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template<typename T>
void gbsv(integer *n, integer *kl, integer *ku, integer *nrhs, T *ab, integer *ldab, integer *ipiv, T *b, integer *ldb, integer *info)# GBSV computes the solution to system of linear equations A * X = B for GB matrices.
Purpose:
GBSV computes the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices.
- Parameters:
N – [in]
N is INTEGER
The number of linear equations, i.e., the order of the matrix A. N >= 0.
KL – [in]
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU – [in]
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS – [in]
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
AB – [inout]
AB is REAL array, dimension (LDAB,N)
On entry, the matrix A in band storage, in rows KL+1 to 2*KL+KU+1; rows 1 to KL of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows:
AB(KL+KU+1+i-j,j) = A(i,j) for fla_max(1,j-KU)<=i<=min(N,j+KL)
On exit, details of the factorization: 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. See below for further details.
LDAB – [in]
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
IPIV – [out]
IPIV is INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).
B – [inout]
B is REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.LDB – [in]
LDB is INTEGER
The leading dimension of the array B. LDB >= fla_max(1,N).
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and the solution has not been computed.