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Mise à jour de Lapack (3.6.0) et du numéro de version du RPL/2.

    1: *> \brief \b ZSYTRF_ROOK
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download ZSYTRF_ROOK + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytrf_rook.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytrf_rook.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrf_rook.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          UPLO
   25: *       INTEGER            INFO, LDA, LWORK, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       INTEGER            IPIV( * )
   29: *       COMPLEX*16         A( LDA, * ), WORK( * )
   30: *       ..
   31: *  
   32: *
   33: *> \par Purpose:
   34: *  =============
   35: *>
   36: *> \verbatim
   37: *>
   38: *> ZSYTRF_ROOK computes the factorization of a complex symmetric matrix A
   39: *> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
   40: *> The form of the factorization is
   41: *>
   42: *>    A = U*D*U**T  or  A = L*D*L**T
   43: *>
   44: *> where U (or L) is a product of permutation and unit upper (lower)
   45: *> triangular matrices, and D is symmetric and block diagonal with
   46: *> 1-by-1 and 2-by-2 diagonal blocks.
   47: *>
   48: *> This is the blocked version of the algorithm, calling Level 3 BLAS.
   49: *> \endverbatim
   50: *
   51: *  Arguments:
   52: *  ==========
   53: *
   54: *> \param[in] UPLO
   55: *> \verbatim
   56: *>          UPLO is CHARACTER*1
   57: *>          = 'U':  Upper triangle of A is stored;
   58: *>          = 'L':  Lower triangle of A is stored.
   59: *> \endverbatim
   60: *>
   61: *> \param[in] N
   62: *> \verbatim
   63: *>          N is INTEGER
   64: *>          The order of the matrix A.  N >= 0.
   65: *> \endverbatim
   66: *>
   67: *> \param[in,out] A
   68: *> \verbatim
   69: *>          A is COMPLEX*16 array, dimension (LDA,N)
   70: *>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
   71: *>          N-by-N upper triangular part of A contains the upper
   72: *>          triangular part of the matrix A, and the strictly lower
   73: *>          triangular part of A is not referenced.  If UPLO = 'L', the
   74: *>          leading N-by-N lower triangular part of A contains the lower
   75: *>          triangular part of the matrix A, and the strictly upper
   76: *>          triangular part of A is not referenced.
   77: *>
   78: *>          On exit, the block diagonal matrix D and the multipliers used
   79: *>          to obtain the factor U or L (see below for further details).
   80: *> \endverbatim
   81: *>
   82: *> \param[in] LDA
   83: *> \verbatim
   84: *>          LDA is INTEGER
   85: *>          The leading dimension of the array A.  LDA >= max(1,N).
   86: *> \endverbatim
   87: *>
   88: *> \param[out] IPIV
   89: *> \verbatim
   90: *>          IPIV is INTEGER array, dimension (N)
   91: *>          Details of the interchanges and the block structure of D.
   92: *>
   93: *>          If UPLO = 'U':
   94: *>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
   95: *>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
   96: *>
   97: *>               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
   98: *>               columns k and -IPIV(k) were interchanged and rows and
   99: *>               columns k-1 and -IPIV(k-1) were inerchaged,
  100: *>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
  101: *>
  102: *>          If UPLO = 'L':
  103: *>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
  104: *>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
  105: *>
  106: *>               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
  107: *>               columns k and -IPIV(k) were interchanged and rows and
  108: *>               columns k+1 and -IPIV(k+1) were inerchaged,
  109: *>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
  110: *> \endverbatim
  111: *>
  112: *> \param[out] WORK
  113: *> \verbatim
  114: *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).
  115: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  116: *> \endverbatim
  117: *>
  118: *> \param[in] LWORK
  119: *> \verbatim
  120: *>          LWORK is INTEGER
  121: *>          The length of WORK.  LWORK >=1.  For best performance
  122: *>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
  123: *>
  124: *>          If LWORK = -1, then a workspace query is assumed; the routine
  125: *>          only calculates the optimal size of the WORK array, returns
  126: *>          this value as the first entry of the WORK array, and no error
  127: *>          message related to LWORK is issued by XERBLA.
  128: *> \endverbatim
  129: *>
  130: *> \param[out] INFO
  131: *> \verbatim
  132: *>          INFO is INTEGER
  133: *>          = 0:  successful exit
  134: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  135: *>          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
  136: *>                has been completed, but the block diagonal matrix D is
  137: *>                exactly singular, and division by zero will occur if it
  138: *>                is used to solve a system of equations.
  139: *> \endverbatim
  140: *
  141: *  Authors:
  142: *  ========
  143: *
  144: *> \author Univ. of Tennessee 
  145: *> \author Univ. of California Berkeley 
  146: *> \author Univ. of Colorado Denver 
  147: *> \author NAG Ltd. 
  148: *
  149: *> \date November 2015
  150: *
  151: *> \ingroup complex16SYcomputational
  152: *
  153: *> \par Further Details:
  154: *  =====================
  155: *>
  156: *> \verbatim
  157: *>
  158: *>  If UPLO = 'U', then A = U*D*U**T, where
  159: *>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
  160: *>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
  161: *>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
  162: *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
  163: *>  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
  164: *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
  165: *>
  166: *>             (   I    v    0   )   k-s
  167: *>     U(k) =  (   0    I    0   )   s
  168: *>             (   0    0    I   )   n-k
  169: *>                k-s   s   n-k
  170: *>
  171: *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
  172: *>  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
  173: *>  and A(k,k), and v overwrites A(1:k-2,k-1:k).
  174: *>
  175: *>  If UPLO = 'L', then A = L*D*L**T, where
  176: *>     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
  177: *>  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
  178: *>  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
  179: *>  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
  180: *>  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
  181: *>  that if the diagonal block D(k) is of order s (s = 1 or 2), then
  182: *>
  183: *>             (   I    0     0   )  k-1
  184: *>     L(k) =  (   0    I     0   )  s
  185: *>             (   0    v     I   )  n-k-s+1
  186: *>                k-1   s  n-k-s+1
  187: *>
  188: *>  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
  189: *>  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
  190: *>  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
  191: *> \endverbatim
  192: *
  193: *> \par Contributors:
  194: *  ==================
  195: *>
  196: *> \verbatim
  197: *>
  198: *>   November 2015, Igor Kozachenko,
  199: *>                  Computer Science Division,
  200: *>                  University of California, Berkeley
  201: *>
  202: *>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
  203: *>                  School of Mathematics,
  204: *>                  University of Manchester
  205: *>
  206: *> \endverbatim
  207: *
  208: *  =====================================================================
  209:       SUBROUTINE ZSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
  210: *
  211: *  -- LAPACK computational routine (version 3.6.0) --
  212: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  213: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  214: *     November 2015
  215: *
  216: *     .. Scalar Arguments ..
  217:       CHARACTER          UPLO
  218:       INTEGER            INFO, LDA, LWORK, N
  219: *     ..
  220: *     .. Array Arguments ..
  221:       INTEGER            IPIV( * )
  222:       COMPLEX*16         A( LDA, * ), WORK( * )
  223: *     ..
  224: *
  225: *  =====================================================================
  226: *
  227: *     .. Local Scalars ..
  228:       LOGICAL            LQUERY, UPPER
  229:       INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
  230: *     ..
  231: *     .. External Functions ..
  232:       LOGICAL            LSAME
  233:       INTEGER            ILAENV
  234:       EXTERNAL           LSAME, ILAENV
  235: *     ..
  236: *     .. External Subroutines ..
  237:       EXTERNAL           ZLASYF_ROOK, ZSYTF2_ROOK, XERBLA
  238: *     ..
  239: *     .. Intrinsic Functions ..
  240:       INTRINSIC          MAX
  241: *     ..
  242: *     .. Executable Statements ..
  243: *
  244: *     Test the input parameters.
  245: *
  246:       INFO = 0
  247:       UPPER = LSAME( UPLO, 'U' )
  248:       LQUERY = ( LWORK.EQ.-1 )
  249:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  250:          INFO = -1
  251:       ELSE IF( N.LT.0 ) THEN
  252:          INFO = -2
  253:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  254:          INFO = -4
  255:       ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
  256:          INFO = -7
  257:       END IF
  258: *
  259:       IF( INFO.EQ.0 ) THEN
  260: *
  261: *        Determine the block size
  262: *
  263:          NB = ILAENV( 1, 'ZSYTRF_ROOK', UPLO, N, -1, -1, -1 )
  264:          LWKOPT = N*NB
  265:          WORK( 1 ) = LWKOPT
  266:       END IF
  267: *
  268:       IF( INFO.NE.0 ) THEN
  269:          CALL XERBLA( 'ZSYTRF_ROOK', -INFO )
  270:          RETURN
  271:       ELSE IF( LQUERY ) THEN
  272:          RETURN
  273:       END IF
  274: *
  275:       NBMIN = 2
  276:       LDWORK = N
  277:       IF( NB.GT.1 .AND. NB.LT.N ) THEN
  278:          IWS = LDWORK*NB
  279:          IF( LWORK.LT.IWS ) THEN
  280:             NB = MAX( LWORK / LDWORK, 1 )
  281:             NBMIN = MAX( 2, ILAENV( 2, 'ZSYTRF_ROOK',
  282:      $                              UPLO, N, -1, -1, -1 ) )
  283:          END IF
  284:       ELSE
  285:          IWS = 1
  286:       END IF
  287:       IF( NB.LT.NBMIN )
  288:      $   NB = N
  289: *
  290:       IF( UPPER ) THEN
  291: *
  292: *        Factorize A as U*D*U**T using the upper triangle of A
  293: *
  294: *        K is the main loop index, decreasing from N to 1 in steps of
  295: *        KB, where KB is the number of columns factorized by ZLASYF_ROOK;
  296: *        KB is either NB or NB-1, or K for the last block
  297: *
  298:          K = N
  299:    10    CONTINUE
  300: *
  301: *        If K < 1, exit from loop
  302: *
  303:          IF( K.LT.1 )
  304:      $      GO TO 40
  305: *
  306:          IF( K.GT.NB ) THEN
  307: *
  308: *           Factorize columns k-kb+1:k of A and use blocked code to
  309: *           update columns 1:k-kb
  310: *
  311:             CALL ZLASYF_ROOK( UPLO, K, NB, KB, A, LDA,
  312:      $                        IPIV, WORK, LDWORK, IINFO )
  313:          ELSE
  314: *
  315: *           Use unblocked code to factorize columns 1:k of A
  316: *
  317:             CALL ZSYTF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
  318:             KB = K
  319:          END IF
  320: *
  321: *        Set INFO on the first occurrence of a zero pivot
  322: *
  323:          IF( INFO.EQ.0 .AND. IINFO.GT.0 )
  324:      $      INFO = IINFO     
  325: *
  326: *        No need to adjust IPIV
  327: *
  328: *        Decrease K and return to the start of the main loop
  329: *
  330:          K = K - KB
  331:          GO TO 10
  332: *
  333:       ELSE
  334: *
  335: *        Factorize A as L*D*L**T using the lower triangle of A
  336: *
  337: *        K is the main loop index, increasing from 1 to N in steps of
  338: *        KB, where KB is the number of columns factorized by ZLASYF_ROOK;
  339: *        KB is either NB or NB-1, or N-K+1 for the last block
  340: *
  341:          K = 1
  342:    20    CONTINUE
  343: *
  344: *        If K > N, exit from loop
  345: *
  346:          IF( K.GT.N )
  347:      $      GO TO 40
  348: *
  349:          IF( K.LE.N-NB ) THEN
  350: *
  351: *           Factorize columns k:k+kb-1 of A and use blocked code to
  352: *           update columns k+kb:n
  353: *
  354:             CALL ZLASYF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
  355:      $                        IPIV( K ), WORK, LDWORK, IINFO )
  356:          ELSE
  357: *
  358: *           Use unblocked code to factorize columns k:n of A
  359: *
  360:             CALL ZSYTF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
  361:      $                   IINFO )
  362:             KB = N - K + 1
  363:          END IF
  364: *
  365: *        Set INFO on the first occurrence of a zero pivot
  366: *
  367:          IF( INFO.EQ.0 .AND. IINFO.GT.0 )
  368:      $      INFO = IINFO + K - 1
  369: *
  370: *        Adjust IPIV
  371: *
  372:          DO 30 J = K, K + KB - 1
  373:             IF( IPIV( J ).GT.0 ) THEN
  374:                IPIV( J ) = IPIV( J ) + K - 1
  375:             ELSE
  376:                IPIV( J ) = IPIV( J ) - K + 1
  377:             END IF
  378:    30    CONTINUE
  379: *
  380: *        Increase K and return to the start of the main loop
  381: *
  382:          K = K + KB
  383:          GO TO 20
  384: *
  385:       END IF
  386: *
  387:    40 CONTINUE
  388:       WORK( 1 ) = LWKOPT
  389:       RETURN
  390: *
  391: *     End of ZSYTRF_ROOK
  392: *
  393:       END