{S,D,C,Z}ROT (n, x, incx, y, incy, c, s) CSROT (n, x, incx, y, incy, c, s) ZDROT (n, x, incx, y, incy, c, s)
n integer*4 On entry, the number of elements in the vectors x and y. On exit, n is unchanged. x real*4 | real*8 | complex*8 | complex*16 On entry, a one-dimensional array X of length at least (1+(n-1)*|incx|), containing the elements of the vector x. On exit, if n<=0 or if c is 1.0 and s is 0.0, x is unchanged. Otherwise, x is overwritten; X contains the rotated vector x. incx integer*4 On entry, the increment for the array X. If incx >= 0, vector x is stored forward in the array, so that x(i) is stored in location X(1+(i-1)*incx). If incx < 0, vector x is stored backward in the array, so that x(i) is stored in location X(1+(n-i)*|incx|). On exit, incx is unchanged. y real*4 | real*8 | complex*8 | complex*16 On entry, a one-dimensional array Y of length at least (1+(n-1)*|incy|). Y contains the n elements of the vector y. On exit, if n<=0 or if c is 1.0 and s is 0.0, y is unchanged. Otherwise, y is overwritten; Y contains the rotated vector y. incy integer*4 On entry, the increment for the array Y. If incy >= 0, vector y is stored forward in the array, so that y(i) is stored in location Y(1+(i-1)*incy). If incy < 0, vector y is stored backward in the array, so that y(i) is stored in location Y(1+(n-i)*|incy|). On exit, incy is unchanged. c real*4 | real*8 On entry, the first rotation element, that is, the cosine of the angle of rotation. The argument c is the first rotation element generated by the _ROTG subroutines. On exit, c is unchanged. s real*4 | real*8 | complex*8 | complex*16 On entry, the second rotation element, that is, the sine of the angle of rotation. The argument s is the second rotation element generated by the _ROTG subroutines. On exit, s is unchanged.
SROT and DROT apply a real Givens plane rotation to each element in the pair of real vectors, x and y. CSROT and ZDROT apply a real Givens plane rotation to elements in the complex vectors, x and y. CROT and ZROT apply a complex Givens plane rotation to each element in the pair of complex vectors x and y. The cosine and sine of the angle of rotation are c and s, respectively, and are provided by the BLAS Level 1 _ROTG subroutines. The Givens plane rotation for SROT, DROT, CSROT, and ZDROT follows: x(i) = c*x(i) + s*y(i) y(i) = -s*x(i) + c*y(i) The elements of the rotated vector x are x(i) = cx(i) + sy(i). The elements of the rotated vector y are y(i) = -sx(i) + cy(i). The Givens plane rotation for CROT and ZROT follows: x(i) = c*x(i) + s*y(i) y(i) = -conjugate(s)*x(i) + c*y(i) The elements of the rotated vector x are x(i) = cx(i) + sy(i). The elements of the rotated vector y are y(i) = -conjugate(s)x(i) + cy(i). If n<=0 or if c = 1.0 and s = 0.0, x and y are unchanged. If any element of x shares a memory location with an element of y, the results are unpredictable. These subroutines can be used to introduce zeros selectively into a matrix.
INTEGER*4 INCX, N REAL X(20,20), A, B, C, S INCX = 20 N = 20 A = X(1,1) B = X(2,1) CALL SROTG(A,B,C,S) CALL SROT(N,X,INCX,X(2,1),INCX,C,S) This FORTRAN code shows how to rotate the first two rows of a matrix and zero out the element in the first column of the second row.