?heequb

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?heequb

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

Syntax

lapack_int LAPACKE_cheequb( int matrix_layout, char uplo, lapack_int n, const lapack_complex_float* a, lapack_int lda, float* s, float* scond, float* amax );

lapack_int LAPACKE_zheequb( int matrix_layout, char uplo, lapack_int n, const lapack_complex_double* a, lapack_int lda, double* s, double* scond, double* amax );

Include Files

mkl.h

Description

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] = 1/sqrt(a_i,i). These factors are chosen so that the scaled matrix B with elements 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

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
uplo	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	The order of the matrix `A`; `n≥ 0`.
a	Array a: size max(1, lda*n) . Contains the n-by-n symmetric indefinite matrix `A` whose scaling factors are to be computed. Only the diagonal elements of `A` are referenced.
lda	The leading dimension of a; `lda≥ max(1, m)`.

Output Parameters

Array, size (n).

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

scond

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

amax

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

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i had an illegal value.

If info = i, the i-th diagonal element of A is nonpositive.

Parent topic: Matrix Equilibration: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?heequb

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

See Also