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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 dtbt03 | ( | character | uplo, |
| character | trans, | ||
| character | diag, | ||
| integer | n, | ||
| integer | kd, | ||
| integer | nrhs, | ||
| double precision, dimension( ldab, * ) | ab, | ||
| integer | ldab, | ||
| double precision | scale, | ||
| double precision, dimension( * ) | cnorm, | ||
| double precision | tscal, | ||
| double precision, dimension( ldx, * ) | x, | ||
| integer | ldx, | ||
| double precision, dimension( ldb, * ) | b, | ||
| integer | ldb, | ||
| double precision, dimension( * ) | work, | ||
| double precision | resid | ||
| ) |
DTBT03
DTBT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b or A'*x = s*b when A is a
triangular band matrix. Here A' is the transpose of A, s is a scalar,
and x and b are N by NRHS matrices. The test ratio is the maximum
over the number of right hand sides of
norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' and EPS is the machine epsilon. | [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 operation applied to A.
= '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 order of the matrix A. N >= 0. |
| [in] | KD | KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0. |
| [in] | NRHS | NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. 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). |
| [in] | LDAB | LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1. |
| [in] | SCALE | SCALE is DOUBLE PRECISION
The scaling factor s used in solving the triangular system. |
| [in] | CNORM | CNORM is DOUBLE PRECISION array, dimension (N)
The 1-norms of the columns of A, not counting the diagonal. |
| [in] | TSCAL | TSCAL is DOUBLE PRECISION
The scaling factor used in computing the 1-norms in CNORM.
CNORM actually contains the column norms of TSCAL*A. |
| [in] | X | X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations. |
| [in] | LDX | LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N). |
| [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). |
| [out] | WORK | WORK is DOUBLE PRECISION array, dimension (N) |
| [out] | RESID | RESID is DOUBLE PRECISION
The maximum over the number of right hand sides of
norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ). |
Definition at line 172 of file dtbt03.f.
1.9.7