VMS Help RTL Routines, MTH$, BLAS1$VxROT  *Conan The Librarian (sorry for the slow response - running on an old VAX)

    The Apply a Givens Plane Rotation routine applies a Givens plane
    rotation to a pair of n-element vectors x and y.

    Format

      BLAS1$VSROT  n ,x ,incx ,y ,incy ,c ,s

      BLAS1$VDROT  n ,x ,incx ,y ,incy ,c ,s

      BLAS1$VGROT  n ,x ,incx ,y ,incy ,c ,s

      BLAS1$VCSROT  n ,x ,incx ,y ,incy ,c ,s

      BLAS1$VZDROT  n ,x ,incx ,y ,incy ,c ,s

      BLAS1$VWGROT  n ,x ,incx ,y ,incy ,c ,s

      Use BLAS1$VSROT for single-precision real operations.
      Use BLAS1$VDROT for double-precision real (D-floating)
      operations.
      Use BLAS1$VGROT for double-precision real (G-floating)
      operations.

      Use BLAS1$VCSROT for single-precision complex operations.
      Use BLAS1$VZDROT for double-precision complex (D-floating)
      operations.
      Use BLAS1$VWGROT for double-precision complex (G-floating)
      operations.
      BLAS1$VCSROT, BLAS1$VZDROT, and BLAS1$VWGROT are real rotations
      applied to a complex vector.

1 - Returns

    None.

2 - Arguments

 n

    OpenVMS usage:longword_signed
    type:         longword integer (signed)
    access:       read only
    mechanism:    by reference

    Number of elements in vectors x and y to be rotated. The n
    argument is the address of a signed longword integer containing
    the number of elements to be rotated. If n is less than or equal
    to 0, then x and y are unchanged.

 x

    OpenVMS usage:floating_point or complex_number
    type:         F_floating, D_floating, G_floating real or
                  F_floating, D_floating, G_floating complex
    access:       modify
    mechanism:    by reference, array reference

    Array containing the elements to be accessed. All elements of
    array x are accessed only if the increment argument of x, called
    incx, is 1. The x argument is the address of a floating-point or
    floating-point complex number that is this array. On entry, this
    argument is an array of length at least:

    1+(n-1)*|incx|

    where:

    n   =  number of vector elements specified in n
    incx=  increment argument for the array x specified in incx

    Specify the data type as follows:

    Routine            Data Type for x

    BLAS1$VSROT        F-floating real
    BLAS1$VDROT        D-floating real
    BLAS1$VGROT        G-floating real
    BLAS1$VCSROT       F-floating complex
    BLAS1$VZDROT       D-floating complex
    BLAS1$VWGROT       G-floating complex

    If n is less than or equal to 0, then x and y are unchanged. If
    c equals 1.0 and s equals 0, then x and y are unchanged. If any
    element of x shares a memory location with an element of y, then
    the results are unpredictable.

    On exit, x contains the rotated vector x, as follows:

    xi< - c*x i+s*y i x[i]< - c*x[i]+s*y[i]

    where:

    x  =  array x specified in x
    y  =  array y specified in y
    i  =  i = 1,2,...,n
    c  =  rotation element generated by the BLAS1$VxROTG routines
    s  =  rotation element generated by the BLAS1$VxROTG routines

 incx

    OpenVMS usage:longword_signed
    type:         longword integer (signed)
    access:       read only
    mechanism:    by reference

    Increment argument for the array x. The incx argument is the
    address of a signed longword integer containing the increment
    argument. If incx is greater than or equal to 0, then x is
    referenced forward in array x; that is, x[i] is referenced in:

    x(1+(i-1)*incx)

    where:

    x   =  array specified in x
    i   =  element of the vector x
    incx=  increment argument for the array x specified in incx

    If incx is less than 0, then x is referenced backward in array x;
    that is, x[i] is referenced in:

    x(1+(n-i)*|incx|)

    where:

    x   =  array specified in x
    n   =  number of vector elements specified in n
    i   =  element of the vector x
    incx=  increment argument for the array x specified in incx

 y

    OpenVMS usage:floating_point or complex_number
    type:         F_floating, D_floating, G_floating real or
                  F_floating, D_floating, G_floating complex
    access:       modify
    mechanism:    by reference, array reference

    Array containing the elements to be accessed. All elements of
    array y are accessed only if the increment argument of y, called
    incy, is 1. The y argument is the address of a floating-point or
    floating-point complex number that is this array. On entry, this
    argument is an array of length at least:

    1+(n-1)*|incx|

    where:

    n   =  number of vector elements specified in n
    incx=  increment argument for the array x specified in incx

    Specify the data type as follows:

    Routine            Data Type for y

    BLAS1$VSROT        F-floating real
    BLAS1$VDROT        D-floating real
    BLAS1$VGROT        G-floating real
    BLAS1$VCSROT       F-floating complex
    BLAS1$VZDROT       D-floating complex
    BLAS1$VWGROT       G-floating complex

    If n is less than or equal to 0, then x and y are unchanged. If
    c equals 1.0 and s equals 0, then x and y are unchanged. If any
    element of x shares a memory location with an element of y, then
    the results are unpredictable.

    On exit, y contains the rotated vector y, as follows:

    yi< - -s*x i +c*y i y[i]< - -s*x[i]+c*y[i]

    where:

    x  =  array x specified in x
    y  =  array y specified in y
    i  =  i = 1,2,...,n
    c  =  real rotation element (can be generated by the BLAS1$VxROTG
          routines)
    s  =  complex rotation element (can be generated by the
          BLAS1$VxROTG routines)

 incy

    OpenVMS usage:longword_signed
    type:         longword integer (signed)
    access:       read only
    mechanism:    by reference

    Increment argument for the array y. The incy argument is the
    address of a signed longword integer containing the increment
    argument. If incy is greater than or equal to 0, then y is
    referenced forward in array y; that is, y[i] is referenced in:

    y(1+(i-1)*incy)

    where:

    y   =  array specified in y
    i   =  element of the vector y
    incy=  increment argument for the array y specified in incy

    If incy is less than 0, then y is referenced backward in array y;
    that is, y[i] is referenced in:

    y(1+(n-i)*|incy|)

    where:

    y   =  array specified in y
    n   =  number of vector elements specified in n
    i   =  element of the vector y
    incy=  increment argument for the array y specified in incy

 c

    OpenVMS usage:floating_point
    type:         F_floating, D_floating, or G_floating real
    access:       read only
    mechanism:    by reference

    First rotation element, which can be interpreted as the cosine
    of the angle of rotation. The c argument is the address of a
    floating-point or floating-point complex number that is this
    vector element. The c argument is the first rotation element
    generated by the BLAS1$VxROTG routines.

    Specify the data type (which is always real) as follows:

    Routine            Data Type for c

    BLAS1$VSROT and    F-floating real
    BLAS1$VCSROT
    BLAS1$VDROT and    D-floating real
    BLAS1$VZDROT
    BLAS1$VGROT and    G-floating real
    BLAS1$VWGROT

 s

    OpenVMS usage:floating_point or complex_number
    type:         F_floating, D_floating, G_floating real or
                  F_floating, D_floating, G_floating complex
    access:       read only
    mechanism:    by reference

    Second rotation element, which can be interpreted as the sine
    of the angle of rotation. The s argument is the address of a
    floating-point or floating-point complex number that is this
    vector element. The s argument is the second rotation element
    generated by the BLAS1$VxROTG routines.

    Specify the data type (which can be either real or complex) as
    follows:

    Routine            Data Type for s

    BLAS1$VSROT and    F-floating real or F-floating complex
    BLAS1$VCSROT
    BLAS1$VDROT and    D-floating real or D-floating complex
    BLAS1$VZDROT
    BLAS1$VGROT and    G-floating real or G-floating complex
    BLAS1$VWGROT