?hptrd

Developer Reference for Intel® oneAPI Math Kernel Library for C

Download PDF

ID 766684

Date 4/28/2026

Version

Public

?hptrd

Reduces a complex Hermitian matrix to tridiagonal form using packed storage.

Syntax

lapack_int LAPACKE_chptrd ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_float*ap , float*d , float*e , lapack_complex_float*tau );

lapack_int LAPACKE_zhptrd ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_double*ap , double*d , double*e , lapack_complex_double*tau );

Include Files

mkl.h

Description

chptrd zhptrd hptrd

The routine reduces a packed complex Hermitian matrix A to symmetric tridiagonal form T by a unitary similarity transformation: A = Q*T*Q^:code:`H` . The unitary matrix Q is not formed explicitly but is represented as a product of n -1 elementary reflectors. Routines are provided for working with Q in this representation (see Application Notes below).

Input Parameters

matrix_layout: Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).

uplo

Must be ‘U’ or ‘L’ .

If uplo = 'U' , ap stores the packed upper triangle of A . If uplo = 'L' , ap stores the packed lower triangle of A .

n

The order of the matrix A ( n≥ 0 ).

ap

COMPLEX for chptrd DOUBLE COMPLEX for zhptrd .

Array, size at least max(1, n(n+1)/2). Contains either upper or lower triangle of A (as specified by uplo ) in the packed form described in “ Matrix Storage Schemes .

Output Parameters

ap

Overwritten by the tridiagonal matrix T and details of the unitary matrix Q , as specified by uplo .

d , e

REAL for chptrd DOUBLE PRECISION for zhptrd . Arrays:

d contains the diagonal elements of the matrix T .

The size of d must be at least max(1, n ).

e contains the off-diagonal elements of T .

The size of e must be at least max(1, n -1).

tau

COMPLEX for chptrd DOUBLE COMPLEX for zhptrd . Array, size at least max(1, n -1). Stores ( n -1) scalars that define elementary reflectors in decomposition of the unitary matrix Q in a product of reflectors.

Return Values

This function returns a value info .

If info=0 , the execution is successful.
If info = -i , the i -th parameter 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.

Application Notes

The computed matrix \(T\) is exactly similar to a matrix \(A\) + \(E\) , where \(||E||_{2} = c(n) \varepsilon ||A||_{2}\) , c(n) is a modestly increasing function of n , and \(\varepsilon\) is the machine precision.

The approximate number of floating-point operations is \((16/3)n^{3}\) .

After calling this routine, you can call the following:

upgtr

to form the computed matrix \(Q\) explicitly

upmtr

to multiply a complex matrix by \(Q\) .

The real counterpart of this routine is sptrd .

Select Your Language

Using Intel.com Search

Quick Links

Recent Searches

Advanced Search

Only search in

Developer Reference for Intel® oneAPI Math Kernel Library for C

?hptrd

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes