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dlaln2 (3)
  • >> dlaln2 (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dlaln2 - solve a system of the form (ca A-wD ) X =  s  B  or
         (ca A'-wD) X = s B with possible scaling ("s") and perturba-
         tion of A
    
    SYNOPSIS
         SUBROUTINE DLALN2( LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2,
                   B, LDB, WR, WI, X, LDX, SCALE, XNORM, INFO )
    
         LOGICAL LTRANS
    
         INTEGER INFO, LDA, LDB, LDX, NA, NW
    
         DOUBLE PRECISION CA, D1, D2, SCALE, SMIN, WI, WR, XNORM
    
         DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * )
    
    
    
         #include <sunperf.h>
    
         void dlaln2(int ltrans, int na, int nw, double smin,  double
                   ca,  double  *da,  int  lda, double d1, double d2,
                   double *db, int ldb, double wr, double wi,  double
                   *dx,  int  ldx, double *dscale, double *xnorm, int
                   *info) ;
    
    PURPOSE
         DLALN2 solves a system of the form  (ca A - w D ) X = s B or
         (ca A' - w D) X = s B   with possible scaling ("s") and per-
         turbation of A.  (A' means A-transpose.)
    
         A is an NA x NA real matrix, ca is a real scalar, D is an NA
         x NA real diagonal matrix, w is a real or complex value, and
         X and B are NA x 1 matrices -- real if w is real, complex if
         w is complex.  NA may be 1 or 2.
    
         If w is complex, X and B are represented as NA x 2 matrices,
         the  first column of each being the real part and the second
         being the imaginary part.
    
         "s" is a scaling factor (.LE. 1), computed by DLALN2,  which
         is  so chosen that X can be computed without overflow.  X is
         further scaled if necessary to assure that  norm(ca  A  -  w
         D)*norm(X) is less than overflow.
    
         If both singular values of (ca A - w D) are less than  SMIN,
         SMIN*identity will be used instead of (ca A - w D).  If only
         one singular value is less than SMIN, one element of (ca A -
         w  D) will be perturbed enough to make the smallest singular
         value roughly SMIN.  If both singular values  are  at  least
         SMIN,  (ca A - w D) will not be perturbed.  In any case, the
         perturbation will be at most some  small  multiple  of  max(
         SMIN,  ulp*norm(ca A - w D) ).  The singular values are com-
         puted by infinity-norm approximations, and thus will only be
         correct to a factor of 2 or so.
    
         Note: all input quantities are assumed to  be  smaller  than
         overflow by a reasonable factor.  (See BIGNUM.)
    
    
    ARGUMENTS
         LTRANS    (input) LOGICAL
                   =.TRUE.:  A-transpose will be used.
                   =.FALSE.: A will be used (not transposed.)
    
         NA        (input) INTEGER
                   The size of the matrix A.  It may (only) be  1  or
                   2.
    
         NW        (input) INTEGER
                   1 if "w" is real, 2 if "w"  is  complex.   It  may
                   only be 1 or 2.
    
         SMIN      (input) DOUBLE PRECISION
                   The desired lower bound on the singular values  of
                   A.   This  should  be  a  safe  distance away from
                   underflow    or     overflow,     say,     between
                   (underflow/machine precision) and  (machine preci-
                   sion * overflow ).  (See BIGNUM and ULP.)
    
         CA        (input) DOUBLE PRECISION
                   The coefficient c, which A is multiplied by.
    
         A         (input) DOUBLE PRECISION array, dimension (LDA,NA)
                   The NA x NA matrix A.
    
         LDA       (input) INTEGER
                   The leading dimension of A.  It must be  at  least
                   NA.
    
         D1        (input) DOUBLE PRECISION
                   The 1,1 element in the diagonal matrix D.
    
         D2        (input) DOUBLE PRECISION
                   The 2,2 element in the  diagonal  matrix  D.   Not
                   used if NW=1.
    
         B         (input) DOUBLE PRECISION array, dimension (LDB,NW)
                   The NA x NW matrix B (right-hand side).   If  NW=2
                   ("w"  is complex), column 1 contains the real part
                   of B and column 2 contains the imaginary part.
    
         LDB       (input) INTEGER
                   The leading dimension of B.  It must be  at  least
                   NA.
    
         WR        (input) DOUBLE PRECISION
                   The real part of the scalar "w".
    
         WI        (input) DOUBLE PRECISION
                   The imaginary part of the scalar "w".  Not used if
                   NW=1.
    
         X         (output)   DOUBLE   PRECISION   array,   dimension
                   (LDX,NW)
                   The NA x NW matrix X (unknowns),  as  computed  by
                   DLALN2.  If NW=2 ("w" is complex), on exit, column
                   1 will contain the real part of  X  and  column  2
                   will contain the imaginary part.
    
         LDX       (input) INTEGER
                   The leading dimension of X.  It must be  at  least
                   NA.
    
         SCALE     (output) DOUBLE PRECISION
                   The scale factor that B must be multiplied  by  to
                   insure that overflow does not occur when computing
                   X.  Thus, (ca A - w D) X  will be SCALE*B,  not  B
                   (ignoring perturbations of A.)  It will be at most
                   1.
    
         XNORM     (output) DOUBLE PRECISION
                   The infinity-norm of X, when X is regarded  as  an
                   NA x NW real matrix.
    
         INFO      (output) INTEGER
                   An error flag.  It will be set to zero if no error
                   occurs,  a  negative  number  if an argument is in
                   error, or a positive number if  ca A - w D  had to
                   be perturbed.  The possible values are:
                   = 0: No error occurred, and (ca A - w D)  did  not
                   have to be perturbed.  = 1: (ca A - w D) had to be
                   perturbed to make its smallest (or only)  singular
                   value  greater  than SMIN.  NOTE: In the interests
                   of speed, this routine does not check  the  inputs
                   for errors.
    
    
    
    


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