OpenBLAS/lapack-netlib/SRC/ctftri.f

*> \brief \b CTFTRI
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE CTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          TRANSR, UPLO, DIAG
*       INTEGER            INFO, N
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( 0: * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CTFTRI computes the inverse of a triangular matrix A stored in RFP
*> format.
*>
*> This is a Level 3 BLAS version of the algorithm.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] TRANSR
*> \verbatim
*>          TRANSR is CHARACTER*1
*>          = 'N':  The Normal TRANSR of RFP A is stored;
*>          = 'C':  The Conjugate-transpose TRANSR of RFP A is stored.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  A is upper triangular;
*>          = 'L':  A is lower triangular.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>          = 'N':  A is non-unit triangular;
*>          = 'U':  A is unit triangular.
*> \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 ( N*(N+1)/2 );
*>          On entry, the triangular matrix A in RFP format. RFP format
*>          is described by TRANSR, UPLO, and N as follows: If TRANSR =
*>          'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
*>          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
*>          the Conjugate-transpose of RFP A as defined when
*>          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
*>          follows: If UPLO = 'U' the RFP A contains the nt elements of
*>          upper packed A; If UPLO = 'L' the RFP A contains the nt
*>          elements of lower packed A. The LDA of RFP A is (N+1)/2 when
*>          TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
*>          even and N is odd. See the Note below for more details.
*>
*>          On exit, the (triangular) inverse of the original matrix, in
*>          the same storage format.
*> \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, A(i,i) is exactly zero.  The triangular
*>               matrix is singular and its inverse can not be computed.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexOTHERcomputational
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  We first consider Standard Packed Format when N is even.
*>  We give an example where N = 6.
*>
*>      AP is Upper             AP is Lower
*>
*>   00 01 02 03 04 05       00
*>      11 12 13 14 15       10 11
*>         22 23 24 25       20 21 22
*>            33 34 35       30 31 32 33
*>               44 45       40 41 42 43 44
*>                  55       50 51 52 53 54 55
*>
*>
*>  Let TRANSR = 'N'. RFP holds AP as follows:
*>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
*>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
*>  conjugate-transpose of the first three columns of AP upper.
*>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
*>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
*>  conjugate-transpose of the last three columns of AP lower.
*>  To denote conjugate we place -- above the element. This covers the
*>  case N even and TRANSR = 'N'.
*>
*>         RFP A                   RFP A
*>
*>                                -- -- --
*>        03 04 05                33 43 53
*>                                   -- --
*>        13 14 15                00 44 54
*>                                      --
*>        23 24 25                10 11 55
*>
*>        33 34 35                20 21 22
*>        --
*>        00 44 45                30 31 32
*>        -- --
*>        01 11 55                40 41 42
*>        -- -- --
*>        02 12 22                50 51 52
*>
*>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
*>  transpose of RFP A above. One therefore gets:
*>
*>
*>           RFP A                   RFP A
*>
*>     -- -- -- --                -- -- -- -- -- --
*>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
*>     -- -- -- -- --                -- -- -- -- --
*>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
*>     -- -- -- -- -- --                -- -- -- --
*>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
*>
*>
*>  We next  consider Standard Packed Format when N is odd.
*>  We give an example where N = 5.
*>
*>     AP is Upper                 AP is Lower
*>
*>   00 01 02 03 04              00
*>      11 12 13 14              10 11
*>         22 23 24              20 21 22
*>            33 34              30 31 32 33
*>               44              40 41 42 43 44
*>
*>
*>  Let TRANSR = 'N'. RFP holds AP as follows:
*>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
*>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
*>  conjugate-transpose of the first two   columns of AP upper.
*>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
*>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
*>  conjugate-transpose of the last two   columns of AP lower.
*>  To denote conjugate we place -- above the element. This covers the
*>  case N odd  and TRANSR = 'N'.
*>
*>         RFP A                   RFP A
*>
*>                                   -- --
*>        02 03 04                00 33 43
*>                                      --
*>        12 13 14                10 11 44
*>
*>        22 23 24                20 21 22
*>        --
*>        00 33 34                30 31 32
*>        -- --
*>        01 11 44                40 41 42
*>
*>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
*>  transpose of RFP A above. One therefore gets:
*>
*>
*>           RFP A                   RFP A
*>
*>     -- -- --                   -- -- -- -- -- --
*>     02 12 22 00 01             00 10 20 30 40 50
*>     -- -- -- --                   -- -- -- -- --
*>     03 13 23 33 11             33 11 21 31 41 51
*>     -- -- -- -- --                   -- -- -- --
*>     04 14 24 34 44             43 44 22 32 42 52
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE CTFTRI( TRANSR, UPLO, DIAG, N, A, 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          TRANSR, UPLO, DIAG
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
      COMPLEX            A( 0: * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            CONE
      PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            LOWER, NISODD, NORMALTRANSR
      INTEGER            N1, N2, K
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, CTRMM, CTRTRI
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MOD
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      NORMALTRANSR = LSAME( TRANSR, 'N' )
      LOWER = LSAME( UPLO, 'L' )
      IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
         INFO = -2
      ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
     $         THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CTFTRI', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     If N is odd, set NISODD = .TRUE.
*     If N is even, set K = N/2 and NISODD = .FALSE.
*
      IF( MOD( N, 2 ).EQ.0 ) THEN
         K = N / 2
         NISODD = .FALSE.
      ELSE
         NISODD = .TRUE.
      END IF
*
*     Set N1 and N2 depending on LOWER
*
      IF( LOWER ) THEN
         N2 = N / 2
         N1 = N - N2
      ELSE
         N1 = N / 2
         N2 = N - N1
      END IF
*
*
*     start execution: there are eight cases
*
      IF( NISODD ) THEN
*
*        N is odd
*
         IF( NORMALTRANSR ) THEN
*
*           N is odd and TRANSR = 'N'
*
            IF( LOWER ) THEN
*
*             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
*             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
*             T1 -> a(0), T2 -> a(n), S -> a(n1)
*
               CALL CTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'R', 'L', 'N', DIAG, N2, N1, -CONE, A( 0 ),
     $                     N, A( N1 ), N )
               CALL CTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
               IF( INFO.GT.0 )
     $            INFO = INFO + N1
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'L', 'U', 'C', DIAG, N2, N1, CONE, A( N ), N,
     $                     A( N1 ), N )
*
            ELSE
*
*             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
*             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
*             T1 -> a(n2), T2 -> a(n1), S -> a(0)
*
               CALL CTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'L', 'L', 'C', DIAG, N1, N2, -CONE, A( N2 ),
     $                     N, A( 0 ), N )
               CALL CTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
               IF( INFO.GT.0 )
     $            INFO = INFO + N1
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'R', 'U', 'N', DIAG, N1, N2, CONE, A( N1 ),
     $                     N, A( 0 ), N )
*
            END IF
*
         ELSE
*
*           N is odd and TRANSR = 'C'
*
            IF( LOWER ) THEN
*
*              SRPA for LOWER, TRANSPOSE and N is odd
*              T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
*
               CALL CTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'L', 'U', 'N', DIAG, N1, N2, -CONE, A( 0 ),
     $                     N1, A( N1*N1 ), N1 )
               CALL CTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
               IF( INFO.GT.0 )
     $            INFO = INFO + N1
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'R', 'L', 'C', DIAG, N1, N2, CONE, A( 1 ),
     $                     N1, A( N1*N1 ), N1 )
*
            ELSE
*
*              SRPA for UPPER, TRANSPOSE and N is odd
*              T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
*
               CALL CTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'R', 'U', 'C', DIAG, N2, N1, -CONE,
     $                     A( N2*N2 ), N2, A( 0 ), N2 )
               CALL CTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
               IF( INFO.GT.0 )
     $            INFO = INFO + N1
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'L', 'L', 'N', DIAG, N2, N1, CONE,
     $                     A( N1*N2 ), N2, A( 0 ), N2 )
            END IF
*
         END IF
*
      ELSE
*
*        N is even
*
         IF( NORMALTRANSR ) THEN
*
*           N is even and TRANSR = 'N'
*
            IF( LOWER ) THEN
*
*              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
*              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
*              T1 -> a(1), T2 -> a(0), S -> a(k+1)
*
               CALL CTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'R', 'L', 'N', DIAG, K, K, -CONE, A( 1 ),
     $                     N+1, A( K+1 ), N+1 )
               CALL CTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
               IF( INFO.GT.0 )
     $            INFO = INFO + K
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'L', 'U', 'C', DIAG, K, K, CONE, A( 0 ), N+1,
     $                     A( K+1 ), N+1 )
*
            ELSE
*
*              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
*              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
*              T1 -> a(k+1), T2 -> a(k), S -> a(0)
*
               CALL CTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'L', 'L', 'C', DIAG, K, K, -CONE, A( K+1 ),
     $                     N+1, A( 0 ), N+1 )
               CALL CTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
               IF( INFO.GT.0 )
     $            INFO = INFO + K
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'R', 'U', 'N', DIAG, K, K, CONE, A( K ), N+1,
     $                     A( 0 ), N+1 )
            END IF
         ELSE
*
*           N is even and TRANSR = 'C'
*
            IF( LOWER ) THEN
*
*              SRPA for LOWER, TRANSPOSE and N is even (see paper)
*              T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
*              T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
*
               CALL CTRTRI( 'U', DIAG, K, A( K ), K, INFO )
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'L', 'U', 'N', DIAG, K, K, -CONE, A( K ), K,
     $                     A( K*( K+1 ) ), K )
               CALL CTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
               IF( INFO.GT.0 )
     $            INFO = INFO + K
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'R', 'L', 'C', DIAG, K, K, CONE, A( 0 ), K,
     $                     A( K*( K+1 ) ), K )
            ELSE
*
*              SRPA for UPPER, TRANSPOSE and N is even (see paper)
*              T1 -> B(0,k+1),     T2 -> B(0,k),   S -> B(0,0)
*              T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
*
               CALL CTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'R', 'U', 'C', DIAG, K, K, -CONE,
     $                     A( K*( K+1 ) ), K, A( 0 ), K )
               CALL CTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
               IF( INFO.GT.0 )
     $            INFO = INFO + K
               IF( INFO.GT.0 )
     $            RETURN
               CALL CTRMM( 'L', 'L', 'N', DIAG, K, K, CONE, A( K*K ), K,
     $                     A( 0 ), K )
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of CTFTRI
*
      END