Developer Reference for Intel® oneAPI Math Kernel Library for C
?gtsv
Computes the solution to the system of linear equations with a tridiagonal coefficient matrix A and multiple right-hand sides.
Syntax
lapack_intLAPACKE_sgtsv ( intmatrix_layout , lapack_intn , lapack_intnrhs , float*dl , float*d , float*du , float*b , lapack_intldb );
lapack_intLAPACKE_dgtsv ( intmatrix_layout , lapack_intn , lapack_intnrhs , double*dl , double*d , double*du , double*b , lapack_intldb );
lapack_intLAPACKE_cgtsv ( intmatrix_layout , lapack_intn , lapack_intnrhs , lapack_complex_float*dl , lapack_complex_float*d , lapack_complex_float*du , lapack_complex_float*b , lapack_intldb );
lapack_intLAPACKE_zgtsv ( intmatrix_layout , lapack_intn , lapack_intnrhs , lapack_complex_double*dl , lapack_complex_double*d , lapack_complex_double*du , lapack_complex_double*b , lapack_intldb );
Include Files
mkl.h
Description
sgtsv dgtsv cgtsv zgtsv gtsv
The routine solves for X the system of linear equations A*X = B , where A is an n -by- n tridiagonal matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The routine uses Gaussian elimination with partial pivoting.
Note that the equation A:code:`T`*X = B may be solved by interchanging the order of the arguments du and dl .
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
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
The array dl (size n - 1) contains the (n - 1) subdiagonal elements of A .
d
The array d (size n ) contains the diagonal elements of A .
du
The array du (size n - 1) contains the (n - 1) superdiagonal elements of A .
b
The array b of size max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout 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)ldb ≥ max(1, n ) for column major layout and ldb ≥ nrhs for row major layout .
Output Parameters
dl
Overwritten by the (n-2) elements of the second superdiagonal of the upper triangular matrix U from the LU factorization of A. These elements are stored in dl(1), ..., dl(n - 2)dl[0], ..., dl[n - 3] .
d
Overwritten by the n diagonal elements of U .
du
Overwritten by the (n-1) elements of the first superdiagonal of U .
b
Overwritten by the solution matrix X .
Return Values
This function returns a value info .
If info = 0 , the execution is successful.
If info = -i , parameter i had an illegal value.
If info = i , Ui, i is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = n .
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.