?lassq

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

Updates a sum of squares represented in scaled form.

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 )

slassq dlassq classq zlassq

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

scl^{2} * smsq = 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 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

scl^{2} * ssq = x(1)^{2} +...+ x(n)^{2} + scale^{2} *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 .

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.

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.