Man page - lahef(3)

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Manual

lahef

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine clahef (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 (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 (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 (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 (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 (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 - la{he,sy}f: step in hetrf

SYNOPSIS

Functions

subroutine clahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
subroutine clasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
subroutine dlasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
DLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
subroutine slasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
subroutine zlahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
subroutine zlasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Detailed Description

Function Documentation

subroutine clahef (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)

CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

Purpose:

CLAHEF computes a partial factorization of a complex Hermitian
matrix A using the Bunch-Kaufman diagonal pivoting method. The
partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ā€™Uā€™, or:
( 0 U22 ) ( 0 D ) ( U12**H U22**H )

A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = ā€™Lā€™
( 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 is an auxiliary routine called by CHETRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ā€™Uā€™) or
A22 (if UPLO = ā€™Lā€™).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 = ā€™Uā€™:
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) = IPIV(k-1) < 0, then rows and columns
k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
is a 2-by-2 diagonal block.

If UPLO = ā€™Lā€™:
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) = IPIV(k+1) < 0, then rows and columns
k+1 and -IPIV(k) were interchanged and 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

subroutine clasyf (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 computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Purpose:

CLASYF computes a partial factorization of a complex symmetric matrix
A using the Bunch-Kaufman diagonal pivoting method. The partial
factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ā€™Uā€™, or:
( 0 U22 ) ( 0 D ) ( U12**T U22**T )

A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = ā€™Lā€™
( 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**T denotes the transpose of U.

CLASYF is an auxiliary routine called by CSYTRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ā€™Uā€™) or
A22 (if UPLO = ā€™Lā€™).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 = ā€™Uā€™:
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) = IPIV(k-1) < 0, then rows and columns
k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
is a 2-by-2 diagonal block.

If UPLO = ā€™Lā€™:
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) = IPIV(k+1) < 0, then rows and columns
k+1 and -IPIV(k) were interchanged and 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

subroutine dlasyf (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 computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Purpose:

DLASYF computes a partial factorization of a real symmetric matrix A
using the Bunch-Kaufman diagonal pivoting method. The partial
factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ā€™Uā€™, or:
( 0 U22 ) ( 0 D ) ( U12**T U22**T )

A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = ā€™Lā€™
( 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 is an auxiliary routine called by DSYTRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ā€™Uā€™) or
A22 (if UPLO = ā€™Lā€™).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 = ā€™Uā€™:
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) = IPIV(k-1) < 0, then rows and columns
k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
is a 2-by-2 diagonal block.

If UPLO = ā€™Lā€™:
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) = IPIV(k+1) < 0, then rows and columns
k+1 and -IPIV(k) were interchanged and 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

subroutine slasyf (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 computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Purpose:

SLASYF computes a partial factorization of a real symmetric matrix A
using the Bunch-Kaufman diagonal pivoting method. The partial
factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ā€™Uā€™, or:
( 0 U22 ) ( 0 D ) ( U12**T U22**T )

A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = ā€™Lā€™
( 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 is an auxiliary routine called by SSYTRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ā€™Uā€™) or
A22 (if UPLO = ā€™Lā€™).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 = ā€™Uā€™:
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) = IPIV(k-1) < 0, then rows and columns
k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
is a 2-by-2 diagonal block.

If UPLO = ā€™Lā€™:
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) = IPIV(k+1) < 0, then rows and columns
k+1 and -IPIV(k) were interchanged and 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

subroutine zlahef (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)

ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

Purpose:

ZLAHEF computes a partial factorization of a complex Hermitian
matrix A using the Bunch-Kaufman diagonal pivoting method. The
partial factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ā€™Uā€™, or:
( 0 U22 ) ( 0 D ) ( U12**H U22**H )

A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = ā€™Lā€™
( 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 is an auxiliary routine called by ZHETRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ā€™Uā€™) or
A22 (if UPLO = ā€™Lā€™).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 = ā€™Uā€™:
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) = IPIV(k-1) < 0, then rows and columns
k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
is a 2-by-2 diagonal block.

If UPLO = ā€™Lā€™:
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) = IPIV(k+1) < 0, then rows and columns
k+1 and -IPIV(k) were interchanged and 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:

December 2016, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

subroutine zlasyf (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 computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Purpose:

ZLASYF computes a partial factorization of a complex symmetric matrix
A using the Bunch-Kaufman diagonal pivoting method. The partial
factorization has the form:

A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ā€™Uā€™, or:
( 0 U22 ) ( 0 D ) ( U12**T U22**T )

A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = ā€™Lā€™
( 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**T denotes the transpose of U.

ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ā€™Uā€™) or
A22 (if UPLO = ā€™Lā€™).

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 = ā€™Uā€™:
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) = IPIV(k-1) < 0, then rows and columns
k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
is a 2-by-2 diagonal block.

If UPLO = ā€™Lā€™:
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) = IPIV(k+1) < 0, then rows and columns
k+1 and -IPIV(k) were interchanged and 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

Author

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