p?lassq

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 11/07/2023

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p?lassq

Updates a sum of squares represented in scaled form.

Syntax

call pslassq(n, x, ix, jx, descx, incx, scale, sumsq)

call pdlassq(n, x, ix, jx, descx, incx, scale, sumsq)

call pclassq(n, x, ix, jx, descx, incx, scale, sumsq)

call pzlassq(n, x, ix, jx, descx, incx, scale, sumsq)

Description

The p?lassqroutine returns the values scl and smsq such that

scl² * smsq = x₁² + ... + x_n² + scale²*sumsq,

where

x_i= sub(X) = X(ix + (jx-1)*m_x + (i - 1)*incx) for pslassq/pdlassq ,

x_i= sub(X) = abs(X(ix + (jx-1)*m_x + (i - 1)*incx) for pclassq/pzlassq.

For real routines pslassq/pdlassq the value of sumsq is assumed to be non-negative and scl returns the value

scl = max(scale, abs(x_i)).

For complex routines pclassq/pzlassq the value of sumsq is assumed to be at least unity and the value of ssq will then satisfy

1.0 ≤ ssq ≤sumsq +2n

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

For all routines p?lassq values scale and sumsq must be supplied in scale and sumsq respectively, and scale and sumsq are overwritten by scl and ssq respectively.

All routines p?lassq make only one pass through the vector sub(X).

Input Parameters

n

(global) INTEGER.

The length of the distributed vector sub(x ).

x

REAL for pslassq

DOUBLE PRECISION for pdlassq

COMPLEX for pclassq

COMPLEX*16 for pzlassq.

The vector for which a scaled sum of squares is computed:

x(ix + (jx-1)*m_x + (i - 1)*incx), 1 ≤ i ≤ n.

ix

(global) INTEGER.

The row index in the global matrix X indicating the first row of sub(X).

jx

(global) INTEGER.

The column index in the global matrix X indicating the first column of sub(X).

descx

(global and local) INTEGER array of size dlen_.

The array descriptor for the distributed matrix X.

incx

(global) INTEGER.

The global increment for the elements of X. Only two values of incx are supported in this version, namely 1 and m_x. The argument incx must not equal zero.

scale

(local).

REAL for pslassq/pclassq

DOUBLE PRECISION for pdlassq/pzlassq.

On entry, the value scale in the equation above.

sumsq

(local)

REAL for pslassq/pclassq

DOUBLE PRECISION for pdlassq/pzlassq.

On entry, the value sumsq in the equation above.

Output Parameters

scale

(local).

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

sumsq

(local).

On exit, sumsq is overwritten with the value smsq, the basic sum of squares from which scl has been factored out.

Parent topic: ScaLAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?lassq

Syntax

Description

Input Parameters

Output Parameters

See Also