lassq(3)

NAME
lassq - lassq: sum-of-squares, avoiding over/underflow

SYNOPSIS

  Functions

subroutine classq (n, x, incx, scale, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
subroutine dlassq (n, x, incx, scale, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
subroutine slassq (n, x, incx, scale, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
subroutine zlassq (n, x, incx, scale, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.

Detailed Description

Function Documentation

  subroutine classq (integer n, complex(wp), dimension(*) x, integer incx, real(wp) scale, real(wp) sumsq)

CLASSQ updates a sum of squares represented in scaled form.

Purpose:

    !>
    !> CLASSQ returns the values scale_out and sumsq_out such that
    !>
    !>    (scale_out**2)*sumsq_out = x( 1 )**2 +...+ x( n )**2 + (scale**2)*sumsq,
    !>
    !> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is
    !> assumed to be non-negative.
    !>
    !> scale and sumsq must be supplied in SCALE and SUMSQ and
    !> scale_out and sumsq_out are overwritten on SCALE and SUMSQ respectively.
    !>
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of elements to be used from the vector x.
    !>

    X

    !>          X is COMPLEX array, dimension (1+(N-1)*abs(INCX))
    !>          The vector for which a scaled sum of squares is computed.
    !>             x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
    !>

    INCX

    !>          INCX is INTEGER
    !>          The increment between successive values of the vector x.
    !>          If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
    !>          If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
    !>          If INCX = 0, x isn't a vector so there is no need to call
    !>          this subroutine. If you call it anyway, it will count x(1)
    !>          in the vector norm N times.
    !>

    SCALE

    !>          SCALE is REAL
    !>          On entry, the value scale in the equation above.
    !>          On exit, SCALE is overwritten by scale_out, the scaling factor
    !>          for the sum of squares.
    !>

    SUMSQ

    !>          SUMSQ is REAL
    !>          On entry, the value sumsq in the equation above.
    !>          On exit, SUMSQ is overwritten by sumsq_out, the basic sum of
    !>          squares from which scale_out has been factored out.
    !>

Author
    Edward Anderson, Lockheed Martin

Contributors:
    Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK

Further Details:

    !>
    !>  Anderson E. (2017)
    !>  Algorithm 978: Safe Scaling in the Level 1 BLAS
    !>  ACM Trans Math Softw 44:1--28
    !>  https://doi.org/10.1145/3061665
    !>
    !>  Blue, James L. (1978)
    !>  A Portable Fortran Program to Find the Euclidean Norm of a Vector
    !>  ACM Trans Math Softw 4:15--23
    !>  https://doi.org/10.1145/355769.355771
    !>
    !>

  subroutine dlassq (integer n, real(wp), dimension(*) x, integer incx, real(wp) scale, real(wp) sumsq)

DLASSQ updates a sum of squares represented in scaled form.

Purpose:

    !>
    !> DLASSQ returns the values scale_out and sumsq_out such that
    !>
    !>    (scale_out**2)*sumsq_out = x( 1 )**2 +...+ x( n )**2 + (scale**2)*sumsq,
    !>
    !> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is
    !> assumed to be non-negative.
    !>
    !> scale and sumsq must be supplied in SCALE and SUMSQ and
    !> scale_out and sumsq_out are overwritten on SCALE and SUMSQ respectively.
    !>
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of elements to be used from the vector x.
    !>

    X

    !>          X is DOUBLE PRECISION array, dimension (1+(N-1)*abs(INCX))
    !>          The vector for which a scaled sum of squares is computed.
    !>             x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
    !>

    INCX

    !>          INCX is INTEGER
    !>          The increment between successive values of the vector x.
    !>          If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
    !>          If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
    !>          If INCX = 0, x isn't a vector so there is no need to call
    !>          this subroutine. If you call it anyway, it will count x(1)
    !>          in the vector norm N times.
    !>

    SCALE

    !>          SCALE is DOUBLE PRECISION
    !>          On entry, the value scale in the equation above.
    !>          On exit, SCALE is overwritten by scale_out, the scaling factor
    !>          for the sum of squares.
    !>

    SUMSQ

    !>          SUMSQ is DOUBLE PRECISION
    !>          On entry, the value sumsq in the equation above.
    !>          On exit, SUMSQ is overwritten by sumsq_out, the basic sum of
    !>          squares from which scale_out has been factored out.
    !>

Author
    Edward Anderson, Lockheed Martin

Contributors:
    Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK

Further Details:

    !>
    !>  Anderson E. (2017)
    !>  Algorithm 978: Safe Scaling in the Level 1 BLAS
    !>  ACM Trans Math Softw 44:1--28
    !>  https://doi.org/10.1145/3061665
    !>
    !>  Blue, James L. (1978)
    !>  A Portable Fortran Program to Find the Euclidean Norm of a Vector
    !>  ACM Trans Math Softw 4:15--23
    !>  https://doi.org/10.1145/355769.355771
    !>
    !>

  subroutine slassq (integer n, real(wp), dimension(*) x, integer incx, real(wp) scale, real(wp) sumsq)

SLASSQ updates a sum of squares represented in scaled form.

Purpose:

    !>
    !> SLASSQ returns the values scale_out and sumsq_out such that
    !>
    !>    (scale_out**2)*sumsq_out = x( 1 )**2 +...+ x( n )**2 + (scale**2)*sumsq,
    !>
    !> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is
    !> assumed to be non-negative.
    !>
    !> scale and sumsq must be supplied in SCALE and SUMSQ and
    !> scale_out and sumsq_out are overwritten on SCALE and SUMSQ respectively.
    !>
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of elements to be used from the vector x.
    !>

    X

    !>          X is REAL array, dimension (1+(N-1)*abs(INCX))
    !>          The vector for which a scaled sum of squares is computed.
    !>             x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
    !>

    INCX

    !>          INCX is INTEGER
    !>          The increment between successive values of the vector x.
    !>          If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
    !>          If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
    !>          If INCX = 0, x isn't a vector so there is no need to call
    !>          this subroutine. If you call it anyway, it will count x(1)
    !>          in the vector norm N times.
    !>

    SCALE

    !>          SCALE is REAL
    !>          On entry, the value scale in the equation above.
    !>          On exit, SCALE is overwritten by scale_out, the scaling factor
    !>          for the sum of squares.
    !>

    SUMSQ

    !>          SUMSQ is REAL
    !>          On entry, the value sumsq in the equation above.
    !>          On exit, SUMSQ is overwritten by sumsq_out, the basic sum of
    !>          squares from which scale_out has been factored out.
    !>

Author
    Edward Anderson, Lockheed Martin

Contributors:
    Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK

Further Details:

    !>
    !>  Anderson E. (2017)
    !>  Algorithm 978: Safe Scaling in the Level 1 BLAS
    !>  ACM Trans Math Softw 44:1--28
    !>  https://doi.org/10.1145/3061665
    !>
    !>  Blue, James L. (1978)
    !>  A Portable Fortran Program to Find the Euclidean Norm of a Vector
    !>  ACM Trans Math Softw 4:15--23
    !>  https://doi.org/10.1145/355769.355771
    !>
    !>

  subroutine zlassq (integer n, complex(wp), dimension(*) x, integer incx, real(wp) scale, real(wp) sumsq)

ZLASSQ updates a sum of squares represented in scaled form.

Purpose:

    !>
    !> ZLASSQ returns the values scale_out and sumsq_out such that
    !>
    !>    (scale_out**2)*sumsq_out = x( 1 )**2 +...+ x( n )**2 + (scale**2)*sumsq,
    !>
    !> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is
    !> assumed to be non-negative.
    !>
    !> scale and sumsq must be supplied in SCALE and SUMSQ and
    !> scale_out and sumsq_out are overwritten on SCALE and SUMSQ respectively.
    !>
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of elements to be used from the vector x.
    !>

    X

    !>          X is DOUBLE COMPLEX array, dimension (1+(N-1)*abs(INCX))
    !>          The vector for which a scaled sum of squares is computed.
    !>             x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
    !>

    INCX

    !>          INCX is INTEGER
    !>          The increment between successive values of the vector x.
    !>          If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
    !>          If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
    !>          If INCX = 0, x isn't a vector so there is no need to call
    !>          this subroutine. If you call it anyway, it will count x(1)
    !>          in the vector norm N times.
    !>

    SCALE

    !>          SCALE is DOUBLE PRECISION
    !>          On entry, the value scale in the equation above.
    !>          On exit, SCALE is overwritten by scale_out, the scaling factor
    !>          for the sum of squares.
    !>

    SUMSQ

    !>          SUMSQ is DOUBLE PRECISION
    !>          On entry, the value sumsq in the equation above.
    !>          On exit, SUMSQ is overwritten by sumsq_out, the basic sum of
    !>          squares from which scale_out has been factored out.
    !>

Author
    Edward Anderson, Lockheed Martin

Contributors:
    Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK

Further Details:

    !>
    !>  Anderson E. (2017)
    !>  Algorithm 978: Safe Scaling in the Level 1 BLAS
    !>  ACM Trans Math Softw 44:1--28
    !>  https://doi.org/10.1145/3061665
    !>
    !>  Blue, James L. (1978)
    !>  A Portable Fortran Program to Find the Euclidean Norm of a Vector
    !>  ACM Trans Math Softw 4:15--23
    !>  https://doi.org/10.1145/355769.355771
    !>
    !>

Author

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