SLA_GBRCOND
Purpose
SLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C)
where op2 is determined by CMODE as follows
CMODE = 1 op2(C) = C
CMODE = 0 op2(C) = I
CMODE = -1 op2(C) = inv(C)
The Skeel condition number cond(A) = norminf( |inv(A)||A| )
is computed by computing scaling factors R such that
diag(R)*A*op2(C) is row equilibrated and computing the standard
infinity-norm condition number.
where op2 is determined by CMODE as follows
CMODE = 1 op2(C) = C
CMODE = 0 op2(C) = I
CMODE = -1 op2(C) = inv(C)
The Skeel condition number cond(A) = norminf( |inv(A)||A| )
is computed by computing scaling factors R such that
diag(R)*A*op2(C) is row equilibrated and computing the standard
infinity-norm condition number.
Arguments
| TRANS |
(input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate Transpose = Transpose) |
| N |
(input) INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0. |
| KL |
(input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
|
| KU |
(input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
|
| AB |
(input) REAL array, dimension (LDAB,N)
On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the array AB as follows: AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) |
| LDAB |
(input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
|
| AFB |
(input) REAL array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
| LDAFB |
(input) INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
|
| IPIV |
(input) INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by SGBTRF; row i of the matrix was interchanged with row IPIV(i). |
| CMODE |
(input) INTEGER
Determines op2(C) in the formula op(A) * op2(C) as follows:
|
| CMODE |
= 1 op2(C) = C
|
| CMODE |
= 0 op2(C) = I
|
| CMODE |
= -1 op2(C) = inv(C)
|
| C |
(input) REAL array, dimension (N)
The vector C in the formula op(A) * op2(C).
|
| INFO |
(output) INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid. |
| WORK |
(input) REAL array, dimension (5*N).
Workspace.
|
| IWORK |
(input) INTEGER array, dimension (N).
Workspace.
|