.TH "laev2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laev2 \- laev2: 2x2 eig
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclaev2\fP (a, b, c, rt1, rt2, cs1, sn1)"
.br
.RI "\fBCLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&. "
.ti -1c
.RI "subroutine \fBdlaev2\fP (a, b, c, rt1, rt2, cs1, sn1)"
.br
.RI "\fBDLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&. "
.ti -1c
.RI "subroutine \fBslaev2\fP (a, b, c, rt1, rt2, cs1, sn1)"
.br
.RI "\fBSLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&. "
.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 "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine claev2 (complex a, complex b, complex c, real rt1, real rt2, real cs1, complex sn1)"

.PP
\fBCLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

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

.SS "subroutine dlaev2 (double precision a, double precision b, double precision c, double precision rt1, double precision rt2, double precision cs1, double precision sn1)"

.PP
\fBDLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

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

.SS "subroutine slaev2 (real a, real b, real c, real rt1, real rt2, real cs1, real sn1)"

.PP
\fBSLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

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

.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
.PP
\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 
.PP
.nf
          C is COMPLEX*16
         The (2,2) element of the 2-by-2 matrix\&.
.fi
.PP
.br
\fIRT1\fP 
.PP
.nf
          RT1 is DOUBLE PRECISION
         The eigenvalue of larger absolute value\&.
.fi
.PP
.br
\fIRT2\fP 
.PP
.nf
          RT2 is DOUBLE PRECISION
         The eigenvalue of smaller absolute value\&.
.fi
.PP
.br
\fICS1\fP 
.PP
.nf
          CS1 is DOUBLE PRECISION
.fi
.PP
.br
\fISN1\fP 
.PP
.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 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.