CTBT03
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
CTBT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b
when A is a triangular band matrix. Here A**T denotes the transpose
of A, A**H denotes the conjugate 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, A**T, or A**H, and EPS is the machine epsilon.
system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b
when A is a triangular band matrix. Here A**T denotes the transpose
of A, A**H denotes the conjugate 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, A**T, or A**H, and EPS is the machine epsilon.
Arguments
| UPLO |
(input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular = 'L': Lower triangular |
| TRANS |
(input) CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = s*b (No transpose) = 'T': A**T *x = s*b (Transpose) = 'C': A**H *x = s*b (Conjugate transpose) |
| DIAG |
(input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular = 'U': Unit triangular |
| N |
(input) INTEGER
The order of the matrix A. N >= 0.
|
| KD |
(input) INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0. |
| NRHS |
(input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0. |
| AB |
(input) COMPLEX 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). |
| LDAB |
(input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
|
| SCALE |
(input) REAL
The scaling factor s used in solving the triangular system.
|
| CNORM |
(input) REAL array, dimension (N)
The 1-norms of the columns of A, not counting the diagonal.
|
| TSCAL |
(input) REAL
The scaling factor used in computing the 1-norms in CNORM.
CNORM actually contains the column norms of TSCAL*A. |
| X |
(input) COMPLEX array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations. |
| LDX |
(input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
|
| B |
(input) COMPLEX array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations. |
| LDB |
(input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
|
| WORK |
(workspace) COMPLEX array, dimension (N)
|
| RESID |
(output) REAL
The maximum over the number of right hand sides of
norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ). |