.TH "laqhp" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laqhp \- laqhp: row/col scale matrix
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclaqhp\fP (uplo, n, ap, s, scond, amax, equed)"
.br
.RI "\fBCLAQHP\fP scales a Hermitian matrix stored in packed form\&. "
.ti -1c
.RI "subroutine \fBclaqsp\fP (uplo, n, ap, s, scond, amax, equed)"
.br
.RI "\fBCLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. "
.ti -1c
.RI "subroutine \fBdlaqsp\fP (uplo, n, ap, s, scond, amax, equed)"
.br
.RI "\fBDLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. "
.ti -1c
.RI "subroutine \fBslaqsp\fP (uplo, n, ap, s, scond, amax, equed)"
.br
.RI "\fBSLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. "
.ti -1c
.RI "subroutine \fBzlaqhp\fP (uplo, n, ap, s, scond, amax, equed)"
.br
.RI "\fBZLAQHP\fP scales a Hermitian matrix stored in packed form\&. "
.ti -1c
.RI "subroutine \fBzlaqsp\fP (uplo, n, ap, s, scond, amax, equed)"
.br
.RI "\fBZLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. "
.in -1c
.SH "Detailed Description"
.PP 

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

.PP
\fBCLAQHP\fP scales a Hermitian matrix stored in packed form\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CLAQHP equilibrates a Hermitian matrix A using the scaling factors
!> in the vector S\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          Hermitian matrix A is stored\&.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 
.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)
!>          On entry, 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\&.
!>
!>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
!>          the same storage format as A\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is REAL array, dimension (N)
!>          The scale factors for A\&.
!> 
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
!>          SCOND is REAL
!>          Ratio of the smallest S(i) to the largest S(i)\&.
!> 
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
!>          AMAX is REAL
!>          Absolute value of largest matrix entry\&.
!> 
.fi
.PP
.br
\fIEQUED\fP 
.PP
.nf
!>          EQUED is CHARACTER*1
!>          Specifies whether or not equilibration was done\&.
!>          = 'N':  No equilibration\&.
!>          = 'Y':  Equilibration was done, i\&.e\&., A has been replaced by
!>                  diag(S) * A * diag(S)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  THRESH is a threshold value used to decide if scaling should be done
!>  based on the ratio of the scaling factors\&.  If SCOND < THRESH,
!>  scaling is done\&.
!>
!>  LARGE and SMALL are threshold values used to decide if scaling should
!>  be done based on the absolute size of the largest matrix element\&.
!>  If AMAX > LARGE or AMAX < SMALL, scaling is done\&.
!> 
.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

.PP
Definition at line \fB125\fP of file \fBclaqhp\&.f\fP\&.
.SS "subroutine claqsp (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)"

.PP
\fBCLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CLAQSP equilibrates a symmetric matrix A using the scaling factors
!> in the vector S\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored\&.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 
.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)
!>          On entry, 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\&.
!>
!>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
!>          the same storage format as A\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is REAL array, dimension (N)
!>          The scale factors for A\&.
!> 
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
!>          SCOND is REAL
!>          Ratio of the smallest S(i) to the largest S(i)\&.
!> 
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
!>          AMAX is REAL
!>          Absolute value of largest matrix entry\&.
!> 
.fi
.PP
.br
\fIEQUED\fP 
.PP
.nf
!>          EQUED is CHARACTER*1
!>          Specifies whether or not equilibration was done\&.
!>          = 'N':  No equilibration\&.
!>          = 'Y':  Equilibration was done, i\&.e\&., A has been replaced by
!>                  diag(S) * A * diag(S)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  THRESH is a threshold value used to decide if scaling should be done
!>  based on the ratio of the scaling factors\&.  If SCOND < THRESH,
!>  scaling is done\&.
!>
!>  LARGE and SMALL are threshold values used to decide if scaling should
!>  be done based on the absolute size of the largest matrix element\&.
!>  If AMAX > LARGE or AMAX < SMALL, scaling is done\&.
!> 
.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

.PP
Definition at line \fB125\fP of file \fBclaqsp\&.f\fP\&.
.SS "subroutine dlaqsp (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)"

.PP
\fBDLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DLAQSP equilibrates a symmetric matrix A using the scaling factors
!> in the vector S\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored\&.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 
.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)
!>          On entry, 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\&.
!>
!>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
!>          the same storage format as A\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is DOUBLE PRECISION array, dimension (N)
!>          The scale factors for A\&.
!> 
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
!>          SCOND is DOUBLE PRECISION
!>          Ratio of the smallest S(i) to the largest S(i)\&.
!> 
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
!>          AMAX is DOUBLE PRECISION
!>          Absolute value of largest matrix entry\&.
!> 
.fi
.PP
.br
\fIEQUED\fP 
.PP
.nf
!>          EQUED is CHARACTER*1
!>          Specifies whether or not equilibration was done\&.
!>          = 'N':  No equilibration\&.
!>          = 'Y':  Equilibration was done, i\&.e\&., A has been replaced by
!>                  diag(S) * A * diag(S)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  THRESH is a threshold value used to decide if scaling should be done
!>  based on the ratio of the scaling factors\&.  If SCOND < THRESH,
!>  scaling is done\&.
!>
!>  LARGE and SMALL are threshold values used to decide if scaling should
!>  be done based on the absolute size of the largest matrix element\&.
!>  If AMAX > LARGE or AMAX < SMALL, scaling is done\&.
!> 
.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

.PP
Definition at line \fB124\fP of file \fBdlaqsp\&.f\fP\&.
.SS "subroutine slaqsp (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)"

.PP
\fBSLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SLAQSP equilibrates a symmetric matrix A using the scaling factors
!> in the vector S\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored\&.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 
.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)
!>          On entry, 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\&.
!>
!>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
!>          the same storage format as A\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is REAL array, dimension (N)
!>          The scale factors for A\&.
!> 
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
!>          SCOND is REAL
!>          Ratio of the smallest S(i) to the largest S(i)\&.
!> 
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
!>          AMAX is REAL
!>          Absolute value of largest matrix entry\&.
!> 
.fi
.PP
.br
\fIEQUED\fP 
.PP
.nf
!>          EQUED is CHARACTER*1
!>          Specifies whether or not equilibration was done\&.
!>          = 'N':  No equilibration\&.
!>          = 'Y':  Equilibration was done, i\&.e\&., A has been replaced by
!>                  diag(S) * A * diag(S)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  THRESH is a threshold value used to decide if scaling should be done
!>  based on the ratio of the scaling factors\&.  If SCOND < THRESH,
!>  scaling is done\&.
!>
!>  LARGE and SMALL are threshold values used to decide if scaling should
!>  be done based on the absolute size of the largest matrix element\&.
!>  If AMAX > LARGE or AMAX < SMALL, scaling is done\&.
!> 
.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

.PP
Definition at line \fB124\fP of file \fBslaqsp\&.f\fP\&.
.SS "subroutine zlaqhp (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)"

.PP
\fBZLAQHP\fP scales a Hermitian matrix stored in packed form\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZLAQHP equilibrates a Hermitian matrix A using the scaling factors
!> in the vector S\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          Hermitian matrix A is stored\&.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 
.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)
!>          On entry, 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\&.
!>
!>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
!>          the same storage format as A\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is DOUBLE PRECISION array, dimension (N)
!>          The scale factors for A\&.
!> 
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
!>          SCOND is DOUBLE PRECISION
!>          Ratio of the smallest S(i) to the largest S(i)\&.
!> 
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
!>          AMAX is DOUBLE PRECISION
!>          Absolute value of largest matrix entry\&.
!> 
.fi
.PP
.br
\fIEQUED\fP 
.PP
.nf
!>          EQUED is CHARACTER*1
!>          Specifies whether or not equilibration was done\&.
!>          = 'N':  No equilibration\&.
!>          = 'Y':  Equilibration was done, i\&.e\&., A has been replaced by
!>                  diag(S) * A * diag(S)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  THRESH is a threshold value used to decide if scaling should be done
!>  based on the ratio of the scaling factors\&.  If SCOND < THRESH,
!>  scaling is done\&.
!>
!>  LARGE and SMALL are threshold values used to decide if scaling should
!>  be done based on the absolute size of the largest matrix element\&.
!>  If AMAX > LARGE or AMAX < SMALL, scaling is done\&.
!> 
.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

.PP
Definition at line \fB125\fP of file \fBzlaqhp\&.f\fP\&.
.SS "subroutine zlaqsp (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)"

.PP
\fBZLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZLAQSP equilibrates a symmetric matrix A using the scaling factors
!> in the vector S\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored\&.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!> 
.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)
!>          On entry, 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\&.
!>
!>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
!>          the same storage format as A\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is DOUBLE PRECISION array, dimension (N)
!>          The scale factors for A\&.
!> 
.fi
.PP
.br
\fISCOND\fP 
.PP
.nf
!>          SCOND is DOUBLE PRECISION
!>          Ratio of the smallest S(i) to the largest S(i)\&.
!> 
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
!>          AMAX is DOUBLE PRECISION
!>          Absolute value of largest matrix entry\&.
!> 
.fi
.PP
.br
\fIEQUED\fP 
.PP
.nf
!>          EQUED is CHARACTER*1
!>          Specifies whether or not equilibration was done\&.
!>          = 'N':  No equilibration\&.
!>          = 'Y':  Equilibration was done, i\&.e\&., A has been replaced by
!>                  diag(S) * A * diag(S)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  THRESH is a threshold value used to decide if scaling should be done
!>  based on the ratio of the scaling factors\&.  If SCOND < THRESH,
!>  scaling is done\&.
!>
!>  LARGE and SMALL are threshold values used to decide if scaling should
!>  be done based on the absolute size of the largest matrix element\&.
!>  If AMAX > LARGE or AMAX < SMALL, scaling is done\&.
!> 
.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

.PP
Definition at line \fB125\fP of file \fBzlaqsp\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.