Subroutine */
| 8563 | } /* sladiv_ */ |
| 8564 | |
| 8565 | /* Subroutine */ int slae2_(real *a, real *b, real *c__, real *rt1, real *rt2) |
| 8566 | { |
| 8567 | /* System generated locals */ |
| 8568 | real r__1; |
| 8569 | |
| 8570 | /* Local variables */ |
| 8571 | static real ab, df, tb, sm, rt, adf, acmn, acmx; |
| 8572 | |
| 8573 | |
| 8574 | /* |
| 8575 | -- LAPACK auxiliary routine (version 3.2) -- |
| 8576 | -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 8577 | -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 8578 | November 2006 |
| 8579 | |
| 8580 | |
| 8581 | Purpose |
| 8582 | ======= |
| 8583 | |
| 8584 | SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix |
| 8585 | [ A B ] |
| 8586 | [ B C ]. |
| 8587 | On return, RT1 is the eigenvalue of larger absolute value, and RT2 |
| 8588 | is the eigenvalue of smaller absolute value. |
| 8589 | |
| 8590 | Arguments |
| 8591 | ========= |
| 8592 | |
| 8593 | A (input) REAL |
| 8594 | The (1,1) element of the 2-by-2 matrix. |
| 8595 | |
| 8596 | B (input) REAL |
| 8597 | The (1,2) and (2,1) elements of the 2-by-2 matrix. |
| 8598 | |
| 8599 | C (input) REAL |
| 8600 | The (2,2) element of the 2-by-2 matrix. |
| 8601 | |
| 8602 | RT1 (output) REAL |
| 8603 | The eigenvalue of larger absolute value. |
| 8604 | |
| 8605 | RT2 (output) REAL |
| 8606 | The eigenvalue of smaller absolute value. |
| 8607 | |
| 8608 | Further Details |
| 8609 | =============== |
| 8610 | |
| 8611 | RT1 is accurate to a few ulps barring over/underflow. |
| 8612 | |
| 8613 | RT2 may be inaccurate if there is massive cancellation in the |
| 8614 | determinant A*C-B*B; higher precision or correctly rounded or |
| 8615 | correctly truncated arithmetic would be needed to compute RT2 |
| 8616 | accurately in all cases. |
| 8617 | |
| 8618 | Overflow is possible only if RT1 is within a factor of 5 of overflow. |
| 8619 | Underflow is harmless if the input data is 0 or exceeds |
| 8620 | underflow_threshold / macheps. |
| 8621 | |
| 8622 | ===================================================================== |