?la_gbrcond_c

Computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.

Syntax

FORTRAN 77:

call cla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork )

call zla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork )

Include Files

• Fortran: mkl.fi
• C: mkl.h

Description

The function computes the infinity norm condition number of

`op(A) * inv(diag(c))`

where the c is a REAL vector for cla_gbrcond_c and a DOUBLE PRECISION vector for zla_gbrcond_c.

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 (No transpose)

If `trans = 'T'`, the system has the form AT*X = B (Transpose)

If `trans = 'C'`, the system has the form AH*X = B (Conjugate Transpose = Transpose)

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, work

COMPLEX for cla_gbrcond_c

DOUBLE COMPLEX for zla_gbrcond_c

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`.

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 DIMENSION n. 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)`.

c, rwork

REAL for cla_gbrcond_c

DOUBLE PRECISION for zla_gbrcond_c

Array c with DIMENSION n. The vector c in the formula

`op(A) * inv(diag(c))`.

Array rwork with DIMENSION n is a workspace.

capply

LOGICAL. If .TRUE., then the function uses the vector c from the formula

`op(A) * inv(diag(c))`.

Output Parameters

info

INTEGER.

If info = 0, the execution is successful.

If i > 0, the i-th parameter is invalid.