALS;
// --------------- LAPACKE --- define variables ----------------------------------------------------------------
//
// Define arguments for LAPACKE_zheevx() routine:
int matrix_layout; // = LAPACK_ROW_MAJOR or LAPACK_COL_MAJOR
char jobz; // It is ="V" to calculate EigenVECTORS and
// ="N" if you don't do it.
char range; // ="A" for ALL values (don't want this),
// ="V" for values in in the half-open interval (vl,vu],
// ="I" for EigenVALUES indexed from il through iu (this is what you want).
char uplo; // ="U" for Upper Triangle of the matrix, or
// ="L" for the Lower triangle of the matrix.
lapack_int n; // the order of matrix "a" to be diagonalized.
lapack_complex_double* a; // complex array of dimension (lda,n).
// On entry it is Hermitian matrix "a".
// uplo="U" means the leading n-by-n upper triangular part of "a" contain the upper triangular part of the Hermitial matrix to be diagonalized.
// uplo="L" means equivalent for the lower triangular part.
// On exit, this content is destroyed.
lapack_int lda; // leading dimension of "a": lda >= max(1,n).
double vl; // taken into account only if range="V": vl<vu. Not referenced if range="I" or range="A".
double vu; // taken into account only if range="V": vl<vu. Not referenced if range="I" or range="A".
lapack_int il; // taken into account only if range="I": il<iu. Indices in ascending order of SMALLEST EigenVALUE to be returned. Not referenced if range="v" or range="A".
lapack_int iu; // taken into account only if range="I": il<iu. Indices in ascending order of LARGEST EigenVALUE to be returned. Not referenced if range="v" or range="A".
double abstol; // The absolute error tolerance for EigenVALUES. If abstop =<0, then EPS*|T| is used. If you get info>0 (some eigenvalues did not converge) then try abstol=2*DLAMCH('S').
lapack_int* m; // total number of EigenVALUES found: 0 =< m =< n, If range="A" then m=n, if range="I" then m = iu-il+1.
double* w; // double precision array of dimension n. On normal exit, the first m elements contain the selected EigenVALUES in ASCENDING ORDER.
lapack_complex_double* z; // double precision array of dimension (ldz, max(1,m)). If jobz="V" and info=0, the first m-columns of z contain normalized EigenVECTORS of a, corresponding to the selected EigenVALUES, with i-th column of z contains the Eigenvectro corresponding to w(i) eigenvalue.
lapack_int ldz; // leading dimension of array z. ldz>=1 and if jobz="V" then ldz >= max(1,n).
// following are used only with LAPACKE_zheevx_work() routine:.
//lapack_complex_double* work; // array of dimension max(1,lwork).
//lapack_int lwork; // lwork=-1 means workspace query. Othewise it has to be length of the array work: lwork=2*n for n>1, and lwork >=1 for N=<1.
//double* rwork; // array dimension is 7*n;
//lapack_int* iwork; // array dimension is 5*n;
lapack_int* ifail; // jobz="V" and info=0: first m elemens of ifail are zero. jobz="V" and info>0: ifail contain indices of the eigenvectors that failed to converge.
lapack_int info; //info=0 means successful exit. info>0 means eigenvectors failed to converge, their indices are in ifail. info<0, info=-i means i-th argument had an illegal value.
//
// ------------------------------------------------------------------------------------------------------------
matrix_layout = LAPACK_ROW_MAJOR;
jobz = 'V'; vl = 0.0; vu =100.0;
il = 1; iu=4; // are ignored now.
range = 'V';
uplo ='U';
n = 4;
lda = n;
ldz = n;
z = new lapack_complex_double [ldz*n];
w = new double [n];
a = new lapack_complex_double [lda*n];
a[0] =lapack_complex_double{6.51,0.0}; a[1] =lapack_make_complex_double(-5.92, 9.53); a[2]=lapack_complex_double{-2.46,2.91}; a[3]=lapack_complex_double{8.84,3.21};
a[4] =lapack_complex_double{0.0,0.0}; a[5] =lapack_make_complex_double(-1.73,0.0); a[6]=lapack_complex_double{6.5,2.09}; a[7]=lapack_complex_double{1.32, 8.81};
a[8] =lapack_complex_double{0.0,0.0}; a[9] =lapack_make_complex_double(0.0,0.0); a[10]=lapack_complex_double{6.90,0.0}; a[11]=lapack_complex_double{-0.59,2.47};
a[12]=lapack_complex_double{0.0,0.0}; a[13]=lapack_make_complex_double(0.0,0.0); a[14]=lapack_complex_double{0.0,0.0}; a[15]=lapack_complex_double{-2.85,0.0};
ifail = new lapack_int [n];
abstol = -1; // set default tolerance for calcuation of EigVals in the assigned interval.
print_matrix( "Entry Matrix A:", n, n, a, lda );
std::cout << std::endl;
info = LAPACKE_zheevx(matrix_layout, jobz, range, uplo, n, a, lda, vl, vu, il, iu, abstol, m, w, z, ldz, ifail);
if (info>0)
{
std::cout << "Error: ZHEEVX failed to compute eigenvalues/vectors.";
exit(1);
}
std::cout << "info = " << info << std::endl;
std::cout << "Number of eigvals found: " << *m << std::endl;
for (int i_e =0; i_e<*m; i_e++)
{
std::cout << "Eigval. " << i_e << " is " << w[i_e] << std::endl;
}
print_matrix( "Selected EigVECTORS (column-wise):", n, n, z, ldz );
std::cout << std::endl;
std::cout << "Done :-) !!!" <<std::endl;
return 0;
}
////////////////////////////////////////////////////////* 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" );
}
}
//=======================================
ここで、main() で 2 行目のコメント記号 (//) を削除すると、次のようになります。 //std::string fn_VALS; これは std::string fn_VALS; になります。これでソースはコンパイルされますが、実行時にセグメンテーション エラー SIGSEGV で失敗します。
より詳しい情報：
Windows 7 Pro と Code::Blocks を使用しています。LAPACKE ヘッダーと dll は 2016 年 6 月 15 日にダウンロードされました。コンソールから: Process returned -1073741819 (0xC0000005) Code::Blocks のコール スタック ウィンドウから
.......... main() 呼び出し LAPACKE_zheevx() [lapacke.dll]
.......... LAPACKE_zheevx() は LAPACKE_zheevx_work() を呼び出します [lapacke.dll]
.......... LAPACKE_zheevx_work() は zheevx_() を呼び出します [lapack.dll]
助けてください。