概要
本サンプルはFortran言語によりLAPACKルーチンDGBSVX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。
は帯行列です。
後方エラーと前方エラーの推定値、条件数、軸要素成長乗数と共に の均衡化についての情報が出力されます。
入力データ
（本ルーチンの詳細はDGBSVX のマニュアルページを参照）| このデータをダウンロード |
DGBSVX Example Program Data
4 2 1 2 :Values of N, NRHS, KL and KU
-0.23 2.54 -3.66
-6.98 2.46 -2.73 -2.13
2.56 2.46 4.07
-4.78 -3.82 :End of matrix A
4.42 -36.01
27.13 -31.67
-6.14 -1.16
10.50 -25.82 :End of matrix B
出力結果
（本ルーチンの詳細はDGBSVX のマニュアルページを参照）| この出力例をダウンロード |
DGBSVX Example Program Results
Solution(s)
1 2
1 -2.0000 1.0000
2 3.0000 -4.0000
3 1.0000 7.0000
4 -4.0000 -2.0000
Backward errors (machine-dependent)
1.1E-16 9.9E-17
Estimated forward error bounds (machine-dependent)
1.6E-14 1.9E-14
Estimate of reciprocal condition number
1.8E-02
A has not been equilibrated
Estimate of reciprocal pivot growth factor
1.0E+00
ソースコード
（本ルーチンの詳細はDGBSVX 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 dgbsvx_example
! DGBSVX 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: dgbsvx
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=dp) :: rcond
Integer :: i, ifail, info, j, k, kl, ku, ldab, ldafb, ldb, ldx, n, nrhs
Character (1) :: equed
! .. Local Arrays ..
Real (Kind=dp), Allocatable :: ab(:, :), afb(:, :), b(:, :), berr(:), &
c(:), ferr(:), r(:), work(:), x(:, :)
Integer, Allocatable :: ipiv(:), iwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, min
! .. Executable Statements ..
Write (nout, *) 'DGBSVX Example Program Results'
Write (nout, *)
Flush (nout)
! Skip heading in data file
Read (nin, *)
Read (nin, *) n, nrhs, kl, ku
ldb = n
ldx = n
ldab = kl + ku + 1
ldafb = ldab + kl
Allocate (ab(ldab,n), afb(ldafb,n), b(ldb,nrhs), berr(nrhs), c(n), &
ferr(nrhs), r(n), work(3*n), x(ldx,nrhs), ipiv(n), iwork(n))
! Read the band matrix A and B from data file
k = ku + 1
Read (nin, *)((ab(k+i-j,j),j=max(i-kl,1),min(i+ku,n)), i=1, n)
Read (nin, *)(b(i,1:nrhs), i=1, n)
! Solve the equations AX = B for X
Call dgbsvx('Equilibration', 'No transpose', n, kl, ku, nrhs, ab, ldab, &
afb, ldafb, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, &
work, iwork, info)
If ((info==0) .Or. (info==n+1)) Then
! Print solution, error bounds, condition number, the form
! of equilibration and the pivot growth factor
! 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=='R') Then
Write (nout, *) 'A has been row scaled as diag(R)*A'
Else If (equed=='C') Then
Write (nout, *) 'A has been column scaled as A*diag(C)'
Else If (equed=='B') Then
Write (nout, *) &
'A has been row and column scaled as diag(R)*A*diag(C)'
End If
Write (nout, *)
Write (nout, *) 'Estimate of reciprocal pivot growth factor'
Write (nout, 100) work(1)
If (info==n+1) Then
Write (nout, *)
Write (nout, *) 'The matrix A is singular to working precision'
End If
Else
Write (nout, 110) 'The (', info, ',', info, ')', &
' element of the factor U is zero'
End If
100 Format ((3X,1P,7E11.1))
110 Format (1X, A, I3, A, I3, A, A)
End Program