###
Symmetric Eigenvalue Problems

**p?sytrd**
reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation.

```
call pssytrd (
```*uplo, n, a, ia, ja, desca, d, e, tau, work, lwork, info*)

call pdsytrd (*uplo, n, a, ia, ja, desca, d, e, tau, work, lwork, info*)

**p?ormtr**
multiplies a general matrix by the orthogonal transformation matrix from a reduction to tridiagonal form determined by
p?sytrd.

```
call psormtr (
```*side, uplo, trans, m, n, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info*)

call pdormtr (*side, uplo, trans, m, n, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info*)

**p?hetrd**
reduces a Hermitian matrix to Hermitian tridiagonal form by a unitary similarity transformation.

```
call pchetrd (
```*uplo, n, a, ia, ja, desca, d, e, tau, work, lwork, info*)

call pzhetrd (*uplo, n, a, ia, ja, desca, d, e, tau, work, lwork, info*)

**p?unmtr**
multiplies a general matrix by the unitary transformation matrix from a reduction to tridiagonal form determined by
p?hetrd.

```
call pcunmtr (
```*side, uplo, trans, m, n, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info*)

call pzunmtr (*side, uplo, trans, m, n, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info*)

**p?stebz**
computes the eigenvalues of a symmetric tridiagonal matrix by bisection.

```
call psstebz (
```*ictxt, range, order, n, vl, vu, il, iu, abstol, d, e, m, nsplit, w, iblock, isplit, w, iblock, work, iwork, liwork, info*)

call pdstebz (*ictxt, range, order, n, vl, vu, il, iu, abstol, d, e, m, nsplit, w, iblock, isplit, w, iblock, work, iwork, liwork, info*)

**p?stein**
computes the eigenvectors of a tridiagonal matrix using inverse iteration.

```
call psstein (
```*n, d, e, m, w, iblock, isplit, orfac, z, iz, jz, descz, work, lwork, iwork, liwork, ifailv, iclustr, gap, info*)

call pdstein (*n, d, e, m, w, iblock, isplit, orfac, z, iz, jz, descz, work, lwork, iwork, liwork, ifailv, iclustr, gap, info*)

call pcstein (*n, d, e, m, w, iblock, isplit, orfac, z, iz, jz, descz, work, lwork, iwork, liwork, ifailv, iclustr, gap, info*)

call pzstein (*n, d, e, m, w, iblock, isplit, orfac, z, iz, jz, descz, work, lwork, iwork, liwork, ifailv, iclustr, gap, info*)

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