MB02CX

Bringing the first blocks of a generator in proper form

Purpose

  To bring the first blocks of a generator in proper form.
  The columns / rows of the positive and negative generators
  are contained in the arrays A and B, respectively.
  Transformation information will be stored and can be applied
  via SLICOT Library routine MB02CY.

      SUBROUTINE MB02CX( TYPET, P, Q, K, A, LDA, B, LDB, CS, LCS,
     $                   DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER         TYPET
      INTEGER           INFO, K, LDA, LDB, LCS, LDWORK, P, Q
C     .. Array Arguments ..
      DOUBLE PRECISION  A(LDA, *), B(LDB, *), CS(*), DWORK(*)

Mode Parameters

  TYPET   CHARACTER*1
          Specifies the type of the generator, as follows:
          = 'R':  A and B are the first blocks of the rows of the
                  positive and negative generators;
          = 'C':  A and B are the first blocks of the columns of the
                  positive and negative generators.
          Note:   in the sequel, the notation x / y means that
                  x corresponds to TYPET = 'R' and y corresponds to
                  TYPET = 'C'.

  P       (input)  INTEGER
          The number of rows / columns in A containing the positive
          generators.  P >= 0.

  Q       (input)  INTEGER
          The number of rows / columns in B containing the negative
          generators.  Q >= 0.

  K       (input)  INTEGER
          The number of columns / rows in A and B to be processed.
          Normally, the size of the first block.  P >= K >= 0.

  A       (input/output)  DOUBLE PRECISION array, dimension
          (LDA, K) / (LDA, P)
          On entry, the leading P-by-K upper / K-by-P lower
          triangular part of this array must contain the rows /
          columns of the positive part in the first block of the
          generator.
          On exit, the leading P-by-K upper / K-by-P lower
          triangular part of this array contains the rows / columns
          of the positive part in the first block of the proper
          generator.
          The lower / upper trapezoidal part is not referenced.

  LDA     INTEGER
          The leading dimension of the array A.
          LDA >= MAX(1,P),    if TYPET = 'R';
          LDA >= MAX(1,K),    if TYPET = 'C'.

  B       (input/output)  DOUBLE PRECISION array, dimension
          (LDB, K) / (LDB, Q)
          On entry, the leading Q-by-K / K-by-Q part of this array
          must contain the rows / columns of the negative part in
          the first block of the generator.
          On exit, the leading Q-by-K / K-by-Q part of this array
          contains part of the necessary information for the
          Householder transformations.

  LDB     INTEGER
          The leading dimension of the array B.
          LDB >= MAX(1,Q),    if TYPET = 'R';
          LDB >= MAX(1,K),    if TYPET = 'C'.

  CS      (output)  DOUBLE PRECISION array, dimension (LCS)
          On exit, the leading 2*K + MIN(K,Q) part of this array
          contains necessary information for the SLICOT Library
          routine MB02CY (modified hyperbolic rotation parameters
          and scalar factors of the Householder transformations).

  LCS     INTEGER
          The length of the array CS.  LCS >= 2*K + MIN(K,Q).

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          On exit, if  INFO = 0,  DWORK(1)  returns the optimal
          value of LDWORK.
          On exit, if  INFO = -12,  DWORK(1)  returns the minimum
          value of LDWORK.

  LDWORK  INTEGER
          The length of the array DWORK.  LDWORK >= MAX(1,K).
          For optimum performance LDWORK should be larger.

  INFO    INTEGER
          = 0:  succesful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value;
          = 1:  the reduction algorithm failed. The matrix
                associated with the generator is not (numerically)
                positive definite.

  If  TYPET = 'R',  a QR decomposition of B is first computed.
  Then, the elements below the first row of each column i of B
  are annihilated by a Householder transformation modifying the
  first element in that column. This first element, in turn, is
  then annihilated by a modified hyperbolic rotation, acting also
  on the i-th row of A.

  If  TYPET = 'C',  an LQ decomposition of B is first computed.
  Then, the elements on the right of the first column of each row i
  of B are annihilated by a Householder transformation modifying the
  first element in that row. This first element, in turn, is
  then annihilated by a modified hyperbolic rotation, acting also
  on the i-th column of A.

  None

Program Text

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