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geql2(3) Library Functions Manual geql2(3)

NAME

geql2 - geql2: QL factor, level 2

SYNOPSIS

Functions


subroutine CGEQL2 (m, n, a, lda, tau, work, info)
CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. subroutine DGEQL2 (m, n, a, lda, tau, work, info)
DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. subroutine SGEQL2 (m, n, a, lda, tau, work, info)
SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. subroutine ZGEQL2 (m, n, a, lda, tau, work, info)
ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Detailed Description

Function Documentation

subroutine CGEQL2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

!>
!> CGEQL2 computes a QL factorization of a complex m by n matrix A:
!> A = Q * L.
!>

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 lower triangle of the subarray
!>          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
!>          if m <= n, the elements on and below the (n-m)-th
!>          superdiagonal contain the m by n lower trapezoidal matrix L;
!>          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 (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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
!>  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
!>

Definition at line 122 of file cgeql2.f.

subroutine DGEQL2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

!>
!> DGEQL2 computes a QL factorization of a real m by n matrix A:
!> A = Q * L.
!>

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 lower triangle of the subarray
!>          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
!>          if m <= n, the elements on and below the (n-m)-th
!>          superdiagonal contain the m by n lower trapezoidal matrix L;
!>          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 (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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
!>  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
!>

Definition at line 122 of file dgeql2.f.

subroutine SGEQL2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

!>
!> SGEQL2 computes a QL factorization of a real m by n matrix A:
!> A = Q * L.
!>

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 lower triangle of the subarray
!>          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
!>          if m <= n, the elements on and below the (n-m)-th
!>          superdiagonal contain the m by n lower trapezoidal matrix L;
!>          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 (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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
!>  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
!>

Definition at line 122 of file sgeql2.f.

subroutine ZGEQL2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

!>
!> ZGEQL2 computes a QL factorization of a complex m by n matrix A:
!> A = Q * L.
!>

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 lower triangle of the subarray
!>          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
!>          if m <= n, the elements on and below the (n-m)-th
!>          superdiagonal contain the m by n lower trapezoidal matrix L;
!>          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 (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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
!>  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
!>

Definition at line 122 of file zgeql2.f.

Author

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