.TH "geequb" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
geequb \- geequb: equilibration, power of 2
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcgeequb\fP (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)"
.br
.RI "\fBCGEEQUB\fP "
.ti -1c
.RI "subroutine \fBdgeequb\fP (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)"
.br
.RI "\fBDGEEQUB\fP "
.ti -1c
.RI "subroutine \fBsgeequb\fP (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)"
.br
.RI "\fBSGEEQUB\fP "
.ti -1c
.RI "subroutine \fBzgeequb\fP (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)"
.br
.RI "\fBZGEEQUB\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgeequb (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)"

.PP
\fBCGEEQUB\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CGEEQUB 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)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          The M-by-N matrix whose equilibration factors are
          to be computed\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is REAL array, dimension (M)
          If INFO = 0 or INFO > M, R contains the row scale factors
          for A\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (N)
          If INFO = 0,  C contains the column scale factors for A\&.
.fi
.PP
.br
\fIROWCND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fICOLCND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine dgeequb (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)"

.PP
\fBDGEEQUB\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DGEEQUB 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)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix whose equilibration factors are
          to be computed\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is DOUBLE PRECISION array, dimension (M)
          If INFO = 0 or INFO > M, R contains the row scale factors
          for A\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (N)
          If INFO = 0,  C contains the column scale factors for A\&.
.fi
.PP
.br
\fIROWCND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fICOLCND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine sgeequb (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)"

.PP
\fBSGEEQUB\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SGEEQUB 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)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
          The M-by-N matrix whose equilibration factors are
          to be computed\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is REAL array, dimension (M)
          If INFO = 0 or INFO > M, R contains the row scale factors
          for A\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (N)
          If INFO = 0,  C contains the column scale factors for A\&.
.fi
.PP
.br
\fIROWCND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fICOLCND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine zgeequb (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)"

.PP
\fBZGEEQUB\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZGEEQUB 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)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          The M-by-N matrix whose equilibration factors are
          to be computed\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is DOUBLE PRECISION array, dimension (M)
          If INFO = 0 or INFO > M, R contains the row scale factors
          for A\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (N)
          If INFO = 0,  C contains the column scale factors for A\&.
.fi
.PP
.br
\fIROWCND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fICOLCND\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIAMAX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.