laqhb - Man Page

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, real scond, 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.
          = 'U':  Upper triangular
          = 'L':  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 = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', 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.
          = '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 140 of file claqhb.f.

subroutine claqsb (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, 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.
          = 'U':  Upper triangular
          = 'L':  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 = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', 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.
          = '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 140 of file claqsb.f.

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.
          = 'U':  Upper triangular
          = 'L':  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 = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', 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.
          = '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 139 of file dlaqsb.f.

subroutine slaqsb (character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, 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.
          = 'U':  Upper triangular
          = 'L':  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 = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', 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.
          = '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 139 of file slaqsb.f.

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.
          = 'U':  Upper triangular
          = 'L':  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 = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', 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.
          = '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 140 of file zlaqhb.f.

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.
          = 'U':  Upper triangular
          = 'L':  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 = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', 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.
          = '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 140 of file zlaqsb.f.

Author

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