zsyconvf.f

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*> \brief \b ZSYCONVF
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO, WAY
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX*16         A( LDA, * ), E( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*> If parameter WAY = 'C':
*> ZSYCONVF converts the factorization output format used in
*> ZSYTRF provided on entry in parameter A into the factorization
*> output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
*> on exit in parameters A and E. It also converts in place details of
*> the interchanges stored in IPIV from the format used in ZSYTRF into
*> the format used in ZSYTRF_RK (or ZSYTRF_BK).
*>
*> If parameter WAY = 'R':
*> ZSYCONVF performs the conversion in reverse direction, i.e.
*> converts the factorization output format used in ZSYTRF_RK
*> (or ZSYTRF_BK) provided on entry in parameters A and E into
*> the factorization output format used in ZSYTRF that is stored
*> on exit in parameter A. It also converts in place details of
*> the interchanges stored in IPIV from the format used in ZSYTRF_RK
*> (or ZSYTRF_BK) into the format used in ZSYTRF.
*>
*> ZSYCONVF can also convert in Hermitian matrix case, i.e. between
*> formats used in ZHETRF and ZHETRF_RK (or ZHETRF_BK).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the details of the factorization are
*>          stored as an upper or lower triangular matrix A.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] WAY
*> \verbatim
*>          WAY is CHARACTER*1
*>          = 'C': Convert
*>          = 'R': Revert
*> \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)
*>
*>          1) If WAY ='C':
*>
*>          On entry, contains factorization details in format used in
*>          ZSYTRF:
*>            a) all elements of the symmetric block diagonal
*>               matrix D on the diagonal of A and on superdiagonal
*>               (or subdiagonal) of A, and
*>            b) If UPLO = 'U': multipliers used to obtain factor U
*>               in the superdiagonal part of A.
*>               If UPLO = 'L': multipliers used to obtain factor L
*>               in the superdiagonal part of A.
*>
*>          On exit, contains factorization details in format used in
*>          ZSYTRF_RK or ZSYTRF_BK:
*>            a) ONLY diagonal elements of the symmetric block diagonal
*>               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
*>               (superdiagonal (or subdiagonal) elements of D
*>                are stored on exit in array E), and
*>            b) If UPLO = 'U': factor U in the superdiagonal part of A.
*>               If UPLO = 'L': factor L in the subdiagonal part of A.
*>
*>          2) If WAY = 'R':
*>
*>          On entry, contains factorization details in format used in
*>          ZSYTRF_RK or ZSYTRF_BK:
*>            a) ONLY diagonal elements of the symmetric block diagonal
*>               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
*>               (superdiagonal (or subdiagonal) elements of D
*>                are stored on exit in array E), and
*>            b) If UPLO = 'U': factor U in the superdiagonal part of A.
*>               If UPLO = 'L': factor L in the subdiagonal part of A.
*>
*>          On exit, contains factorization details in format used in
*>          ZSYTRF:
*>            a) all elements of the symmetric block diagonal
*>               matrix D on the diagonal of A and on superdiagonal
*>               (or subdiagonal) of A, and
*>            b) If UPLO = 'U': multipliers used to obtain factor U
*>               in the superdiagonal part of A.
*>               If UPLO = 'L': multipliers used to obtain factor L
*>               in the superdiagonal part of A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*>          E is COMPLEX*16 array, dimension (N)
*>
*>          1) If WAY ='C':
*>
*>          On entry, just a workspace.
*>
*>          On exit, contains the superdiagonal (or subdiagonal)
*>          elements of the symmetric block diagonal matrix D
*>          with 1-by-1 or 2-by-2 diagonal blocks, where
*>          If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
*>          If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
*>
*>          2) If WAY = 'R':
*>
*>          On entry, contains the superdiagonal (or subdiagonal)
*>          elements of the symmetric block diagonal matrix D
*>          with 1-by-1 or 2-by-2 diagonal blocks, where
*>          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
*>          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
*>
*>          On exit, is not changed
*> \endverbatim
*.
*> \param[in,out] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>
*>          1) If WAY ='C':
*>          On entry, details of the interchanges and the block
*>          structure of D in the format used in ZSYTRF.
*>          On exit, details of the interchanges and the block
*>          structure of D in the format used in ZSYTRF_RK
*>          ( or ZSYTRF_BK).
*>
*>          1) If WAY ='R':
*>          On entry, details of the interchanges and the block
*>          structure of D in the format used in ZSYTRF_RK
*>          ( or ZSYTRF_BK).
*>          On exit, details of the interchanges and the block
*>          structure of D in the format used in ZSYTRF.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup syconvf
*
*> \par Contributors:
*  ==================
*>
*> \verbatim
*>
*>  November 2017,  Igor Kozachenko,
*>                  Computer Science Division,
*>                  University of California, Berkeley
*>
*> \endverbatim
*  =====================================================================
      SUBROUTINE zsyconvf( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO, WAY
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * ), E( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      parameter( zero = ( 0.0d+0, 0.0d+0 ) )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*
*     .. External Subroutines ..
      EXTERNAL           zswap, xerbla
*     .. Local Scalars ..
      LOGICAL            UPPER, CONVERT
      INTEGER            I, IP
*     ..
*     .. Executable Statements ..
*
      info = 0
      upper = lsame( uplo, 'U' )
      convert = lsame( way, 'C' )
      IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
         info = -1
      ELSE IF( .NOT.convert .AND. .NOT.lsame( way, 'R' ) ) THEN
         info = -2
      ELSE IF( n.LT.0 ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -5
 
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZSYCONVF', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      IF( upper ) THEN
*
*        Begin A is UPPER
*
         IF ( convert ) THEN
*
*           Convert A (A is upper)
*
*
*           Convert VALUE
*
*           Assign superdiagonal entries of D to array E and zero out
*           corresponding entries in input storage A
*
            i = n
            e( 1 ) = zero
            DO WHILE ( i.GT.1 )
               IF( ipiv( i ).LT.0 ) THEN
                  e( i ) = a( i-1, i )
                  e( i-1 ) = zero
                  a( i-1, i ) = zero
                  i = i - 1
               ELSE
                  e( i ) = zero
               END IF
               i = i - 1
            END DO
*
*           Convert PERMUTATIONS and IPIV
*
*           Apply permutations to submatrices of upper part of A
*           in factorization order where i decreases from N to 1
*
            i = n
            DO WHILE ( i.GE.1 )
               IF( ipiv( i ).GT.0 ) THEN
*
*                 1-by-1 pivot interchange
*
*                 Swap rows i and IPIV(i) in A(1:i,N-i:N)
*
                  ip = ipiv( i )
                  IF( i.LT.n ) THEN
                     IF( ip.NE.i ) THEN
                        CALL zswap( n-i, a( i, i+1 ), lda,
     $                              a( ip, i+1 ), lda )
                     END IF
                  END IF
*
               ELSE
*
*                 2-by-2 pivot interchange
*
*                 Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
*
                  ip = -ipiv( i )
                  IF( i.LT.n ) THEN
                     IF( ip.NE.(i-1) ) THEN
                        CALL zswap( n-i, a( i-1, i+1 ), lda,
     $                              a( ip, i+1 ), lda )
                     END IF
                  END IF
*
*                 Convert IPIV
*                 There is no interchange of rows i and and IPIV(i),
*                 so this should be reflected in IPIV format for
*                 *SYTRF_RK ( or *SYTRF_BK)
*
                  ipiv( i ) = i
*
                  i = i - 1
*
               END IF
               i = i - 1
            END DO
*
         ELSE
*
*           Revert A (A is upper)
*
*
*           Revert PERMUTATIONS and IPIV
*
*           Apply permutations to submatrices of upper part of A
*           in reverse factorization order where i increases from 1 to N
*
            i = 1
            DO WHILE ( i.LE.n )
               IF( ipiv( i ).GT.0 ) THEN
*
*                 1-by-1 pivot interchange
*
*                 Swap rows i and IPIV(i) in A(1:i,N-i:N)
*
                  ip = ipiv( i )
                  IF( i.LT.n ) THEN
                     IF( ip.NE.i ) THEN
                        CALL zswap( n-i, a( ip, i+1 ), lda,
     $                              a( i, i+1 ), lda )
                     END IF
                  END IF
*
               ELSE
*
*                 2-by-2 pivot interchange
*
*                 Swap rows i-1 and IPIV(i) in A(1:i,N-i:N)
*
                  i = i + 1
                  ip = -ipiv( i )
                  IF( i.LT.n ) THEN
                     IF( ip.NE.(i-1) ) THEN
                        CALL zswap( n-i, a( ip, i+1 ), lda,
     $                              a( i-1, i+1 ), lda )
                     END IF
                  END IF
*
*                 Convert IPIV
*                 There is one interchange of rows i-1 and IPIV(i-1),
*                 so this should be recorded in two consecutive entries
*                 in IPIV format for *SYTRF
*
                  ipiv( i ) = ipiv( i-1 )
*
               END IF
               i = i + 1
            END DO
*
*           Revert VALUE
*           Assign superdiagonal entries of D from array E to
*           superdiagonal entries of A.
*
            i = n
            DO WHILE ( i.GT.1 )
               IF( ipiv( i ).LT.0 ) THEN
                  a( i-1, i ) = e( i )
                  i = i - 1
               END IF
               i = i - 1
            END DO
*
*        End A is UPPER
*
         END IF
*
      ELSE
*
*        Begin A is LOWER
*
         IF ( convert ) THEN
*
*           Convert A (A is lower)
*
*
*           Convert VALUE
*           Assign subdiagonal entries of D to array E and zero out
*           corresponding entries in input storage A
*
            i = 1
            e( n ) = zero
            DO WHILE ( i.LE.n )
               IF( i.LT.n .AND. ipiv(i).LT.0 ) THEN
                  e( i ) = a( i+1, i )
                  e( i+1 ) = zero
                  a( i+1, i ) = zero
                  i = i + 1
               ELSE
                  e( i ) = zero
               END IF
               i = i + 1
            END DO
*
*           Convert PERMUTATIONS and IPIV
*
*           Apply permutations to submatrices of lower part of A
*           in factorization order where k increases from 1 to N
*
            i = 1
            DO WHILE ( i.LE.n )
               IF( ipiv( i ).GT.0 ) THEN
*
*                 1-by-1 pivot interchange
*
*                 Swap rows i and IPIV(i) in A(i:N,1:i-1)
*
                  ip = ipiv( i )
                  IF ( i.GT.1 ) THEN
                     IF( ip.NE.i ) THEN
                        CALL zswap( i-1, a( i, 1 ), lda,
     $                              a( ip, 1 ), lda )
                     END IF
                  END IF
*
               ELSE
*
*                 2-by-2 pivot interchange
*
*                 Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
*
                  ip = -ipiv( i )
                  IF ( i.GT.1 ) THEN
                     IF( ip.NE.(i+1) ) THEN
                        CALL zswap( i-1, a( i+1, 1 ), lda,
     $                              a( ip, 1 ), lda )
                     END IF
                  END IF
*
*                 Convert IPIV
*                 There is no interchange of rows i and and IPIV(i),
*                 so this should be reflected in IPIV format for
*                 *SYTRF_RK ( or *SYTRF_BK)
*
                  ipiv( i ) = i
*
                  i = i + 1
*
               END IF
               i = i + 1
            END DO
*
         ELSE
*
*           Revert A (A is lower)
*
*
*           Revert PERMUTATIONS and IPIV
*
*           Apply permutations to submatrices of lower part of A
*           in reverse factorization order where i decreases from N to 1
*
            i = n
            DO WHILE ( i.GE.1 )
               IF( ipiv( i ).GT.0 ) THEN
*
*                 1-by-1 pivot interchange
*
*                 Swap rows i and IPIV(i) in A(i:N,1:i-1)
*
                  ip = ipiv( i )
                  IF ( i.GT.1 ) THEN
                     IF( ip.NE.i ) THEN
                        CALL zswap( i-1, a( ip, 1 ), lda,
     $                              a( i, 1 ), lda )
                     END IF
                  END IF
*
               ELSE
*
*                 2-by-2 pivot interchange
*
*                 Swap rows i+1 and IPIV(i) in A(i:N,1:i-1)
*
                  i = i - 1
                  ip = -ipiv( i )
                  IF ( i.GT.1 ) THEN
                     IF( ip.NE.(i+1) ) THEN
                        CALL zswap( i-1, a( ip, 1 ), lda,
     $                              a( i+1, 1 ), lda )
                     END IF
                  END IF
*
*                 Convert IPIV
*                 There is one interchange of rows i+1 and IPIV(i+1),
*                 so this should be recorded in consecutive entries
*                 in IPIV format for *SYTRF
*
                  ipiv( i ) = ipiv( i+1 )
*
               END IF
               i = i - 1
            END DO
*
*           Revert VALUE
*           Assign subdiagonal entries of D from array E to
*           subdiagonal entries of A.
*
            i = 1
            DO WHILE ( i.LE.n-1 )
               IF( ipiv( i ).LT.0 ) THEN
                  a( i + 1, i ) = e( i )
                  i = i + 1
               END IF
               i = i + 1
            END DO
*
         END IF
*
*        End A is LOWER
*
      END IF
 
      RETURN
*
*     End of ZSYCONVF
*
      END