cgbequ.f (3) Linux Manual Page

cgbequ.f –

Synopsis

Functions/Subroutines

subroutine cgbequ (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO)
CGBEQU

Function/Subroutine Documentation

subroutine cgbequ (integerM, integerN, integerKL, integerKU, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND, realAMAX, integerINFO)

CGBEQU

Purpose:

 CGBEQU computes row and column scalings intended to equilibrate an

 M-by-N band 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 absolute value 1.

 R(i) and C(j) are restricted to be 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.

 

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)

 The band matrix A, stored 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).

LDAB

 LDAB is INTEGER

 The leading dimension of the array AB. LDAB >= KL+KU+1.

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.

Date:

November 2011

Definition at line 154 of file cgbequ.f.

Author

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