slag2 (l) - Linux Manuals
slag2: computes the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
NAME
SLAG2 - computes the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflowSYNOPSIS
- SUBROUTINE SLAG2(
- A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI )
- INTEGER LDA, LDB
- REAL SAFMIN, SCALE1, SCALE2, WI, WR1, WR2
- REAL A( LDA, * ), B( LDB, * )
PURPOSE
SLAG2 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 equationwhere 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.
ARGUMENTS
- A (input) REAL 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) REAL 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.
- LDB (input) INTEGER
- The leading dimension of the array B. LDB >= 2.
- SAFMIN (input) REAL
- The smallest positive number s.t. 1/SAFMIN does not overflow. (This should always be SLAMCH(aqSaq) -- it is an argument in order to avoid having to call SLAMCH frequently.)
- SCALE1 (output) REAL
- 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) REAL
- 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) REAL
- 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) REAL
- 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) REAL
-
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.