hetrf_rook(3)

NAME
hetrf_rook - {he,sy}trf_rook: triangular factor

SYNOPSIS

  Functions

subroutine chetrf_rook (uplo, n, a, lda, ipiv, work, lwork, info)
CHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman (rook")diagonalpivotingmethod(blockedalgorithm,callingLevel3BLAS).
subroutine csytrf_rook (uplo, n, a, lda, ipiv, work, lwork, info)
CSYTRF_ROOK
subroutine dsytrf_rook (uplo, n, a, lda, ipiv, work, lwork, info)
DSYTRF_ROOK
subroutine ssytrf_rook (uplo, n, a, lda, ipiv, work, lwork, info)
SSYTRF_ROOK
subroutine zhetrf_rook (uplo, n, a, lda, ipiv, work, lwork, info)
ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman (rook")diagonalpivotingmethod(blockedalgorithm,callingLevel3BLAS).
subroutine zsytrf_rook (uplo, n, a, lda, ipiv, work, lwork, info)
ZSYTRF_ROOK

Detailed Description

Function Documentation

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

CHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

Purpose:

    !>
    !> CHETRF_ROOK computes the factorization of a complex Hermitian matrix A
    !> using the bounded Bunch-Kaufman () diagonal pivoting method.
    !> The form of the factorization is
    !>
    !>    A = U*D*U**T  or  A = L*D*L**T
    !>
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is Hermitian and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.
    !>
    !> 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 block diagonal matrix D and the multipliers used
    !>          to obtain the factor U or L (see below for further details).
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D.
    !>
    !>          If UPLO = 'U':
    !>             Only the last KB elements of IPIV are set.
    !>
    !>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
    !>             interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>             columns k and -IPIV(k) were interchanged and rows and
    !>             columns k-1 and -IPIV(k-1) were inerchaged,
    !>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>             Only the first KB elements of IPIV are set.
    !>
    !>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>             columns k and -IPIV(k) were interchanged and rows and
    !>             columns k+1 and -IPIV(k+1) were inerchaged,
    !>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
    !>

    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.  For best performance
    !>          LWORK >= N*NB, where NB is the block size 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
    !>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
    !>                has been completed, but the block diagonal matrix D is
    !>                exactly singular, and division by zero will occur if it
    !>                is used to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  If UPLO = 'U', then A = U*D*U**T, where
    !>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
    !>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
    !>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    v    0   )   k-s
    !>     U(k) =  (   0    I    0   )   s
    !>             (   0    0    I   )   n-k
    !>                k-s   s   n-k
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
    !>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
    !>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
    !>
    !>  If UPLO = 'L', then A = L*D*L**T, where
    !>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
    !>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
    !>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    0     0   )  k-1
    !>     L(k) =  (   0    I     0   )  s
    !>             (   0    v     I   )  n-k-s+1
    !>                k-1   s  n-k-s+1
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
    !>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
    !>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
    !>

Contributors:

    !>
    !>  June 2016,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

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

CSYTRF_ROOK

Purpose:

    !>
    !> CSYTRF_ROOK computes the factorization of a complex symmetric matrix A
    !> using the bounded Bunch-Kaufman () diagonal pivoting method.
    !> The form of the factorization is
    !>
    !>    A = U*D*U**T  or  A = L*D*L**T
    !>
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is symmetric and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.
    !>
    !> 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 block diagonal matrix D and the multipliers used
    !>          to obtain the factor U or L (see below for further details).
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D.
    !>
    !>          If UPLO = 'U':
    !>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k-1 and -IPIV(k-1) were inerchaged,
    !>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k+1 and -IPIV(k+1) were inerchaged,
    !>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
    !>

    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.  For best performance
    !>          LWORK >= N*NB, where NB is the block size 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
    !>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
    !>                has been completed, but the block diagonal matrix D is
    !>                exactly singular, and division by zero will occur if it
    !>                is used to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  If UPLO = 'U', then A = U*D*U**T, where
    !>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
    !>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
    !>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    v    0   )   k-s
    !>     U(k) =  (   0    I    0   )   s
    !>             (   0    0    I   )   n-k
    !>                k-s   s   n-k
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
    !>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
    !>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
    !>
    !>  If UPLO = 'L', then A = L*D*L**T, where
    !>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
    !>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
    !>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    0     0   )  k-1
    !>     L(k) =  (   0    I     0   )  s
    !>             (   0    v     I   )  n-k-s+1
    !>                k-1   s  n-k-s+1
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
    !>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
    !>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
    !>

Contributors:

    !>
    !>   June 2016, Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

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

DSYTRF_ROOK

Purpose:

    !>
    !> DSYTRF_ROOK computes the factorization of a real symmetric matrix A
    !> using the bounded Bunch-Kaufman () diagonal pivoting method.
    !> The form of the factorization is
    !>
    !>    A = U*D*U**T  or  A = L*D*L**T
    !>
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is symmetric and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.
    !>
    !> 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 block diagonal matrix D and the multipliers used
    !>          to obtain the factor U or L (see below for further details).
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D.
    !>
    !>          If UPLO = 'U':
    !>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k-1 and -IPIV(k-1) were inerchaged,
    !>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k+1 and -IPIV(k+1) were inerchaged,
    !>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
    !>

    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.  For best performance
    !>          LWORK >= N*NB, where NB is the block size 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
    !>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
    !>                has been completed, but the block diagonal matrix D is
    !>                exactly singular, and division by zero will occur if it
    !>                is used to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  If UPLO = 'U', then A = U*D*U**T, where
    !>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
    !>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
    !>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    v    0   )   k-s
    !>     U(k) =  (   0    I    0   )   s
    !>             (   0    0    I   )   n-k
    !>                k-s   s   n-k
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
    !>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
    !>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
    !>
    !>  If UPLO = 'L', then A = L*D*L**T, where
    !>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
    !>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
    !>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    0     0   )  k-1
    !>     L(k) =  (   0    I     0   )  s
    !>             (   0    v     I   )  n-k-s+1
    !>                k-1   s  n-k-s+1
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
    !>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
    !>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
    !>

Contributors:

    !>
    !>   April 2012, Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

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

SSYTRF_ROOK

Purpose:

    !>
    !> SSYTRF_ROOK computes the factorization of a real symmetric matrix A
    !> using the bounded Bunch-Kaufman () diagonal pivoting method.
    !> The form of the factorization is
    !>
    !>    A = U*D*U**T  or  A = L*D*L**T
    !>
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is symmetric and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.
    !>
    !> 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 block diagonal matrix D and the multipliers used
    !>          to obtain the factor U or L (see below for further details).
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D.
    !>
    !>          If UPLO = 'U':
    !>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k-1 and -IPIV(k-1) were inerchaged,
    !>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k+1 and -IPIV(k+1) were inerchaged,
    !>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
    !>

    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.  For best performance
    !>          LWORK >= N*NB, where NB is the block size 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
    !>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
    !>                has been completed, but the block diagonal matrix D is
    !>                exactly singular, and division by zero will occur if it
    !>                is used to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  If UPLO = 'U', then A = U*D*U**T, where
    !>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
    !>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
    !>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    v    0   )   k-s
    !>     U(k) =  (   0    I    0   )   s
    !>             (   0    0    I   )   n-k
    !>                k-s   s   n-k
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
    !>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
    !>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
    !>
    !>  If UPLO = 'L', then A = L*D*L**T, where
    !>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
    !>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
    !>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    0     0   )  k-1
    !>     L(k) =  (   0    I     0   )  s
    !>             (   0    v     I   )  n-k-s+1
    !>                k-1   s  n-k-s+1
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
    !>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
    !>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
    !>

Contributors:

    !>
    !>   June 2016, Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

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

ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

Purpose:

    !>
    !> ZHETRF_ROOK computes the factorization of a complex Hermitian matrix A
    !> using the bounded Bunch-Kaufman () diagonal pivoting method.
    !> The form of the factorization is
    !>
    !>    A = U*D*U**T  or  A = L*D*L**T
    !>
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is Hermitian and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.
    !>
    !> 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 block diagonal matrix D and the multipliers used
    !>          to obtain the factor U or L (see below for further details).
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D.
    !>
    !>          If UPLO = 'U':
    !>             Only the last KB elements of IPIV are set.
    !>
    !>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
    !>             interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>             columns k and -IPIV(k) were interchanged and rows and
    !>             columns k-1 and -IPIV(k-1) were inerchaged,
    !>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>             Only the first KB elements of IPIV are set.
    !>
    !>             If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>             were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>             columns k and -IPIV(k) were interchanged and rows and
    !>             columns k+1 and -IPIV(k+1) were inerchaged,
    !>             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
    !>

    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.  For best performance
    !>          LWORK >= N*NB, where NB is the block size 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
    !>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
    !>                has been completed, but the block diagonal matrix D is
    !>                exactly singular, and division by zero will occur if it
    !>                is used to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  If UPLO = 'U', then A = U*D*U**T, where
    !>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
    !>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
    !>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    v    0   )   k-s
    !>     U(k) =  (   0    I    0   )   s
    !>             (   0    0    I   )   n-k
    !>                k-s   s   n-k
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
    !>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
    !>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
    !>
    !>  If UPLO = 'L', then A = L*D*L**T, where
    !>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
    !>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
    !>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    0     0   )  k-1
    !>     L(k) =  (   0    I     0   )  s
    !>             (   0    v     I   )  n-k-s+1
    !>                k-1   s  n-k-s+1
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
    !>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
    !>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
    !>

Contributors:

    !>
    !>  June 2016,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

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

ZSYTRF_ROOK

Purpose:

    !>
    !> ZSYTRF_ROOK computes the factorization of a complex symmetric matrix A
    !> using the bounded Bunch-Kaufman () diagonal pivoting method.
    !> The form of the factorization is
    !>
    !>    A = U*D*U**T  or  A = L*D*L**T
    !>
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is symmetric and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.
    !>
    !> 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 block diagonal matrix D and the multipliers used
    !>          to obtain the factor U or L (see below for further details).
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D.
    !>
    !>          If UPLO = 'U':
    !>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k-1 and -IPIV(k-1) were inerchaged,
    !>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
    !>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
    !>
    !>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k+1 and -IPIV(k+1) were inerchaged,
    !>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
    !>

    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.  For best performance
    !>          LWORK >= N*NB, where NB is the block size 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
    !>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
    !>                has been completed, but the block diagonal matrix D is
    !>                exactly singular, and division by zero will occur if it
    !>                is used to solve a system of equations.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  If UPLO = 'U', then A = U*D*U**T, where
    !>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
    !>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
    !>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    v    0   )   k-s
    !>     U(k) =  (   0    I    0   )   s
    !>             (   0    0    I   )   n-k
    !>                k-s   s   n-k
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
    !>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
    !>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
    !>
    !>  If UPLO = 'L', then A = L*D*L**T, where
    !>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
    !>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
    !>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
    !>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
    !>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
    !>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
    !>
    !>             (   I    0     0   )  k-1
    !>     L(k) =  (   0    I     0   )  s
    !>             (   0    v     I   )  n-k-s+1
    !>                k-1   s  n-k-s+1
    !>
    !>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
    !>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
    !>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
    !>

Contributors:

    !>
    !>   June 2016, Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

Author

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