cpbequ-f(3)

cpbequ.f –

Synopsis

Functions/Subroutines

subroutine cpbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)
CPBEQU

Function/Subroutine Documentation

subroutine cpbequ (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )S, realSCOND, realAMAX, integerINFO)

CPBEQU

Purpose:

 CPBEQU computes row and column scalings intended to equilibrate a
 Hermitian positive definite band matrix A and reduce its condition
 number (with respect to the two-norm). S contains the scale factors,
 S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
 elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
 choice of S puts the condition number of B within a factor N of the
 smallest possible condition number over all possible diagonal
 scalings.

Parameters:

UPLO

 UPLO is CHARACTER*1
 = 'U': Upper triangular of A is stored;
 = 'L': Lower triangular of A is stored.

 N is INTEGER
 The order of the matrix A. N >= 0.

 KD is INTEGER
 The number of superdiagonals of the matrix A if UPLO = 'U',
 or the number of subdiagonals if UPLO = 'L'. KD >= 0.

 AB is COMPLEX array, dimension (LDAB,N)
 The upper or lower triangle of the Hermitian band matrix A,
 stored in the first KD+1 rows of the array. The j-th column
 of A is stored in the j-th column of the array AB as follows:
 if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
 if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

LDAB

 LDAB is INTEGER
 The leading dimension of the array A. LDAB >= KD+1.

 S is REAL array, dimension (N)
 If INFO = 0, S contains the scale factors for A.

SCOND

 SCOND is REAL
 If INFO = 0, S contains the ratio of the smallest S(i) to
 the largest S(i). If SCOND >= 0.1 and AMAX is neither too
 large nor too small, it is not worth scaling by S.

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, the i-th diagonal element is nonpositive.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 131 of file cpbequ.f.

Author

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