NAME

largv - largv: generate vector of plane rotations

SYNOPSIS

Functions

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.

Detailed Description

Function Documentation

subroutine clargv (integer n, complex, dimension( * ) x, integer incx, complex, dimension( * ) y, integer incy, real, dimension( * ) c, integer incc)

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 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 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 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 Tennessee

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.

Definition at line 121 of file clargv.f.

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

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 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 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 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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 103 of file dlargv.f.

subroutine slargv (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real, dimension( * ) c, integer incc)

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 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 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 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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 103 of file slargv.f.

subroutine zlargv (integer n, complex16, dimension( ) x, integer incx, complex16, dimension( ) y, integer incy, double precision, dimension( * ) c, integer incc)

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 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 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 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 Tennessee

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.

Definition at line 121 of file zlargv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.