Library Functions Manual

NAME¶

launhr_col_getrfnp - la{un,or}hr_col_getrfnp: LU factor without pivoting

SYNOPSIS¶

Functions¶

subroutine CLAUNHR_COL_GETRFNP (m, n, a, lda, d, info)
CLAUNHR_COL_GETRFNP subroutine DLAORHR_COL_GETRFNP (m, n, a, lda, d, info)
DLAORHR_COL_GETRFNP subroutine SLAORHR_COL_GETRFNP (m, n, a, lda, d, info)
SLAORHR_COL_GETRFNP subroutine ZLAUNHR_COL_GETRFNP (m, n, a, lda, d, info)
ZLAUNHR_COL_GETRFNP

Detailed Description¶

Function Documentation¶

subroutine CLAUNHR_COL_GETRFNP (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) d, integer info)¶

CLAUNHR_COL_GETRFNP

Purpose:

!>
!> CLAUNHR_COL_GETRFNP computes the modified LU factorization without
!> pivoting of a complex general M-by-N matrix A. The factorization has
!> the form:
!>
!>     A - S = L * U,
!>
!> where:
!>    S is a m-by-n diagonal sign matrix with the diagonal D, so that
!>    D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
!>    as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
!>    i-1 steps of Gaussian elimination. This means that the diagonal
!>    element at each step of  Gaussian elimination is
!>    at least one in absolute value (so that division-by-zero not
!>    not possible during the division by the diagonal element);
!>
!>    L is a M-by-N lower triangular matrix with unit diagonal elements
!>    (lower trapezoidal if M > N);
!>
!>    and U is a M-by-N upper triangular matrix
!>    (upper trapezoidal if M < N).
!>
!> This routine is an auxiliary routine used in the Householder
!> reconstruction routine CUNHR_COL. In CUNHR_COL, this routine is
!> applied to an M-by-N matrix A with orthonormal columns, where each
!> element is bounded by one in absolute value. With the choice of
!> the matrix S above, one can show that the diagonal element at each
!> step of Gaussian elimination is the largest (in absolute value) in
!> the column on or below the diagonal, so that no pivoting is required
!> for numerical stability [1].
!>
!> For more details on the Householder reconstruction algorithm,
!> including the modified LU factorization, see [1].
!>
!> This is the blocked right-looking version of the algorithm,
!> calling Level 3 BLAS to update the submatrix. To factorize a block,
!> this routine calls the recursive routine CLAUNHR_COL_GETRFNP2.
!>
!> [1] ,
!>     G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
!>     E. Solomonik, J. Parallel Distrib. Comput.,
!>     vol. 85, pp. 3-31, 2015.
!>

Parameters

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the M-by-N matrix to be factored.
!>          On exit, the factors L and U from the factorization
!>          A-S=L*U; the unit diagonal elements of L are not stored.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

!>          D is COMPLEX array, dimension min(M,N)
!>          The diagonal elements of the diagonal M-by-N sign matrix S,
!>          D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can be
!>          only ( +1.0, 0.0 ) or (-1.0, 0.0 ).
!>

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.

Contributors:

!>
!> November 2019, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>

Definition at line 145 of file claunhr_col_getrfnp.f.

subroutine DLAORHR_COL_GETRFNP (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, integer info)¶

DLAORHR_COL_GETRFNP

Purpose:

!>
!> DLAORHR_COL_GETRFNP computes the modified LU factorization without
!> pivoting of a real general M-by-N matrix A. The factorization has
!> the form:
!>
!>     A - S = L * U,
!>
!> where:
!>    S is a m-by-n diagonal sign matrix with the diagonal D, so that
!>    D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
!>    as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
!>    i-1 steps of Gaussian elimination. This means that the diagonal
!>    element at each step of  Gaussian elimination is
!>    at least one in absolute value (so that division-by-zero not
!>    not possible during the division by the diagonal element);
!>
!>    L is a M-by-N lower triangular matrix with unit diagonal elements
!>    (lower trapezoidal if M > N);
!>
!>    and U is a M-by-N upper triangular matrix
!>    (upper trapezoidal if M < N).
!>
!> This routine is an auxiliary routine used in the Householder
!> reconstruction routine DORHR_COL. In DORHR_COL, this routine is
!> applied to an M-by-N matrix A with orthonormal columns, where each
!> element is bounded by one in absolute value. With the choice of
!> the matrix S above, one can show that the diagonal element at each
!> step of Gaussian elimination is the largest (in absolute value) in
!> the column on or below the diagonal, so that no pivoting is required
!> for numerical stability [1].
!>
!> For more details on the Householder reconstruction algorithm,
!> including the modified LU factorization, see [1].
!>
!> This is the blocked right-looking version of the algorithm,
!> calling Level 3 BLAS to update the submatrix. To factorize a block,
!> this routine calls the recursive routine DLAORHR_COL_GETRFNP2.
!>
!> [1] ,
!>     G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
!>     E. Solomonik, J. Parallel Distrib. Comput.,
!>     vol. 85, pp. 3-31, 2015.
!>

Parameters

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the M-by-N matrix to be factored.
!>          On exit, the factors L and U from the factorization
!>          A-S=L*U; the unit diagonal elements of L are not stored.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

!>          D is DOUBLE PRECISION array, dimension min(M,N)
!>          The diagonal elements of the diagonal M-by-N sign matrix S,
!>          D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can
!>          be only plus or minus one.
!>

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.

Contributors:

!>
!> November 2019, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>

Definition at line 145 of file dlaorhr_col_getrfnp.f.

subroutine SLAORHR_COL_GETRFNP (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) d, integer info)¶

SLAORHR_COL_GETRFNP

Purpose:

!>
!> SLAORHR_COL_GETRFNP computes the modified LU factorization without
!> pivoting of a real general M-by-N matrix A. The factorization has
!> the form:
!>
!>     A - S = L * U,
!>
!> where:
!>    S is a m-by-n diagonal sign matrix with the diagonal D, so that
!>    D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
!>    as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
!>    i-1 steps of Gaussian elimination. This means that the diagonal
!>    element at each step of  Gaussian elimination is
!>    at least one in absolute value (so that division-by-zero not
!>    not possible during the division by the diagonal element);
!>
!>    L is a M-by-N lower triangular matrix with unit diagonal elements
!>    (lower trapezoidal if M > N);
!>
!>    and U is a M-by-N upper triangular matrix
!>    (upper trapezoidal if M < N).
!>
!> This routine is an auxiliary routine used in the Householder
!> reconstruction routine SORHR_COL. In SORHR_COL, this routine is
!> applied to an M-by-N matrix A with orthonormal columns, where each
!> element is bounded by one in absolute value. With the choice of
!> the matrix S above, one can show that the diagonal element at each
!> step of Gaussian elimination is the largest (in absolute value) in
!> the column on or below the diagonal, so that no pivoting is required
!> for numerical stability [1].
!>
!> For more details on the Householder reconstruction algorithm,
!> including the modified LU factorization, see [1].
!>
!> This is the blocked right-looking version of the algorithm,
!> calling Level 3 BLAS to update the submatrix. To factorize a block,
!> this routine calls the recursive routine SLAORHR_COL_GETRFNP2.
!>
!> [1] ,
!>     G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
!>     E. Solomonik, J. Parallel Distrib. Comput.,
!>     vol. 85, pp. 3-31, 2015.
!>

Parameters

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the M-by-N matrix to be factored.
!>          On exit, the factors L and U from the factorization
!>          A-S=L*U; the unit diagonal elements of L are not stored.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

!>          D is REAL array, dimension min(M,N)
!>          The diagonal elements of the diagonal M-by-N sign matrix S,
!>          D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can
!>          be only plus or minus one.
!>

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.

Contributors:

!>
!> November 2019, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>

Definition at line 145 of file slaorhr_col_getrfnp.f.

subroutine ZLAUNHR_COL_GETRFNP (integer m, integer n, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) d, integer info)¶

ZLAUNHR_COL_GETRFNP

Purpose:

!>
!> ZLAUNHR_COL_GETRFNP computes the modified LU factorization without
!> pivoting of a complex general M-by-N matrix A. The factorization has
!> the form:
!>
!>     A - S = L * U,
!>
!> where:
!>    S is a m-by-n diagonal sign matrix with the diagonal D, so that
!>    D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
!>    as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
!>    i-1 steps of Gaussian elimination. This means that the diagonal
!>    element at each step of  Gaussian elimination is
!>    at least one in absolute value (so that division-by-zero not
!>    not possible during the division by the diagonal element);
!>
!>    L is a M-by-N lower triangular matrix with unit diagonal elements
!>    (lower trapezoidal if M > N);
!>
!>    and U is a M-by-N upper triangular matrix
!>    (upper trapezoidal if M < N).
!>
!> This routine is an auxiliary routine used in the Householder
!> reconstruction routine ZUNHR_COL. In ZUNHR_COL, this routine is
!> applied to an M-by-N matrix A with orthonormal columns, where each
!> element is bounded by one in absolute value. With the choice of
!> the matrix S above, one can show that the diagonal element at each
!> step of Gaussian elimination is the largest (in absolute value) in
!> the column on or below the diagonal, so that no pivoting is required
!> for numerical stability [1].
!>
!> For more details on the Householder reconstruction algorithm,
!> including the modified LU factorization, see [1].
!>
!> This is the blocked right-looking version of the algorithm,
!> calling Level 3 BLAS to update the submatrix. To factorize a block,
!> this routine calls the recursive routine ZLAUNHR_COL_GETRFNP2.
!>
!> [1] ,
!>     G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
!>     E. Solomonik, J. Parallel Distrib. Comput.,
!>     vol. 85, pp. 3-31, 2015.
!>

Parameters

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix to be factored.
!>          On exit, the factors L and U from the factorization
!>          A-S=L*U; the unit diagonal elements of L are not stored.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

!>          D is COMPLEX*16 array, dimension min(M,N)
!>          The diagonal elements of the diagonal M-by-N sign matrix S,
!>          D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can be
!>          only ( +1.0, 0.0 ) or (-1.0, 0.0 ).
!>

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.

Contributors:

!>
!> November 2019, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>

Definition at line 145 of file zlaunhr_col_getrfnp.f.

Author¶

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NAME¶

SYNOPSIS¶

Functions¶

Detailed Description¶

Function Documentation¶

subroutine CLAUNHR_COL_GETRFNP (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) d, integer info)¶

subroutine DLAORHR_COL_GETRFNP (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, integer info)¶

subroutine SLAORHR_COL_GETRFNP (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) d, integer info)¶

subroutine ZLAUNHR_COL_GETRFNP (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) d, integer info)¶

Author¶

subroutine ZLAUNHR_COL_GETRFNP (integer m, integer n, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) d, integer info)¶