hesv_aa(3)

NAME
hesv_aa - {he,sy}sv_aa: Aasen

SYNOPSIS

  Functions

subroutine chesv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CHESV_AA computes the solution to system of linear equations A * X = B for HE matrices
subroutine csysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine dsysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine ssysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine zhesv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices
subroutine zsysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Detailed Description

Function Documentation

  subroutine chesv_aa (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CHESV_AA computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

    !>
    !> CHESV_AA computes the solution to a complex system of linear equations
    !>    A * X = B,
    !> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
    !> matrices.
    !>
    !> Aasen's algorithm is used to factor A as
    !>    A = U**H * T * U,  if UPLO = 'U', or
    !>    A = L * T * L**H,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and T is Hermitian and tridiagonal. The factored form
    !> of A is then used to solve the system of equations A * X = B.
    !>

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 number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 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, if INFO = 0, the tridiagonal matrix T and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U**H*T*U or A = L*T*L**H as computed by
    !>          CHETRF_AA.
    !>

    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).
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          On entry, the N-by-NRHS right hand side matrix B.
    !>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDB

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

    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,3*N-2), and for best
    !>          performance LWORK >= MAX(1,N*NB), where NB is the optimal
    !>          blocksize for CHETRF.
    !>
    !>          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, D(i,i) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular, so the solution could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine csysv_aa (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> CSYSV computes the solution to a complex system of linear equations
    !>    A * X = B,
    !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
    !> matrices.
    !>
    !> Aasen's algorithm is used to factor A as
    !>    A = U**T * T * U,  if UPLO = 'U', or
    !>    A = L * T * L**T,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and T is symmetric tridiagonal. The factored
    !> form of A is then used to solve the system of equations A * X = B.
    !>

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 number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 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, if INFO = 0, the tridiagonal matrix T and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U**T*T*U or A = L*T*L**T as computed by
    !>          CSYTRF.
    !>

    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).
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          On entry, the N-by-NRHS right hand side matrix B.
    !>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDB

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

    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(2*N, 3*N-2), and for
    !>          the best performance, LWORK >= max(1,N*NB), where NB is
    !>          the optimal blocksize for CSYTRF_AA.
    !>
    !>          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, D(i,i) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular, so the solution could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dsysv_aa (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> DSYSV computes the solution to a real system of linear equations
    !>    A * X = B,
    !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
    !> matrices.
    !>
    !> Aasen's algorithm is used to factor A as
    !>    A = U**T * T * U,  if UPLO = 'U', or
    !>    A = L * T * L**T,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and T is symmetric tridiagonal. The factored
    !> form of A is then used to solve the system of equations A * X = B.
    !>

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 number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 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, if INFO = 0, the tridiagonal matrix T and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U**T*T*U or A = L*T*L**T as computed by
    !>          DSYTRF.
    !>

    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).
    !>

    B

    !>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
    !>          On entry, the N-by-NRHS right hand side matrix B.
    !>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDB

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

    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 >= MAX(1,2*N,3*N-2), and for
    !>          the best performance, LWORK >= MAX(1,N*NB), where NB is
    !>          the optimal blocksize for DSYTRF_AA.
    !>
    !>          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, D(i,i) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular, so the solution could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine ssysv_aa (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)

SSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> SSYSV computes the solution to a real system of linear equations
    !>    A * X = B,
    !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
    !> matrices.
    !>
    !> Aasen's algorithm is used to factor A as
    !>    A = U**T * T * U,  if UPLO = 'U', or
    !>    A = L * T * L**T,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and T is symmetric tridiagonal. The factored
    !> form of A is then used to solve the system of equations A * X = B.
    !>

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 number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 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, if INFO = 0, the tridiagonal matrix T and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U**T*T*U or A = L*T*L**T as computed by
    !>          SSYTRF.
    !>

    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).
    !>

    B

    !>          B is REAL array, dimension (LDB,NRHS)
    !>          On entry, the N-by-NRHS right hand side matrix B.
    !>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDB

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

    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 >= MAX(1,2*N,3*N-2), and for
    !>          the best performance, LWORK >= MAX(1,N*NB), where NB is
    !>          the optimal blocksize for SSYTRF_AA.
    !>
    !>          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, D(i,i) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular, so the solution could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zhesv_aa (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)

ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

    !>
    !> ZHESV_AA computes the solution to a complex system of linear equations
    !>    A * X = B,
    !> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
    !> matrices.
    !>
    !> Aasen's algorithm is used to factor A as
    !>    A = U**H * T * U,  if UPLO = 'U', or
    !>    A = L * T * L**H,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and T is Hermitian and tridiagonal. The factored form
    !> of A is then used to solve the system of equations A * X = B.
    !>

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 number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 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, if INFO = 0, the tridiagonal matrix T and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U**H*T*U or A = L*T*L**H as computed by
    !>          ZHETRF_AA.
    !>

    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).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          On entry, the N-by-NRHS right hand side matrix B.
    !>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDB

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

    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,3*N-2), and for best
    !>          performance LWORK >= max(1,N*NB), where NB is the optimal
    !>          blocksize for ZHETRF_AA.
    !>
    !>          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, D(i,i) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular, so the solution could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zsysv_aa (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)

ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> ZSYSV computes the solution to a complex system of linear equations
    !>    A * X = B,
    !> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
    !> matrices.
    !>
    !> Aasen's algorithm is used to factor A as
    !>    A = U**T * T * U,  if UPLO = 'U', or
    !>    A = L * T * L**T,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and T is symmetric tridiagonal. The factored
    !> form of A is then used to solve the system of equations A * X = B.
    !>

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 number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 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, if INFO = 0, the tridiagonal matrix T and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U**T*T*U or A = L*T*L**T as computed by
    !>          ZSYTRF.
    !>

    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).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          On entry, the N-by-NRHS right hand side matrix B.
    !>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDB

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

    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,3*N-2), and for
    !>          the best performance, LWORK >= MAX(1,N*NB), where NB is
    !>          the optimal blocksize for ZSYTRF_AA.
    !>
    !>          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, D(i,i) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular, so the solution could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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