laev2 - laev2: 2x2 eig

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subroutineclaev2(complexa,complexb,complexc,realrt1,realrt2,realcs1,complexsn1)CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. ParametersA A is COMPLEX The (1,1) element of the 2-by-2 matrix. B B is COMPLEX The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. C C is COMPLEX The (2,2) element of the 2-by-2 matrix. RT1 RT1 is REAL The eigenvalue of larger absolute value. RT2 RT2 is REAL The eigenvalue of smaller absolute value. CS1 CS1 is REAL SN1 SN1 is COMPLEX The vector (CS1, SN1) is a unit right eigenvector for RT1. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. CS1 and SN1 are accurate to a few ulps barring over/underflow. 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. subroutinedlaev2(doubleprecisiona,doubleprecisionb,doubleprecisionc,doubleprecisionrt1,doubleprecisionrt2,doubleprecisioncs1,doubleprecisionsn1)DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. ParametersA A is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix. B B is DOUBLE PRECISION The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. C C is DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix. RT1 RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value. RT2 RT2 is DOUBLE PRECISION The eigenvalue of smaller absolute value. CS1 CS1 is DOUBLE PRECISION SN1 SN1 is DOUBLE PRECISION The vector (CS1, SN1) is a unit right eigenvector for RT1. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. CS1 and SN1 are accurate to a few ulps barring over/underflow. 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. subroutineslaev2(reala,realb,realc,realrt1,realrt2,realcs1,realsn1)SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. ParametersA A is REAL The (1,1) element of the 2-by-2 matrix. B B is REAL The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. C C is REAL The (2,2) element of the 2-by-2 matrix. RT1 RT1 is REAL The eigenvalue of larger absolute value. RT2 RT2 is REAL The eigenvalue of smaller absolute value. CS1 CS1 is REAL SN1 SN1 is REAL The vector (CS1, SN1) is a unit right eigenvector for RT1. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. CS1 and SN1 are accurate to a few ulps barring over/underflow. 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. subroutinezlaev2(complex*16a,complex*16b,complex*16c,doubleprecisionrt1,doubleprecisionrt2,doubleprecisioncs1,complex*16sn1)ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. ParametersA A is COMPLEX*16 The (1,1) element of the 2-by-2 matrix. B B is COMPLEX*16 The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. C C is COMPLEX*16 The (2,2) element of the 2-by-2 matrix. RT1 RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value. RT2 RT2 is DOUBLE PRECISION The eigenvalue of smaller absolute value. CS1 CS1 is DOUBLE PRECISION SN1 SN1 is COMPLEX*16 The vector (CS1, SN1) is a unit right eigenvector for RT1. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. CS1 and SN1 are accurate to a few ulps barring over/underflow. 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.

laev2 - laev2: 2x2 eig

Functions subroutine claev2 (a, b, c, rt1, rt2, cs1, sn1) CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. subroutine dlaev2 (a, b, c, rt1, rt2, cs1, sn1) DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. subroutine slaev2 (a, b, c, rt1, rt2, cs1, sn1) SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. subroutine zlaev2 (a, b, c, rt1, rt2, cs1, sn1) ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.