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    1: *> \brief \b DTPQRT
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DTPQRT + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtpqrt.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtpqrt.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtpqrt.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
   22: *                          INFO )
   23: * 
   24: *       .. Scalar Arguments ..
   25: *       INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
   29: *       ..
   30: *  
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> DTPQRT computes a blocked QR factorization of a real 
   38: *> "triangular-pentagonal" matrix C, which is composed of a 
   39: *> triangular block A and pentagonal block B, using the compact 
   40: *> WY representation for Q.
   41: *> \endverbatim
   42: *
   43: *  Arguments:
   44: *  ==========
   45: *
   46: *> \param[in] M
   47: *> \verbatim
   48: *>          M is INTEGER
   49: *>          The number of rows of the matrix B.  
   50: *>          M >= 0.
   51: *> \endverbatim
   52: *>
   53: *> \param[in] N
   54: *> \verbatim
   55: *>          N is INTEGER
   56: *>          The number of columns of the matrix B, and the order of the
   57: *>          triangular matrix A.
   58: *>          N >= 0.
   59: *> \endverbatim
   60: *>
   61: *> \param[in] L
   62: *> \verbatim
   63: *>          L is INTEGER
   64: *>          The number of rows of the upper trapezoidal part of B.
   65: *>          MIN(M,N) >= L >= 0.  See Further Details.
   66: *> \endverbatim
   67: *>
   68: *> \param[in] NB
   69: *> \verbatim
   70: *>          NB is INTEGER
   71: *>          The block size to be used in the blocked QR.  N >= NB >= 1.
   72: *> \endverbatim
   73: *>
   74: *> \param[in,out] A
   75: *> \verbatim
   76: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   77: *>          On entry, the upper triangular N-by-N matrix A.
   78: *>          On exit, the elements on and above the diagonal of the array
   79: *>          contain the upper triangular matrix R.
   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[in,out] B
   89: *> \verbatim
   90: *>          B is DOUBLE PRECISION array, dimension (LDB,N)
   91: *>          On entry, the pentagonal M-by-N matrix B.  The first M-L rows 
   92: *>          are rectangular, and the last L rows are upper trapezoidal.
   93: *>          On exit, B contains the pentagonal matrix V.  See Further Details.
   94: *> \endverbatim
   95: *>
   96: *> \param[in] LDB
   97: *> \verbatim
   98: *>          LDB is INTEGER
   99: *>          The leading dimension of the array B.  LDB >= max(1,M).
  100: *> \endverbatim
  101: *>
  102: *> \param[out] T
  103: *> \verbatim
  104: *>          T is DOUBLE PRECISION array, dimension (LDT,N)
  105: *>          The upper triangular block reflectors stored in compact form
  106: *>          as a sequence of upper triangular blocks.  See Further Details.
  107: *> \endverbatim
  108: *>          
  109: *> \param[in] LDT
  110: *> \verbatim
  111: *>          LDT is INTEGER
  112: *>          The leading dimension of the array T.  LDT >= NB.
  113: *> \endverbatim
  114: *>
  115: *> \param[out] WORK
  116: *> \verbatim
  117: *>          WORK is DOUBLE PRECISION array, dimension (NB*N)
  118: *> \endverbatim
  119: *>
  120: *> \param[out] INFO
  121: *> \verbatim
  122: *>          INFO is INTEGER
  123: *>          = 0:  successful exit
  124: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  125: *> \endverbatim
  126: *
  127: *  Authors:
  128: *  ========
  129: *
  130: *> \author Univ. of Tennessee 
  131: *> \author Univ. of California Berkeley 
  132: *> \author Univ. of Colorado Denver 
  133: *> \author NAG Ltd. 
  134: *
  135: *> \date November 2013
  136: *
  137: *> \ingroup doubleOTHERcomputational
  138: *
  139: *> \par Further Details:
  140: *  =====================
  141: *>
  142: *> \verbatim
  143: *>
  144: *>  The input matrix C is a (N+M)-by-N matrix  
  145: *>
  146: *>               C = [ A ]
  147: *>                   [ B ]        
  148: *>
  149: *>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
  150: *>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
  151: *>  upper trapezoidal matrix B2:
  152: *>
  153: *>               B = [ B1 ]  <- (M-L)-by-N rectangular
  154: *>                   [ B2 ]  <-     L-by-N upper trapezoidal.
  155: *>
  156: *>  The upper trapezoidal matrix B2 consists of the first L rows of a
  157: *>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0, 
  158: *>  B is rectangular M-by-N; if M=L=N, B is upper triangular.  
  159: *>
  160: *>  The matrix W stores the elementary reflectors H(i) in the i-th column
  161: *>  below the diagonal (of A) in the (N+M)-by-N input matrix C
  162: *>
  163: *>               C = [ A ]  <- upper triangular N-by-N
  164: *>                   [ B ]  <- M-by-N pentagonal
  165: *>
  166: *>  so that W can be represented as
  167: *>
  168: *>               W = [ I ]  <- identity, N-by-N
  169: *>                   [ V ]  <- M-by-N, same form as B.
  170: *>
  171: *>  Thus, all of information needed for W is contained on exit in B, which
  172: *>  we call V above.  Note that V has the same form as B; that is, 
  173: *>
  174: *>               V = [ V1 ] <- (M-L)-by-N rectangular
  175: *>                   [ V2 ] <-     L-by-N upper trapezoidal.
  176: *>
  177: *>  The columns of V represent the vectors which define the H(i)'s.  
  178: *>
  179: *>  The number of blocks is B = ceiling(N/NB), where each
  180: *>  block is of order NB except for the last block, which is of order 
  181: *>  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
  182: *>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB 
  183: *>  for the last block) T's are stored in the NB-by-N matrix T as
  184: *>
  185: *>               T = [T1 T2 ... TB].
  186: *> \endverbatim
  187: *>
  188: *  =====================================================================
  189:       SUBROUTINE DTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
  190:      $                   INFO )
  191: *
  192: *  -- LAPACK computational routine (version 3.5.0) --
  193: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  194: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  195: *     November 2013
  196: *
  197: *     .. Scalar Arguments ..
  198:       INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
  199: *     ..
  200: *     .. Array Arguments ..
  201:       DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
  202: *     ..
  203: *
  204: * =====================================================================
  205: *
  206: *     ..
  207: *     .. Local Scalars ..
  208:       INTEGER    I, IB, LB, MB, IINFO
  209: *     ..
  210: *     .. External Subroutines ..
  211:       EXTERNAL   DTPQRT2, DTPRFB, XERBLA
  212: *     ..
  213: *     .. Executable Statements ..
  214: *
  215: *     Test the input arguments
  216: *
  217:       INFO = 0
  218:       IF( M.LT.0 ) THEN
  219:          INFO = -1
  220:       ELSE IF( N.LT.0 ) THEN
  221:          INFO = -2
  222:       ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN
  223:          INFO = -3
  224:       ELSE IF( NB.LT.1 .OR. (NB.GT.N .AND. N.GT.0)) THEN
  225:          INFO = -4
  226:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  227:          INFO = -6
  228:       ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
  229:          INFO = -8
  230:       ELSE IF( LDT.LT.NB ) THEN
  231:          INFO = -10
  232:       END IF
  233:       IF( INFO.NE.0 ) THEN
  234:          CALL XERBLA( 'DTPQRT', -INFO )
  235:          RETURN
  236:       END IF
  237: *
  238: *     Quick return if possible
  239: *
  240:       IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
  241: *
  242:       DO I = 1, N, NB
  243: *     
  244: *     Compute the QR factorization of the current block
  245: *
  246:          IB = MIN( N-I+1, NB )
  247:          MB = MIN( M-L+I+IB-1, M )
  248:          IF( I.GE.L ) THEN
  249:             LB = 0
  250:          ELSE
  251:             LB = MB-M+L-I+1
  252:          END IF
  253: *
  254:          CALL DTPQRT2( MB, IB, LB, A(I,I), LDA, B( 1, I ), LDB, 
  255:      $                 T(1, I ), LDT, IINFO )
  256: *
  257: *     Update by applying H**T to B(:,I+IB:N) from the left
  258: *
  259:          IF( I+IB.LE.N ) THEN
  260:             CALL DTPRFB( 'L', 'T', 'F', 'C', MB, N-I-IB+1, IB, LB,
  261:      $                    B( 1, I ), LDB, T( 1, I ), LDT, 
  262:      $                    A( I, I+IB ), LDA, B( 1, I+IB ), LDB, 
  263:      $                    WORK, IB )
  264:          END IF
  265:       END DO
  266:       RETURN
  267: *     
  268: *     End of DTPQRT
  269: *
  270:       END