.TH "lar2v" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lar2v \- lar2v: apply vector of plane rotations to 2x2 matrices
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclar2v\fP (n, x, y, z, incx, c, s, incc)"
.br
.RI "\fBCLAR2V\fP applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices\&. "
.ti -1c
.RI "subroutine \fBdlar2v\fP (n, x, y, z, incx, c, s, incc)"
.br
.RI "\fBDLAR2V\fP applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices\&. "
.ti -1c
.RI "subroutine \fBslar2v\fP (n, x, y, z, incx, c, s, incc)"
.br
.RI "\fBSLAR2V\fP applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices\&. "
.ti -1c
.RI "subroutine \fBzlar2v\fP (n, x, y, z, incx, c, s, incc)"
.br
.RI "\fBZLAR2V\fP applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clar2v (integer n, complex, dimension( * ) x, complex, dimension( * ) y, complex, dimension( * ) z, integer incx, real, dimension( * ) c, complex, dimension( * ) s, integer incc)"

.PP
\fBCLAR2V\fP applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLAR2V applies a vector of complex plane rotations with real cosines
 from both sides to a sequence of 2-by-2 complex Hermitian matrices,
 defined by the elements of the vectors x, y and z\&. For i = 1,2,\&.\&.\&.,n

    (       x(i)  z(i) ) :=
    ( conjg(z(i)) y(i) )

      (  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
      ( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of plane rotations to be applied\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX array, dimension (1+(N-1)*INCX)
          The vector x; the elements of x are assumed to be real\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is COMPLEX array, dimension (1+(N-1)*INCX)
          The vector y; the elements of y are assumed to be real\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is COMPLEX array, dimension (1+(N-1)*INCX)
          The vector z\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between elements of X, Y and Z\&. INCX > 0\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (1+(N-1)*INCC)
          The cosines of the plane rotations\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is COMPLEX array, dimension (1+(N-1)*INCC)
          The sines of the plane rotations\&.
.fi
.PP
.br
\fIINCC\fP 
.PP
.nf
          INCC is INTEGER
          The increment between elements of C and S\&. INCC > 0\&.
.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

.SS "subroutine dlar2v (integer n, double precision, dimension( * ) x, double precision, dimension( * ) y, double precision, dimension( * ) z, integer incx, double precision, dimension( * ) c, double precision, dimension( * ) s, integer incc)"

.PP
\fBDLAR2V\fP applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAR2V applies a vector of real plane rotations from both sides to
 a sequence of 2-by-2 real symmetric matrices, defined by the elements
 of the vectors x, y and z\&. For i = 1,2,\&.\&.\&.,n

    ( x(i)  z(i) ) := (  c(i)  s(i) ) ( x(i)  z(i) ) ( c(i) -s(i) )
    ( z(i)  y(i) )    ( -s(i)  c(i) ) ( z(i)  y(i) ) ( s(i)  c(i) )
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of plane rotations to be applied\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is DOUBLE PRECISION array,
                         dimension (1+(N-1)*INCX)
          The vector x\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is DOUBLE PRECISION array,
                         dimension (1+(N-1)*INCX)
          The vector y\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is DOUBLE PRECISION array,
                         dimension (1+(N-1)*INCX)
          The vector z\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between elements of X, Y and Z\&. INCX > 0\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
          The cosines of the plane rotations\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
          The sines of the plane rotations\&.
.fi
.PP
.br
\fIINCC\fP 
.PP
.nf
          INCC is INTEGER
          The increment between elements of C and S\&. INCC > 0\&.
.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

.SS "subroutine slar2v (integer n, real, dimension( * ) x, real, dimension( * ) y, real, dimension( * ) z, integer incx, real, dimension( * ) c, real, dimension( * ) s, integer incc)"

.PP
\fBSLAR2V\fP applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLAR2V applies a vector of real plane rotations from both sides to
 a sequence of 2-by-2 real symmetric matrices, defined by the elements
 of the vectors x, y and z\&. For i = 1,2,\&.\&.\&.,n

    ( x(i)  z(i) ) := (  c(i)  s(i) ) ( x(i)  z(i) ) ( c(i) -s(i) )
    ( z(i)  y(i) )    ( -s(i)  c(i) ) ( z(i)  y(i) ) ( s(i)  c(i) )
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of plane rotations to be applied\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is REAL array,
                         dimension (1+(N-1)*INCX)
          The vector x\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is REAL array,
                         dimension (1+(N-1)*INCX)
          The vector y\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is REAL array,
                         dimension (1+(N-1)*INCX)
          The vector z\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between elements of X, Y and Z\&. INCX > 0\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (1+(N-1)*INCC)
          The cosines of the plane rotations\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is REAL array, dimension (1+(N-1)*INCC)
          The sines of the plane rotations\&.
.fi
.PP
.br
\fIINCC\fP 
.PP
.nf
          INCC is INTEGER
          The increment between elements of C and S\&. INCC > 0\&.
.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

.SS "subroutine zlar2v (integer n, complex*16, dimension( * ) x, complex*16, dimension( * ) y, complex*16, dimension( * ) z, integer incx, double precision, dimension( * ) c, complex*16, dimension( * ) s, integer incc)"

.PP
\fBZLAR2V\fP applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLAR2V applies a vector of complex plane rotations with real cosines
 from both sides to a sequence of 2-by-2 complex Hermitian matrices,
 defined by the elements of the vectors x, y and z\&. For i = 1,2,\&.\&.\&.,n

    (       x(i)  z(i) ) :=
    ( conjg(z(i)) y(i) )

      (  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
      ( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of plane rotations to be applied\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
          The vector x; the elements of x are assumed to be real\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is COMPLEX*16 array, dimension (1+(N-1)*INCX)
          The vector y; the elements of y are assumed to be real\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is COMPLEX*16 array, dimension (1+(N-1)*INCX)
          The vector z\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between elements of X, Y and Z\&. INCX > 0\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
          The cosines of the plane rotations\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is COMPLEX*16 array, dimension (1+(N-1)*INCC)
          The sines of the plane rotations\&.
.fi
.PP
.br
\fIINCC\fP 
.PP
.nf
          INCC is INTEGER
          The increment between elements of C and S\&. INCC > 0\&.
.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

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