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gerq2(3) Library Functions Manual gerq2(3)

NAME

gerq2 - gerq2: RQ factor, level 2

SYNOPSIS

Functions


subroutine CGERQ2 (m, n, a, lda, tau, work, info)
CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. subroutine DGERQ2 (m, n, a, lda, tau, work, info)
DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. subroutine SGERQ2 (m, n, a, lda, tau, work, info)
SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. subroutine ZGERQ2 (m, n, a, lda, tau, work, info)
ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Detailed Description

Function Documentation

subroutine CGERQ2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

!>
!> CGERQ2 computes an RQ factorization of a complex m by n matrix A:
!> A = R * Q.
!>

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 >= 0.
!>

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the m by n matrix A.
!>          On exit, if m <= n, the upper triangle of the subarray
!>          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
!>          if m >= n, the elements on and above the (m-n)-th subdiagonal
!>          contain the m by n upper trapezoidal matrix R; the remaining
!>          elements, with the array TAU, represent the unitary matrix
!>          Q as a product of elementary reflectors (see Further
!>          Details).
!>

LDA

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

TAU

!>          TAU is COMPLEX array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>

WORK

!>          WORK is COMPLEX array, dimension (M)
!>

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 Q is represented as a product of elementary reflectors
!>
!>     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
!>  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
!>

Definition at line 122 of file cgerq2.f.

subroutine DGERQ2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

!>
!> DGERQ2 computes an RQ factorization of a real m by n matrix A:
!> A = R * Q.
!>

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 >= 0.
!>

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the m by n matrix A.
!>          On exit, if m <= n, the upper triangle of the subarray
!>          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
!>          if m >= n, the elements on and above the (m-n)-th subdiagonal
!>          contain the m by n upper trapezoidal matrix R; the remaining
!>          elements, with the array TAU, represent the orthogonal matrix
!>          Q as a product of elementary reflectors (see Further
!>          Details).
!>

LDA

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

TAU

!>          TAU is DOUBLE PRECISION array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (M)
!>

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 Q is represented as a product of elementary reflectors
!>
!>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
!>
!>  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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
!>  A(m-k+i,1:n-k+i-1), and tau in TAU(i).
!>

Definition at line 122 of file dgerq2.f.

subroutine SGERQ2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

!>
!> SGERQ2 computes an RQ factorization of a real m by n matrix A:
!> A = R * Q.
!>

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 >= 0.
!>

A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the m by n matrix A.
!>          On exit, if m <= n, the upper triangle of the subarray
!>          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
!>          if m >= n, the elements on and above the (m-n)-th subdiagonal
!>          contain the m by n upper trapezoidal matrix R; the remaining
!>          elements, with the array TAU, represent the orthogonal matrix
!>          Q as a product of elementary reflectors (see Further
!>          Details).
!>

LDA

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

TAU

!>          TAU is REAL array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>

WORK

!>          WORK is REAL array, dimension (M)
!>

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 Q is represented as a product of elementary reflectors
!>
!>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
!>
!>  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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
!>  A(m-k+i,1:n-k+i-1), and tau in TAU(i).
!>

Definition at line 122 of file sgerq2.f.

subroutine ZGERQ2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

!>
!> ZGERQ2 computes an RQ factorization of a complex m by n matrix A:
!> A = R * Q.
!>

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 >= 0.
!>

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the m by n matrix A.
!>          On exit, if m <= n, the upper triangle of the subarray
!>          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
!>          if m >= n, the elements on and above the (m-n)-th subdiagonal
!>          contain the m by n upper trapezoidal matrix R; the remaining
!>          elements, with the array TAU, represent the unitary matrix
!>          Q as a product of elementary reflectors (see Further
!>          Details).
!>

LDA

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

TAU

!>          TAU is COMPLEX*16 array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>

WORK

!>          WORK is COMPLEX*16 array, dimension (M)
!>

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 Q is represented as a product of elementary reflectors
!>
!>     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
!>  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
!>

Definition at line 122 of file zgerq2.f.

Author

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