# lar2v - Man Page

lar2v: apply vector of plane rotations to 2x2 matrices

## Synopsis

### Functions

subroutine **clar2v** (n, x, y, z, incx, c, s, incc)**CLAR2V** applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

subroutine **dlar2v** (n, x, y, z, incx, c, s, incc)**DLAR2V** applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

subroutine **slar2v** (n, x, y, z, incx, c, s, incc)**SLAR2V** applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

subroutine **zlar2v** (n, x, y, z, incx, c, s, incc)**ZLAR2V** applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

## Detailed Description

## Function Documentation

### subroutine clar2v (integer n, complex, dimension( * ) x, complex, dimension( * ) y, complex, dimension( * ) z, integer incx, real, dimension( * ) c, complex, dimension( * ) s, integer incc)

**CLAR2V** applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

**Purpose:**

CLAR2V applies a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, defined by the elements of the vectors x, y and z. For i = 1,2,...,n ( x(i) z(i) ) := ( conjg(z(i)) y(i) ) ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) ) ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(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; the elements of x are assumed to be real.

*Y*Y is COMPLEX array, dimension (1+(N-1)*INCX) The vector y; the elements of y are assumed to be real.

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

*INCX*INCX is INTEGER The increment between elements of X, Y and Z. INCX > 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 **110** of file **clar2v.f**.

### subroutine dlar2v (integer n, double precision, dimension( * ) x, double precision, dimension( * ) y, double precision, dimension( * ) z, integer incx, double precision, dimension( * ) c, double precision, dimension( * ) s, integer incc)

**DLAR2V** applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

**Purpose:**

DLAR2V applies a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z. For i = 1,2,...,n ( x(i) z(i) ) := ( c(i) s(i) ) ( x(i) z(i) ) ( c(i) -s(i) ) ( z(i) y(i) ) ( -s(i) c(i) ) ( z(i) y(i) ) ( s(i) c(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.

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

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

*INCX*INCX is INTEGER The increment between elements of X, Y and Z. INCX > 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 **109** of file **dlar2v.f**.

### subroutine slar2v (integer n, real, dimension( * ) x, real, dimension( * ) y, real, dimension( * ) z, integer incx, real, dimension( * ) c, real, dimension( * ) s, integer incc)

**SLAR2V** applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

**Purpose:**

SLAR2V applies a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z. For i = 1,2,...,n ( x(i) z(i) ) := ( c(i) s(i) ) ( x(i) z(i) ) ( c(i) -s(i) ) ( z(i) y(i) ) ( -s(i) c(i) ) ( z(i) y(i) ) ( s(i) c(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.

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

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

*INCX*INCX is INTEGER The increment between elements of X, Y and Z. INCX > 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 **109** of file **slar2v.f**.

### subroutine zlar2v (integer n, complex*16, dimension( * ) x, complex*16, dimension( * ) y, complex*16, dimension( * ) z, integer incx, double precision, dimension( * ) c, complex*16, dimension( * ) s, integer incc)

**ZLAR2V** applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

**Purpose:**

ZLAR2V applies a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, defined by the elements of the vectors x, y and z. For i = 1,2,...,n ( x(i) z(i) ) := ( conjg(z(i)) y(i) ) ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) ) ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(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; the elements of x are assumed to be real.

*Y*Y is COMPLEX*16 array, dimension (1+(N-1)*INCX) The vector y; the elements of y are assumed to be real.

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

*INCX*INCX is INTEGER The increment between elements of X, Y and Z. INCX > 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 **110** of file **zlar2v.f**.

## Author

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