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geqr2p(3) Library Functions Manual 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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