(S|D|C|Z)POSV
=============
Single, double, single complex, and double complex POSV.

Description
-----------
Solves a system of linear equations for multiple right-hand sides
for positive definite matrices.

.. math::

    A \mult X = B

Uses Cholesky decomposition to factor A.

If UPLO is 'U' then A is factored using an upper triangular matrix U:

.. math::

    A = \herm{U} \mult U

If UPLO is 'L' then A is factored using a lower triangular matrix L:

.. math::

    A = L \mult \herm{L}

The factored form is used to solve the system of equations.


LAPACK Interface
----------------
.. code-block:: c

    void sposv(const char *UPLO, const qml_long *N, const qml_long *NRHS, float *A,
        const qml_long *LDA, float *B, const qml_long *LDB, qml_long *INFO);

    void dposv(const char *UPLO, const qml_long *N, const qml_long *NRHS, double *A,
        const qml_long *LDA, double *B, const qml_long *LDB, qml_long *INFO);

    void cposv(const char *UPLO, const qml_long *N, const qml_long *NRHS,
        qml_single_complex *A, const qml_long *LDA, qml_single_complex *B,
        const qml_long *LDB, qml_long *INFO);

    void zposv(const char *UPLO, const qml_long *N, const qml_long *NRHS,
        qml_double_complex *A, const qml_long *LDA, qml_double_complex *B,
        const qml_long *LDB, qml_long *INFO);


Arguments
---------
======   =====================================================================
UPLO     Specify whether to factor using 'U' upper triangular or 'L' lower triangular
N        Number of linear equations, order of the matrix A
NRHS     Number of right hand sides, number of columns of B
A        Matrix of size N x N, overwritten with factorization on exit
LDA      Leading dimension of A
B        On entry, the N x NRHS matrix B, on exit the solution matrix
LDB      Leading dimension of B
INFO     0 on success, <0 on illegal arguments, >0 if not positive definite
======   =====================================================================
