?lassq

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?lassq

Updates a sum of squares represented in scaled form.

Syntax

call slassq( n, x, incx, scale, sumsq )

call dlassq( n, x, incx, scale, sumsq )

call classq( n, x, incx, scale, sumsq )

call zlassq( n, x, incx, scale, sumsq )

Include Files

mkl.fi

Description

The real routines slassq/dlassq return the values scl and smsq such that

scl² * smsq = x(1)² +...+ x(n)² + scale² *sumsq,

where x( i ) = x(1 + ( i - 1) incx).

The value of sumsq is assumed to be non-negative and scl returns the value

scl = max( scale, abs(x(i))).

Values scale and sumsq must be supplied in scale and sumsq, and scl and smsq are overwritten on scale and sumsq, respectively.

The complex routines classq/zlassq return the values scl and ssq such that

scl² * ssq = x(1)² +...+ x(n)² + scale² *sumsq,

where x(i) = abs(x(1 +(i - 1)*incx)).

The value of sumsq is assumed to be at least unity and the value of ssq will then satisfy 1.0 ≤ ssq ≤ sumsq + 2n

scale is assumed to be non-negative and scl returns the value

scl = max( scale, abs(real(x(i))), abs(aimag(x(i)))).

Values scale and sumsq must be supplied in scale and sumsq, and scl and ssq are overwritten on scale and sumsq, respectively.

All routines ?lassq make only one pass through the vector x.

Input Parameters

n

INTEGER. The number of elements to be used from the vector x.

x

REAL for slassq

DOUBLE PRECISION for dlassq

COMPLEX for classq

DOUBLE COMPLEX for zlassq.

The vector for which a scaled sum of squares is computed: x(i) = x(1+(i-1)*incx), 1 ≤ i ≤ n.

incx

INTEGER. The increment between successive values of the vector x. incx > 0.

scale

REAL for slassq/classq

DOUBLE PRECISION for dlassq/zlassq.

On entry, the value scale in the equation above.

sumsq

REAL for slassq/classq

DOUBLE PRECISION for dlassq/zlassq.

On entry, the value sumsq in the equation above.

Output Parameters

scale

On exit, scale is overwritten with scl, the scaling factor for the sum of squares.

sumsq

For real flavors:

On exit, sumsq is overwritten with the value smsq in the equation above.

For complex flavors:

On exit, sumsq is overwritten with the value ssq in the equation above.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lassq