IRIX Base Documentation 2002 November/SGI IRIX Base Documentation 2002 November.iso/usr/share/catman/p_man/cat3/SCSL/dlag2.z/dlag2

Text File | 2002-10-03 | 5.6 KB | 133 lines

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     DLAG2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem
     A - w B, with scaling as necessary to avoid over-/underflow

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     SUBROUTINE DLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI )

         INTEGER       LDA, LDB

         DOUBLE        PRECISION SAFMIN, SCALE1, SCALE2, WI, WR1, WR2

         DOUBLE        PRECISION A( LDA, * ), B( LDB, * )

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     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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     DLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue problem
     A - w B, with scaling as necessary to avoid over-/underflow. The scaling
     factor "s" results in a modified eigenvalue equation

         s A - w B

     where  s  is a non-negative scaling factor chosen so that  w,  w B, and
     s A  do not overflow and, if possible, do not underflow, either.


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     A       (input) DOUBLE PRECISION array, dimension (LDA, 2)
             On entry, the 2 x 2 matrix A.  It is assumed that its 1-norm is
             less than 1/SAFMIN.  Entries less than sqrt(SAFMIN)*norm(A) are
             subject to being treated as zero.

     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= 2.

     B       (input) DOUBLE PRECISION array, dimension (LDB, 2)
             On entry, the 2 x 2 upper triangular matrix B.  It is assumed
             that the one-norm of B is less than 1/SAFMIN.  The diagonals
             should be at least sqrt(SAFMIN) times the largest element of B
             (in absolute value); if a diagonal is smaller than that, then
             +/- sqrt(SAFMIN) will be used instead of that diagonal.



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DDDDLLLLAAAAGGGG2222((((3333SSSS))))                                                            DDDDLLLLAAAAGGGG2222((((3333SSSS))))



     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= 2.

     SAFMIN  (input) DOUBLE PRECISION
             The smallest positive number s.t. 1/SAFMIN does not overflow.
             (This should always be DLAMCH('S') -- it is an argument in order
             to avoid having to call DLAMCH frequently.)

     SCALE1  (output) DOUBLE PRECISION
             A scaling factor used to avoid over-/underflow in the eigenvalue
             equation which defines the first eigenvalue.  If the eigenvalues
             are complex, then the eigenvalues are ( WR1  +/-  WI i ) / SCALE1
             (which may lie outside the exponent range of the machine),
             SCALE1=SCALE2, and SCALE1 will always be positive.  If the
             eigenvalues are real, then the first (real) eigenvalue is  WR1 /
             SCALE1 , but this may overflow or underflow, and in fact, SCALE1
             may be zero or less than the underflow threshhold if the exact
             eigenvalue is sufficiently large.

     SCALE2  (output) DOUBLE PRECISION
             A scaling factor used to avoid over-/underflow in the eigenvalue
             equation which defines the second eigenvalue.  If the eigenvalues
             are complex, then SCALE2=SCALE1.  If the eigenvalues are real,
             then the second (real) eigenvalue is WR2 / SCALE2 , but this may
             overflow or underflow, and in fact, SCALE2 may be zero or less
             than the underflow threshhold if the exact eigenvalue is
             sufficiently large.

     WR1     (output) DOUBLE PRECISION
             If the eigenvalue is real, then WR1 is SCALE1 times the
             eigenvalue closest to the (2,2) element of A B**(-1).  If the
             eigenvalue is complex, then WR1=WR2 is SCALE1 times the real part
             of the eigenvalues.

     WR2     (output) DOUBLE PRECISION
             If the eigenvalue is real, then WR2 is SCALE2 times the other
             eigenvalue.  If the eigenvalue is complex, then WR1=WR2 is SCALE1
             times the real part of the eigenvalues.

     WI      (output) DOUBLE PRECISION
             If the eigenvalue is real, then WI is zero.  If the eigenvalue is
             complex, then WI is SCALE1 times the imaginary part of the
             eigenvalues.  WI will always be non-negative.

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     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.







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