.TH "SRC/zlaev2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/zlaev2.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlaev2\fP (a, b, c, rt1, rt2, cs1, sn1)"
.br
.RI "\fBZLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlaev2 (complex*16 a, complex*16 b, complex*16 c, double precision rt1, double precision rt2, double precision cs1, complex*16 sn1)"

.PP
\fBZLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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 ]\&.
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is COMPLEX*16
         The (1,1) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX*16
         The (1,2) element and the conjugate of the (2,1) element of
         the 2-by-2 matrix\&.
.fi
.PP
.br
\fIC\fP 
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.nf
          C is COMPLEX*16
         The (2,2) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIRT1\fP 
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          RT1 is DOUBLE PRECISION
         The eigenvalue of larger absolute value\&.
.fi
.PP
.br
\fIRT2\fP 
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.nf
          RT2 is DOUBLE PRECISION
         The eigenvalue of smaller absolute value\&.
.fi
.PP
.br
\fICS1\fP 
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.nf
          CS1 is DOUBLE PRECISION
.fi
.PP
.br
\fISN1\fP 
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.nf
          SN1 is COMPLEX*16
         The vector (CS1, SN1) is a unit right eigenvector for RT1\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
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Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB120\fP of file \fBzlaev2\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.