概要
本サンプルはFortran言語によりLAPACKルーチンZHPEVX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ZHPEVX のマニュアルページを参照）1 2 3 4 5 6 7 8 9
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ZHPEVX 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ZHPEVX のマニュアルページを参照）1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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ZHPEVX 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ZHPEVX 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。
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Program zhpevx_example
! ZHPEVX Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use blas_interfaces, Only: dznrm2
Use lapack_example_aux, Only: nagf_file_print_matrix_complex_gen
Use lapack_interfaces, Only: zhpevx
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Real (Kind=dp), Parameter :: zero = 0.0E+0_dp
Integer, Parameter :: nin = 5, nout = 6
Character (1), Parameter :: uplo = 'U'
! .. Local Scalars ..
Complex (Kind=dp) :: scal
Real (Kind=dp) :: abstol, vl, vu
Integer :: i, ifail, il, info, iu, j, k, ldz, m, n
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: ap(:), work(:), z(:, :)
Real (Kind=dp), Allocatable :: rwork(:), w(:)
Integer, Allocatable :: iwork(:), jfail(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, conjg, maxloc
! .. Executable Statements ..
Write (nout, *) 'ZHPEVX Example Program Results'
Write (nout, *)
! Skip heading in data file
Read (nin, *)
Read (nin, *) n
ldz = n
m = n
Allocate (ap((n*(n+1))/2), work(2*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,
! and read the upper or lower triangular part of the matrix A
! from data file
Read (nin, *) vl, vu
If (uplo=='U') Then
Read (nin, *)((ap(i+(j*(j-1))/2),j=i,n), i=1, n)
Else If (uplo=='L') Then
Read (nin, *)((ap(i+((2*n-j)*(j-1))/2),j=1,i), i=1, n)
End If
! 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 zhpevx('Vectors', 'Values in range', uplo, n, ap, vl, vu, il, iu, &
abstol, m, w, z, ldz, work, 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, largest element real
Do i = 1, m
rwork(1:n) = abs(z(1:n,i))
k = maxloc(rwork(1:n), 1)
scal = conjg(z(k,i))/abs(z(k,i))/dznrm2(n, z(1,i), 1)
z(1:n, i) = z(1:n, i)*scal
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 ZHPEVX. INFO =', info
End If
100 Format (1X, A, I5)
110 Format (3X, (8F8.4))
120 Format (3X, (8I8))
End Program