?heequb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?heequb

Computes row and column scaling factors intended to equilibrate a Hermitian indefinite matrix and reduce its condition number.

Syntax

call cheequb ( uplo , n , a , lda , s , scond , amax , work , info )

call zheequb ( uplo , n , a , lda , s , scond , amax , work , info )

Include Files

mkl.fi , mkl_lapack.f90

Description

cheequb zheequb

The routine computes row and column scalings intended to equilibrate a Hermitian indefinite matrix A and reduce its condition number (with respect to the two-norm).

The array s contains the scale factors, s(i) = 1/sqrt(A(i,i))s[i-1] = 1/sqrt(a_{i,i}) . These factors are chosen so that the scaled matrix B with elements b(i,j)=s(i)*a(i,j)*s(j)b_{i,j}=s[i-1]*a_{i,j}*s[j-1] has ones on the diagonal.

This choice of s puts the condition number of B within a factor n of the smallest possible condition number over all possible diagonal scalings.

Input Parameters

uplo

CHARACTER*1 . Must be ‘U’ or ‘L’ .

Indicates whether the upper or lower triangular part of A is stored:

If uplo = 'U' , the array a stores the upper triangular part of the matrix A .

If uplo = 'L' , the array a stores the lower triangular part of the matrix A .

n

INTEGER . The order of the matrix A ; n≥ 0 .

a , work

COMPLEX for cheequb

DOUBLE COMPLEX for zheequb .

Array a : size lda by * .

Contains the n -by- n symmetric indefinite matrix A whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

The second dimension of a must be at least max(1,n) .

work(*) is a workspace array. The dimension of work is at least max(1,3*n) .

lda

INTEGER . The leading dimension of a ; lda≥ max(1, m) .

Output Parameters

s

REAL for cheequb

DOUBLE PRECISION for zheequb .

Array, size ( n ).

If info = 0 , the array s contains the scale factors for A .

scond

REAL for cheequb

DOUBLE PRECISION for zheequb .

If info = 0 , scond contains the ratio of the smallest s(i)s[i] to the largest s(i)s[i] . If scond≥ 0.1 , and amax is neither too large nor too small, it is not worth scaling by s .

amax

REAL for cheequb

DOUBLE PRECISION for zheequb .

Absolute value of the largest element of the matrix A . If amax is very close to SMLNUM or BIGNUM , the matrix should be scaled.

info

INTEGER .

If info = 0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.
If info = i , the i -th diagonal element of A is nonpositive.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?heequb

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values