gerq2 - Man Page

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.

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.

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.

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.

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.