概要
本サンプルはFortran言語によりLAPACKルーチンZHBGVXを利用するサンプルプログラムです。
一般化帯エルミート固有値問題
で半開区間 ![$ (0.0, 2.0]$](img/img101.gif){kind=small}
の固有値と対応する固有ベクトルを求めます。
及び
入力データ
（本ルーチンの詳細はZHBGVX 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
| このデータをダウンロード |
ZHBGVX Example Program Data
4 2 1 :Values of N, KA and KB
0.0 2.0 :Values of VL and VU
(-1.13, 0.00) ( 1.94,-2.10) (-1.40, 0.25)
(-1.91, 0.00) (-0.82,-0.89) (-0.67, 0.34)
(-1.87, 0.00) (-1.10,-0.16)
( 0.50, 0.00) :End of matrix A
( 9.89, 0.00) ( 1.08,-1.73)
( 1.69, 0.00) (-0.04, 0.29)
( 2.65, 0.00) (-0.33, 2.24)
( 2.17, 0.00) :End of matrix B
出力結果
（本ルーチンの詳細はZHBGVX 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
| この出力例をダウンロード |
ZHBGVX Example Program Results
Number of eigenvalues found = 2
Eigenvalues
0.1603 1.7712
Selected eigenvectors
1 2
1 0.1908 0.0494
0.0137 -0.0045
2 0.1413 0.2505
0.1012 0.4427
3 -0.0437 -0.9705
-0.0905 0.0679
4 -0.2135 0.0606
0.2880 -1.3227
ソースコード
（本ルーチンの詳細はZHBGVX 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 97 98 99 100
| このソースコードをダウンロード |
Program zhbgvx_example
! ZHBGVX Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use lapack_example_aux, Only: nagf_file_print_matrix_complex_gen
Use lapack_interfaces, Only: zhbgvx
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 ..
Real (Kind=dp) :: abstol, vl, vu
Integer :: i, ifail, il, info, iu, j, ka, kb, ldab, ldbb, ldq, ldz, m, n
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: ab(:, :), bb(:, :), q(:, :), work(:), &
z(:, :)
Real (Kind=dp), Allocatable :: rwork(:), w(:)
Integer, Allocatable :: iwork(:), jfail(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, min
! .. Executable Statements ..
Write (nout, *) 'ZHBGVX Example Program Results'
Write (nout, *)
! Skip heading in data file
Read (nin, *)
Read (nin, *) n, ka, kb
ldab = ka + 1
ldbb = kb + 1
ldq = n
ldz = n
m = n
Allocate (ab(ldab,n), bb(ldbb,n), q(ldq,n), work(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 parts of the matrices A
! and B from data file
Read (nin, *) vl, vu
If (uplo=='U') Then
Read (nin, *)((ab(ka+1+i-j,j),j=i,min(n,i+ka)), i=1, n)
Read (nin, *)((bb(kb+1+i-j,j),j=i,min(n,i+kb)), i=1, n)
Else If (uplo=='L') Then
Read (nin, *)((ab(1+i-j,j),j=max(1,i-ka),i), i=1, n)
Read (nin, *)((bb(1+i-j,j),j=max(1,i-kb),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 generalized symmetric eigenvalue problem
! A*x = lambda*B*x
Call zhbgvx('Vectors', 'Values in range', uplo, n, ka, kb, ab, ldab, bb, &
ldbb, q, ldq, vl, vu, il, iu, abstol, m, w, z, ldz, work, rwork, &
iwork, jfail, info)
If (info>=0 .And. info<=n) Then
! Print solution
Write (nout, 100) 'Number of eigenvalues found =', m
Write (nout, *)
Write (nout, *) 'Eigenvalues'
Write (nout, 110) w(1:m)
Flush (nout)
! 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 If (info>n .And. info<=2*n) Then
i = info - n
Write (nout, 130) 'The leading minor of order ', i, &
' of B is not positive definite'
Else
Write (nout, 100) 'Failure in ZHBGVX. INFO =', info
End If
100 Format (1X, A, I5)
110 Format (3X, (8F8.4))
120 Format (3X, (8I8))
130 Format (1X, A, I4, A)
End Program