Intel® oneAPI Math Kernel Library Developer Reference - Fortran
Estimates the Skeel condition number for a symmetric indefinite matrix.
call sla_syrcond( uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork )
call dla_syrcond( uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork )
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.
CHARACTER*1. Must be 'U' or 'L'.
Specifies the triangle of A to store:
If uplo = 'U', the upper triangle of A is stored,
If uplo = 'L', the lower triangle of A is stored.
INTEGER. The number of linear equations, that is, the order of the matrix A; n≥ 0.
REAL for sla_syrcond
DOUBLE PRECISION for dla_syrcond
Arrays:
ab (lda,*) contains the n-by-n matrix A.
af (ldaf,*) contains the The block diagonal matrix D and the multipliers used to obtain the factor L or U as computed by ?sytrf.
The second dimension of a and af must be at least max(1, n).
c, DIMENSIONn. The vector C in the formula op(A) * op2(C).
work is a workspace array of DIMENSION (3*n).
INTEGER. The leading dimension of the array ab. lda≥max(1,n).
INTEGER. The leading dimension of af. ldaf≥max(1,n).
INTEGER.
Array with DIMENSIONn. Details of the interchanges and the block structure of D as determined by ?sytrf.
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).
INTEGER. Workspace array with DIMENSIONn.
INTEGER.
If info = 0, the execution is successful.
If i > 0, the i-th parameter is invalid.