.TH "zsyequb.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
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.SH NAME
zsyequb.f \- 
.SH SYNOPSIS
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.SS "Functions/Subroutines"

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.ti -1c
.RI "subroutine \fBzsyequb\fP (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)"
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.RI "\fI\fBZSYEQUB\fP \fP"
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.SH "Function/Subroutine Documentation"
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.SS "subroutine zsyequb (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, complex*16, dimension( * )WORK, integerINFO)"

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\fBZSYEQUB\fP  
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\fBPurpose: \fP
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.nf
 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.
.fi
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.RE
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\fBParameters:\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          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.
.fi
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\fIN\fP 
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          N is INTEGER
          The order of the matrix A.  N >= 0.
.fi
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\fIA\fP 
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          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.
.fi
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\fILDA\fP 
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          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
.fi
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\fIS\fP 
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          S is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, S contains the scale factors for A.
.fi
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.br
\fISCOND\fP 
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          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.
.fi
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.br
\fIAMAX\fP 
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          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.
.fi
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\fIWORK\fP 
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          WORK is COMPLEX*16 array, dimension (3*N)
.fi
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\fIINFO\fP 
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          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.
.fi
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.RE
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\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
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Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
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\fBDate:\fP
.RS 4
November 2011 
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\fBReferences: \fP
.RS 4
Livne, O\&.E\&. and Golub, G\&.H\&., 'Scaling by Binormalization', 
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 Numerical Algorithms, vol\&. 35, no\&. 1, pp\&. 97-120, January 2004\&. 
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 DOI 10\&.1023/B:NUMA\&.0000016606\&.32820\&.69 
.br
 Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf 
.RE
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Definition at line 137 of file zsyequb\&.f\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.