IRIX 6.2 Development Libraries/SGI IRIX 6.2 Development Libraries.iso/dist/complib.idb/usr/share/catman/p_man/cat3/complib/SQRSL.z/SQRSL

Text File | 1996-03-14 | 6KB | 199 lines

SSSSQQQQRRRRSSSSLLLL((((3333FFFF))))                                                            SSSSQQQQRRRRSSSSLLLL((((3333FFFF))))



NNNNAAAAMMMMEEEE
     SQRSL   - SQRSL applies the output of SQRDC to compute coordinate
     transformations, projections, and least squares solutions.  For K .LE.
     MIN(N,P), let XK be the matrix

        XK = (X(JPVT(1)),X(JPVT(2)), ... ,X(JPVT(K)))

     formed from columnns JPVT(1), ... ,JPVT(K) of the original N x P matrix X
     that was input to SQRDC (if no pivoting was done, XK consists of the
     first K columns of X in their original order).  SQRDC produces a factored
     orthogonal matrix Q and an upper triangular matrix R such that

        XK = Q * (R)
        (0)

     This information is contained in coded form in the arrays X and QRAUX.


SSSSYYYYNNNNOOOOPPPPSSSSYYYYSSSS
      SUBROUTINE SQRSL(X,LDX,N,K,QRAUX,Y,QY,QTY,B,RSD,XB,JOB,INFO)

DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     On Entry

     XXXX REAL(LDX,P)
        X contains the output of SQRDC.

     LLLLDDDDXXXX INTEGER
        LDX is the leading dimension of the array X.

     NNNN INTEGER
        N is the number of rows of the matrix XK.  It must
        have the same value as N in SQRDC.

     KKKK INTEGER
        K is the number of columns of the matrix XK.  K
        must not be greater than MIN(N,P), where P is the
        same as in the calling sequence to SQRDC.

     QQQQRRRRAAAAUUUUXXXX REAL(P)
        QRAUX contains the auxiliary output from SQRDC.

     YYYY REAL(N)
        Y contains an N-vector that is to be manipulated
        by SQRSL.

     JJJJOOOOBBBB INTEGER
        JOB specifies what is to be computed.  JOB has
        the decimal expansion ABCDE, with the following
        meaning.
        If A .NE. 0, compute QY.
        If B,C,D, or E .NE. 0, compute QTY.



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SSSSQQQQRRRRSSSSLLLL((((3333FFFF))))                                                            SSSSQQQQRRRRSSSSLLLL((((3333FFFF))))



        If C .NE. 0, compute B.
        If D .NE. 0, compute RSD.
        If E .NE. 0, compute XB.
        Note that a request to compute B, RSD, or XB
        automatically triggers the computation of QTY, for
        which an array must be provided in the calling
        sequence.  On Return

     QQQQYYYY REAL(N).
        QY contains Q*Y, if its computation has been
        requested.

     QQQQTTTTYYYY REAL(N).
        QTY contains TRANS(Q)*Y, if its computation has
        been requested.  Here TRANS(Q) is the
        transpose of the matrix Q.

     BBBB REAL(K)
        B contains the solution of the least squares problem
        minimize norm2(Y - XK*B),
        if its computation has been requested.  (Note that
        if pivoting was requested in SQRDC, the J-th
        component of B will be associated with column JPVT(J)
        of the original matrix X that was input into SQRDC.)

     RRRRSSSSDDDD REAL(N).
        RSD contains the least squares residual Y - XK*B,
        if its computation has been requested.  RSD is
        also the orthogonal projection of Y onto the
        orthogonal complement of the column space of XK.

     XXXXBBBB REAL(N).
        XB contains the least squares approximation XK*B,
        if its computation has been requested.  XB is also
        the orthogonal projection of Y onto the column space
        of X.

     IIIINNNNFFFFOOOO INTEGER.
        INFO is zero unless the computation of B has
        been requested and R is exactly singular.  In
        this case, INFO is the index of the first zero
        diagonal element of R and B is left unaltered.  The parameters QY,
     QTY, B, RSD, and XB are not referenced if their computation is not
     requested and in this case can be replaced by dummy variables in the
     calling program.  To save storage, the user may in some cases use the
     same array for different parameters in the calling sequence.  A
     frequently occuring example is when one wishes to compute any of B, RSD,
     or XB and does not need Y or QTY.  In this case one may identify Y, QTY,
     and one of B, RSD, or XB, while providing separate arrays for anything
     else that is to be computed.  Thus the calling sequence CALL
     SQRSL(X,LDX,N,K,QRAUX,Y,DUM,Y,B,Y,DUM,110,INFO) will result in the
     computation of B and RSD, with RSD overwriting Y.  More generally, each



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SSSSQQQQRRRRSSSSLLLL((((3333FFFF))))                                                            SSSSQQQQRRRRSSSSLLLL((((3333FFFF))))



     item in the following list contains groups of permissible identifications
     for a single callinng sequence.  1. (Y,QTY,B) (RSD) (XB) (QY) 2.
     (Y,QTY,RSD) (B) (XB) (QY) 3. (Y,QTY,XB) (B) (RSD) (QY) 4. (Y,QY) (QTY,B)
     (RSD) (XB) 5. (Y,QY) (QTY,RSD) (B) (XB) 6. (Y,QY) (QTY,XB) (B) (RSD) In
     any group the value returned in the array allocated to the group
     corresponds to the last member of the group.  LINPACK.  This version
     dated 08/14/78 .  G. W. Stewart, University of Maryland, Argonne National
     Lab.

     SSSSQQQQRRRRSSSSLLLL uses the following functions and subprograms. BLAS SAXPY,SCOPY,SDOT
     Fortran ABS,MIN0,MOD












































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