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tzrzf - Man Page

tzrzf: RZ factor

Synopsis

Functions

subroutine ctzrzf (m, n, a, lda, tau, work, lwork, info)
CTZRZF
subroutine dtzrzf (m, n, a, lda, tau, work, lwork, info)
DTZRZF
subroutine stzrzf (m, n, a, lda, tau, work, lwork, info)
STZRZF
subroutine ztzrzf (m, n, a, lda, tau, work, lwork, info)
ZTZRZF

Detailed Description

Function Documentation

subroutine ctzrzf (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

CTZRZF  

Purpose:

 CTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
 to upper triangular form by means of unitary transformations.

 The upper trapezoidal matrix A is factored as

    A = ( R  0 ) * Z,

 where Z is an N-by-N unitary matrix and R is an M-by-M upper
 triangular matrix.
Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

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

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the leading M-by-N upper trapezoidal part of the
          array A must contain the matrix to be factorized.
          On exit, the leading M-by-M upper triangular part of A
          contains the upper triangular matrix R, and elements M+1 to
          N of the first M rows of A, with the array TAU, represent the
          unitary matrix Z as a product of M elementary reflectors.

LDA

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

TAU

          TAU is COMPLEX array, dimension (M)
          The scalar factors of the elementary reflectors.

WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,M).
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

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.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

  The N-by-N matrix Z can be computed by

     Z =  Z(1)*Z(2)* ... *Z(M)

  where each N-by-N Z(k) is given by

     Z(k) = I - tau(k)*v(k)*v(k)**H

  with v(k) is the kth row vector of the M-by-N matrix

     V = ( I   A(:,M+1:N) )

  I is the M-by-M identity matrix, A(:,M+1:N)
  is the output stored in A on exit from CTZRZF,
  and tau(k) is the kth element of the array TAU.

Definition at line 150 of file ctzrzf.f.

subroutine dtzrzf (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DTZRZF  

Purpose:

 DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
 to upper triangular form by means of orthogonal transformations.

 The upper trapezoidal matrix A is factored as

    A = ( R  0 ) * Z,

 where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
 triangular matrix.
Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

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

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the leading M-by-N upper trapezoidal part of the
          array A must contain the matrix to be factorized.
          On exit, the leading M-by-M upper triangular part of A
          contains the upper triangular matrix R, and elements M+1 to
          N of the first M rows of A, with the array TAU, represent the
          orthogonal matrix Z as a product of M elementary reflectors.

LDA

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

TAU

          TAU is DOUBLE PRECISION array, dimension (M)
          The scalar factors of the elementary reflectors.

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,M).
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

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.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

  The N-by-N matrix Z can be computed by

     Z =  Z(1)*Z(2)* ... *Z(M)

  where each N-by-N Z(k) is given by

     Z(k) = I - tau(k)*v(k)*v(k)**T

  with v(k) is the kth row vector of the M-by-N matrix

     V = ( I   A(:,M+1:N) )

  I is the M-by-M identity matrix, A(:,M+1:N)
  is the output stored in A on exit from DTZRZF,
  and tau(k) is the kth element of the array TAU.

Definition at line 150 of file dtzrzf.f.

subroutine stzrzf (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

STZRZF  

Purpose:

 STZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
 to upper triangular form by means of orthogonal transformations.

 The upper trapezoidal matrix A is factored as

    A = ( R  0 ) * Z,

 where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
 triangular matrix.
Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

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

A

          A is REAL array, dimension (LDA,N)
          On entry, the leading M-by-N upper trapezoidal part of the
          array A must contain the matrix to be factorized.
          On exit, the leading M-by-M upper triangular part of A
          contains the upper triangular matrix R, and elements M+1 to
          N of the first M rows of A, with the array TAU, represent the
          orthogonal matrix Z as a product of M elementary reflectors.

LDA

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

TAU

          TAU is REAL array, dimension (M)
          The scalar factors of the elementary reflectors.

WORK

          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,M).
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

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.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

  The N-by-N matrix Z can be computed by

     Z =  Z(1)*Z(2)* ... *Z(M)

  where each N-by-N Z(k) is given by

     Z(k) = I - tau(k)*v(k)*v(k)**T

  with v(k) is the kth row vector of the M-by-N matrix

     V = ( I   A(:,M+1:N) )

  I is the M-by-M identity matrix, A(:,M+1:N)
  is the output stored in A on exit from STZRZF,
  and tau(k) is the kth element of the array TAU.

Definition at line 150 of file stzrzf.f.

subroutine ztzrzf (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZTZRZF  

Purpose:

 ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
 to upper triangular form by means of unitary transformations.

 The upper trapezoidal matrix A is factored as

    A = ( R  0 ) * Z,

 where Z is an N-by-N unitary matrix and R is an M-by-M upper
 triangular matrix.
Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

N

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

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the leading M-by-N upper trapezoidal part of the
          array A must contain the matrix to be factorized.
          On exit, the leading M-by-M upper triangular part of A
          contains the upper triangular matrix R, and elements M+1 to
          N of the first M rows of A, with the array TAU, represent the
          unitary matrix Z as a product of M elementary reflectors.

LDA

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

TAU

          TAU is COMPLEX*16 array, dimension (M)
          The scalar factors of the elementary reflectors.

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,M).
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

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.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

  The N-by-N matrix Z can be computed by

     Z =  Z(1)*Z(2)* ... *Z(M)

  where each N-by-N Z(k) is given by

     Z(k) = I - tau(k)*v(k)*v(k)**H

  with v(k) is the kth row vector of the M-by-N matrix

     V = ( I   A(:,M+1:N) )

  I is the M-by-M identity matrix, A(:,M+1:N)
  is the output stored in A on exit from ZTZRZF,
  and tau(k) is the kth element of the array TAU.

Definition at line 150 of file ztzrzf.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK