SYEQUB - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void syequb(char *uplo, integer *n, T *a, integer *lda, T *s, T *scond, T *amax, T *work, integer *info)#

SYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A.

Purpose:

  SYEQUB computes row and column scalings intended to equilibrate a
  symmetric matrix A (with respect to the Euclidean norm) and reduce
  its condition number. The scale factors S are computed by the BIN
  algorithm (see references) so that the scaled matrix B with elements
  B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
  the smallest possible condition number over all possible diagonal
  scalings.
Parameters:
  • UPLO[in]

    UPLO is CHARACTER*1

    = ‘U’: Upper triangle of A is stored;

    = ‘L’: Lower triangle of A is stored.
  • N[in]

    N is INTEGER

    The order of the matrix A. N >= 0.

  • A[in]

    A is REAL array, dimension (LDA,N)

    The N-by-N symmetric matrix whose scaling factors are to be computed.

  • LDA[in]

    LDA is INTEGER

    The leading dimension of the array A. LDA >= fla_max(1,N).

  • S[out]

    S is REAL array, dimension (N)

    If INFO = 0, S contains the scale factors for A.

  • SCOND[out]

    SCOND is REAL

    If INFO = 0, S 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[out]

    AMAX is REAL

    Largest absolute value of any matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.

  • WORK[out] WORK is REAL array, dimension (2*N)

  • INFO[out]

    INFO is INTEGER

    = 0: successful exit

    < 0: if INFO = -i, the i-th argument had an illegal value

    > 0: if INFO = i, the i-th diagonal element is nonpositive.

template<typename T, typename Ta>
void syequb(char *uplo, integer *n, T *a, integer *lda, Ta *s, Ta *scond, Ta *amax, T *work, integer *info)#