dpbequ.f File Reference

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Functions/Subroutines
subroutine	dpbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)
	DPBEQU

---

Function/Subroutine Documentation

subroutine dpbequ	(	character	UPLO,
		integer	N,
		integer	KD,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision, dimension( * )	S,
		double precision	SCOND,
		double precision	AMAX,
		integer	INFO
	)

DPBEQU

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Purpose:

 DPBEQU computes row and column scalings intended to equilibrate a
 symmetric 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:

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
[in]	AB	AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangle of the symmetric 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).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array A. LDAB >= KD+1.
[out]	S	S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.
[out]	SCOND	SCOND is DOUBLE PRECISION 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.
[out]	AMAX	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.
[out]	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 130 of file dpbequ.f.

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