概要
本サンプルはFortran言語によりLAPACKルーチンDPPSVXを利用するサンプルプログラムです。
以下の式を解きます。
は対称正定値行列です。
解のエラー推定値、均衡化についての情報、スケーリングされた行列の条件数の逆数の推定値も合わせて出力されます。
入力データ
（本ルーチンの詳細はDPPSVX のマニュアルページを参照）| このデータをダウンロード |
DPPSVX Example Program Data
4 2 :Values of N and NRHS
4.16 -3.12 0.56 -0.10
5.03 -0.83 1.18
0.76 0.34
1.18 :End of matrix A
8.70 8.30
-13.35 2.13
1.89 1.61
-4.14 5.00 :End of matrix B
出力結果
（本ルーチンの詳細はDPPSVX のマニュアルページを参照）| この出力例をダウンロード |
DPPSVX Example Program Results
Solution(s)
1 2
1 1.0000 4.0000
2 -1.0000 3.0000
3 2.0000 2.0000
4 -3.0000 1.0000
Backward errors (machine-dependent)
6.7E-17 7.9E-17
Estimated forward error bounds (machine-dependent)
2.3E-14 2.3E-14
Estimate of reciprocal condition number
1.0E-02
A has not been equilibrated
ソースコード
（本ルーチンの詳細はDPPSVX 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 dppsvx_example
! DPPSVX 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: dppsvx
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) :: rcond
Integer :: i, ifail, info, j, ldb, ldx, n, nrhs
Character (1) :: equed
! .. Local Arrays ..
Real (Kind=dp), Allocatable :: afp(:), ap(:), b(:, :), berr(:), ferr(:), &
s(:), work(:), x(:, :)
Integer, Allocatable :: iwork(:)
! .. Executable Statements ..
Write (nout, *) 'DPPSVX Example Program Results'
Write (nout, *)
Flush (nout)
! Skip heading in data file
Read (nin, *)
Read (nin, *) n, nrhs
ldb = n
ldx = n
Allocate (afp((n*(n+1))/2), ap((n*(n+1))/2), b(ldb,nrhs), berr(nrhs), &
ferr(nrhs), s(n), work(3*n), x(ldx,nrhs), iwork(n))
! Read the upper or lower triangular part of the matrix A from
! data file
If (uplo=='U') Then
Read (nin, *)((ap(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)
End If
! Read B from data file
Read (nin, *)(b(i,1:nrhs), i=1, n)
! Solve the equations AX = B for X
Call dppsvx('Equilibration', uplo, n, nrhs, ap, afp, equed, s, b, ldb, &
x, ldx, rcond, ferr, berr, work, iwork, info)
If ((info==0) .Or. (info==n+1)) Then
! Print solution, error bounds, condition number and the form
! of equilibration
! 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, nrhs, x, ldx, &
'Solution(s)', ifail)
Write (nout, *)
Write (nout, *) 'Backward errors (machine-dependent)'
Write (nout, 100) berr(1:nrhs)
Write (nout, *)
Write (nout, *) 'Estimated forward error bounds (machine-dependent)'
Write (nout, 100) ferr(1:nrhs)
Write (nout, *)
Write (nout, *) 'Estimate of reciprocal condition number'
Write (nout, 100) rcond
Write (nout, *)
If (equed=='N') Then
Write (nout, *) 'A has not been equilibrated'
Else If (equed=='Y') Then
Write (nout, *) &
'A has been row and column scaled as diag(S)*A*diag(S)'
End If
If (info==n+1) Then
Write (nout, *)
Write (nout, *) 'The matrix A is singular to working precision'
End If
Else
Write (nout, 110) 'The leading minor of order ', info, &
' is not positive definite'
End If
100 Format ((3X,1P,7E11.1))
110 Format (1X, A, I3, A)
End Program