.TH "lassq" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lassq \- lassq: sum-of-squares, avoiding over/underflow
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclassq\fP (n, x, incx, scale, sumsq)"
.br
.RI "\fBCLASSQ\fP updates a sum of squares represented in scaled form\&. "
.ti -1c
.RI "subroutine \fBdlassq\fP (n, x, incx, scale, sumsq)"
.br
.RI "\fBDLASSQ\fP updates a sum of squares represented in scaled form\&. "
.ti -1c
.RI "subroutine \fBslassq\fP (n, x, incx, scale, sumsq)"
.br
.RI "\fBSLASSQ\fP updates a sum of squares represented in scaled form\&. "
.ti -1c
.RI "subroutine \fBzlassq\fP (n, x, incx, scale, sumsq)"
.br
.RI "\fBZLASSQ\fP updates a sum of squares represented in scaled form\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine classq (integer n, complex(wp), dimension(*) x, integer incx, real(wp) scale, real(wp) sumsq)"

.PP
\fBCLASSQ\fP updates a sum of squares represented in scaled form\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of elements to be used from the vector x\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fISCALE\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fISUMSQ\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Edward Anderson, Lockheed Martin 
.RE
.PP
\fBContributors:\fP
.RS 4
Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

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

.PP
\fBDLASSQ\fP updates a sum of squares represented in scaled form\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of elements to be used from the vector x\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fISCALE\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fISUMSQ\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Edward Anderson, Lockheed Martin 
.RE
.PP
\fBContributors:\fP
.RS 4
Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

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

.PP
\fBSLASSQ\fP updates a sum of squares represented in scaled form\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of elements to be used from the vector x\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fISCALE\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fISUMSQ\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Edward Anderson, Lockheed Martin 
.RE
.PP
\fBContributors:\fP
.RS 4
Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

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

.PP
\fBZLASSQ\fP updates a sum of squares represented in scaled form\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of elements to be used from the vector x\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fISCALE\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fISUMSQ\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Edward Anderson, Lockheed Martin 
.RE
.PP
\fBContributors:\fP
.RS 4
Weslley Pereira, University of Colorado Denver, USA Nick Papior, Technical University of Denmark, DK 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.