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template<typename T>
void tbtrs(char *uplo, char *trans, char *diag, integer *n, integer *kd, integer *nrhs, T *ab, integer *ldab, T *b, integer *ldb, integer *info)# TBTRS solves a triangular system of the form A * X = B or A**T * X = B.
Purpose:
TBTRS solves a triangular system of the form A * X = B or A**T * X = B, where A is a triangular band matrix of order N, and B is an N-by NRHS matrix. A check is made to verify that A is nonsingular.
- Parameters:
UPLO – [in]
UPLO is CHARACTER*1
= ‘U’: A is upper triangular;
= ‘L’: A is lower triangular.TRANS – [in]
TRANS is CHARACTER*1
Specifies the form the system of equations:
= ‘N’: A * X = B (No transpose)
= ‘T’: A**T * X = B (Transpose)
= ‘C’: A**H * X = B (Conjugate transpose = Transpose)DIAG – [in]
DIAG is CHARACTER*1
= ‘N’: A is non-unit triangular;
= ‘U’: A is unit triangular.N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
KD – [in]
KD is INTEGER
The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 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 – [in]
AB is REAL array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the first kd+1 rows of AB. 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 fla_max(1,j-kd)<=i<=j;
if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ‘U’, the diagonal elements of A are not referenced and are assumed to be 1.LDAB – [in]
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B – [inout]
B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B. On exit, if INFO = 0, the 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, the i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been computed.