?laic1

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?laic1

Applies one step of incremental condition estimation.

Syntax

call slaic1(job, j, x, sest, w, gamma, sestpr, s, c)
call dlaic1(job, j, x, sest, w, gamma, sestpr, s, c)
call claic1(job, j, x, sest, w, gamma, sestpr, s, c)
call zlaic1(job, j, x, sest, w, gamma, sestpr, s, c)

Include Files

mkl.fi

Description

The routine ?laic1 applies one step of incremental condition estimation in its simplest version.

Let x , ||x||_{2} = 1 (where ||a||_{2} denotes the 2-norm of a ), be an approximate singular vector of an j -by- j lower triangular matrix L , such that

||L*x||_{2} = sest

Then ?laic1 computes sestpr , s , c such that the vector

is an approximate singular vector of

(for complex flavors), or

(for real flavors), in the sense that

||Lhat*xhat||_{2} = sestpr .

Depending on job , an estimate for the largest or smallest singular value is computed.

For real flavors, [sc]^{T} and sestpr^{2} is an eigenpair of the system

where alpha = x^{T}*w .

For complex flavors, [sc]^{H} and sestpr^{2} is an eigenpair of the system

where alpha = x^{H}*w .

Input Parameters

job: INTEGER . If job =1 , an estimate for the largest singular value is computed; If job =2 , an estimate for the smallest singular value is computed;
j: INTEGER . Length of x and w .
x , w: REAL for slaic1 DOUBLE PRECISION for dlaic1 COMPLEX for claic1 DOUBLE COMPLEX for zlaic1 . Arrays, dimension ( j ) each. Contain vectors x and w , respectively.
sest: REAL for slaic1 / claic1 ; DOUBLE PRECISION for dlaic1 / zlaic1 . Estimated singular value of j -by- j matrix L .
gamma: REAL for slaic1 DOUBLE PRECISION for dlaic1 COMPLEX for claic1 DOUBLE COMPLEX for zlaic1 . The diagonal element gamma .

Output Parameters

sestpr: REAL for slaic1 / claic1 ; DOUBLE PRECISION for dlaic1 / zlaic1 . Estimated singular value of ( j +1)-by-( j +1) matrix Lhat .
s , c: REAL for slaic1 DOUBLE PRECISION for dlaic1 COMPLEX for claic1 DOUBLE COMPLEX for zlaic1 . Sine and cosine needed in forming xhat .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laic1

Syntax

Include Files

Description

Input Parameters

Output Parameters