ZHET22(3)

💖 NAME 💖

Manual: Library Functions Manual ✨

This page is for: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zhet22.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

Okay so the star of the show is the ZHET22 subroutine, and the docs also list it as ZHET22. Here’s the exact call shape, bestie:

       subroutine ZHET22 (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v,
           ldv, tau, work, rwork, result)
           ZHET22

🧚 Function/Subroutine Documentation 🧚

🌟 The signature 🌟

subroutine ZHET22 (integer itype, character uplo, integer n, integer m,
       integer kband, complex*16, dimension( lda, * ) a, integer lda, double
       precision, dimension( * ) d, double precision, dimension( * ) e,
       complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension(
       ldv, * ) v, integer ldv, complex*16, dimension( * ) tau, complex*16,
       dimension( * ) work, double precision, dimension( * ) rwork, double
       precision, dimension( 2 ) result)
       ZHET22

💅 Purpose 💅

ZHET22 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 U is expressed as a product of Householder transformations, whose vectors are stored in the array and whose scaling constants are in — yes, the source text literally leaves those names blank, so don’t come for me 😭 — and we shall use the letter (also blank in the source) to refer to the product of Householder transformations, which should be equal to U.

Specifically, if ITYPE=1, then:

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

🎀 Parameters — the whole cast 🎀

• 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, ZHET22 does nothing. It must be at least zero. Not modified.
• M — INTEGER. The number of columns of U. If it is zero, ZHET22 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*16 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 — DOUBLE PRECISION array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix. Not modified.
• E — DOUBLE PRECISION 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*16 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*16 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*16 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*16 array, dimension (2*N**2). Workspace. Modified.
• RWORK — DOUBLE PRECISION array, dimension (N). Workspace. Modified.
• RESULT — DOUBLE PRECISION 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 zhet22.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the whole page, bestie — LAPACK Version 3.12.0, from /home/abui...IG/zhet22.f(3). Periodt. 🎀