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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine spbt05 | ( | character | UPLO, |
| integer | N, | ||
| integer | KD, | ||
| integer | NRHS, | ||
| real, dimension( ldab, * ) | AB, | ||
| integer | LDAB, | ||
| real, dimension( ldb, * ) | B, | ||
| integer | LDB, | ||
| real, dimension( ldx, * ) | X, | ||
| integer | LDX, | ||
| real, dimension( ldxact, * ) | XACT, | ||
| integer | LDXACT, | ||
| real, dimension( * ) | FERR, | ||
| real, dimension( * ) | BERR, | ||
| real, dimension( * ) | RESLTS | ||
| ) |
SPBT05
SPBT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
symmetric 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 upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower 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 REAL array, dimension (LDAB,N)
The upper or lower triangle of the symmetric 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). |
| [in] | LDAB | LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1. |
| [in] | B | B is REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 + (*) ) |
1.9.4