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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine dtbt05 | ( | character | uplo, |
| character | trans, | ||
| character | diag, | ||
| integer | n, | ||
| integer | kd, | ||
| integer | nrhs, | ||
| double precision, dimension( ldab, * ) | ab, | ||
| integer | ldab, | ||
| double precision, dimension( ldb, * ) | b, | ||
| integer | ldb, | ||
| double precision, dimension( ldx, * ) | x, | ||
| integer | ldx, | ||
| double precision, dimension( ldxact, * ) | xact, | ||
| integer | ldxact, | ||
| double precision, dimension( * ) | ferr, | ||
| double precision, dimension( * ) | berr, | ||
| double precision, dimension( * ) | reslts | ||
| ) |
DTBT05
DTBT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
triangular band matrix.
RESLTS(1) = test of the error bound
= norm(X - XACT) / ( norm(X) * FERR )
A large value is returned if this ratio is not less than one.
RESLTS(2) = residual from the iterative refinement routine
= the maximum of BERR / ( NZ*EPS + (*) ), where
(*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
and NZ = max. number of nonzeros in any row of A, plus 1 | [in] | UPLO | UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular |
| [in] | TRANS | TRANS is CHARACTER*1
Specifies the form of the system of equations.
= 'N': A * X = B (No transpose)
= 'T': A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose) |
| [in] | DIAG | DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular |
| [in] | N | N is INTEGER
The number of rows of the matrices X, B, and XACT, and the
order of the matrix A. N >= 0. |
| [in] | KD | KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0. |
| [in] | NRHS | NRHS is INTEGER
The number of columns of the matrices X, B, and XACT.
NRHS >= 0. |
| [in] | AB | AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1. |
| [in] | LDAB | LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1. |
| [in] | B | B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations. |
| [in] | LDB | LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N). |
| [in] | X | X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors. Each vector is stored as a
column of the matrix X. |
| [in] | LDX | LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N). |
| [in] | XACT | XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
The exact solution vectors. Each vector is stored as a
column of the matrix XACT. |
| [in] | LDXACT | LDXACT is INTEGER
The leading dimension of the array XACT. LDXACT >= max(1,N). |
| [in] | FERR | FERR is DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution vector
X. If XTRUE is the true solution, FERR bounds the magnitude
of the largest entry in (X - XTRUE) divided by the magnitude
of the largest entry in X. |
| [in] | BERR | BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector (i.e., the smallest relative change in any entry of A
or B that makes X an exact solution). |
| [out] | RESLTS | RESLTS is DOUBLE PRECISION array, dimension (2)
The maximum over the NRHS solution vectors of the ratios:
RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) ) |
Definition at line 187 of file dtbt05.f.
1.9.7