table of contents
| laqhp(3) | LAPACK | laqhp(3) |
NAME¶
laqhp - laqhp: row/col scale matrix
SYNOPSIS¶
Functions¶
subroutine claqhp (uplo, n, ap, s, scond, amax, equed)
CLAQHP scales a Hermitian matrix stored in packed form. subroutine
claqsp (uplo, n, ap, s, scond, amax, equed)
CLAQSP scales a symmetric/Hermitian matrix in packed storage, using
scaling factors computed by sppequ. subroutine dlaqsp (uplo, n, ap,
s, scond, amax, equed)
DLAQSP scales a symmetric/Hermitian matrix in packed storage, using
scaling factors computed by sppequ. subroutine slaqsp (uplo, n, ap,
s, scond, amax, equed)
SLAQSP scales a symmetric/Hermitian matrix in packed storage, using
scaling factors computed by sppequ. subroutine zlaqhp (uplo, n, ap,
s, scond, amax, equed)
ZLAQHP scales a Hermitian matrix stored in packed form. subroutine
zlaqsp (uplo, n, ap, s, scond, amax, equed)
ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using
scaling factors computed by sppequ.
Detailed Description¶
Function Documentation¶
subroutine claqhp (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)¶
CLAQHP scales a Hermitian matrix stored in packed form.
Purpose:
CLAQHP equilibrates a Hermitian matrix A using the scaling factors
in the vector S.
Parameters
UPLO
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
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
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.
S
S is REAL array, dimension (N)
The scale factors for A.
SCOND
SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).
AMAX
AMAX is REAL
Absolute value of largest matrix entry.
EQUED
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= 'Y': Equilibration was done, i.e., A has been replaced by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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine claqsp (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)¶
CLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
Purpose:
CLAQSP equilibrates a symmetric matrix A using the scaling factors
in the vector S.
Parameters
UPLO
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
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
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.
S
S is REAL array, dimension (N)
The scale factors for A.
SCOND
SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).
AMAX
AMAX is REAL
Absolute value of largest matrix entry.
EQUED
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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dlaqsp (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)¶
DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
Purpose:
DLAQSP equilibrates a symmetric matrix A using the scaling factors
in the vector S.
Parameters
UPLO
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
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
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.
S
S is DOUBLE PRECISION array, dimension (N)
The scale factors for A.
SCOND
SCOND is DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).
AMAX
AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED
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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine slaqsp (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)¶
SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
Purpose:
SLAQSP equilibrates a symmetric matrix A using the scaling factors
in the vector S.
Parameters
UPLO
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
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
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.
S
S is REAL array, dimension (N)
The scale factors for A.
SCOND
SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).
AMAX
AMAX is REAL
Absolute value of largest matrix entry.
EQUED
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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zlaqhp (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)¶
ZLAQHP scales a Hermitian matrix stored in packed form.
Purpose:
ZLAQHP equilibrates a Hermitian matrix A using the scaling factors
in the vector S.
Parameters
UPLO
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
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
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.
S
S is DOUBLE PRECISION array, dimension (N)
The scale factors for A.
SCOND
SCOND is DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).
AMAX
AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED
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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zlaqsp (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)¶
ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
Purpose:
ZLAQSP equilibrates a symmetric matrix A using the scaling factors
in the vector S.
Parameters
UPLO
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
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
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.
S
S is DOUBLE PRECISION array, dimension (N)
The scale factors for A.
SCOND
SCOND is DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).
AMAX
AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED
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).
Internal Parameters:
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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