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author | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
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committer | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
commit | baba851215b44ac3b60b9248eb02bcce7eb76247 (patch) | |
tree | 8c0f5c006875532a30d4409f5e94b0f310ff00a7 /SRC/dlae2.f | |
download | lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.gz lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.bz2 lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.zip |
Move LAPACK trunk into position.
Diffstat (limited to 'SRC/dlae2.f')
-rw-r--r-- | SRC/dlae2.f | 123 |
1 files changed, 123 insertions, 0 deletions
diff --git a/SRC/dlae2.f b/SRC/dlae2.f new file mode 100644 index 00000000..8e81c608 --- /dev/null +++ b/SRC/dlae2.f @@ -0,0 +1,123 @@ + SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) +* +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B, C, RT1, RT2 +* .. +* +* Purpose +* ======= +* +* DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix +* [ A B ] +* [ B C ]. +* On return, RT1 is the eigenvalue of larger absolute value, and RT2 +* is the eigenvalue of smaller absolute value. +* +* Arguments +* ========= +* +* A (input) DOUBLE PRECISION +* The (1,1) element of the 2-by-2 matrix. +* +* B (input) DOUBLE PRECISION +* The (1,2) and (2,1) elements of the 2-by-2 matrix. +* +* C (input) DOUBLE PRECISION +* The (2,2) element of the 2-by-2 matrix. +* +* RT1 (output) DOUBLE PRECISION +* The eigenvalue of larger absolute value. +* +* RT2 (output) DOUBLE PRECISION +* The eigenvalue of smaller absolute value. +* +* Further Details +* =============== +* +* RT1 is accurate to a few ulps barring over/underflow. +* +* RT2 may be inaccurate if there is massive cancellation in the +* determinant A*C-B*B; higher precision or correctly rounded or +* correctly truncated arithmetic would be needed to compute RT2 +* accurately in all cases. +* +* Overflow is possible only if RT1 is within a factor of 5 of overflow. +* Underflow is harmless if the input data is 0 or exceeds +* underflow_threshold / macheps. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D0 ) + DOUBLE PRECISION TWO + PARAMETER ( TWO = 2.0D0 ) + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) + DOUBLE PRECISION HALF + PARAMETER ( HALF = 0.5D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, SQRT +* .. +* .. Executable Statements .. +* +* Compute the eigenvalues +* + SM = A + C + DF = A - C + ADF = ABS( DF ) + TB = B + B + AB = ABS( TB ) + IF( ABS( A ).GT.ABS( C ) ) THEN + ACMX = A + ACMN = C + ELSE + ACMX = C + ACMN = A + END IF + IF( ADF.GT.AB ) THEN + RT = ADF*SQRT( ONE+( AB / ADF )**2 ) + ELSE IF( ADF.LT.AB ) THEN + RT = AB*SQRT( ONE+( ADF / AB )**2 ) + ELSE +* +* Includes case AB=ADF=0 +* + RT = AB*SQRT( TWO ) + END IF + IF( SM.LT.ZERO ) THEN + RT1 = HALF*( SM-RT ) +* +* Order of execution important. +* To get fully accurate smaller eigenvalue, +* next line needs to be executed in higher precision. +* + RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B + ELSE IF( SM.GT.ZERO ) THEN + RT1 = HALF*( SM+RT ) +* +* Order of execution important. +* To get fully accurate smaller eigenvalue, +* next line needs to be executed in higher precision. +* + RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B + ELSE +* +* Includes case RT1 = RT2 = 0 +* + RT1 = HALF*RT + RT2 = -HALF*RT + END IF + RETURN +* +* End of DLAE2 +* + END |