.TH "laqgb" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laqgb \- laqgb: row/col scale matrix .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclaqgb\fP (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)" .br .RI "\fBCLAQGB\fP scales a general band matrix, using row and column scaling factors computed by sgbequ\&. " .ti -1c .RI "subroutine \fBdlaqgb\fP (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)" .br .RI "\fBDLAQGB\fP scales a general band matrix, using row and column scaling factors computed by sgbequ\&. " .ti -1c .RI "subroutine \fBslaqgb\fP (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)" .br .RI "\fBSLAQGB\fP scales a general band matrix, using row and column scaling factors computed by sgbequ\&. " .ti -1c .RI "subroutine \fBzlaqgb\fP (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)" .br .RI "\fBZLAQGB\fP scales a general band matrix, using row and column scaling factors computed by sgbequ\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine claqgb (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, character equed)" .PP \fBCLAQGB\fP scales a general band matrix, using row and column scaling factors computed by sgbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C\&. .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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A\&. See EQUED for the form of the equilibrated matrix\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDA >= KL+KU+1\&. .fi .PP .br \fIR\fP .PP .nf R is REAL array, dimension (M) The row scale factors for A\&. .fi .PP .br \fIC\fP .PP .nf C is REAL array, dimension (N) The column scale factors for A\&. .fi .PP .br \fIROWCND\fP .PP .nf ROWCND is REAL Ratio of the smallest R(i) to the largest R(i)\&. .fi .PP .br \fICOLCND\fP .PP .nf COLCND is REAL Ratio of the smallest C(i) to the largest C(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is REAL Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies the form of equilibration that was done\&. = 'N': No equilibration = 'R': Row equilibration, i\&.e\&., A has been premultiplied by diag(R)\&. = 'C': Column equilibration, i\&.e\&., A has been postmultiplied by diag(C)\&. = 'B': Both row and column equilibration, i\&.e\&., A has been replaced by diag(R) * A * diag(C)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors\&. If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done\&. LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, row scaling is done\&. .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 dlaqgb (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, character equed)" .PP \fBDLAQGB\fP scales a general band matrix, using row and column scaling factors computed by sgbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C\&. .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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A\&. See EQUED for the form of the equilibrated matrix\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDA >= KL+KU+1\&. .fi .PP .br \fIR\fP .PP .nf R is DOUBLE PRECISION array, dimension (M) The row scale factors for A\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension (N) The column scale factors for A\&. .fi .PP .br \fIROWCND\fP .PP .nf ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i)\&. .fi .PP .br \fICOLCND\fP .PP .nf COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies the form of equilibration that was done\&. = 'N': No equilibration = 'R': Row equilibration, i\&.e\&., A has been premultiplied by diag(R)\&. = 'C': Column equilibration, i\&.e\&., A has been postmultiplied by diag(C)\&. = 'B': Both row and column equilibration, i\&.e\&., A has been replaced by diag(R) * A * diag(C)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors\&. If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done\&. LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, row scaling is done\&. .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 slaqgb (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, character equed)" .PP \fBSLAQGB\fP scales a general band matrix, using row and column scaling factors computed by sgbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C\&. .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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A\&. See EQUED for the form of the equilibrated matrix\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDA >= KL+KU+1\&. .fi .PP .br \fIR\fP .PP .nf R is REAL array, dimension (M) The row scale factors for A\&. .fi .PP .br \fIC\fP .PP .nf C is REAL array, dimension (N) The column scale factors for A\&. .fi .PP .br \fIROWCND\fP .PP .nf ROWCND is REAL Ratio of the smallest R(i) to the largest R(i)\&. .fi .PP .br \fICOLCND\fP .PP .nf COLCND is REAL Ratio of the smallest C(i) to the largest C(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is REAL Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies the form of equilibration that was done\&. = 'N': No equilibration = 'R': Row equilibration, i\&.e\&., A has been premultiplied by diag(R)\&. = 'C': Column equilibration, i\&.e\&., A has been postmultiplied by diag(C)\&. = 'B': Both row and column equilibration, i\&.e\&., A has been replaced by diag(R) * A * diag(C)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors\&. If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done\&. LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, row scaling is done\&. .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 zlaqgb (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, character equed)" .PP \fBZLAQGB\fP scales a general band matrix, using row and column scaling factors computed by sgbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C\&. .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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A\&. See EQUED for the form of the equilibrated matrix\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDA >= KL+KU+1\&. .fi .PP .br \fIR\fP .PP .nf R is DOUBLE PRECISION array, dimension (M) The row scale factors for A\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension (N) The column scale factors for A\&. .fi .PP .br \fIROWCND\fP .PP .nf ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i)\&. .fi .PP .br \fICOLCND\fP .PP .nf COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies the form of equilibration that was done\&. = 'N': No equilibration = 'R': Row equilibration, i\&.e\&., A has been premultiplied by diag(R)\&. = 'C': Column equilibration, i\&.e\&., A has been postmultiplied by diag(C)\&. = 'B': Both row and column equilibration, i\&.e\&., A has been replaced by diag(R) * A * diag(C)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if row or column scaling should be done based on the ratio of the row or column scaling factors\&. If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column scaling is done\&. LARGE and SMALL are threshold values used to decide if row scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, row scaling is done\&. .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\&.