Developer Reference for Intel® oneAPI Math Kernel Library for C
?dtsvb
Computes the solution to the system of linear equations with a diagonally dominant tridiagonal coefficient matrix A and multiple right-hand sides.
Syntax
voidsdtsvb ( constMKL_INT*n , constMKL_INT*nrhs , float*dl , float*d , constfloat*du , float*b , constMKL_INT*ldb , MKL_INT*info );
voidddtsvb ( constMKL_INT*n , constMKL_INT*nrhs , double*dl , double*d , constdouble*du , double*b , constMKL_INT*ldb , MKL_INT*info );
voidcdtsvb ( constMKL_INT*n , constMKL_INT*nrhs , MKL_Complex8*dl , MKL_Complex8*d , constMKL_Complex8*du , MKL_Complex8*b , constMKL_INT*ldb , MKL_INT*info );
voidzdtsvb ( constMKL_INT*n , constMKL_INT*nrhs , MKL_Complex16*dl , MKL_Complex16*d , constMKL_Complex16*du , MKL_Complex16*b , constMKL_INT*ldb , MKL_INT*info );
Include Files
mkl.h
Description
sdtsvb ddtsvb cdtsvb zdtsvb
The ?dtsvb routine solves a system of linear equations A*X = B for X , where A is an n -by- n diagonally dominant tridiagonal matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The routine uses the BABE (Burning At Both Ends) algorithm.
Note that the equation A:code:`T` * X = B may be solved by interchanging the order of the arguments du and dl .
Input Parameters
n
The order of A , the number of rows in B ; n ≥ 0.
nrhs
The number of right-hand sides, the number of columns in B ; nrhs ≥ 0.
dl , d , du , b
Arrays: dl (size n - 1), d (size n ), du (size n - 1), b (max( ldb * nrhs ) for column major layout and max( ldb * n ) for row major layout) .
The array dl contains the (n - 1) subdiagonal elements of A .
The array d contains the diagonal elements of A .
The array du contains the (n - 1) superdiagonal elements of A .
The array b contains the matrix B whose columns are the right-hand sides for the systems of equations.
ldb
The leading dimension of b ; ldb≥ max(1, n) .
Output Parameters
dl
Overwritten by the (n-1) elements of the subdiagonal of the lower triangular matrices L1 , L2 from the factorization of A (see dttrfb ).
d
Overwritten by the n diagonal element reciprocals of U .
b
Overwritten by the solution matrix X .
info
-
If info = 0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.
If info = i , u_{ii} is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = n .
Application Notes
A diagonally dominant tridiagonal system is defined such that \(|d_{i}| > |dl_{i-1}| + |du_{i}|\) for any i :
1 < i < n , and \(|d_{1}| > |du_{1}|, |d_{n}| > |dl_{n-1}|\)
The underlying BABE algorithm is designed for diagonally dominant systems. Such systems have no numerical stability issue unlike the canonical systems that use elimination with partial pivoting (see ?gtsv (Computes the solution to the system of linear equations with a tridiagonal coefficient matrix A and multiple right-hand sides.) ). The diagonally dominant systems are much faster than the canonical systems.