DLA_GBRCOND (3) - Linux Manuals
DOUBLE PRECISION function dla_gbrcond (characterTRANS, integerN, integerKL, integerKU, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, integerCMODE, double precision, dimension( * )C, integerINFO, double precision, dimension( * )WORK, integer, dimension( * )IWORK)
DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.
TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate Transpose = Transpose)
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.
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(N,j+kl)
LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
AFB is DOUBLE PRECISION array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by DGBTRF. 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.
IPIV is INTEGER array, dimension (N) The pivot indices from the factorization A = P*L*U as computed by DGBTRF; row i of the matrix was interchanged with row IPIV(i).
CMODE is INTEGER Determines op2(C) in the formula op(A) * op2(C) as follows: CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C)
C is DOUBLE PRECISION array, dimension (N) The vector C in the formula op(A) * op2(C).
INFO is INTEGER = 0: Successful exit. i > 0: The ith argument is invalid.
WORK is DOUBLE PRECISION array, dimension (5*N). Workspace.
IWORK is INTEGER array, dimension (N). Workspace.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- September 2012
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