?sytd2/?hetd2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?sytd2/?hetd2

Reduces a symmetric/Hermitian matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation(unblocked algorithm).

Syntax

call ssytd2 ( uplo , n , a , lda , d , e , tau , info )

call dsytd2 ( uplo , n , a , lda , d , e , tau , info )

call chetd2 ( uplo , n , a , lda , d , e , tau , info )

call zhetd2 ( uplo , n , a , lda , d , e , tau , info )

Include Files

mkl.fi

Description

The routine ?sytd2 / ?hetd2 reduces a real symmetric/complex Hermitian matrix A to real symmetric tridiagonal form T by an orthogonal/unitary similarity transformation: Q^{T}*A*Q = T ( Q^{H}*A*Q = T ).

Input Parameters

uplo: CHARACTER*1 . Specifies whether the upper or lower triangular part of the symmetric/Hermitian matrix A is stored: = ‘U’ : upper triangular = ‘L’ : lower triangular
n: INTEGER . The order of the matrix A . n≥ 0 .
a: REAL for ssytd2 DOUBLE PRECISION for dsytd2 COMPLEX for chetd2 DOUBLE COMPLEX for zhetd2 . Array, DIMENSION ( lda , n ). On entry, the symmetric/Hermitian matrix A . If uplo = 'U' , the leading n -by- n upper triangular part of a contains the upper triangular part of the matrix A , and the strictly lower triangular part of a is not referenced. If uplo = 'L' , the leading n -by- n lower triangular part of a contains the lower triangular part of the matrix A , and the strictly upper triangular part of a is not referenced.
lda: INTEGER . The leading dimension of the array a . lda≥ max(1,n) .

Output Parameters

a: On exit, if uplo = 'U' , the diagonal and first superdiagonal of a are overwritten by the corresponding elements of the tridiagonal matrix T , and the elements above the first superdiagonal, with the array tau , represent the orthogonal/unitary matrix Q as a product of elementary reflectors; if uplo = 'L' , the diagonal and first subdiagonal of a are overwritten by the corresponding elements of the tridiagonal matrix T , and the elements below the first subdiagonal, with the array tau , represent the orthogonal/unitary matrix Q as a product of elementary reflectors.
d: REAL for ssytd2 / chetd2 DOUBLE PRECISION for dsytd2 / zhetd2 . Array, DIMENSION ( n ). The diagonal elements of the tridiagonal matrix T : d(i) = a(i,i) .
e: REAL for ssytd2 / chetd2 DOUBLE PRECISION for dsytd2 / zhetd2 . Array, DIMENSION ( n -1). The off-diagonal elements of the tridiagonal matrix T : e(i) = a ( i , i +1) if uplo = 'U' , e(i) = a ( i +1, i ) if uplo = 'L' .
tau: REAL for ssytd2 DOUBLE PRECISION for dsytd2 COMPLEX for chetd2 DOUBLE COMPLEX for zhetd2 . Array, DIMENSION ( n ). The first n-1 elements contain scalar factors of the elementary reflectors. tau(n) is used as workspace.

info

INTEGER .

= 0: successful exit
< 0: if info = -i , the i -th argument had an illegal value.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sytd2/?hetd2

Syntax

Include Files

Description

Input Parameters

Output Parameters