| largv(3) | LAPACK | largv(3) |
largv - largv: generate vector of plane rotations
subroutine clargv (n, x, incx, y, incy, c, incc)
CLARGV generates a vector of plane rotations with real cosines and
complex sines. subroutine dlargv (n, x, incx, y, incy, c, incc)
DLARGV generates a vector of plane rotations with real cosines and real
sines. subroutine slargv (n, x, incx, y, incy, c, incc)
SLARGV generates a vector of plane rotations with real cosines and real
sines. subroutine zlargv (n, x, incx, y, incy, c, incc)
ZLARGV generates a vector of plane rotations with real cosines and
complex sines.
CLARGV generates a vector of plane rotations with real cosines and complex sines.
Purpose:
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.
Parameters
N is INTEGER
The number of plane rotations to be generated.
X
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.
INCX
INCX is INTEGER
The increment between elements of X. INCX > 0.
Y
Y is COMPLEX array, dimension (1+(N-1)*INCY)
On entry, the vector y.
On exit, the sines of the plane rotations.
INCY
INCY is INTEGER
The increment between elements of Y. INCY > 0.
C
C is REAL array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.
INCC
INCC is INTEGER
The increment between elements of C. INCC > 0.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
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.
DLARGV generates a vector of plane rotations with real cosines and real sines.
Purpose:
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 )
Parameters
N is INTEGER
The number of plane rotations to be generated.
X
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.
INCX
INCX is INTEGER
The increment between elements of X. INCX > 0.
Y
Y is DOUBLE PRECISION array,
dimension (1+(N-1)*INCY)
On entry, the vector y.
On exit, the sines of the plane rotations.
INCY
INCY is INTEGER
The increment between elements of Y. INCY > 0.
C
C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.
INCC
INCC is INTEGER
The increment between elements of C. INCC > 0.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
SLARGV generates a vector of plane rotations with real cosines and real sines.
Purpose:
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 )
Parameters
N is INTEGER
The number of plane rotations to be generated.
X
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.
INCX
INCX is INTEGER
The increment between elements of X. INCX > 0.
Y
Y is REAL array,
dimension (1+(N-1)*INCY)
On entry, the vector y.
On exit, the sines of the plane rotations.
INCY
INCY is INTEGER
The increment between elements of Y. INCY > 0.
C
C is REAL array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.
INCC
INCC is INTEGER
The increment between elements of C. INCC > 0.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZLARGV generates a vector of plane rotations with real cosines and complex sines.
Purpose:
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.
Parameters
N is INTEGER
The number of plane rotations to be generated.
X
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.
INCX
INCX is INTEGER
The increment between elements of X. INCX > 0.
Y
Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
On entry, the vector y.
On exit, the sines of the plane rotations.
INCY
INCY is INTEGER
The increment between elements of Y. INCY > 0.
C
C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.
INCC
INCC is INTEGER
The increment between elements of C. INCC > 0.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
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.
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