Library Functions Manual

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

Definition at line 123 of file classq.f90.

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

Definition at line 123 of file dlassq.f90.

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

Definition at line 123 of file slassq.f90.

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

Definition at line 123 of file zlassq.f90.

Author¶

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