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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| real function sla_gbrcond | ( | character | TRANS, |
| integer | N, | ||
| integer | KL, | ||
| integer | KU, | ||
| real, dimension( ldab, * ) | AB, | ||
| integer | LDAB, | ||
| real, dimension( ldafb, * ) | AFB, | ||
| integer | LDAFB, | ||
| integer, dimension( * ) | IPIV, | ||
| integer | CMODE, | ||
| real, dimension( * ) | C, | ||
| integer | INFO, | ||
| real, dimension( * ) | WORK, | ||
| integer, dimension( * ) | IWORK | ||
| ) |
SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
Download SLA_GBRCOND + dependencies [TGZ] [ZIP] [TXT]
SLA_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. | [in] | TRANS | 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) |
| [in] | N | N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0. |
| [in] | KL | KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0. |
| [in] | KU | KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0. |
| [in] | AB | 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) |
| [in] | LDAB | LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1. |
| [in] | AFB | 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. |
| [in] | LDAFB | LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. |
| [in] | IPIV | IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by SGBTRF; row i of the matrix was interchanged
with row IPIV(i). |
| [in] | CMODE | 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) |
| [in] | C | C is REAL array, dimension (N)
The vector C in the formula op(A) * op2(C). |
| [out] | INFO | INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid. |
| [out] | WORK | WORK is REAL array, dimension (5*N).
Workspace. |
| [out] | IWORK | IWORK is INTEGER array, dimension (N).
Workspace. |
1.9.4