# dsytd2.f man page

dsytd2.f —

## Synopsis

### Functions/Subroutines

subroutinedsytd2(UPLO, N, A, LDA, D, E, TAU, INFO)DSYTD2reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine dsytd2 (characterUPLO, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )D, double precision, dimension( * )E, double precision, dimension( * )TAU, integerINFO)

**DSYTD2** reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation (unblocked algorithm).

**Purpose:**

```
DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal
form T by an orthogonal similarity transformation: Q**T * A * Q = T.
```

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
```

*N*

```
N is INTEGER
The order of the matrix A. N >= 0.
```

*A*

```
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric 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.
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
matrix Q as a product of elementary reflectors; if UPLO
= 'L', the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
```

*LDA*

```
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
```

*D*

```
D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
```

*E*

```
E is DOUBLE PRECISION 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*

```
TAU is DOUBLE PRECISION array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
```

*INFO*

```
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**Further Details:**

```
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v**T
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v**T
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
```

Definition at line 174 of file dsytd2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dsytd2(3) is an alias of dsytd2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK