LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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dlaln2.f File Reference

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Functions/Subroutines

subroutine dlaln2 (LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, LDB, WR, WI, X, LDX, SCALE, XNORM, INFO)
 DLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.

Function/Subroutine Documentation

subroutine dlaln2 ( logical  LTRANS,
integer  NA,
integer  NW,
double precision  SMIN,
double precision  CA,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision  D1,
double precision  D2,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision  WR,
double precision  WI,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision  SCALE,
double precision  XNORM,
integer  INFO 
)

DLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form.

Download DLALN2 + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 DLALN2 solves a system of the form  (ca A - w D ) X = s B
 or (ca A**T - w D) X = s B   with possible scaling ("s") and
 perturbation of A.  (A**T 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 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.)
Parameters:
[in]LTRANS
          LTRANS is LOGICAL
          =.TRUE.:  A-transpose will be used.
          =.FALSE.: A will be used (not transposed.)
[in]NA
          NA is INTEGER
          The size of the matrix A.  It may (only) be 1 or 2.
[in]NW
          NW is INTEGER
          1 if "w" is real, 2 if "w" is complex.  It may only be 1
          or 2.
[in]SMIN
          SMIN is 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
          precision * overflow ).  (See BIGNUM and ULP.)
[in]CA
          CA is DOUBLE PRECISION
          The coefficient c, which A is multiplied by.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,NA)
          The NA x NA matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  It must be at least NA.
[in]D1
          D1 is DOUBLE PRECISION
          The 1,1 element in the diagonal matrix D.
[in]D2
          D2 is DOUBLE PRECISION
          The 2,2 element in the diagonal matrix D.  Not used if NW=1.
[in]B
          B is 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.
[in]LDB
          LDB is INTEGER
          The leading dimension of B.  It must be at least NA.
[in]WR
          WR is DOUBLE PRECISION
          The real part of the scalar "w".
[in]WI
          WI is DOUBLE PRECISION
          The imaginary part of the scalar "w".  Not used if NW=1.
[out]X
          X is 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.
[in]LDX
          LDX is INTEGER
          The leading dimension of X.  It must be at least NA.
[out]SCALE
          SCALE is 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.
[out]XNORM
          XNORM is DOUBLE PRECISION
          The infinity-norm of X, when X is regarded as an NA x NW
          real matrix.
[out]INFO
          INFO is 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012

Definition at line 218 of file dlaln2.f.

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