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hetrf_aa_2stage(3) Library Functions Manual hetrf_aa_2stage(3)

NAME

hetrf_aa_2stage - {he,sy}trf_aa_2stage: triangular factor

SYNOPSIS

Functions


subroutine CHETRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
CHETRF_AA_2STAGE subroutine CSYTRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
CSYTRF_AA_2STAGE subroutine DSYTRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
DSYTRF_AA_2STAGE subroutine SSYTRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
SSYTRF_AA_2STAGE subroutine ZHETRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
ZHETRF_AA_2STAGE subroutine ZSYTRF_AA_2STAGE (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
ZSYTRF_AA_2STAGE

Detailed Description

Function Documentation

subroutine CHETRF_AA_2STAGE (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( * ) work, integer lwork, integer info)

CHETRF_AA_2STAGE

Purpose:

!>
!> CHETRF_AA_2STAGE computes the factorization of a real hermitian matrix A
!> using the Aasen's algorithm.  The form of the factorization is
!>
!>    A = U**T*T*U  or  A = L*T*L**T
!>
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is a hermitian band matrix with the
!> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is 
!> LU factorized with partial pivoting).
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

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, L is stored below (or above) the subdiagonal blocks,
!>          when UPLO  is 'L' (or 'U').
!>

LDA

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

TB

!>          TB is COMPLEX array, dimension (LTB)
!>          On exit, details of the LU factorization of the band matrix.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N, internally
!>          used to select NB such that LTB >= (3*NB+1)*N.
!>
!>          If LTB = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of LTB, 
!>          returns this value as the first entry of TB, and
!>          no error message related to LTB is issued by XERBLA.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of T were interchanged with the
!>          row and column IPIV(k).
!>

WORK

!>          WORK is COMPLEX workspace of size LWORK
!>

LWORK

!>          LWORK is INTEGER
!>          The size of WORK. LWORK >= N, internally used to select NB
!>          such that LWORK >= N*NB.
!>
!>          If LWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of the WORK array,
!>          returns this value as the first entry of the WORK array, and
!>          no error message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = i, band LU factorization failed on i-th column
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file chetrf_aa_2stage.f.

subroutine CSYTRF_AA_2STAGE (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( * ) work, integer lwork, integer info)

CSYTRF_AA_2STAGE

Purpose:

!>
!> CSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
!> using the Aasen's algorithm.  The form of the factorization is
!>
!>    A = U**T*T*U  or  A = L*T*L**T
!>
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is a complex symmetric band matrix with the
!> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is 
!> LU factorized with partial pivoting).
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

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, L is stored below (or above) the subdiagonal blocks,
!>          when UPLO  is 'L' (or 'U').
!>

LDA

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

TB

!>          TB is COMPLEX array, dimension (LTB)
!>          On exit, details of the LU factorization of the band matrix.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N, internally
!>          used to select NB such that LTB >= (3*NB+1)*N.
!>
!>          If LTB = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of LTB, 
!>          returns this value as the first entry of TB, and
!>          no error message related to LTB is issued by XERBLA.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of T were interchanged with the
!>          row and column IPIV(k).
!>

WORK

!>          WORK is COMPLEX workspace of size LWORK
!>

LWORK

!>          LWORK is INTEGER
!>          The size of WORK. LWORK >= N, internally used to select NB
!>          such that LWORK >= N*NB.
!>
!>          If LWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of the WORK array,
!>          returns this value as the first entry of the WORK array, and
!>          no error message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = i, band LU factorization failed on i-th column
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file csytrf_aa_2stage.f.

subroutine DSYTRF_AA_2STAGE (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRF_AA_2STAGE

Purpose:

!>
!> DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
!> using the Aasen's algorithm.  The form of the factorization is
!>
!>    A = U**T*T*U  or  A = L*T*L**T
!>
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is a symmetric band matrix with the
!> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is 
!> LU factorized with partial pivoting).
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

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, L is stored below (or above) the subdiagonal blocks,
!>          when UPLO  is 'L' (or 'U').
!>

LDA

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

TB

!>          TB is DOUBLE PRECISION array, dimension (LTB)
!>          On exit, details of the LU factorization of the band matrix.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N, internally
!>          used to select NB such that LTB >= (3*NB+1)*N.
!>
!>          If LTB = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of LTB, 
!>          returns this value as the first entry of TB, and
!>          no error message related to LTB is issued by XERBLA.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of T were interchanged with the
!>          row and column IPIV2(k).
!>

WORK

!>          WORK is DOUBLE PRECISION workspace of size LWORK
!>

LWORK

!>          LWORK is INTEGER
!>          The size of WORK. LWORK >= N, internally used to select NB
!>          such that LWORK >= N*NB.
!>
!>          If LWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of the WORK array,
!>          returns this value as the first entry of the WORK array, and
!>          no error message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = i, band LU factorization failed on i-th column
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file dsytrf_aa_2stage.f.

subroutine SSYTRF_AA_2STAGE (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( * ) work, integer lwork, integer info)

SSYTRF_AA_2STAGE

Purpose:

!>
!> SSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
!> using the Aasen's algorithm.  The form of the factorization is
!>
!>    A = U**T*T*U  or  A = L*T*L**T
!>
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is a symmetric band matrix with the
!> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is 
!> LU factorized with partial pivoting).
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

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, L is stored below (or above) the subdiagonal blocks,
!>          when UPLO  is 'L' (or 'U').
!>

LDA

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

TB

!>          TB is REAL array, dimension (LTB)
!>          On exit, details of the LU factorization of the band matrix.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N, internally
!>          used to select NB such that LTB >= (3*NB+1)*N.
!>
!>          If LTB = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of LTB, 
!>          returns this value as the first entry of TB, and
!>          no error message related to LTB is issued by XERBLA.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of T were interchanged with the
!>          row and column IPIV(k).
!>

WORK

!>          WORK is REAL workspace of size LWORK
!>

LWORK

!>          LWORK is INTEGER
!>          The size of WORK. LWORK >= N, internally used to select NB
!>          such that LWORK >= N*NB.
!>
!>          If LWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of the WORK array,
!>          returns this value as the first entry of the WORK array, and
!>          no error message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = i, band LU factorization failed on i-th column
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file ssytrf_aa_2stage.f.

subroutine ZHETRF_AA_2STAGE (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( * ) work, integer lwork, integer info)

ZHETRF_AA_2STAGE

Purpose:

!>
!> ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A
!> using the Aasen's algorithm.  The form of the factorization is
!>
!>    A = U**H*T*U  or  A = L*T*L**H
!>
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is a hermitian band matrix with the
!> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is 
!> LU factorized with partial pivoting).
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

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, L is stored below (or above) the subdiagonal blocks,
!>          when UPLO  is 'L' (or 'U').
!>

LDA

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

TB

!>          TB is COMPLEX*16 array, dimension (LTB)
!>          On exit, details of the LU factorization of the band matrix.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N, internally
!>          used to select NB such that LTB >= (3*NB+1)*N.
!>
!>          If LTB = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of LTB, 
!>          returns this value as the first entry of TB, and
!>          no error message related to LTB is issued by XERBLA.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of T were interchanged with the
!>          row and column IPIV(k).
!>

WORK

!>          WORK is COMPLEX*16 workspace of size LWORK
!>

LWORK

!>          LWORK is INTEGER
!>          The size of WORK. LWORK >= N, internally used to select NB
!>          such that LWORK >= N*NB.
!>
!>          If LWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of the WORK array,
!>          returns this value as the first entry of the WORK array, and
!>          no error message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = i, band LU factorization failed on i-th column
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file zhetrf_aa_2stage.f.

subroutine ZSYTRF_AA_2STAGE (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( * ) work, integer lwork, integer info)

ZSYTRF_AA_2STAGE

Purpose:

!>
!> ZSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
!> using the Aasen's algorithm.  The form of the factorization is
!>
!>    A = U**T*T*U  or  A = L*T*L**T
!>
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is a complex symmetric band matrix with the
!> bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is 
!> LU factorized with partial pivoting).
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

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

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, L is stored below (or above) the subdiagonal blocks,
!>          when UPLO  is 'L' (or 'U').
!>

LDA

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

TB

!>          TB is COMPLEX*16 array, dimension (LTB)
!>          On exit, details of the LU factorization of the band matrix.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N, internally
!>          used to select NB such that LTB >= (3*NB+1)*N.
!>
!>          If LTB = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of LTB, 
!>          returns this value as the first entry of TB, and
!>          no error message related to LTB is issued by XERBLA.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of T were interchanged with the
!>          row and column IPIV(k).
!>

WORK

!>          WORK is COMPLEX*16 workspace of size LWORK
!>

LWORK

!>          LWORK is INTEGER
!>          The size of WORK. LWORK >= N, internally used to select NB
!>          such that LWORK >= N*NB.
!>
!>          If LWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of the WORK array,
!>          returns this value as the first entry of the WORK array, and
!>          no error message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = i, band LU factorization failed on i-th column
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file zsytrf_aa_2stage.f.

Author

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