.TH "ppequ" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ppequ \- ppequ: equilibration
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcppequ\fP (uplo, n, ap, s, scond, amax, info)"
.br
.RI "\fBCPPEQU\fP "
.ti -1c
.RI "subroutine \fBdppequ\fP (uplo, n, ap, s, scond, amax, info)"
.br
.RI "\fBDPPEQU\fP "
.ti -1c
.RI "subroutine \fBsppequ\fP (uplo, n, ap, s, scond, amax, info)"
.br
.RI "\fBSPPEQU\fP "
.ti -1c
.RI "subroutine \fBzppequ\fP (uplo, n, ap, s, scond, amax, info)"
.br
.RI "\fBZPPEQU\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cppequ (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, integer info)"

.PP
\fBCPPEQU\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CPPEQU computes row and column scalings intended to equilibrate a
 Hermitian positive definite matrix A in packed storage 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
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangle of the Hermitian matrix A, packed
          columnwise in a linear array\&.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A\&.
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine dppequ (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)"

.PP
\fBDPPEQU\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DPPEQU computes row and column scalings intended to equilibrate a
 symmetric positive definite matrix A in packed storage 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
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The upper or lower triangle of the symmetric matrix A, packed
          columnwise in a linear array\&.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, S contains the scale factors for A\&.
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
          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
.PP
.br
\fIAMAX\fP 
.PP
.nf
          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
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine sppequ (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, integer info)"

.PP
\fBSPPEQU\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SPPEQU computes row and column scalings intended to equilibrate a
 symmetric positive definite matrix A in packed storage 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
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is REAL array, dimension (N*(N+1)/2)
          The upper or lower triangle of the symmetric matrix A, packed
          columnwise in a linear array\&.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is REAL array, dimension (N)
          If INFO = 0, S contains the scale factors for A\&.
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine zppequ (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)"

.PP
\fBZPPEQU\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZPPEQU computes row and column scalings intended to equilibrate a
 Hermitian positive definite matrix A in packed storage 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
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
          The upper or lower triangle of the Hermitian matrix A, packed
          columnwise in a linear array\&.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, S contains the scale factors for A\&.
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
          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
.PP
.br
\fIAMAX\fP 
.PP
.nf
          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
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.