# dsptrd.f man page

dsptrd.f —

## Synopsis

### Functions/Subroutines

subroutinedsptrd(UPLO, N, AP, D, E, TAU, INFO)DSPTRD

## Function/Subroutine Documentation

### subroutine dsptrd (characterUPLO, integerN, double precision, dimension( * )AP, double precision, dimension( * )D, double precision, dimension( * )E, double precision, dimension( * )TAU, integerINFO)

**DSPTRD**

**Purpose:**

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

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
```

*N*

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

*AP*

```
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
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.
```

*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:**

November 2011

**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 AP,
overwriting A(1:i-1,i+1), and tau is stored 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 AP,
overwriting A(i+2:n,i), and tau is stored in TAU(i).
```

Definition at line 151 of file dsptrd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK