LAHR2 - 5.2 English - 68552

LAHR2 reduces the specified number of first columns of a general

rectangular matrix A so that elements below the specified subdiagonal

are zero, and returns auxiliary matrices which are needed to apply the

transformation to the unreduced part of A.

Purpose:

 LAHR2 reduces the first NB columns of A real general n-BY-(n-k+1)
 matrix A so that elements below the k-th subdiagonal are zero. The
 reduction is performed by an orthogonal similarity transformation
 Q**T * A * Q. The routine   returns the matrices V and T which determine
 Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.

 This is an auxiliary routine called by GEHRD.

Parameters:

• N – [in]

  N is INTEGER

  The order of the matrix A.

• K – [in]

  K is INTEGER

  The offset for the reduction. Elements below the k-th subdiagonal in the first NB columns are reduced to zero. K < N.

• NB – [in]

  NB is INTEGER

  The number of columns to be reduced.

• A – [inout]

  A is REAL array, dimension (LDA,N-K+1)

  On entry, the n-by-(n-k+1) general matrix A.

  On exit, the elements on and above the k-th subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix Q as a product of elementary reflectors. The other columns of A are unchanged. See Further Details.

• LDA – [in]

  LDA is INTEGER

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

• TAU – [out]

  TAU is REAL array, dimension (NB)

  The scalar factors of the elementary reflectors. See Further Details.

• T – [out]

  T is REAL array, dimension (LDT,NB)

  The upper triangular matrix T.

• LDT – [in]

  LDT is INTEGER

  The leading dimension of the array T. LDT >= NB.

• Y – [out]

  Y is REAL array, dimension (LDY,NB)

  The n-by-nb matrix Y.

• LDY – [in]

  LDY is INTEGER

  The leading dimension of the array Y. LDY >= N.