gbequb(3)

NAME
gbequb - gbequb: equilibration, power of 2

SYNOPSIS

  Functions
subroutine cgbequb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
CGBEQUB
subroutine dgbequb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
DGBEQUB
subroutine sgbequb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
SGBEQUB
subroutine zgbequb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
ZGBEQUB

Detailed Description

Function Documentation

  subroutine cgbequb (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)

CGBEQUB

Purpose:

    !>
    !> CGBEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N 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 an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix 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.
    !>
    !> This routine differs from CGEEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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)
    !>          On entry, the matrix A in band storage, 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(N,j+kl)
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array A.  LDAB >= max(1,M).
    !>

    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.

Definition at line 159 of file cgbequb.f.

  subroutine dgbequb (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)

DGBEQUB

Purpose:

    !>
    !> DGBEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N 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 an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix 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.
    !>
    !> This routine differs from DGEEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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)
    !>          On entry, the matrix A in band storage, 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(N,j+kl)
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array A.  LDAB >= max(1,M).
    !>

    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.

Definition at line 158 of file dgbequb.f.

  subroutine sgbequb (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)

SGBEQUB

Purpose:

    !>
    !> SGBEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N 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 an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix 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.
    !>
    !> This routine differs from SGEEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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)
    !>          On entry, the matrix A in band storage, 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(N,j+kl)
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array A.  LDAB >= max(1,M).
    !>

    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.

Definition at line 158 of file sgbequb.f.

  subroutine zgbequb (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)

ZGBEQUB

Purpose:

    !>
    !> ZGBEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N 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 an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix 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.
    !>
    !> This routine differs from ZGEEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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)
    !>          On entry, the matrix A in band storage, 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(N,j+kl)
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array A.  LDAB >= max(1,M).
    !>

    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.

Definition at line 159 of file zgbequb.f.

Author

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