?ptsv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

Version

Public

Visible to Intel only — GUID: GUID-3F01B6CD-6B58-4D39-8DF2-0321CD37CF49

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?ptsv

Computes the solution to the system of linear equations with a symmetric or Hermitian positive definite tridiagonal coefficient matrix A and multiple right-hand sides.

Syntax

lapack_int LAPACKE_sptsv( int matrix_layout, lapack_int n, lapack_int nrhs, float* d, float* e, float* b, lapack_int ldb );

lapack_int LAPACKE_dptsv( int matrix_layout, lapack_int n, lapack_int nrhs, double* d, double* e, double* b, lapack_int ldb );

lapack_int LAPACKE_cptsv( int matrix_layout, lapack_int n, lapack_int nrhs, float* d, lapack_complex_float* e, lapack_complex_float* b, lapack_int ldb );

lapack_int LAPACKE_zptsv( int matrix_layout, lapack_int n, lapack_int nrhs, double* d, lapack_complex_double* e, lapack_complex_double* b, lapack_int ldb );

Include Files

mkl.h

Description

The routine solves for X the real or complex system of linear equations A*X = B, where A is an n-by-n symmetric/Hermitian positive-definite tridiagonal matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.

A is factored as A = L*D*L^T (real flavors) or A = L*D*L^H (complex flavors), and the factored form of A is then used to solve the system of equations A*X = B.

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 matrix `A`; `n`≥ 0.
nrhs	The number of right-hand sides, the number of columns in `B; nrhs≥ 0`.
d	Array, dimension at least `max(1, n)`. Contains the diagonal elements of the tridiagonal matrix `A`.
e, b	Arrays: `e` (size `n` - 1), `b`of size max(1, ldbnrhs) for column major layout and max(1, ldbn) for row major layout. The array `e` contains the `(n - 1)` subdiagonal 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) for column major layout and `ldb`≥nrhs for row major layout.

Output Parameters

d	Overwritten by the `n` diagonal elements of the diagonal matrix `D` from the `LDL^T` (real)/ `LDL^H` (complex) factorization of `A`.
e	Overwritten by the `(n - 1)` subdiagonal elements of the unit bidiagonal factor `L` from the factorization of `A`.
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, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the solution has not been computed. The factorization has not been completed unless i = n.

Parent topic: LAPACK Linear Equation Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?ptsv

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

See Also