ssptrd.f −

**Functions/Subroutines**

subroutine **ssptrd** (UPLO, N, AP, D, E, TAU, INFO)

SSPTRD

**subroutine ssptrd (characterUPLO, integerN, real, dimension( * )AP, real, dimension( * )D, real, dimension( * )E, real, dimension( * )TAU, integerINFO)
SSPTRD**

**Purpose:**

SSPTRD 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 REAL 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 REAL array, dimension (N)

The diagonal elements of the tridiagonal matrix T:

D(i) = A(i,i).

*E*

E is REAL 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 REAL 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

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

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 ssptrd.f.

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