?la_gbrcond

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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 A^:code:`T` * X = B .

If trans = 'C' , the system has the form A^:code:`H` * 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 , DIMENSION n . 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 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) .

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 DIMENSION n .

Output Parameters

info

INTEGER .

If info = 0, the execution is successful.
If i > 0, the i -th parameter is invalid.

NOTE:

?gbtrf

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?la_gbrcond

Syntax

Include Files

Description

Input Parameters

Output Parameters