概要
本サンプルはFortran言語によりLAPACKルーチンDSYGVXを利用するサンプルプログラムです。
一般化対称固有値問題
の半開区間 ![$ (-1.0, 1.0]$](img/img97.gif){kind=small}
の固有値と対応する固有ベクトルを求めます。
DSYGVDの例題プログラムは一般化対称固有値問題
の解き方を示します。
入力データ
（本ルーチンの詳細はDSYGVX 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
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DSYGVX Example Program Data
4 :Value of N
-1.0 1.0 :Values of VL and VU
0.24 0.39 0.42 -0.16
-0.11 0.79 0.63
-0.25 0.48
-0.03 :End of matrix A
4.16 -3.12 0.56 -0.10
5.03 -0.83 1.09
0.76 0.34
1.18 :End of matrix B
出力結果
（本ルーチンの詳細はDSYGVX 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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DSYGVX Example Program Results
Number of eigenvalues found = 2
Eigenvalues
-0.4548 0.1001
Selected eigenvectors
1 2
1 -0.3080 -0.4469
2 -0.5329 -0.0371
3 0.3496 0.0505
4 0.6211 0.4743
ソースコード
（本ルーチンの詳細はDSYGVX 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 99 100 101 102 103 104 105 106 107 108 109
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Program dsygvx_example
! DSYGVX Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use lapack_example_aux, Only: nagf_blas_damax_val, &
nagf_file_print_matrix_real_gen
Use lapack_interfaces, Only: dsygvx
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Real (Kind=dp), Parameter :: zero = 0.0_dp
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=dp) :: abstol, r, vl, vu
Integer :: i, ifail, il, info, iu, k, lda, ldb, ldz, lwork, m, n
! .. Local Arrays ..
Real (Kind=dp), Allocatable :: a(:, :), b(:, :), w(:), work(:), z(:, :)
Real (Kind=dp) :: dummy(1)
Integer, Allocatable :: iwork(:), jfail(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, nint
! .. Executable Statements ..
Write (nout, *) 'DSYGVX Example Program Results'
Write (nout, *)
! Skip heading in data file
Read (nin, *)
Read (nin, *) n
lda = n
ldb = n
ldz = n
m = n
Allocate (a(lda,n), b(ldb,n), w(n), z(ldz,m), 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 dsygvx(1, 'Vectors', 'Values in range', 'Upper', n, a, lda, b, ldb, &
vl, vu, il, iu, abstol, m, w, z, ldz, dummy, lwork, iwork, jfail, &
info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+3)*n, nint(dummy(1)))
Allocate (work(lwork))
! Read the upper triangular parts of the matrices A and B
Read (nin, *)(a(i,i:n), i=1, n)
Read (nin, *)(b(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 generalized symmetric eigenvalue problem
! A*x = lambda*B*x (ITYPE = 1)
Call dsygvx(1, 'Vectors', 'Values in range', 'Upper', n, a, lda, b, ldb, &
vl, vu, il, iu, abstol, m, w, z, ldz, work, lwork, 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)
! Normalize the eigenvectors, largest positive
Do i = 1, m
Call nagf_blas_damax_val(n, z(1,i), 1, k, r)
If (z(k,i)<zero) Then
z(1:n, i) = -z(1:n, i)
End If
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_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'
Else
Write (nout, 100) 'Failure in DSYGVX. 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