hetrf_aa(3)

NAME
hetrf_aa - {he,sy}trf_aa: triangular factor

SYNOPSIS

  Functions

subroutine chetrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
CHETRF_AA
subroutine csytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
CSYTRF_AA
subroutine dsytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
DSYTRF_AA
subroutine ssytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
SSYTRF_AA
subroutine zhetrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
ZHETRF_AA
subroutine zsytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
ZSYTRF_AA

Detailed Description

Function Documentation

  subroutine chetrf_aa (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)

CHETRF_AA

Purpose:

    !>
    !> CHETRF_AA computes the factorization of a complex 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 tridiagonal matrix.
    !>
    !> 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, the tridiagonal matrix is stored in the diagonals
    !>          and the subdiagonals of A just below (or above) the diagonals,
    !>          and L is stored below (or above) the subdiagonals, when UPLO
    !>          is 'L' (or 'U').
    !>

    LDA

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

    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).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of WORK.
    !>          LWORK >= 1, if N <= 1, and LWORK >= 2*N, otherwise.
    !>          For optimum performance LWORK >= N*(1+NB), where NB is
    !>          the optimal blocksize, returned by ILAENV.
    !>
    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine csytrf_aa (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)

CSYTRF_AA

Purpose:

    !>
    !> CSYTRF_AA 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 tridiagonal matrix.
    !>
    !> 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 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, the tridiagonal matrix is stored in the diagonals
    !>          and the subdiagonals of A just below (or above) the diagonals,
    !>          and L is stored below (or above) the subdiagonals, when UPLO
    !>          is 'L' (or 'U').
    !>

    LDA

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

    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).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of WORK. LWORK >= MAX(1,2*N). For optimum performance
    !>          LWORK >= N*(1+NB), where NB is the optimal blocksize.
    !>
    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dsytrf_aa (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRF_AA

Purpose:

    !>
    !> DSYTRF_AA 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 tridiagonal matrix.
    !>
    !> 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, the tridiagonal matrix is stored in the diagonals
    !>          and the subdiagonals of A just below (or above) the diagonals,
    !>          and L is stored below (or above) the subdiagonals, when UPLO
    !>          is 'L' (or 'U').
    !>

    LDA

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

    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).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of WORK.
    !>          LWORK >= 1, if N <= 1, and LWORK >= 2*N, otherwise.
    !>          For optimum performance LWORK >= N*(1+NB), where NB is
    !>          the optimal blocksize, returned by ILAENV.
    !>
    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine ssytrf_aa (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info)

SSYTRF_AA

Purpose:

    !>
    !> SSYTRF_AA 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 tridiagonal matrix.
    !>
    !> 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, the tridiagonal matrix is stored in the diagonals
    !>          and the subdiagonals of A just below (or above) the diagonals,
    !>          and L is stored below (or above) the subdiagonals, when UPLO
    !>          is 'L' (or 'U').
    !>

    LDA

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

    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).
    !>

    WORK

    !>          WORK is REAL array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of WORK.
    !>          LWORK >= 1, if N <= 1, and LWORK >= 2*N, otherwise.
    !>          For optimum performance LWORK >= N*(1+NB), where NB is
    !>          the optimal blocksize, returned by ILAENV.
    !>
    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zhetrf_aa (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)

ZHETRF_AA

Purpose:

    !>
    !> ZHETRF_AA computes the factorization of a complex 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 tridiagonal matrix.
    !>
    !> 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, the tridiagonal matrix is stored in the diagonals
    !>          and the subdiagonals of A just below (or above) the diagonals,
    !>          and L is stored below (or above) the subdiagonals, when UPLO
    !>          is 'L' (or 'U').
    !>

    LDA

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

    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).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of WORK.
    !>          LWORK >= 1, if N >= 1, and LWORK >= 2*N, otherwise.
    !>          For optimum performance LWORK >= N*(1+NB), where NB is
    !>          the optimal blocksize, returned by ILAENV.
    !>
    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zsytrf_aa (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)

ZSYTRF_AA

Purpose:

    !>
    !> ZSYTRF_AA 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 tridiagonal matrix.
    !>
    !> 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 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, the tridiagonal matrix is stored in the diagonals
    !>          and the subdiagonals of A just below (or above) the diagonals,
    !>          and L is stored below (or above) the subdiagonals, when UPLO
    !>          is 'L' (or 'U').
    !>

    LDA

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

    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).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of WORK. LWORK >=MAX(1,2*N). For optimum performance
    !>          LWORK >= N*(1+NB), where NB is the optimal blocksize.
    !>
    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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