gelqt3(3) LAPACK gelqt3(3)

gelqt3 - gelqt3: LQ factor, with T, recursive


recursive subroutine cgelqt3 (m, n, a, lda, t, ldt, info)
CGELQT3 recursive subroutine dgelqt3 (m, n, a, lda, t, ldt, info)
DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. recursive subroutine sgelqt3 (m, n, a, lda, t, ldt, info)
SGELQT3 recursive subroutine zgelqt3 (m, n, a, lda, t, ldt, info)
ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

CGELQT3

Purpose:

 CGELQT3 recursively computes a LQ factorization of a complex M-by-N
 matrix A, using the compact WY representation of Q.
 Based on the algorithm of Elmroth and Gustavson,
 IBM J. Res. Develop. Vol 44 No. 4 July 2000.

Parameters

M 

          M is INTEGER
          The number of rows of the matrix A.  M =< N.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the complex M-by-N matrix A.  On exit, the elements on and
          below the diagonal contain the N-by-N lower triangular matrix L; the
          elements above the diagonal are the rows of V.  See below for
          further details.

LDA

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

T

          T is COMPLEX array, dimension (LDT,N)
          The N-by-N upper triangular factor of the block reflector.
          The elements on and above the diagonal contain the block
          reflector T; the elements below the diagonal are not used.
          See below for further details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,N).

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.

Further Details:

  The matrix V stores the elementary reflectors H(i) in the i-th row
  above the diagonal. For example, if M=5 and N=3, the matrix V is
               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (     1  v3 v3 v3 )
  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
  block reflector H is then given by
               H = I - V * T * V**T
  where V**T is the transpose of V.
  For details of the algorithm, see Elmroth and Gustavson (cited above).

DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

 DGELQT3 recursively computes a LQ factorization of a real M-by-N
 matrix A, using the compact WY representation of Q.
 Based on the algorithm of Elmroth and Gustavson,
 IBM J. Res. Develop. Vol 44 No. 4 July 2000.

Parameters

M 

          M is INTEGER
          The number of rows of the matrix A.  M =< N.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the real M-by-N matrix A.  On exit, the elements on and
          below the diagonal contain the N-by-N lower triangular matrix L; the
          elements above the diagonal are the rows of V.  See below for
          further details.

LDA

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

T

          T is DOUBLE PRECISION array, dimension (LDT,N)
          The N-by-N upper triangular factor of the block reflector.
          The elements on and above the diagonal contain the block
          reflector T; the elements below the diagonal are not used.
          See below for further details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,N).

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.

Further Details:

  The matrix V stores the elementary reflectors H(i) in the i-th row
  above the diagonal. For example, if M=5 and N=3, the matrix V is
               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (     1  v3 v3 v3 )
  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
  block reflector H is then given by
               H = I - V * T * V**T
  where V**T is the transpose of V.
  For details of the algorithm, see Elmroth and Gustavson (cited above).

SGELQT3

Purpose:

 SGELQT3 recursively computes a LQ factorization of a real M-by-N
 matrix A, using the compact WY representation of Q.
 Based on the algorithm of Elmroth and Gustavson,
 IBM J. Res. Develop. Vol 44 No. 4 July 2000.

Parameters

M 

          M is INTEGER
          The number of rows of the matrix A.  M =< N.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is REAL array, dimension (LDA,N)
          On entry, the real M-by-N matrix A.  On exit, the elements on and
          below the diagonal contain the N-by-N lower triangular matrix L; the
          elements above the diagonal are the rows of V.  See below for
          further details.

LDA

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

T

          T is REAL array, dimension (LDT,N)
          The N-by-N upper triangular factor of the block reflector.
          The elements on and above the diagonal contain the block
          reflector T; the elements below the diagonal are not used.
          See below for further details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,N).

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.

Further Details:

  The matrix V stores the elementary reflectors H(i) in the i-th row
  above the diagonal. For example, if M=5 and N=3, the matrix V is
               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (     1  v3 v3 v3 )
  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
  block reflector H is then given by
               H = I - V * T * V**T
  where V**T is the transpose of V.
  For details of the algorithm, see Elmroth and Gustavson (cited above).

ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

 ZGELQT3 recursively computes a LQ factorization of a complex M-by-N
 matrix A, using the compact WY representation of Q.
 Based on the algorithm of Elmroth and Gustavson,
 IBM J. Res. Develop. Vol 44 No. 4 July 2000.

Parameters

M 

          M is INTEGER
          The number of rows of the matrix A.  M =< N.

N

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the complex M-by-N matrix A.  On exit, the elements on and
          below the diagonal contain the N-by-N lower triangular matrix L; the
          elements above the diagonal are the rows of V.  See below for
          further details.

LDA

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

T

          T is COMPLEX*16 array, dimension (LDT,N)
          The N-by-N upper triangular factor of the block reflector.
          The elements on and above the diagonal contain the block
          reflector T; the elements below the diagonal are not used.
          See below for further details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,N).

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.

Further Details:

  The matrix V stores the elementary reflectors H(i) in the i-th row
  above the diagonal. For example, if M=5 and N=3, the matrix V is
               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (     1  v3 v3 v3 )
  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
  block reflector H is then given by
               H = I - V * T * V**T
  where V**T is the transpose of V.
  For details of the algorithm, see Elmroth and Gustavson (cited above).

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