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

Definition at line 133 of file cgeqr2p.f.

  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

Definition at line 133 of file dgeqr2p.f.

  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

Definition at line 133 of file sgeqr2p.f.

  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

Definition at line 133 of file zgeqr2p.f.

Author

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