hesv_aa_2stage(3)

NAME
hesv_aa_2stage - {he,sy}sv_aa_2stage: Aasen, blocked 2-stage

SYNOPSIS

  Functions

subroutine chesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices
subroutine csysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
subroutine dsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
subroutine ssysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
subroutine zhesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices
subroutine zsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Detailed Description

Function Documentation

  subroutine chesv_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

    !>
    !> CHESV_AA_2STAGE 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 2-stage 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 band. The matrix T is
    !> then LU-factored with partial pivoting. The factored form of A
    !> is then used to solve the system of equations A * X = B.
    !>
    !> 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.
    !>

    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, 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).
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the solution matrix X.
    !>

    LDB

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

    WORK

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

  subroutine csysv_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> CSYSV_AA_2STAGE 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 2-stage 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 and band. The matrix T is
    !> then LU-factored with partial pivoting. The factored form of A
    !> is then used to solve the system of equations A * X = B.
    !>
    !> 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.
    !>

    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, 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).
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the solution matrix X.
    !>

    LDB

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

    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.

  subroutine dsysv_aa_2stage (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> DSYSV_AA_2STAGE 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 2-stage 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 and band. The matrix T is
    !> then LU-factored with partial pivoting. The factored form of A
    !> is then used to solve the system of equations A * X = B.
    !>
    !> 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.
    !>

    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, 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 IPIV(k).
    !>

    B

    !>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the solution matrix X.
    !>

    LDB

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

    WORK

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

  subroutine ssysv_aa_2stage (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)

SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> SSYSV_AA_2STAGE 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 2-stage 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 and band. The matrix T is
    !> then LU-factored with partial pivoting. The factored form of A
    !> is then used to solve the system of equations A * X = B.
    !>
    !> 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.
    !>

    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, 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 (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).
    !>

    B

    !>          B is REAL array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the solution matrix X.
    !>

    LDB

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

    WORK

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

  subroutine zhesv_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)

ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

    !>
    !> ZHESV_AA_2STAGE 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 2-stage 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 band. The matrix T is
    !> then LU-factored with partial pivoting. The factored form of A
    !> is then used to solve the system of equations A * X = B.
    !>
    !> 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.
    !>

    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, 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).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the solution matrix X.
    !>

    LDB

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

    WORK

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

  subroutine zsysv_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)

ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> ZSYSV_AA_2STAGE 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 2-stage 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 and band. The matrix T is
    !> then LU-factored with partial pivoting. The factored form of A
    !> is then used to solve the system of equations A * X = B.
    !>
    !> 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.
    !>

    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, 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).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the solution matrix X.
    !>

    LDB

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

    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.

Author

Generated automatically by Doxygen for LAPACK from the source code.