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RedHat 9 (Linux i386) - man page for dlaln2 (redhat section l)

DLALN2(l)					)					DLALN2(l)

NAME
       DLALN2  -  solve  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 perturbation 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, * )

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 perturbation 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  com-
       plex.  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 computed 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 dis-
	       tance away from underflow or overflow, say, between (underflow/machine  precision)
	       and  (machine precision * 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 con-
	       tains 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.

LAPACK version 3.0			   15 June 2000 				DLALN2(l)


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