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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