CHET22(3)

💖 NAME 💖

okay bestie, this is CHET22(3) from the Library Functions Manual — welcome to the group chat ✨ The file it's documenting is exactly this path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/chet22.f

That's the whole NAME section, periodt. 💅

🌸 SYNOPSIS 🌸

🦋 Functions/Subroutines 🦋

subroutine CHET22 (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v,
    ldv, tau, work, rwork, result)
    CHET22

🎀 Function/Subroutine Documentation 🎀

here's the full signature, copied exactly, bestie:

subroutine CHET22 (integer itype, character uplo, integer n, integer m,
    integer kband, complex, dimension( lda, * ) a, integer lda, real,
    dimension( * ) d, real, dimension( * ) e, complex, dimension( ldu, * )
    u, integer ldu, complex, dimension( ldv, * ) v, integer ldv, complex,
    dimension( * ) tau, complex, dimension( * ) work, real, dimension( * )
    rwork, real, dimension( 2 ) result)
    CHET22

💅 Purpose 💅

okay so CHET22 generally checks a decomposition of the form:

A U = U S

where A is complex Hermitian, the columns of U are orthonormal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as a dense matrix, otherwise the U is expressed as a product of Householder transformations, whose vectors are stored in the array [blank] and whose scaling constants are in [blank]; then it says "we shall use the letter" [blank] "to refer to the product of Householder transformations" (which should be equal to U).

bestie, those blanks are literally how the source text came through — I'm not guessing array names here, I'm preserving the gaps. 🫶

Specifically, if ITYPE=1, then:

RESULT(1) = | U**H A U - S | / ( |A| m ulp ) and
RESULT(2) = | I - U**H U | / ( m ulp )

and yes, the argument list below has its own ITYPE=1 formulas too — both sets are in the page, so both are staying. 🫡

and here are all the arguments, one by one:

• ITYPE — INTEGER. Specifies the type of tests to be performed.
  • 1: U expressed as a dense orthogonal matrix:

RESULT(1) = | A - U S U**H | / ( |A| n ulp )  and
RESULT(2) = | I - U U**H | / ( n ulp )

• UPLO — CHARACTER. If UPLO='U', the upper triangle of A will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A will be used and the (strictly) upper triangle will not be referenced. Not modified.
• N — INTEGER. The size of the matrix. If it is zero, CHET22 does nothing. It must be at least zero. Not modified.
• M — INTEGER. The number of columns of U. If it is zero, CHET22 does nothing. It must be at least zero. Not modified.
• KBAND — INTEGER. The bandwidth of the matrix. It may only be zero or one. If zero, then S is diagonal, and E is not referenced. If one, then S is symmetric tri-diagonal. Not modified.
• A — COMPLEX array, dimension (LDA , N). The original (unfactored) matrix. It is assumed to be symmetric, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced. Not modified.
• LDA — INTEGER. The leading dimension of A. It must be at least 1 and at least N. Not modified.
• D — REAL array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix. Not modified.
• E — REAL array, dimension (N). The off-diagonal of the (symmetric tri-) diagonal matrix. E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. Not referenced if KBAND=0. Not modified.
• U — COMPLEX array, dimension (LDU, N). If ITYPE=1, this contains the orthogonal matrix in the decomposition, expressed as a dense matrix. Not modified.
• LDU — INTEGER. The leading dimension of U. LDU must be at least N and at least 1. Not modified.
• V — COMPLEX array, dimension (LDV, N). If ITYPE=2 or 3, the lower triangle of this array contains the Householder vectors used to describe the orthogonal matrix in the decomposition. If ITYPE=1, then it is not referenced. Not modified.
• LDV — INTEGER. The leading dimension of V. LDV must be at least N and at least 1. Not modified.
• TAU — COMPLEX array, dimension (N). If ITYPE >= 2, then TAU(j) is the scalar factor of v(j) v(j)**H in the Householder transformation H(j) of the product U = H(1)...H(n-2). If ITYPE < 2, then TAU is not referenced. Not modified.
• WORK — COMPLEX array, dimension (2*N**2). Workspace. Modified.
• RWORK — REAL array, dimension (N). Workspace. Modified.
• RESULT — REAL array, dimension (2). The values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow. RESULT(1) is always modified. RESULT(2) is modified only if LDU is at least N. Modified.

🌸 Author 🌸

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 159 of file chet22.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page, bestie — byeee 🫶💅 This one comes from LAPACK Version 3.12.0, and the footer also shows /home/abui...IG/chet22.f(3). There's no separate date printed on it, so that's the version/source situation, periodt. ✨