Visible to Intel only — GUID: GUID-6E1C4E98-77B7-4726-B5DE-A43B856FCDE2
Visible to Intel only — GUID: GUID-6E1C4E98-77B7-4726-B5DE-A43B856FCDE2
?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: QT*A*Q = T (QH*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.