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

.in +1c
.ti -1c
.RI "subroutine \fBclartv\fP (n, x, incx, y, incy, c, s, incc)"
.br
.RI "\fBCLARTV\fP applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors\&. "
.ti -1c
.RI "subroutine \fBdlartv\fP (n, x, incx, y, incy, c, s, incc)"
.br
.RI "\fBDLARTV\fP applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors\&. "
.ti -1c
.RI "subroutine \fBslartv\fP (n, x, incx, y, incy, c, s, incc)"
.br
.RI "\fBSLARTV\fP applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors\&. "
.ti -1c
.RI "subroutine \fBzlartv\fP (n, x, incx, y, incy, c, s, incc)"
.br
.RI "\fBZLARTV\fP applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors\&. "
.in -1c
.SH "Detailed Description"
.PP 

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

.PP
\fBCLARTV\fP applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLARTV applies a vector of complex plane rotations with real cosines
 to elements of the complex vectors x and y\&. For i = 1,2,\&.\&.\&.,n

    ( x(i) ) := (        c(i)   s(i) ) ( x(i) )
    ( y(i) )    ( -conjg(s(i))  c(i) ) ( y(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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between elements of X\&. INCX > 0\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is COMPLEX array, dimension (1+(N-1)*INCY)
          The vector y\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between elements of Y\&. INCY > 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 dlartv (integer n, double precision, dimension( * ) x, integer incx, double precision, dimension( * ) y, integer incy, double precision, dimension( * ) c, double precision, dimension( * ) s, integer incc)"

.PP
\fBDLARTV\fP applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLARTV applies a vector of real plane rotations to elements of the
 real vectors x and y\&. For i = 1,2,\&.\&.\&.,n

    ( x(i) ) := (  c(i)  s(i) ) ( x(i) )
    ( y(i) )    ( -s(i)  c(i) ) ( y(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
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between elements of X\&. INCX > 0\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is DOUBLE PRECISION array,
                         dimension (1+(N-1)*INCY)
          The vector y\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between elements of Y\&. INCY > 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 slartv (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real, dimension( * ) c, real, dimension( * ) s, integer incc)"

.PP
\fBSLARTV\fP applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLARTV applies a vector of real plane rotations to elements of the
 real vectors x and y\&. For i = 1,2,\&.\&.\&.,n

    ( x(i) ) := (  c(i)  s(i) ) ( x(i) )
    ( y(i) )    ( -s(i)  c(i) ) ( y(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
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between elements of X\&. INCX > 0\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is REAL array,
                         dimension (1+(N-1)*INCY)
          The vector y\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between elements of Y\&. INCY > 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 zlartv (integer n, complex*16, dimension( * ) x, integer incx, complex*16, dimension( * ) y, integer incy, double precision, dimension( * ) c, complex*16, dimension( * ) s, integer incc)"

.PP
\fBZLARTV\fP applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLARTV applies a vector of complex plane rotations with real cosines
 to elements of the complex vectors x and y\&. For i = 1,2,\&.\&.\&.,n

    ( x(i) ) := (        c(i)   s(i) ) ( x(i) )
    ( y(i) )    ( -conjg(s(i))  c(i) ) ( y(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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between elements of X\&. INCX > 0\&.
.fi
.PP
.br
\fIY\fP 
.PP
.nf
          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
          The vector y\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between elements of Y\&. INCY > 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 
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