Visible to Intel only — GUID: GUID-FAD7A2ED-0194-4C4C-836E-F321AF3C2994
Visible to Intel only — GUID: GUID-FAD7A2ED-0194-4C4C-836E-F321AF3C2994
?la_gbrcond
Estimates the Skeel condition number for a general banded matrix.
Syntax
call sla_gbrcond( trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork )
call dla_gbrcond( trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork )
Include Files
- mkl.fi
Description
The function estimates the Skeel condition number of
op(A) * op2(C)
where
the cmode parameter determines op2 as follows:
cmode Value |
op2(C) |
---|---|
1 |
C |
0 |
I |
-1 |
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 by computing the standard infinity-norm condition number.
Input Parameters
- trans
-
CHARACTER*1. Must be 'N' or 'T' or 'C'.
Specifies the form of the system of equations:
If trans = 'N', the system has the form A*X = B.
If trans = 'T', the system has the form AT*X = B.
If trans = 'C', the system has the form AH*X = B.
- n
-
INTEGER. The number of linear equations, that is, the order of the matrix A; n≥ 0.
- kl
-
INTEGER. The number of subdiagonals within the band of A; kl≥ 0.
- ku
-
INTEGER. The number of superdiagonals within the band of A; ku≥ 0.
- ab, afb, c, work
-
REAL for sla_gbrcond
DOUBLE PRECISION for dla_gbrcond
Arrays:
ab(ldab,*) contains the original band matrix A stored in rows from 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)
afb(ldafb,*) contains details of the LU factorization of the band matrix A, as returned by ?gbtrf. 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.
c, DIMENSIONn. The vector C in the formula op(A) * op2(C).
work is a workspace array of DIMENSION (5*n).
The second dimension of ab and afb must be at least max(1, n).
- ldab
-
INTEGER. The leading dimension of the array ab. ldab≥kl+ku+1.
- ldafb
-
INTEGER. The leading dimension of afb. ldafb≥2*kl+ku+1.
- ipiv
-
INTEGER.
Array with DIMENSIONn. The pivot indices from the factorization A = P*L*U as computed by ?gbtrf. Row i of the matrix was interchanged with row ipiv(i).
- cmode
-
INTEGER. Determines op2(C) in the formula op(A) * op2(C) as follows:
If cmode = 1, op2(C) = C.
If cmode = 0, op2(C) = I.
If cmode = -1, op2(C) = inv(C).
- iwork
-
INTEGER. Workspace array with DIMENSIONn.
Output Parameters
- info
-
INTEGER.
If info = 0, the execution is successful.
If i > 0, the i-th parameter is invalid.