added LAPACK routine (c,z)hesv_rook.f

2 files changed, 590 insertions, 0 deletions

diff --git a/SRC/chesv_rook.f b/SRC/chesv_rook.f
new file mode 100644
index 00000000..4a4569f4
--- /dev/null
+++ b/SRC/chesv_rook.f
@@ -0,0 +1,295 @@
+*> \brief \b CHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHESV_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chesv_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chesv_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chesv_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE CHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+*                              LWORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> CHESV_ROOK 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.
+*>
+*> The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used
+*> to factor A as
+*>    A = U * D * U**T,  if UPLO = 'U', or
+*>    A = L * D * L**T,  if UPLO = 'L',
+*> 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.
+*>
+*> CHETRF_ROOK is called to compute the factorization of a complex
+*> Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal
+*> pivoting method.
+*>
+*> The factored form of A is then used to solve the system
+*> of equations A * X = B by calling CHETRS_ROOK (uses BLAS 2).
+*> \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 number of linear equations, i.e., the order of the
+*>          matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 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, if INFO = 0, the block diagonal matrix D and the
+*>          multipliers used to obtain the factor U or L from the
+*>          factorization A = U*D*U**H or A = L*D*L**H as computed by
+*>          CHETRF_ROOK.
+*> \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[in,out] B
+*> \verbatim
+*>          B is COMPLEX array, dimension (LDB,NRHS)
+*>          On entry, the N-by-NRHS right hand side matrix B.
+*>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \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, and for best performance
+*>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
+*>          CHETRF_ROOK.
+*>          for LWORK < N, TRS will be done with Level BLAS 2
+*>          for LWORK >= N, TRS will be done with Level BLAS 3
+*>
+*>          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, so the solution could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2012
+*
+*> \ingroup complexHEsolve
+*>
+*> \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 CHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+     $                       LWORK, INFO )
+*
+*  -- LAPACK driver 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 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY
+      INTEGER            LWKOPT, NB
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ILAENV
+      EXTERNAL           LSAME, ILAENV
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA, CHETRF_ROOK, CHETRS_ROOK
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -5
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -10
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+         IF( N.EQ.0 ) THEN
+            LWKOPT = 1
+         ELSE
+            NB = ILAENV( 1, 'CHETRF_ROOK', UPLO, N, -1, -1, -1 )
+            LWKOPT = N*NB
+         END IF
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'CHESV_ROOK ', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Compute the factorization A = U*D*U**H or A = L*D*L**H.
+*
+      CALL CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+      IF( INFO.EQ.0 ) THEN
+*
+*        Solve the system A*X = B, overwriting B with X.
+*
+*        Solve with TRS ( Use Level BLAS 2)
+*
+         CALL CHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+*
+      END IF
+*
+      WORK( 1 ) = LWKOPT
+*
+      RETURN
+*
+*     End of CHESV_ROOK
+*
+      END
diff --git a/SRC/zhesv_rook.f b/SRC/zhesv_rook.f
new file mode 100644
index 00000000..9d35d650
--- /dev/null
+++ b/SRC/zhesv_rook.f
@@ -0,0 +1,295 @@
+*> \brief \b ZHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHESV_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhesv_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhesv_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhesv_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+*                              LWORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZHESV_ROOK 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.
+*>
+*> The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used
+*> to factor A as
+*>    A = U * D * U**T,  if UPLO = 'U', or
+*>    A = L * D * L**T,  if UPLO = 'L',
+*> 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.
+*>
+*> ZHETRF_ROOK is called to compute the factorization of a complex
+*> Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal
+*> pivoting method.
+*>
+*> The factored form of A is then used to solve the system
+*> of equations A * X = B by calling ZHETRS_ROOK (uses BLAS 2).
+*> \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 number of linear equations, i.e., the order of the
+*>          matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 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, if INFO = 0, the block diagonal matrix D and the
+*>          multipliers used to obtain the factor U or L from the
+*>          factorization A = U*D*U**H or A = L*D*L**H as computed by
+*>          ZHETRF_ROOK.
+*> \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[in,out] B
+*> \verbatim
+*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
+*>          On entry, the N-by-NRHS right hand side matrix B.
+*>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \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, and for best performance
+*>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
+*>          ZHETRF_ROOK.
+*>          for LWORK < N, TRS will be done with Level BLAS 2
+*>          for LWORK >= N, TRS will be done with Level BLAS 3
+*>
+*>          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, so the solution could not be computed.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2012
+*
+*> \ingroup complex16HEsolve
+*>
+*> \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 ZHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
+     $                       LWORK, INFO )
+*
+*  -- LAPACK driver 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 2012
+*
+*     .. Scalar Arguments ..
+      CHARACTER          UPLO
+      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
+*     ..
+*     .. Array Arguments ..
+      INTEGER            IPIV( * )
+      COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Local Scalars ..
+      LOGICAL            LQUERY
+      INTEGER            LWKOPT, NB
+*     ..
+*     .. External Functions ..
+      LOGICAL            LSAME
+      INTEGER            ILAENV
+      EXTERNAL           LSAME, ILAENV
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           XERBLA, ZHETRF_ROOK, ZHETRS_ROOK
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      LQUERY = ( LWORK.EQ.-1 )
+      IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( NRHS.LT.0 ) THEN
+         INFO = -3
+      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+         INFO = -5
+      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+         INFO = -8
+      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
+         INFO = -10
+      END IF
+*
+      IF( INFO.EQ.0 ) THEN
+         IF( N.EQ.0 ) THEN
+            LWKOPT = 1
+         ELSE
+            NB = ILAENV( 1, 'ZHETRF_ROOK', UPLO, N, -1, -1, -1 )
+            LWKOPT = N*NB
+         END IF
+         WORK( 1 ) = LWKOPT
+      END IF
+*
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'ZHESV_ROOK ', -INFO )
+         RETURN
+      ELSE IF( LQUERY ) THEN
+         RETURN
+      END IF
+*
+*     Compute the factorization A = U*D*U**H or A = L*D*L**H.
+*
+      CALL ZHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
+      IF( INFO.EQ.0 ) THEN
+*
+*        Solve the system A*X = B, overwriting B with X.
+*
+*        Solve with TRS ( Use Level BLAS 2)
+*
+         CALL ZHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
+*
+      END IF
+*
+      WORK( 1 ) = LWKOPT
+*
+      RETURN
+*
+*     End of ZHESV_ROOK
+*
+      END