.TH "gbequb" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gbequb \- gbequb: equilibration, power of 2 .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgbequb\fP (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)" .br .RI "\fBCGBEQUB\fP " .ti -1c .RI "subroutine \fBdgbequb\fP (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)" .br .RI "\fBDGBEQUB\fP " .ti -1c .RI "subroutine \fBsgbequb\fP (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)" .br .RI "\fBSGBEQUB\fP " .ti -1c .RI "subroutine \fBzgbequb\fP (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)" .br .RI "\fBZGBEQUB\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "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)" .PP \fBCGBEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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)\&. !> .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 \fIKL\fP .PP .nf !> KL is INTEGER !> The number of subdiagonals within the band of A\&. KL >= 0\&. !> .fi .PP .br \fIKU\fP .PP .nf !> KU is INTEGER !> The number of superdiagonals within the band of A\&. KU >= 0\&. !> .fi .PP .br \fIAB\fP .PP .nf !> 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) !> .fi .PP .br \fILDAB\fP .PP .nf !> LDAB is INTEGER !> The leading dimension of the array A\&. LDAB >= 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 .PP Definition at line \fB159\fP of file \fBcgbequb\&.f\fP\&. .SS "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)" .PP \fBDGBEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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)\&. !> .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 \fIKL\fP .PP .nf !> KL is INTEGER !> The number of subdiagonals within the band of A\&. KL >= 0\&. !> .fi .PP .br \fIKU\fP .PP .nf !> KU is INTEGER !> The number of superdiagonals within the band of A\&. KU >= 0\&. !> .fi .PP .br \fIAB\fP .PP .nf !> 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) !> .fi .PP .br \fILDAB\fP .PP .nf !> LDAB is INTEGER !> The leading dimension of the array A\&. LDAB >= 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 .PP Definition at line \fB158\fP of file \fBdgbequb\&.f\fP\&. .SS "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)" .PP \fBSGBEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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)\&. !> .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 \fIKL\fP .PP .nf !> KL is INTEGER !> The number of subdiagonals within the band of A\&. KL >= 0\&. !> .fi .PP .br \fIKU\fP .PP .nf !> KU is INTEGER !> The number of superdiagonals within the band of A\&. KU >= 0\&. !> .fi .PP .br \fIAB\fP .PP .nf !> 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) !> .fi .PP .br \fILDAB\fP .PP .nf !> LDAB is INTEGER !> The leading dimension of the array A\&. LDAB >= 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 .PP Definition at line \fB158\fP of file \fBsgbequb\&.f\fP\&. .SS "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)" .PP \fBZGBEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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)\&. !> .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 \fIKL\fP .PP .nf !> KL is INTEGER !> The number of subdiagonals within the band of A\&. KL >= 0\&. !> .fi .PP .br \fIKU\fP .PP .nf !> KU is INTEGER !> The number of superdiagonals within the band of A\&. KU >= 0\&. !> .fi .PP .br \fIAB\fP .PP .nf !> 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) !> .fi .PP .br \fILDAB\fP .PP .nf !> LDAB is INTEGER !> The leading dimension of the array A\&. LDAB >= 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 .PP Definition at line \fB159\fP of file \fBzgbequb\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.