概要
本サンプルはFortran言語によりLAPACKルーチンDSBGVXを利用するサンプルプログラムです。
帯対称固有値問題
の半開区間 ![$ (0.0, 1.0]$](img/img93.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DSBGVX 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
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DSBGVX Example Program Data
4 2 1 :Values of N, KA and KB
0.0 1.0 :Values of VL and VU
0.24 0.39 0.42
-0.11 0.79 0.63
-0.25 0.48
-0.03 :End of matrix A
2.07 0.95
1.69 -0.29
0.65 -0.33
1.17 :End of matrix B
出力結果
（本ルーチンの詳細はDSBGVX のマニュアルページを参照）1 2 3 4 5 6 7 8 9 10 11 12
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DSBGVX Example Program Results
Number of eigenvalues found = 1
Eigenvalues
0.0992
Selected eigenvectors
1
1 0.6729
2 -0.1009
3 0.0155
4 -0.3806
ソースコード
（本ルーチンの詳細はDSBGVX 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 dsbgvx_example
! DSBGVX Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use lapack_example_aux, Only: nagf_file_print_matrix_real_gen
Use lapack_interfaces, Only: dsbgvx
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 ..
Real (Kind=dp), Allocatable :: ab(:, :), bb(:, :), q(:, :), w(:), &
work(:), z(:, :)
Integer, Allocatable :: iwork(:), jfail(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, min
! .. Executable Statements ..
Write (nout, *) 'DSBGVX 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), w(n), work(7*n), z(ldz,m), &
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 dsbgvx('Vectors', 'Values in range', uplo, n, ka, kb, ab, ldab, bb, &
ldbb, q, ldq, vl, vu, il, iu, abstol, m, w, z, ldz, work, 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_real_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'
Write (nout, 100) 'Failure in DSBGVX. 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