SLA_GBRPVGRW (3) - Linux Manuals
REAL function sla_gbrpvgrw (integerN, integerKL, integerKU, integerNCOLS, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB, integerLDAFB)
SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The "max absolute element" norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.
N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
NCOLS is INTEGER The number of columns of the matrix A. NCOLS >= 0.
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(N,j+kl)
LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
AFB is REAL array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- September 2012
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