lassq - Man Page

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

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

          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

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

          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

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

          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

Definition at line 123 of file zlassq.f90.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK