geqr2p(3)

NAME
geqr2p - geqr2p: QR factor, diag( R ) ≥ 0, level 2

SYNOPSIS

  Functions

subroutine cgeqr2p (m, n, a, lda, tau, work, info)
CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
subroutine dgeqr2p (m, n, a, lda, tau, work, info)
DGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
subroutine sgeqr2p (m, n, a, lda, tau, work, info)
SGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
subroutine zgeqr2p (m, n, a, lda, tau, work, info)
ZGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Detailed Description

Function Documentation

  subroutine cgeqr2p (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Purpose:

    !>
    !> CGEQR2P computes a QR factorization of a complex m-by-n matrix A:
    !>
    !>    A = Q * ( R ),
    !>            ( 0 )
    !>
    !> where:
    !>
    !>    Q is a m-by-m orthogonal matrix;
    !>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
    !>    entries;
    !>    0 is a (m-n)-by-n zero matrix, if m > n.
    !>
    !>

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, the elements on and above the diagonal of the array
    !>          contain the min(m,n) by n upper trapezoidal matrix R (R is
    !>          upper triangular if m >= n). The diagonal entries of R are
    !>          real and nonnegative; the elements below the diagonal,
    !>          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 (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 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**H
    !>
    !>  where tau is a complex scalar, and v is a complex vector with
    !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
    !>  and tau in TAU(i).
    !>
    !> See Lapack Working Note 203 for details
    !>

  subroutine dgeqr2p (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Purpose:

    !>
    !> DGEQR2P computes a QR factorization of a real m-by-n matrix A:
    !>
    !>    A = Q * ( R ),
    !>            ( 0 )
    !>
    !> where:
    !>
    !>    Q is a m-by-m orthogonal matrix;
    !>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
    !>    entries;
    !>    0 is a (m-n)-by-n zero matrix, if m > n.
    !>
    !>

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, the elements on and above the diagonal of the array
    !>          contain the min(m,n) by n upper trapezoidal matrix R (R is
    !>          upper triangular if m >= n). The diagonal entries of R are
    !>          nonnegative; the elements below the diagonal,
    !>          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 (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 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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
    !>  and tau in TAU(i).
    !>
    !> See Lapack Working Note 203 for details
    !>

  subroutine sgeqr2p (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Purpose:

    !>
    !> SGEQR2P computes a QR factorization of a real m-by-n matrix A:
    !>
    !>    A = Q * ( R ),
    !>            ( 0 )
    !>
    !> where:
    !>
    !>    Q is a m-by-m orthogonal matrix;
    !>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
    !>    entries;
    !>    0 is a (m-n)-by-n zero matrix, if m > n.
    !>
    !>

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, the elements on and above the diagonal of the array
    !>          contain the min(m,n) by n upper trapezoidal matrix R (R is
    !>          upper triangular if m >= n). The diagonal entries of R
    !>          are nonnegative; the elements below the diagonal,
    !>          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 (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 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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
    !>  and tau in TAU(i).
    !>
    !> See Lapack Working Note 203 for details
    !>

  subroutine zgeqr2p (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

Purpose:

    !>
    !> ZGEQR2P computes a QR factorization of a complex m-by-n matrix A:
    !>
    !>    A = Q * ( R ),
    !>            ( 0 )
    !>
    !> where:
    !>
    !>    Q is a m-by-m orthogonal matrix;
    !>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
    !>    entries;
    !>    0 is a (m-n)-by-n zero matrix, if m > n.
    !>
    !>

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, the elements on and above the diagonal of the array
    !>          contain the min(m,n) by n upper trapezoidal matrix R (R is
    !>          upper triangular if m >= n). The diagonal entries of R
    !>          are real and nonnegative; the elements below the diagonal,
    !>          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 (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 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**H
    !>
    !>  where tau is a complex scalar, and v is a complex vector with
    !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
    !>  and tau in TAU(i).
    !>
    !> See Lapack Working Note 203 for details
    !>

Author

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