laqhe - Man Page

laqhe: row/col scale matrix

Synopsis

Functions

subroutine claqhe (uplo, n, a, lda, s, scond, amax, equed)
CLAQHE scales a Hermitian matrix.
subroutine claqsy (uplo, n, a, lda, s, scond, amax, equed)
CLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
subroutine dlaqsy (uplo, n, a, lda, s, scond, amax, equed)
DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
subroutine slaqsy (uplo, n, a, lda, s, scond, amax, equed)
SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
subroutine zlaqhe (uplo, n, a, lda, s, scond, amax, equed)
ZLAQHE scales a Hermitian matrix.
subroutine zlaqsy (uplo, n, a, lda, s, scond, amax, equed)
ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Detailed Description

Function Documentation

subroutine claqhe (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)

CLAQHE scales a Hermitian matrix.  

Purpose:

 CLAQHE 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.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
          n by n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n by n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix:
          diag(S) * A * diag(S).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,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.
          = '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.

Definition at line 133 of file claqhe.f.

subroutine claqsy (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)

CLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.  

Purpose:

 CLAQSY 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.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
          n by n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n by n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix:
          diag(S) * A * diag(S).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,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.
          = '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.

Definition at line 133 of file claqsy.f.

subroutine dlaqsy (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.  

Purpose:

 DLAQSY 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.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
          n by n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n by n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix:
          diag(S) * A * diag(S).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,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.
          = '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.

Definition at line 132 of file dlaqsy.f.

subroutine slaqsy (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)

SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.  

Purpose:

 SLAQSY 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.

A

          A is REAL array, dimension (LDA,N)
          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
          n by n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n by n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix:
          diag(S) * A * diag(S).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,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.
          = '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.

Definition at line 132 of file slaqsy.f.

subroutine zlaqhe (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

ZLAQHE scales a Hermitian matrix.  

Purpose:

 ZLAQHE 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.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
          n by n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n by n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix:
          diag(S) * A * diag(S).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,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.
          = '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.

Definition at line 133 of file zlaqhe.f.

subroutine zlaqsy (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.  

Purpose:

 ZLAQSY 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.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
          n by n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n by n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix:
          diag(S) * A * diag(S).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,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.
          = '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.

Definition at line 133 of file zlaqsy.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK