Solving a Positive Definite System of Linear Equations (potrs)

potrs solves a system of linear equations \( A X = B \) with a symmetric positive definite matrix A using the Cholesky factorization computed by potrf.

Real Variant

The Cholesky factorization reads \( A = U^T U \) or \( A = L L^T \).

A

(input/output) real valued SyMatrix
The triangular factor \( U \) or \( L \) from the Cholesky factorization \( A = U^T U \) or \( A = L L^T \), as computed by potrf.

B

(input/output) real valued GeMatrix
On entry, the right hand side matrix \( B \).
On exit, the solution matrix \( X \).

Complex Variant

The Cholesky factorization reads \( A = U^H U \) or \( A = L L^H \).

A

(input/output) complex valued HeMatrix
The triangular factor \( U \) or \( L \) from the Cholesky factorization \( A = U^H U \) or \( A = L L^H \), as computed by potrf.

B

(input/output) complex valued GeMatrix
On entry, the right hand side matrix \( B \).
On exit, the solution matrix \( X \).

Single Right-Hand Side (Real and Complex Variant)

A

(input/output) complex valued HeMatrix
The triangular factor \( U \) or \( L \) from the Cholesky factorization.

b

(input/output) complex valued GeMatrix
On entry, the right hand side vector \( b \).
On exit, the solution vector \( x \).