added LAPACK routine (c,z)hetrf_rook.f

2 files changed, 794 insertions, 0 deletions

diff --git a/SRC/chetrf_rook.f b/SRC/chetrf_rook.f
new file mode 100644
index 00000000..0af0604d
--- /dev/null
+++ b/SRC/chetrf_rook.f
@@ -0,0 +1,397 @@
+*> \brief \b 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).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHETRF_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrf_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrf_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrf_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LWORK, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CHETRF_ROOK computes the factorization of a comlex Hermitian matrix A
+*> using the bounded Bunch-Kaufman ("rook") 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.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          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).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          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.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK)).
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          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.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          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.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complexHEcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  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).
+*> \endverbatim
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 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
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LWORK, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY, UPPER
+      INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ILAENV
+      EXTERNAL           LSAME, ILAENV
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           CLAHEF_ROOK, CHETF2_ROOK, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -7
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+*
+*        Determine the block size
+*
+         NB = ILAENV( 1, 'CHETRF_ROOK', UPLO, N, -1, -1, -1 )
+         LWKOPT = N*NB
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CHETRF_ROOK', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+      NBMIN = 2
+      LDWORK = N
+      IF( NB.GT.1 .AND. NB.LT.N ) THEN
+         IWS = LDWORK*NB
+         IF( LWORK.LT.IWS ) THEN
+            NB = MAX( LWORK / LDWORK, 1 )
+            NBMIN = MAX( 2, ILAENV( 2, 'CHETRF_ROOK',
+     $                              UPLO, N, -1, -1, -1 ) )
+         END IF
+      ELSE
+         IWS = 1
+      END IF
+      IF( NB.LT.NBMIN )
+     $   NB = N
+*
+      IF( UPPER ) THEN
+*
+*        Factorize A as U*D*U**T using the upper triangle of A
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        KB, where KB is the number of columns factorized by CLAHEF_ROOK;
+*        KB is either NB or NB-1, or K for the last block
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop
+*
+         IF( K.LT.1 )
+     $      GO TO 40
+*
+         IF( K.GT.NB ) THEN
+*
+*           Factorize columns k-kb+1:k of A and use blocked code to
+*           update columns 1:k-kb
+*
+            CALL CLAHEF_ROOK( UPLO, K, NB, KB, A, LDA,
+     $                        IPIV, WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns 1:k of A
+*
+            CALL CHETF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
+            KB = K
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO
+*
+*        No need to adjust IPIV
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KB
+         GO TO 10
+*
+      ELSE
+*
+*        Factorize A as L*D*L**T using the lower triangle of A
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        KB, where KB is the number of columns factorized by CLAHEF_ROOK;
+*        KB is either NB or NB-1, or N-K+1 for the last block
+*
+         K = 1
+   20    CONTINUE
+*
+*        If K > N, exit from loop
+*
+         IF( K.GT.N )
+     $      GO TO 40
+*
+         IF( K.LE.N-NB ) THEN
+*
+*           Factorize columns k:k+kb-1 of A and use blocked code to
+*           update columns k+kb:n
+*
+            CALL CLAHEF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
+     $                        IPIV( K ), WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns k:n of A
+*
+            CALL CHETF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
+     $                        IINFO )
+            KB = N - K + 1
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO + K - 1
+*
+*        Adjust IPIV
+*
+         DO 30 J = K, K + KB - 1
+            IF( IPIV( J ).GT.0 ) THEN
+               IPIV( J ) = IPIV( J ) + K - 1
+            ELSE
+               IPIV( J ) = IPIV( J ) - K + 1
+            END IF
+   30    CONTINUE
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KB
+         GO TO 20
+*
+      END IF
+*
+   40 CONTINUE
+      WORK( 1 ) = LWKOPT
+      RETURN
+*
+*     End of CHETRF_ROOK
+*
+      END
diff --git a/SRC/zhetrf_rook.f b/SRC/zhetrf_rook.f
new file mode 100644
index 00000000..4e4e8f8b
--- /dev/null
+++ b/SRC/zhetrf_rook.f
@@ -0,0 +1,397 @@
+*> \brief \b 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).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHETRF_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrf_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetrf_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrf_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LWORK, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX*16         A( LDA, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZHETRF_ROOK computes the factorization of a complex Hermitian matrix A
+*> using the bounded Bunch-Kaufman ("rook") 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.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          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).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          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.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*>          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.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          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.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16HEcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  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).
+*> \endverbatim
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*>  November 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
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE ZHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+*
+*  -- LAPACK computational routine (version 3.4.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LWORK, N
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX*16         A( LDA, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY, UPPER
+      INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ILAENV
+      EXTERNAL           LSAME, ILAENV
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           ZLAHEF_ROOK, ZHETF2_ROOK, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      UPPER = LSAME( UPLO, 'U' )
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -4
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -7
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+*
+*        Determine the block size
+*
+         NB = ILAENV( 1, 'ZHETRF_ROOK', UPLO, N, -1, -1, -1 )
+         LWKOPT = N*NB
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'ZHETRF_ROOK', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+      NBMIN = 2
+      LDWORK = N
+      IF( NB.GT.1 .AND. NB.LT.N ) THEN
+         IWS = LDWORK*NB
+         IF( LWORK.LT.IWS ) THEN
+            NB = MAX( LWORK / LDWORK, 1 )
+            NBMIN = MAX( 2, ILAENV( 2, 'ZHETRF_ROOK',
+     $                              UPLO, N, -1, -1, -1 ) )
+         END IF
+      ELSE
+         IWS = 1
+      END IF
+      IF( NB.LT.NBMIN )
+     $   NB = N
+*
+      IF( UPPER ) THEN
+*
+*        Factorize A as U*D*U**T using the upper triangle of A
+*
+*        K is the main loop index, decreasing from N to 1 in steps of
+*        KB, where KB is the number of columns factorized by ZLAHEF_ROOK;
+*        KB is either NB or NB-1, or K for the last block
+*
+         K = N
+   10    CONTINUE
+*
+*        If K < 1, exit from loop
+*
+         IF( K.LT.1 )
+     $      GO TO 40
+*
+         IF( K.GT.NB ) THEN
+*
+*           Factorize columns k-kb+1:k of A and use blocked code to
+*           update columns 1:k-kb
+*
+            CALL ZLAHEF_ROOK( UPLO, K, NB, KB, A, LDA,
+     $                        IPIV, WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns 1:k of A
+*
+            CALL ZHETF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
+            KB = K
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO
+*
+*        No need to adjust IPIV
+*
+*        Decrease K and return to the start of the main loop
+*
+         K = K - KB
+         GO TO 10
+*
+      ELSE
+*
+*        Factorize A as L*D*L**T using the lower triangle of A
+*
+*        K is the main loop index, increasing from 1 to N in steps of
+*        KB, where KB is the number of columns factorized by ZLAHEF_ROOK;
+*        KB is either NB or NB-1, or N-K+1 for the last block
+*
+         K = 1
+   20    CONTINUE
+*
+*        If K > N, exit from loop
+*
+         IF( K.GT.N )
+     $      GO TO 40
+*
+         IF( K.LE.N-NB ) THEN
+*
+*           Factorize columns k:k+kb-1 of A and use blocked code to
+*           update columns k+kb:n
+*
+            CALL ZLAHEF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
+     $                        IPIV( K ), WORK, LDWORK, IINFO )
+         ELSE
+*
+*           Use unblocked code to factorize columns k:n of A
+*
+            CALL ZHETF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
+     $                        IINFO )
+            KB = N - K + 1
+         END IF
+*
+*        Set INFO on the first occurrence of a zero pivot
+*
+         IF( INFO.EQ.0 .AND. IINFO.GT.0 )
+     $      INFO = IINFO + K - 1
+*
+*        Adjust IPIV
+*
+         DO 30 J = K, K + KB - 1
+            IF( IPIV( J ).GT.0 ) THEN
+               IPIV( J ) = IPIV( J ) + K - 1
+            ELSE
+               IPIV( J ) = IPIV( J ) - K + 1
+            END IF
+   30    CONTINUE
+*
+*        Increase K and return to the start of the main loop
+*
+         K = K + KB
+         GO TO 20
+*
+      END IF
+*
+   40 CONTINUE
+      WORK( 1 ) = LWKOPT
+      RETURN
+*
+*     End of ZHETRF_ROOK
+*
+      END