概要
本サンプルはFortran言語によりLAPACKルーチンZHPGVXを利用するサンプルプログラムです。
一般化エルミート固有値問題
の半開区間 ![$ (-3, 3]$](img/img71.gif){kind=small}
の全ての固有値と対応する固有ベクトルを求めます。
及び
ZHPGVD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ZHPGVX のマニュアルページを参照）| このデータをダウンロード |
ZHPGVX Example Program Data
4 :Value of N
-3.0 3.0 :Values of VL and VU
(-7.36, 0.00) ( 0.77, -0.43) (-0.64, -0.92) ( 3.01, -6.97)
( 3.49, 0.00) ( 2.19, 4.45) ( 1.90, 3.73)
( 0.12, 0.00) ( 2.88, -3.17)
(-2.54, 0.00) :End of matrix A
( 3.23, 0.00) ( 1.51, -1.92) ( 1.90, 0.84) ( 0.42, 2.50)
( 3.58, 0.00) (-0.23, 1.11) (-1.18, 1.37)
( 4.09, 0.00) ( 2.33, -0.14)
( 4.29, 0.00) :End of matrix B
出力結果
（本ルーチンの詳細はZHPGVX のマニュアルページを参照）| この出力例をダウンロード |
ZHPGVX Example Program Results
Number of eigenvalues found = 2
Eigenvalues
-2.9936 0.5047
Selected eigenvectors
1 2
1 -0.6626 0.2835
0.2258 -0.5806
2 -0.1164 -0.3769
-0.0178 -0.3194
3 0.9098 -0.3338
-0.0000 -0.0134
4 -0.6120 0.6663
-0.5348 0.0000
ソースコード
（本ルーチンの詳細はZHPGVX 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。
| このソースコードをダウンロード |
Program zhpgvx_example
! ZHPGVX 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: zhpgvx
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(:), bp(:), work(:), z(:, :)
Real (Kind=dp), Allocatable :: rwork(:), w(:)
Integer, Allocatable :: iwork(:), jfail(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, conjg, maxloc
! .. Executable Statements ..
Write (nout, *) 'ZHPGVX 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), bp((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 parts of the matrices A
! and B 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)
Read (nin, *)((bp(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)
Read (nin, *)((bp(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 generalized Hermitian eigenvalue problem
! A*x = lambda*B*x (itype = 1)
Call zhpgvx(1, 'Vectors', 'Values in range', uplo, n, ap, bp, 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)
! 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))
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 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 ZHPGVX. 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