table of contents
| lassq(3) | LAPACK | 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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