?hptrd

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?hptrd

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

Syntax

lapack_int LAPACKE_chptrd(int matrix_layout, char uplo, lapack_int n,
                          lapack_complex_float *ap, float *d, float *e,
                          lapack_complex_float *tau);

lapack_int LAPACKE_zhptrd(int matrix_layout, char uplo, lapack_int n,
                          lapack_complex_double *ap, double *d, double *e,
                          lapack_complex_double *tau);

Include Files

mkl.h

Description

The routine reduces a packed complex Hermitian matrix A to symmetric tridiagonal form T by a unitary similarity transformation: A = Q*T*Q^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: Specifies the order of the matrix A . The value of n must be at least zero.

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 .

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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