Man page - gerq2(3)

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Manual

gerq2(3) LAPACK gerq2(3)

gerq2 - gerq2: RQ factor, level 2


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).

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).

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).

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).

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