概要
本サンプルはFortran言語によりLAPACKルーチンZHEEVXを利用するサンプルプログラムです。
エルミート行列の半開区間![$ (-2, 2]$](img/img82.gif){kind=small}
の固有値と対応する固有ベクトルを求めます。
入力データ
（本ルーチンの詳細はZHEEVX のマニュアルページを参照）| このデータをダウンロード |
ZHEEVX Example Program Data
4 :Value of N
-2.0 2.0 :Values of VL and VU
(1.0, 0.0) (2.0, -1.0) (3.0, -1.0) (4.0, -1.0)
(2.0, 0.0) (3.0, -2.0) (4.0, -2.0)
(3.0, 0.0) (4.0, -3.0)
(4.0, 0.0) :End of matrix A
出力結果
（本ルーチンの詳細はZHEEVX のマニュアルページを参照）| この出力例をダウンロード |
ZHEEVX Example Program Results
Number of eigenvalues found = 2
Eigenvalues
-0.6886 1.1412
Selected eigenvectors
1 2
1 0.6470 0.0179
0.0000 -0.4453
2 -0.4984 0.5706
-0.1130 0.0000
3 0.2949 -0.1530
0.3165 0.5273
4 -0.2241 -0.2118
-0.2878 -0.3598
ソースコード
（本ルーチンの詳細はZHEEVX のマニュアルページを参照）※本サンプルソースコードのご利用手順は「サンプルのコンパイル及び実行方法」をご参照下さい。
| このソースコードをダウンロード |
Program zheevx_example
! ZHEEVX Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use blas_interfaces, Only: zscal
Use lapack_example_aux, Only: nagf_file_print_matrix_complex_gen
Use lapack_interfaces, Only: zheevx
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Real (Kind=dp), Parameter :: zero = 0.0E+0_dp
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=dp) :: abstol, vl, vu
Integer :: i, ifail, il, info, iu, k, lda, ldz, lwork, m, n
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: a(:, :), work(:), z(:, :)
Complex (Kind=dp) :: dummy(1)
Real (Kind=dp), Allocatable :: rwork(:), w(:)
Integer, Allocatable :: iwork(:), jfail(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, cmplx, conjg, max, maxloc, nint, real
! .. Executable Statements ..
Write (nout, *) 'ZHEEVX Example Program Results'
Write (nout, *)
! Skip heading in data file
Read (nin, *)
Read (nin, *) n
lda = n
ldz = n
m = n
Allocate (a(lda,n), z(ldz,m), rwork(7*n), w(n), iwork(5*n), jfail(n))
! Read the lower and upper bounds of the interval to be searched.
Read (nin, *) vl, vu
! Use routine workspace query to get optimal workspace.
lwork = -1
Call zheevx('Vectors', 'Values in range', 'Upper', n, a, lda, vl, vu, &
il, iu, abstol, m, w, z, ldz, dummy, lwork, rwork, iwork, jfail, info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+1)*n, nint(real(dummy(1))))
Allocate (work(lwork))
! Read the upper triangular part of the matrix A.
Read (nin, *)(a(i,i:n), i=1, n)
! Set the absolute error tolerance for eigenvalues. With ABSTOL
! set to zero, the default value is used instead
abstol = zero
! Solve the Hermitian eigenvalue problem
Call zheevx('Vectors', 'Values in range', 'Upper', n, a, lda, vl, vu, &
il, iu, abstol, m, w, z, ldz, work, lwork, rwork, iwork, jfail, info)
If (info>=0) Then
! Print solution
Write (nout, 100) 'Number of eigenvalues found =', m
Write (nout, *)
Write (nout, *) 'Eigenvalues'
Write (nout, 110) w(1:m)
Flush (nout)
! Normalize the eigenvectors so that the element of largest absolute
! value is real.
Do i = 1, m
rwork(1:n) = abs(z(1:n,i))
k = maxloc(rwork(1:n), 1)
Call zscal(n, conjg(z(k,i))/cmplx(abs(z(k,i)),kind=dp), z(1,i), 1)
End Do
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call nagf_file_print_matrix_complex_gen('General', ' ', n, m, z, ldz, &
'Selected eigenvectors', ifail)
If (info>0) Then
Write (nout, 100) 'INFO eigenvectors failed to converge, INFO =', &
info
Write (nout, *) 'Indices of eigenvectors that did not converge'
Write (nout, 120) jfail(1:m)
End If
Else
Write (nout, 100) 'Failure in ZHEEVX. INFO =', info
End If
100 Format (1X, A, I5)
110 Format (3X, (8F8.4))
120 Format (3X, (8I8))
End Program