LATRD - 5.2 English - 68552

LATRD reduces the first nb rows and columns of a symmetric/Hermitian

matrix A to real tridiagonal form by an orthogonal similarity transformation.

Purpose:

 LATRD reduces NB rows and columns of a real symmetric matrix A to
 symmetric tridiagonal form by an orthogonal similarity
 transformation Q**T * A * Q, and   returns the matrices V and W which are
 needed to apply the transformation to the unreduced part of A.

 If UPLO = 'U', SLATRD reduces the last NB rows and columns of a
 matrix, of which the upper triangle is supplied;
 if UPLO = 'L', SLATRD reduces the first NB rows and columns of a
 matrix, of which the lower triangle is supplied.

 This is an auxiliary routine called by SSYTRD.

Parameters:

• UPLO – [in]

  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 – [in]

  N is INTEGER

  The order of the matrix A.

• NB – [in]

  NB is INTEGER

  The number of rows and columns to be reduced.

• A – [inout]

  A is REAL 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 last NB columns have been reduced to tridiagonal form, with the diagonal elements overwriting the diagonal elements of A; the elements above the diagonal with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors;

  if UPLO = ‘L’, the first NB columns have been reduced to tridiagonal form, with the diagonal elements overwriting the diagonal elements of A; the elements below the diagonal with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors.

  See Further Details.

• LDA – [in]

  LDA is INTEGER

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

• E – [out]

  E is REAL array, dimension (N-1)

  If UPLO = ‘U’, E(n-nb:n-1) contains the superdiagonal elements of the last NB columns of the reduced matrix;

  if UPLO = ‘L’, E(1:nb) contains the subdiagonal elements of the first NB columns of the reduced matrix.

• TAU – [out]

  TAU is REAL array, dimension (N-1)

  The scalar factors of the elementary reflectors, stored in TAU(n-nb:n-1) if UPLO = ‘U’, and in TAU(1:nb) if UPLO = ‘L’. See Further Details.

• W – [out]

  W is REAL array, dimension (LDW,NB)

  The n-by-nb matrix W required to update the unreduced part of A.

• LDW – [in]

  LDW is INTEGER

  The leading dimension of the array W. LDW >= fla_max(1,N).