Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

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?larfy

Applies an elementary reflector, or Householder matrix, H, to an n by n symmetric or Hermitian matrix C, from both the left and the right.

call slarfy(uplo, n, v, incv, tau, C, ldc, work)

call dlarfy(uplo, n, v, incv, tau, C, ldc, work)

call clarfy(uplo, n, v, incv, tau, C, ldc, work)

call zlarfy(uplo, n, v, incv, tau, C, ldc, work)

Description

?larfy applies an elementary reflector, or Householder matrix, H, to an n by n symmetric or Hermitian matrix C, from both the left and the right. H is represented in the form H = I - tau * v * vT (for real flavors) or H = I - tau * v * vH (for complex flavors), where tau is a scalar and v is a vector. If tau is zero, H is taken to be the unit matrix.

Input Parameters

uplo

CHARACTER*1

Specifies whether the upper or lower triangular part of the symmetric or Hermitian matrix C is stored.

  • = 'U': Upper triangular part of C is stored.
  • = 'L': Lower triangular part of C is stored.
n

INTEGER

The number of rows and columns of the matrix C. n ≥ 0.

v

REAL for slarfy

DOUBLE PRECISION for dlarfy

COMPLEX for clarfy

COMPLEX*16 for zlarfy

Array, dimension (1 + (n-1)*abs(incv)). The vector v as described above.

incv

INTEGER

The increment between successive elements of v. incv must not be zero.

tau

REAL for slarfy

DOUBLE PRECISION for dlarfy

COMPLEX for clarfy

COMPLEX*16 for zlarfy

The value tau as described above.

C

REAL for slarfy

DOUBLE PRECISION for dlarfy

COMPLEX for clarfy

COMPLEX*16 for zlarfy

Array, dimension (ldc, n). On entry, the matrix C.

ldc

INTEGER

The leading dimension of the array C. ldc ≥ max( 1, n ).

Output Parameters

C

REAL for slarfy

DOUBLE PRECISION for dlarfy

COMPLEX for clarfy

COMPLEX*16 for zlarfy

On exit, C is overwritten by H * C * HT (for real flavors) or H * C * HH (for complex flavors).

work

REAL for slarfy

DOUBLE PRECISION for dlarfy

COMPLEX for clarfy

COMPLEX*16 for zlarfy

Array, dimension (n).