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

.in +1c
.ti -1c
.RI "subroutine \fBclargv\fP (n, x, incx, y, incy, c, incc)"
.br
.RI "\fBCLARGV\fP generates a vector of plane rotations with real cosines and complex sines\&. "
.ti -1c
.RI "subroutine \fBdlargv\fP (n, x, incx, y, incy, c, incc)"
.br
.RI "\fBDLARGV\fP generates a vector of plane rotations with real cosines and real sines\&. "
.ti -1c
.RI "subroutine \fBslargv\fP (n, x, incx, y, incy, c, incc)"
.br
.RI "\fBSLARGV\fP generates a vector of plane rotations with real cosines and real sines\&. "
.ti -1c
.RI "subroutine \fBzlargv\fP (n, x, incx, y, incy, c, incc)"
.br
.RI "\fBZLARGV\fP generates a vector of plane rotations with real cosines and complex sines\&. "
.in -1c
.SH "Detailed Description"
.PP 

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

.PP
\fBCLARGV\fP generates a vector of plane rotations with real cosines and complex sines\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLARGV generates a vector of complex plane rotations with real
 cosines, determined by elements of the complex vectors x and y\&.
 For i = 1,2,\&.\&.\&.,n

    (        c(i)   s(i) ) ( x(i) ) = ( r(i) )
    ( -conjg(s(i))  c(i) ) ( y(i) ) = (   0  )

    where c(i)**2 + ABS(s(i))**2 = 1

 The following conventions are used (these are the same as in CLARTG,
 but differ from the BLAS1 routine CROTG):
    If y(i)=0, then c(i)=1 and s(i)=0\&.
    If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of plane rotations to be generated\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX array, dimension (1+(N-1)*INCX)
          On entry, the vector x\&.
          On exit, x(i) is overwritten by r(i), for i = 1,\&.\&.\&.,n\&.
.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)
          On entry, the vector y\&.
          On exit, the sines of the plane rotations\&.
.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
\fIINCC\fP 
.PP
.nf
          INCC is INTEGER
          The increment between elements of C\&. 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  6-6-96 - Modified with a new algorithm by W\&. Kahan and J\&. Demmel

  This version has a few statements commented out for thread safety
  (machine parameters are computed on each entry)\&. 10 feb 03, SJH\&.
.fi
.PP
 
.RE
.PP

.SS "subroutine dlargv (integer n, double precision, dimension( * ) x, integer incx, double precision, dimension( * ) y, integer incy, double precision, dimension( * ) c, integer incc)"

.PP
\fBDLARGV\fP generates a vector of plane rotations with real cosines and real sines\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLARGV generates a vector of real plane rotations, determined by
 elements of the real vectors x and y\&. For i = 1,2,\&.\&.\&.,n

    (  c(i)  s(i) ) ( x(i) ) = ( a(i) )
    ( -s(i)  c(i) ) ( y(i) ) = (   0  )
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of plane rotations to be generated\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is DOUBLE PRECISION array,
                         dimension (1+(N-1)*INCX)
          On entry, the vector x\&.
          On exit, x(i) is overwritten by a(i), for i = 1,\&.\&.\&.,n\&.
.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)
          On entry, the vector y\&.
          On exit, the sines of the plane rotations\&.
.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
\fIINCC\fP 
.PP
.nf
          INCC is INTEGER
          The increment between elements of C\&. 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 slargv (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real, dimension( * ) c, integer incc)"

.PP
\fBSLARGV\fP generates a vector of plane rotations with real cosines and real sines\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLARGV generates a vector of real plane rotations, determined by
 elements of the real vectors x and y\&. For i = 1,2,\&.\&.\&.,n

    (  c(i)  s(i) ) ( x(i) ) = ( a(i) )
    ( -s(i)  c(i) ) ( y(i) ) = (   0  )
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of plane rotations to be generated\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is REAL array,
                         dimension (1+(N-1)*INCX)
          On entry, the vector x\&.
          On exit, x(i) is overwritten by a(i), for i = 1,\&.\&.\&.,n\&.
.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)
          On entry, the vector y\&.
          On exit, the sines of the plane rotations\&.
.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
\fIINCC\fP 
.PP
.nf
          INCC is INTEGER
          The increment between elements of C\&. 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 zlargv (integer n, complex*16, dimension( * ) x, integer incx, complex*16, dimension( * ) y, integer incy, double precision, dimension( * ) c, integer incc)"

.PP
\fBZLARGV\fP generates a vector of plane rotations with real cosines and complex sines\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLARGV generates a vector of complex plane rotations with real
 cosines, determined by elements of the complex vectors x and y\&.
 For i = 1,2,\&.\&.\&.,n

    (        c(i)   s(i) ) ( x(i) ) = ( r(i) )
    ( -conjg(s(i))  c(i) ) ( y(i) ) = (   0  )

    where c(i)**2 + ABS(s(i))**2 = 1

 The following conventions are used (these are the same as in ZLARTG,
 but differ from the BLAS1 routine ZROTG):
    If y(i)=0, then c(i)=1 and s(i)=0\&.
    If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of plane rotations to be generated\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
          On entry, the vector x\&.
          On exit, x(i) is overwritten by r(i), for i = 1,\&.\&.\&.,n\&.
.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)
          On entry, the vector y\&.
          On exit, the sines of the plane rotations\&.
.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
\fIINCC\fP 
.PP
.nf
          INCC is INTEGER
          The increment between elements of C\&. 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  6-6-96 - Modified with a new algorithm by W\&. Kahan and J\&. Demmel

  This version has a few statements commented out for thread safety
  (machine parameters are computed on each entry)\&. 10 feb 03, SJH\&.
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
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