CHET21(3)

🎀 chet21.f(3) — Library Functions Manual 🎀

okay bestie, this is the chet21.f(3) page from the Library Functions Manual 💅. The header path vibe is /home/abui...IG/chet21.f(3), and this whole page is about the LAPACK test file in NAME. ngl, it's lowkey giving main character energy for a test subroutine, and I'm obsessed. 🦋

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/chet21.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine CHET21 (itype, uplo, n, kband, a, lda, d, e, u, ldu, v, ldv,
    tau, work, rwork, result)
    CHET21

💖 Function/Subroutine Documentation 💖

CHET21

subroutine CHET21 (integer itype, character uplo, integer n, 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)

Purpose

okay so CHET21 generally checks a decomposition of the form

A = U S U**H

where **H means conjugate transpose, A is hermitian, U is unitary, and S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if KBAND=1). iconic linear algebra behavior ✨ fr fr.

If ITYPE=1, then U is represented as a dense matrix; otherwise U is expressed as a product of Householder transformations, whose vectors are stored in the array [blank in the source] and whose scaling constants are in [blank in the source]. We shall use the letter [blank in the source] to refer to the product of Householder transformations (which should be equal to U). the source literally has blanks there, so I'm not inventing names, no cap — iykyk 🫶

Specifically, if ITYPE=1, then:

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

If ITYPE=2, then:

RESULT(1) = | A - V S V**H | / ( |A| n ulp )

If ITYPE=3, then:

RESULT(1) = | I - U V**H | / ( n ulp )

For ITYPE > 1, the transformation U is expressed as a product

V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)**H

and each vector v(j) has its first j elements 0 and the remaining n-j elements stored in V(j+1:n,j). math ate that 🔥

Parameters

• ITYPE — ITYPE is INTEGER. Specifies the type of tests to be performed.
  • 1: U expressed as a dense unitary matrix: RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and RESULT(2) = | I - U U**H | / ( n ulp )
  • 2: U expressed as a product V of Householder transformations: RESULT(1) = | A - V S V**H | / ( |A| n ulp )
  • 3: U expressed both as a dense unitary matrix and as a product of Householder transformations: RESULT(1) = | I - U V**H | / ( n ulp )
• UPLO — UPLO is CHARACTER.
  • If UPLO='U', the upper triangle of A and V will be used and the (strictly) lower triangle will not be referenced.
  • If UPLO='L', the lower triangle of A and V will be used and the (strictly) upper triangle will not be referenced.
• N — N is INTEGER. The size of the matrix. If it is zero, CHET21 does nothing. It must be at least zero.
• KBAND — KBAND is 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.
• A — A is COMPLEX array, dimension (LDA, N). The original (unfactored) matrix. It is assumed to be hermitian, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced.
• LDA — LDA is INTEGER. The leading dimension of A. It must be at least 1 and at least N.
• D — D is REAL array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix.
• E — E is REAL array, dimension (N-1). The off-diagonal of the (symmetric tri-) diagonal matrix. E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and (3,2) element, etc. Not referenced if KBAND=0.
• U — U is COMPLEX array, dimension (LDU, N). If ITYPE=1 or 3, this contains the unitary matrix in the decomposition, expressed as a dense matrix. If ITYPE=2, then it is not referenced.
• LDU — LDU is INTEGER. The leading dimension of U. LDU must be at least N and at least 1.
• V — V is COMPLEX array, dimension (LDV, N). If ITYPE=2 or 3, the columns of this array contain the Householder vectors used to describe the unitary matrix in the decomposition. If UPLO='L', then the vectors are in the lower triangle, if UPLO='U', then in the upper triangle.

NOTE — If ITYPE=2 or 3, V is modified and restored. The subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U') is set to one, and later reset to its original value, during the course of the calculation. If ITYPE=1, then it is neither referenced nor modified. 💀

• LDV — LDV is INTEGER. The leading dimension of V. LDV must be at least N and at least 1.
• TAU — TAU is 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.
• WORK — WORK is COMPLEX array, dimension (2*N**2).
• RWORK — RWORK is REAL array, dimension (N).
• RESULT — RESULT is 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 ITYPE=1.

Author

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

Definition at line 212 of file chet21.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie. Cute footer sign-off: LAPACK, Version 3.12.0, with footer path /home/abui...IG/chet21.f(3). the source didn't give a date, so I'm not making one up, periodt 🫶✨💖