# lartv - Man Page

lartv: apply vector of plane rotations to vectors

## Synopsis

### Functions

subroutine **clartv** (n, x, incx, y, incy, c, s, incc)**CLARTV** applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

subroutine **dlartv** (n, x, incx, y, incy, c, s, incc)**DLARTV** applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.

subroutine **slartv** (n, x, incx, y, incy, c, s, incc)**SLARTV** applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.

subroutine **zlartv** (n, x, incx, y, incy, c, s, incc)**ZLARTV** applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

## Detailed Description

## Function Documentation

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

**CLARTV** applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

**Purpose:**

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) )

**Parameters***N*N is INTEGER The number of plane rotations to be applied.

*X*X is COMPLEX array, dimension (1+(N-1)*INCX) The vector x.

*INCX*INCX is INTEGER The increment between elements of X. INCX > 0.

*Y*Y is COMPLEX array, dimension (1+(N-1)*INCY) The vector y.

*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.

*S*S is COMPLEX array, dimension (1+(N-1)*INCC) The sines of the plane rotations.

*INCC*INCC is INTEGER The increment between elements of C and S. INCC > 0.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **106** of file **clartv.f**.

### 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)

**DLARTV** applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.

**Purpose:**

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) )

**Parameters***N*N is INTEGER The number of plane rotations to be applied.

*X*X is DOUBLE PRECISION array, dimension (1+(N-1)*INCX) The vector x.

*INCX*INCX is INTEGER The increment between elements of X. INCX > 0.

*Y*Y is DOUBLE PRECISION array, dimension (1+(N-1)*INCY) The vector y.

*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.

*S*S is DOUBLE PRECISION array, dimension (1+(N-1)*INCC) The sines of the plane rotations.

*INCC*INCC is INTEGER The increment between elements of C and S. INCC > 0.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **107** of file **dlartv.f**.

### subroutine slartv (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real, dimension( * ) c, real, dimension( * ) s, integer incc)

**SLARTV** applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.

**Purpose:**

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) )

**Parameters***N*N is INTEGER The number of plane rotations to be applied.

*X*X is REAL array, dimension (1+(N-1)*INCX) The vector x.

*INCX*INCX is INTEGER The increment between elements of X. INCX > 0.

*Y*Y is REAL array, dimension (1+(N-1)*INCY) The vector y.

*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.

*S*S is REAL array, dimension (1+(N-1)*INCC) The sines of the plane rotations.

*INCC*INCC is INTEGER The increment between elements of C and S. INCC > 0.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **107** of file **slartv.f**.

### 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)

**ZLARTV** applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

**Purpose:**

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) )

**Parameters***N*N is INTEGER The number of plane rotations to be applied.

*X*X is COMPLEX*16 array, dimension (1+(N-1)*INCX) The vector x.

*INCX*INCX is INTEGER The increment between elements of X. INCX > 0.

*Y*Y is COMPLEX*16 array, dimension (1+(N-1)*INCY) The vector y.

*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.

*S*S is COMPLEX*16 array, dimension (1+(N-1)*INCC) The sines of the plane rotations.

*INCC*INCC is INTEGER The increment between elements of C and S. INCC > 0.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **106** of file **zlartv.f**.

## Author

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