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 (MAX(1,LTB))
    !>          On exit, details of the LU factorization of the band matrix.
    !>

    LTB

    !>          LTB is INTEGER
    !>          The size of the array TB. LTB >= MAX(1,4*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 (MAX(1,LWORK))
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The size of WORK. LWORK >= MAX(1,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 (MAX(1,LTB))
    !>          On exit, details of the LU factorization of the band matrix.
    !>

    LTB

    !>          LTB is INTEGER
    !>          The size of the array TB. LTB >= MAX(1,4*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 (MAX(1,LWORK))
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The size of WORK. LWORK >= MAX(1,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 >= MAX(1,4*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 (MAX(1,LWORK))
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The size of WORK. LWORK >= MAX(1,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 (MAX(1,LTB))
    !>          On exit, details of the LU factorization of the band matrix.
    !>

    LTB

    !>          LTB is INTEGER
    !>          The size of the array TB. LTB >= MAX(1,4*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 (MAX(1,LWORK))
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The size of WORK. LWORK >= MAX(1,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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