概要
本サンプルはFortran言語によりLAPACKルーチンDSPGVD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
の全ての固有値と固有ベクトルを求めます。
の条件数の推定値、計算された固有値と固有ベクトルの誤差限界の近似値も合わせて求めます。DSPGV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DSPGVD のマニュアルページを参照）| このデータをダウンロード |
DSPGVD Example Program Data
4 :Value of N
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DSPGVD のマニュアルページを参照）| この出力例をダウンロード |
DSPGVD Example Program Results
Eigenvalues
-3.5411 -0.3347 0.2983 2.2544
Estimate of reciprocal condition number for B
5.8E-03
Error estimates for the eigenvalues
1.4E-13 1.7E-14 1.6E-14 9.1E-14
ソースコード
（本ルーチンの詳細はDSPGVD 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 dspgvd_example
! DSPGVD Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use lapack_interfaces, Only: dlansp, dspgvd, dtpcon
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
Character (1), Parameter :: uplo = 'U'
! .. Local Scalars ..
Real (Kind=dp) :: anorm, bnorm, eps, rcond, rcondb, t1
Integer :: aplen, i, info, j, liwork, lwork, n
! .. Local Arrays ..
Real (Kind=dp), Allocatable :: ap(:), bp(:), eerbnd(:), w(:), work(:)
Real (Kind=dp) :: dummy(1, 1)
Integer :: idum(1)
Integer, Allocatable :: iwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, epsilon, max, nint
! .. Executable Statements ..
Write (nout, *) 'DSPGVD Example Program Results'
Write (nout, *)
! Skip heading in data file
Read (nin, *)
Read (nin, *) n
aplen = (n*(n+1))/2
Allocate (ap(aplen), bp(aplen), eerbnd(n), w(n))
! Use routine workspace query to get optimal workspace.
lwork = -1
liwork = -1
Call dspgvd(2, 'No vectors', uplo, n, ap, bp, w, dummy, n, dummy, lwork, &
idum, liwork, info)
! Make sure that there is at least minimum workspace.
lwork = max(3*n, nint(dummy(1,1)))
liwork = max(n, idum(1))
Allocate (work(lwork), iwork(liwork))
! Read the upper or lower triangular parts of the matrices A and
! B from data file
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
! Compute the one-norms of the symmetric matrices A and B
anorm = dlansp('One norm', uplo, n, ap, work)
bnorm = dlansp('One norm', uplo, n, bp, work)
! Solve the generalized symmetric eigenvalue problem
! A*B*x = lambda*x (itype = 2)
! In the following call the 9th argument is set to n rather
! than 1 to avoid an incorrect error message in some vendor
! versions of LAPACK.
Call dspgvd(2, 'No vectors', uplo, n, ap, bp, w, dummy, n, work, lwork, &
iwork, liwork, info)
If (info==0) Then
! Print solution
Write (nout, *) 'Eigenvalues'
Write (nout, 100) w(1:n)
! Call DTPCON to estimate the reciprocal condition
! number of the Cholesky factor of B. Note that:
! cond(B) = 1/rcond**2. DTPCON requires WORK and IWORK to be
! of length at least 3*n and n respectively
Call dtpcon('One norm', uplo, 'Non-unit', n, bp, rcond, work, iwork, &
info)
! Print the reciprocal condition number of B
rcondb = rcond**2
Write (nout, *)
Write (nout, *) 'Estimate of reciprocal condition number for B'
Write (nout, 110) rcondb
! Get the machine precision, eps, and if rcondb is not less
! than eps**2, compute error estimates for the eigenvalues
eps = epsilon(1.0E0_dp)
If (rcond>=eps) Then
t1 = anorm*bnorm
Do i = 1, n
eerbnd(i) = eps*(t1+abs(w(i))/rcondb)
End Do
! Print the approximate error bounds for the eigenvalues
Write (nout, *)
Write (nout, *) 'Error estimates for the eigenvalues'
Write (nout, 110) eerbnd(1:n)
Else
Write (nout, *)
Write (nout, *) 'B is very ill-conditioned, error ', &
'estimates have not been computed'
End If
Else If (info>n .And. info<=2*n) Then
i = info - n
Write (nout, 120) 'The leading minor of order ', i, &
' of B is not positive definite'
Else
Write (nout, 130) 'Failure in DSPGVD. INFO =', info
End If
100 Format (3X, (6F11.4))
110 Format (4X, 1P, 6E11.1)
120 Format (1X, A, I4, A)
130 Format (1X, A, I4)
End Program