# laqgb - Man Page

laqgb: row/col scale matrix

## Synopsis

### Functions

subroutine **claqgb** (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)**CLAQGB** scales a general band matrix, using row and column scaling factors computed by sgbequ.

subroutine **dlaqgb** (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)**DLAQGB** scales a general band matrix, using row and column scaling factors computed by sgbequ.

subroutine **slaqgb** (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)**SLAQGB** scales a general band matrix, using row and column scaling factors computed by sgbequ.

subroutine **zlaqgb** (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)**ZLAQGB** scales a general band matrix, using row and column scaling factors computed by sgbequ.

## Detailed Description

## Function Documentation

### 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)

**CLAQGB** scales a general band matrix, using row and column scaling factors computed by sgbequ.

**Purpose:**

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.

**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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix.

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

*R*R is REAL array, dimension (M) The row scale factors for A.

*C*C is REAL array, dimension (N) The column scale factors for A.

*ROWCND*ROWCND is REAL Ratio of the smallest R(i) to the largest R(i).

*COLCND*COLCND is REAL Ratio of the smallest C(i) to the largest C(i).

*AMAX*AMAX is REAL Absolute value of largest matrix entry.

*EQUED*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).

**Internal Parameters:**

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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **158** of file **claqgb.f**.

### 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)

**DLAQGB** scales a general band matrix, using row and column scaling factors computed by sgbequ.

**Purpose:**

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.

**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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix.

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

*R*R is DOUBLE PRECISION array, dimension (M) The row scale factors for A.

*C*C is DOUBLE PRECISION array, dimension (N) The column scale factors for A.

*ROWCND*ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i).

*COLCND*COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i).

*AMAX*AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.

*EQUED*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).

**Internal Parameters:**

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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **157** of file **dlaqgb.f**.

### 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)

**SLAQGB** scales a general band matrix, using row and column scaling factors computed by sgbequ.

**Purpose:**

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.

**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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix.

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

*R*R is REAL array, dimension (M) The row scale factors for A.

*C*C is REAL array, dimension (N) The column scale factors for A.

*ROWCND*ROWCND is REAL Ratio of the smallest R(i) to the largest R(i).

*COLCND*COLCND is REAL Ratio of the smallest C(i) to the largest C(i).

*AMAX*AMAX is REAL Absolute value of largest matrix entry.

*EQUED*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).

**Internal Parameters:**

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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **157** of file **slaqgb.f**.

### 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)

**ZLAQGB** scales a general band matrix, using row and column scaling factors computed by sgbequ.

**Purpose:**

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.

**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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix.

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

*R*R is DOUBLE PRECISION array, dimension (M) The row scale factors for A.

*C*C is DOUBLE PRECISION array, dimension (N) The column scale factors for A.

*ROWCND*ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i).

*COLCND*COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i).

*AMAX*AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.

*EQUED*

**Internal Parameters:**

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **158** of file **zlaqgb.f**.

## Author

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