概要
本サンプルはFortran言語によりLAPACKルーチンZHEEVRを利用するサンプルプログラムです。
エルミート行列の指標が![$ [2, 3]$](img/img78.gif){kind=small}
の範囲の固有値と対応する固有ベクトルを求めます。
必要とされ利用されたワークスペースの情報も合わせて出力されます。
入力データ
（本ルーチンの詳細はZHEEVR のマニュアルページを参照）1 2 3 4 5 6 7 8
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ZHEEVR Example Program Data
4 2 3 :Values of N, IL and IU
(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ZHEEVR 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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ZHEEVR Example Program Results
Selected eigenvalues
-0.6886 1.1412
Warning: Floating invalid operation occurred
Warning: Floating divide by zero occurred
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ZHEEVR 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。
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
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Program zheevr_example
! ZHEEVR 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: zheevr
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, liwork, lrwork, lwork, &
m, n
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: a(:, :), work(:), z(:, :)
Complex (Kind=dp) :: dummy(1)
Real (Kind=dp) :: rdum(1)
Real (Kind=dp), Allocatable :: rwork(:), w(:)
Integer :: idum(1)
Integer, Allocatable :: isuppz(:), iwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, cmplx, conjg, max, maxloc, nint, real
! .. Executable Statements ..
Write (nout, *) 'ZHEEVR Example Program Results'
Write (nout, *)
! Skip heading in data file and read N and the lower and upper
! indices of the smallest and largest eigenvalues to be found
Read (nin, *)
Read (nin, *) n, il, iu
lda = n
ldz = n
m = n
Allocate (a(lda,n), z(ldz,m), w(n), isuppz(2*m))
! Use routine workspace query to get optimal workspace.
lwork = -1
liwork = -1
lrwork = -1
Call zheevr('Vectors', 'I', 'Upper', n, a, lda, vl, vu, il, iu, abstol, &
m, w, z, ldz, isuppz, dummy, lwork, rdum, lrwork, idum, liwork, info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+1)*n, nint(real(dummy(1))))
lrwork = max(24*n, nint(rdum(1)))
liwork = max(10*n, idum(1))
Allocate (work(lwork), rwork(lrwork), iwork(liwork))
! Read the upper triangular part of the matrix A from data file
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 symmetric eigenvalue problem
Call zheevr('Vectors', 'I', 'Upper', n, a, lda, vl, vu, il, iu, abstol, &
m, w, z, ldz, isuppz, work, lwork, rwork, lrwork, iwork, liwork, info)
If (info==0) Then
! Print solution
Write (nout, *) 'Selected eigenvalues'
Write (nout, 100) 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)
Else
Write (nout, 110) 'Failure in ZHEEVR. INFO =', info
End If
100 Format (3X, (8F8.4))
110 Format (1X, A, I5)
End Program