Man page - laqhb(3)

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Manual

laqhb

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine claqhb (character uplo, integer n, integer kd, complex,dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, realscond, real amax, character equed)
subroutine claqsb (character uplo, integer n, integer kd, complex,dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, realscond, real amax, character equed)
subroutine dlaqsb (character uplo, integer n, integer kd, double precision,dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )s, double precision scond, double precision amax, character equed)
subroutine slaqsb (character uplo, integer n, integer kd, real, dimension(ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, realamax, character equed)
subroutine zlaqhb (character uplo, integer n, integer kd, complex*16,dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )s, double precision scond, double precision amax, character equed)
subroutine zlaqsb (character uplo, integer n, integer kd, complex*16,dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )s, double precision scond, double precision amax, character equed)
Author

NAME

laqhb - laqhb: row/col scale matrix

SYNOPSIS

Functions

subroutine claqhb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.
subroutine claqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
subroutine dlaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
subroutine slaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.
subroutine zlaqhb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.
subroutine zlaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Detailed Description

Function Documentation

subroutine claqhb (character uplo, integer n, integer kd, complex,dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, realscond, real amax, character equed)

CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

Purpose:

CLAQHB equilibrates an Hermitian band 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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: Lower triangular

N

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

KD

KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of sub-diagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H *U or A = L*L**H of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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.
= ā€™Nā€™: No equilibration.
= ā€™Yā€™: 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 claqsb (character uplo, integer n, integer kd, complex,dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, realscond, real amax, character equed)

CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

CLAQSB equilibrates a symmetric band 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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: Lower triangular

N

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

KD

KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of sub-diagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H *U or A = L*L**H of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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.
= ā€™Nā€™: No equilibration.
= ā€™Yā€™: 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 dlaqsb (character uplo, integer n, integer kd, double precision,dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )s, double precision scond, double precision amax, character equed)

DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

DLAQSB equilibrates a symmetric band 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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: Lower triangular

N

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

KD

KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of sub-diagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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.
= ā€™Nā€™: No equilibration.
= ā€™Yā€™: 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 slaqsb (character uplo, integer n, integer kd, real, dimension(ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, realamax, character equed)

SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

SLAQSB equilibrates a symmetric band 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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: Lower triangular

N

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

KD

KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of sub-diagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is REAL array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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.
= ā€™Nā€™: No equilibration.
= ā€™Yā€™: 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 zlaqhb (character uplo, integer n, integer kd, complex*16,dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )s, double precision scond, double precision amax, character equed)

ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

Purpose:

ZLAQHB equilibrates a Hermitian band 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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: Lower triangular

N

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

KD

KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of sub-diagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H *U or A = L*L**H of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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.
= ā€™Nā€™: No equilibration.
= ā€™Yā€™: 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 zlaqsb (character uplo, integer n, integer kd, complex*16,dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )s, double precision scond, double precision amax, character equed)

ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

ZLAQSB equilibrates a symmetric band 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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: Lower triangular

N

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

KD

KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of sub-diagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H *U or A = L*L**H of the band
matrix A, in the same storage format as A.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

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.
= ā€™Nā€™: No equilibration.
= ā€™Yā€™: 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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