# zsyequb.f(3) [centos man page]

```zsyequb.f(3)							      LAPACK							      zsyequb.f(3)

NAME
zsyequb.f -

SYNOPSIS
Functions/Subroutines
subroutine zsyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
ZSYEQUB

Function/Subroutine Documentation
subroutine zsyequb (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double
precisionSCOND, double precisionAMAX, complex*16, dimension( * )WORK, integerINFO)
ZSYEQUB

Purpose:

ZSYEQUB computes row and column scalings intended to equilibrate a
symmetric matrix A and reduce its condition number
(with respect to the two-norm).  S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) 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.

Parameters:
UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U':  Upper triangular, form is A = U*D*U**T;
= 'L':  Lower triangular, form is A = L*D*L**T.

N

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

A

A is COMPLEX*16 array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling
factors are to be computed.  Only the diagonal elements of A
are referenced.

LDA

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

S

S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is DOUBLE PRECISION
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

AMAX is DOUBLE PRECISION
Absolute value of largest matrix element.	If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.

WORK

WORK is COMPLEX*16 array, dimension (3*N)

INFO

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.

Author:
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:
November 2011

References:
Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf

Definition at line 137 of file zsyequb.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						      zsyequb.f(3)```

## Check Out this Related Man Page

```csyequb.f(3)							      LAPACK							      csyequb.f(3)

NAME
csyequb.f -

SYNOPSIS
Functions/Subroutines
subroutine csyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
CSYEQUB

Function/Subroutine Documentation
subroutine csyequb (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )S, realSCOND, realAMAX, complex,
dimension( * )WORK, integerINFO)
CSYEQUB

Purpose:

CSYEQUB computes row and column scalings intended to equilibrate a
symmetric matrix A and reduce its condition number
(with respect to the two-norm).  S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) 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.

Parameters:
UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U':  Upper triangular, form is A = U*D*U**T;
= 'L':  Lower triangular, form is A = L*D*L**T.

N

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

A

A is COMPLEX array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling
factors are to be computed.  Only the diagonal elements of A
are referenced.

LDA

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

S

S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

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

AMAX is REAL
Absolute value of largest matrix element.	If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.

WORK

WORK is COMPLEX array, dimension (3*N)

INFO

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.

Author:
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:
November 2011

References:
Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf

Definition at line 137 of file csyequb.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						      csyequb.f(3)```
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