Man page - lahef_rook(3)

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Manual

lahef_rook

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine clahef_rook (character uplo, integer n, integer nb, integer kb,complex, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)
subroutine clasyf_rook (character uplo, integer n, integer nb, integer kb,complex, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)
subroutine dlasyf_rook (character uplo, integer n, integer nb, integer kb,double precision, dimension( lda, * ) a, integer lda, integer,dimension( * ) ipiv, double precision, dimension( ldw, * ) w, integerldw, integer info)
subroutine slasyf_rook (character uplo, integer n, integer nb, integer kb,real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,real, dimension( ldw, * ) w, integer ldw, integer info)
subroutine zlahef_rook (character uplo, integer n, integer nb, integer kb,complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)
subroutine zlasyf_rook (character uplo, integer n, integer nb, integer kb,complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)
Author

NAME

lahef_rook - la{he,sy}f_rook: triangular factor step

SYNOPSIS

Functions

subroutine clahef_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
subroutine clasyf_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
CLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.
subroutine dlasyf_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
DLASYF_ROOK *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.
subroutine slasyf_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
SLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.
subroutine zlahef_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
subroutine zlasyf_rook (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
ZLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.

Detailed Description

Function Documentation

subroutine clahef_rook (character uplo, integer n, integer nb, integer kb,complex, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)

Purpose:

CLAHEF_ROOK computes a partial factorization of a complex Hermitian
matrix A using the bounded Bunch-Kaufman (’rook’) diagonal pivoting
method. The partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ’U’, or:
( 0 U22 ) ( 0 D ) ( U12**H U22**H )

A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = ’L’
( L21 I ) ( 0 A22 ) ( 0 I )

where the order of D is at most NB. The actual order is returned in
the argument KB, and is either NB or NB-1, or N if N <= NB.
Note that U**H denotes the conjugate transpose of U.

CLAHEF_ROOK is an auxiliary routine called by CHETRF_ROOK. It uses
blocked code (calling Level 3 BLAS) to update the submatrix
A11 (if UPLO = ’U’) or A22 (if UPLO = ’L’).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= ’U’: Upper triangular
= ’L’: Lower triangular

N

N is INTEGER
The order of the matrix A. N >= 0.

NB

NB is INTEGER
The maximum number of columns of the matrix A that should be
factored. NB should be at least 2 to allow for 2-by-2 pivot
blocks.

KB

KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB.

A

A is COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = ’U’, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = ’L’, the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, A contains details of the partial factorization.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.

If UPLO = ’U’:
Only the last KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = ’L’:
Only the first KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

W

W is COMPLEX array, dimension (LDW,NB)

LDW

LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
> 0: if INFO = k, D(k,k) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine clasyf_rook (character uplo, integer n, integer nb, integer kb,complex, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)

CLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.

Purpose:

CLASYF_ROOK computes a partial factorization of a complex symmetric
matrix A using the bounded Bunch-Kaufman (’rook’) diagonal
pivoting method. The partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ’U’, or:
( 0 U22 ) ( 0 D ) ( U12**T U22**T )

A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = ’L’
( L21 I ) ( 0 A22 ) ( 0 I )

where the order of D is at most NB. The actual order is returned in
the argument KB, and is either NB or NB-1, or N if N <= NB.

CLASYF_ROOK is an auxiliary routine called by CSYTRF_ROOK. It uses
blocked code (calling Level 3 BLAS) to update the submatrix
A11 (if UPLO = ’U’) or A22 (if UPLO = ’L’).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= ’U’: Upper triangular
= ’L’: Lower triangular

N

N is INTEGER
The order of the matrix A. N >= 0.

NB

NB is INTEGER
The maximum number of columns of the matrix A that should be
factored. NB should be at least 2 to allow for 2-by-2 pivot
blocks.

KB

KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB.

A

A is COMPLEX array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = ’U’, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = ’L’, the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, A contains details of the partial factorization.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.

If UPLO = ’U’:
Only the last KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = ’L’:
Only the first KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

W

W is COMPLEX array, dimension (LDW,NB)

LDW

LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
> 0: if INFO = k, D(k,k) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine dlasyf_rook (character uplo, integer n, integer nb, integer kb,double precision, dimension( lda, * ) a, integer lda, integer,dimension( * ) ipiv, double precision, dimension( ldw, * ) w, integerldw, integer info)

DLASYF_ROOK *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.

Purpose:

DLASYF_ROOK computes a partial factorization of a real symmetric
matrix A using the bounded Bunch-Kaufman (’rook’) diagonal
pivoting method. The partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ’U’, or:
( 0 U22 ) ( 0 D ) ( U12**T U22**T )

A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = ’L’
( L21 I ) ( 0 A22 ) ( 0 I )

where the order of D is at most NB. The actual order is returned in
the argument KB, and is either NB or NB-1, or N if N <= NB.

DLASYF_ROOK is an auxiliary routine called by DSYTRF_ROOK. It uses
blocked code (calling Level 3 BLAS) to update the submatrix
A11 (if UPLO = ’U’) or A22 (if UPLO = ’L’).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= ’U’: Upper triangular
= ’L’: Lower triangular

N

N is INTEGER
The order of the matrix A. N >= 0.

NB

NB is INTEGER
The maximum number of columns of the matrix A that should be
factored. NB should be at least 2 to allow for 2-by-2 pivot
blocks.

KB

KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = ’U’, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = ’L’, the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, A contains details of the partial factorization.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.

If UPLO = ’U’:
Only the last KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = ’L’:
Only the first KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

W

W is DOUBLE PRECISION array, dimension (LDW,NB)

LDW

LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
> 0: if INFO = k, D(k,k) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine slasyf_rook (character uplo, integer n, integer nb, integer kb,real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,real, dimension( ldw, * ) w, integer ldw, integer info)

SLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.

Purpose:

SLASYF_ROOK computes a partial factorization of a real symmetric
matrix A using the bounded Bunch-Kaufman (’rook’) diagonal
pivoting method. The partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ’U’, or:
( 0 U22 ) ( 0 D ) ( U12**T U22**T )

A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = ’L’
( L21 I ) ( 0 A22 ) ( 0 I )

where the order of D is at most NB. The actual order is returned in
the argument KB, and is either NB or NB-1, or N if N <= NB.

SLASYF_ROOK is an auxiliary routine called by SSYTRF_ROOK. It uses
blocked code (calling Level 3 BLAS) to update the submatrix
A11 (if UPLO = ’U’) or A22 (if UPLO = ’L’).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= ’U’: Upper triangular
= ’L’: Lower triangular

N

N is INTEGER
The order of the matrix A. N >= 0.

NB

NB is INTEGER
The maximum number of columns of the matrix A that should be
factored. NB should be at least 2 to allow for 2-by-2 pivot
blocks.

KB

KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB.

A

A is REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = ’U’, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = ’L’, the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, A contains details of the partial factorization.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.

If UPLO = ’U’:
Only the last KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = ’L’:
Only the first KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

W

W is REAL array, dimension (LDW,NB)

LDW

LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
> 0: if INFO = k, D(k,k) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine zlahef_rook (character uplo, integer n, integer nb, integer kb,complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

Purpose:

ZLAHEF_ROOK computes a partial factorization of a complex Hermitian
matrix A using the bounded Bunch-Kaufman (’rook’) diagonal pivoting
method. The partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ’U’, or:
( 0 U22 ) ( 0 D ) ( U12**H U22**H )

A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = ’L’
( L21 I ) ( 0 A22 ) ( 0 I )

where the order of D is at most NB. The actual order is returned in
the argument KB, and is either NB or NB-1, or N if N <= NB.
Note that U**H denotes the conjugate transpose of U.

ZLAHEF_ROOK is an auxiliary routine called by ZHETRF_ROOK. It uses
blocked code (calling Level 3 BLAS) to update the submatrix
A11 (if UPLO = ’U’) or A22 (if UPLO = ’L’).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= ’U’: Upper triangular
= ’L’: Lower triangular

N

N is INTEGER
The order of the matrix A. N >= 0.

NB

NB is INTEGER
The maximum number of columns of the matrix A that should be
factored. NB should be at least 2 to allow for 2-by-2 pivot
blocks.

KB

KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB.

A

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = ’U’, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = ’L’, the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, A contains details of the partial factorization.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.

If UPLO = ’U’:
Only the last KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = ’L’:
Only the first KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

W

W is COMPLEX*16 array, dimension (LDW,NB)

LDW

LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
> 0: if INFO = k, D(k,k) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine zlasyf_rook (character uplo, integer n, integer nb, integer kb,complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

ZLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.

Purpose:

ZLASYF_ROOK computes a partial factorization of a complex symmetric
matrix A using the bounded Bunch-Kaufman (’rook’) diagonal
pivoting method. The partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ’U’, or:
( 0 U22 ) ( 0 D ) ( U12**T U22**T )

A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = ’L’
( L21 I ) ( 0 A22 ) ( 0 I )

where the order of D is at most NB. The actual order is returned in
the argument KB, and is either NB or NB-1, or N if N <= NB.

ZLASYF_ROOK is an auxiliary routine called by ZSYTRF_ROOK. It uses
blocked code (calling Level 3 BLAS) to update the submatrix
A11 (if UPLO = ’U’) or A22 (if UPLO = ’L’).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= ’U’: Upper triangular
= ’L’: Lower triangular

N

N is INTEGER
The order of the matrix A. N >= 0.

NB

NB is INTEGER
The maximum number of columns of the matrix A that should be
factored. NB should be at least 2 to allow for 2-by-2 pivot
blocks.

KB

KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB.

A

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = ’U’, the leading
n-by-n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = ’L’, the
leading n-by-n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, A contains details of the partial factorization.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.

If UPLO = ’U’:
Only the last KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = ’L’:
Only the first KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

W

W is COMPLEX*16 array, dimension (LDW,NB)

LDW

LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
> 0: if INFO = k, D(k,k) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

Author

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