.TH "rot" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
rot \- rot: apply plane rotation ([cz]rot in LAPACK)
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcsrot\fP (n, cx, incx, cy, incy, c, s)"
.br
.RI "\fBCSROT\fP "
.ti -1c
.RI "subroutine \fBdrot\fP (n, dx, incx, dy, incy, c, s)"
.br
.RI "\fBDROT\fP "
.ti -1c
.RI "subroutine \fBsrot\fP (n, sx, incx, sy, incy, c, s)"
.br
.RI "\fBSROT\fP "
.ti -1c
.RI "subroutine \fBzdrot\fP (n, zx, incx, zy, incy, c, s)"
.br
.RI "\fBZDROT\fP "
.ti -1c
.RI "subroutine \fBcrot\fP (n, cx, incx, cy, incy, c, s)"
.br
.RI "\fBCROT\fP applies a plane rotation with real cosine and complex sine to a pair of complex vectors\&. "
.ti -1c
.RI "subroutine \fBzrot\fP (n, cx, incx, cy, incy, c, s)"
.br
.RI "\fBZROT\fP applies a plane rotation with real cosine and complex sine to a pair of complex vectors\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine crot (integer n, complex, dimension( * ) cx, integer incx, complex, dimension( * ) cy, integer incy, real c, complex s)"

.PP
\fBCROT\fP applies a plane rotation with real cosine and complex sine to a pair of complex vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CROT applies a plane rotation, where the cos (C) is real and the
 sin (S) is complex, and the vectors CX and CY are complex\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of elements in the vectors CX and CY\&.
.fi
.PP
.br
\fICX\fP 
.PP
.nf
          CX is COMPLEX array, dimension (N)
          On input, the vector X\&.
          On output, CX is overwritten with C*X + S*Y\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between successive values of CX\&.  INCX <> 0\&.
.fi
.PP
.br
\fICY\fP 
.PP
.nf
          CY is COMPLEX array, dimension (N)
          On input, the vector Y\&.
          On output, CY is overwritten with -CONJG(S)*X + C*Y\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between successive values of CY\&.  INCX <> 0\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is COMPLEX
          C and S define a rotation
             [  C          S  ]
             [ -conjg(S)   C  ]
          where C*C + S*CONJG(S) = 1\&.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 csrot (integer n, complex, dimension( * ) cx, integer incx, complex, dimension( * ) cy, integer incy, real c, real s)"

.PP
\fBCSROT\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CSROT applies a plane rotation, where the cos and sin (c and s) are real
 and the vectors cx and cy are complex\&.
 jack dongarra, linpack, 3/11/78\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the order of the vectors cx and cy\&.
           N must be at least zero\&.
.fi
.PP
.br
\fICX\fP 
.PP
.nf
          CX is COMPLEX array, dimension at least
           ( 1 + ( N - 1 )*abs( INCX ) )\&.
           Before entry, the incremented array CX must contain the n
           element vector cx\&. On exit, CX is overwritten by the updated
           vector cx\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           CX\&. INCX must not be zero\&.
.fi
.PP
.br
\fICY\fP 
.PP
.nf
          CY is COMPLEX array, dimension at least
           ( 1 + ( N - 1 )*abs( INCY ) )\&.
           Before entry, the incremented array CY must contain the n
           element vector cy\&. On exit, CY is overwritten by the updated
           vector cy\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           CY\&. INCY must not be zero\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL
           On entry, C specifies the cosine, cos\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is REAL
           On entry, S specifies the sine, sin\&.
.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 drot (integer n, double precision, dimension(*) dx, integer incx, double precision, dimension(*) dy, integer incy, double precision c, double precision s)"

.PP
\fBDROT\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    DROT applies a plane rotation\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
         number of elements in input vector(s)
.fi
.PP
.br
\fIDX\fP 
.PP
.nf
          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
         storage spacing between elements of DX
.fi
.PP
.br
\fIDY\fP 
.PP
.nf
          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
         storage spacing between elements of DY
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is DOUBLE PRECISION
.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
     jack dongarra, linpack, 3/11/78\&.
     modified 12/3/93, array(1) declarations changed to array(*)
.fi
.PP
 
.RE
.PP

.SS "subroutine srot (integer n, real, dimension(*) sx, integer incx, real, dimension(*) sy, integer incy, real c, real s)"

.PP
\fBSROT\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    applies a plane rotation\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
         number of elements in input vector(s)
.fi
.PP
.br
\fISX\fP 
.PP
.nf
          SX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
         storage spacing between elements of SX
.fi
.PP
.br
\fISY\fP 
.PP
.nf
          SY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
         storage spacing between elements of SY
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is REAL
.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
     jack dongarra, linpack, 3/11/78\&.
     modified 12/3/93, array(1) declarations changed to array(*)
.fi
.PP
 
.RE
.PP

.SS "subroutine zdrot (integer n, complex*16, dimension( * ) zx, integer incx, complex*16, dimension( * ) zy, integer incy, double precision c, double precision s)"

.PP
\fBZDROT\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 Applies a plane rotation, where the cos and sin (c and s) are real
 and the vectors cx and cy are complex\&.
 jack dongarra, linpack, 3/11/78\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the order of the vectors cx and cy\&.
           N must be at least zero\&.
.fi
.PP
.br
\fIZX\fP 
.PP
.nf
          ZX is COMPLEX*16 array, dimension at least
           ( 1 + ( N - 1 )*abs( INCX ) )\&.
           Before entry, the incremented array ZX must contain the n
           element vector cx\&. On exit, ZX is overwritten by the updated
           vector cx\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           ZX\&. INCX must not be zero\&.
.fi
.PP
.br
\fIZY\fP 
.PP
.nf
          ZY is COMPLEX*16 array, dimension at least
           ( 1 + ( N - 1 )*abs( INCY ) )\&.
           Before entry, the incremented array ZY must contain the n
           element vector cy\&. On exit, ZY is overwritten by the updated
           vector cy\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           ZY\&. INCY must not be zero\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION
           On entry, C specifies the cosine, cos\&.
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is DOUBLE PRECISION
           On entry, S specifies the sine, sin\&.
.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 zrot (integer n, complex*16, dimension( * ) cx, integer incx, complex*16, dimension( * ) cy, integer incy, double precision c, complex*16 s)"

.PP
\fBZROT\fP applies a plane rotation with real cosine and complex sine to a pair of complex vectors\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZROT applies a plane rotation, where the cos (C) is real and the
 sin (S) is complex, and the vectors CX and CY are complex\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of elements in the vectors CX and CY\&.
.fi
.PP
.br
\fICX\fP 
.PP
.nf
          CX is COMPLEX*16 array, dimension (N)
          On input, the vector X\&.
          On output, CX is overwritten with C*X + S*Y\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
          The increment between successive values of CX\&.  INCX <> 0\&.
.fi
.PP
.br
\fICY\fP 
.PP
.nf
          CY is COMPLEX*16 array, dimension (N)
          On input, the vector Y\&.
          On output, CY is overwritten with -CONJG(S)*X + C*Y\&.
.fi
.PP
.br
\fIINCY\fP 
.PP
.nf
          INCY is INTEGER
          The increment between successive values of CY\&.  INCX <> 0\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION
.fi
.PP
.br
\fIS\fP 
.PP
.nf
          S is COMPLEX*16
          C and S define a rotation
             [  C          S  ]
             [ -conjg(S)   C  ]
          where C*C + S*CONJG(S) = 1\&.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\&.