Developer Reference for Intel® oneAPI Math Kernel Library for C
?pttrs
Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix using the factorization computed by ?pttrf .
Syntax
lapack_int LAPACKE_spttrs ( intmatrix_layout , lapack_intn , lapack_intnrhs , const float*d , const float*e , float*b , lapack_intldb );
lapack_int LAPACKE_dpttrs ( intmatrix_layout , lapack_intn , lapack_intnrhs , const double*d , const double*e , double*b , lapack_intldb );
lapack_int LAPACKE_cpttrs ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , const float*d , const lapack_complex_float*e , lapack_complex_float*b , lapack_intldb );
lapack_int LAPACKE_zpttrs ( intmatrix_layout , charuplo , lapack_intn , lapack_intnrhs , const double*d , const lapack_complex_double*e , lapack_complex_double*b , lapack_intldb );
Include Files
mkl.h
Description
spttrs dpttrs cpttrs zpttrs pttrs
The routine solves for X a system of linear equations A*X = B with a symmetric (Hermitian) positive-definite tridiagonal matrix A . Before calling this routine, call ?pttrf (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) to compute the L*D*L^{T} or U^{T}*D*U for real data and the L*D*L^{H} or U^{H}*D*U factorization of A for complex data.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
uplo
Used for cpttrs / zpttrs only. Must be ‘U’ or ‘L’ .
Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and how A is factored:
If uplo = 'U' , the array e stores the conjugated values of the superdiagonal of U , and A is factored as U^{H}*D*U .
If uplo = 'L' , the array e stores the subdiagonal of L , and A is factored as L*D*L^{H} .
n
The order of A ; n ≥ 0.
nrhs
The number of right-hand sides, that is, the number of columns of the matrix B ; nrhs ≥ 0.
d
Array, dimension ( n ). Contains the diagonal elements of the diagonal matrix D from the factorization computed by ?pttrf (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) .
e , b
Array e is of size ( n -1).
The array e contains the ( n - 1) sub-diagonal elements of the unit bidiagonal factor L or the conjugated values of the superdiagonal of U from the factorization computed by ?pttrf (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) (see uplo ).
e , b
The array b contains the matrix B whose columns are the right-hand sides for the systems of equations.
The size of b is at least max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout.
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
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.
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.