gbequ(3)

NAME
gbequ - gbequ: equilibration

SYNOPSIS

  Functions

subroutine cgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
CGBEQU
subroutine dgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
DGBEQU
subroutine sgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
SGBEQU
subroutine zgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
ZGBEQU

Detailed Description

Function Documentation

  subroutine cgbequ (integer m, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

CGBEQU

Purpose:

    !>
    !> CGBEQU computes row and column scalings intended to equilibrate an
    !> M-by-N band matrix A and reduce its condition number.  R returns the
    !> row scale factors and C the column scale factors, chosen to try to
    !> make the largest element in each row and column of the matrix B with
    !> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
    !>
    !> R(i) and C(j) are restricted to be between SMLNUM = smallest safe
    !> number and BIGNUM = largest safe number.  Use of these scaling
    !> factors is not guaranteed to reduce the condition number of A but
    !> works well in practice.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is COMPLEX array, dimension (LDAB,N)
    !>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
    !>          column of A is stored in the j-th column of the array AB as
    !>          follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
    !>

    R

    !>          R is REAL array, dimension (M)
    !>          If INFO = 0, or INFO > M, R contains the row scale factors
    !>          for A.
    !>

    C

    !>          C is REAL array, dimension (N)
    !>          If INFO = 0, C contains the column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is REAL
    !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
    !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
    !>          AMAX is neither too large nor too small, it is not worth
    !>          scaling by R.
    !>

    COLCND

    !>          COLCND is REAL
    !>          If INFO = 0, COLCND contains the ratio of the smallest
    !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
    !>          worth scaling by C.
    !>

    AMAX

    !>          AMAX is REAL
    !>          Absolute value of largest matrix element.  If AMAX is very
    !>          close to overflow or very close to underflow, the matrix
    !>          should be scaled.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, and i is
    !>                <= M:  the i-th row of A is exactly zero
    !>                >  M:  the (i-M)-th column of A is exactly zero
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dgbequ (integer m, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)

DGBEQU

Purpose:

    !>
    !> DGBEQU computes row and column scalings intended to equilibrate an
    !> M-by-N band matrix A and reduce its condition number.  R returns the
    !> row scale factors and C the column scale factors, chosen to try to
    !> make the largest element in each row and column of the matrix B with
    !> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
    !>
    !> R(i) and C(j) are restricted to be between SMLNUM = smallest safe
    !> number and BIGNUM = largest safe number.  Use of these scaling
    !> factors is not guaranteed to reduce the condition number of A but
    !> works well in practice.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
    !>          column of A is stored in the j-th column of the array AB as
    !>          follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
    !>

    R

    !>          R is DOUBLE PRECISION array, dimension (M)
    !>          If INFO = 0, or INFO > M, R contains the row scale factors
    !>          for A.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0, C contains the column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
    !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
    !>          AMAX is neither too large nor too small, it is not worth
    !>          scaling by R.
    !>

    COLCND

    !>          COLCND is DOUBLE PRECISION
    !>          If INFO = 0, COLCND contains the ratio of the smallest
    !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
    !>          worth scaling by C.
    !>

    AMAX

    !>          AMAX is DOUBLE PRECISION
    !>          Absolute value of largest matrix element.  If AMAX is very
    !>          close to overflow or very close to underflow, the matrix
    !>          should be scaled.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, and i is
    !>                <= M:  the i-th row of A is exactly zero
    !>                >  M:  the (i-M)-th column of A is exactly zero
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sgbequ (integer m, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

SGBEQU

Purpose:

    !>
    !> SGBEQU computes row and column scalings intended to equilibrate an
    !> M-by-N band matrix A and reduce its condition number.  R returns the
    !> row scale factors and C the column scale factors, chosen to try to
    !> make the largest element in each row and column of the matrix B with
    !> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
    !>
    !> R(i) and C(j) are restricted to be between SMLNUM = smallest safe
    !> number and BIGNUM = largest safe number.  Use of these scaling
    !> factors is not guaranteed to reduce the condition number of A but
    !> works well in practice.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is REAL array, dimension (LDAB,N)
    !>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
    !>          column of A is stored in the j-th column of the array AB as
    !>          follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
    !>

    R

    !>          R is REAL array, dimension (M)
    !>          If INFO = 0, or INFO > M, R contains the row scale factors
    !>          for A.
    !>

    C

    !>          C is REAL array, dimension (N)
    !>          If INFO = 0, C contains the column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is REAL
    !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
    !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
    !>          AMAX is neither too large nor too small, it is not worth
    !>          scaling by R.
    !>

    COLCND

    !>          COLCND is REAL
    !>          If INFO = 0, COLCND contains the ratio of the smallest
    !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
    !>          worth scaling by C.
    !>

    AMAX

    !>          AMAX is REAL
    !>          Absolute value of largest matrix element.  If AMAX is very
    !>          close to overflow or very close to underflow, the matrix
    !>          should be scaled.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, and i is
    !>                <= M:  the i-th row of A is exactly zero
    !>                >  M:  the (i-M)-th column of A is exactly zero
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zgbequ (integer m, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)

ZGBEQU

Purpose:

    !>
    !> ZGBEQU computes row and column scalings intended to equilibrate an
    !> M-by-N band matrix A and reduce its condition number.  R returns the
    !> row scale factors and C the column scale factors, chosen to try to
    !> make the largest element in each row and column of the matrix B with
    !> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
    !>
    !> R(i) and C(j) are restricted to be between SMLNUM = smallest safe
    !> number and BIGNUM = largest safe number.  Use of these scaling
    !> factors is not guaranteed to reduce the condition number of A but
    !> works well in practice.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is COMPLEX*16 array, dimension (LDAB,N)
    !>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
    !>          column of A is stored in the j-th column of the array AB as
    !>          follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
    !>

    R

    !>          R is DOUBLE PRECISION array, dimension (M)
    !>          If INFO = 0, or INFO > M, R contains the row scale factors
    !>          for A.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0, C contains the column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
    !>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
    !>          AMAX is neither too large nor too small, it is not worth
    !>          scaling by R.
    !>

    COLCND

    !>          COLCND is DOUBLE PRECISION
    !>          If INFO = 0, COLCND contains the ratio of the smallest
    !>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
    !>          worth scaling by C.
    !>

    AMAX

    !>          AMAX is DOUBLE PRECISION
    !>          Absolute value of largest matrix element.  If AMAX is very
    !>          close to overflow or very close to underflow, the matrix
    !>          should be scaled.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, and i is
    !>                <= M:  the i-th row of A is exactly zero
    !>                >  M:  the (i-M)-th column of A is exactly zero
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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