SSYT22(3)

okay bestie, this is ssyt22.f(3) from the Library Functions Manual — the raw header path is /home/abui...IG/ssyt22.f(3), and it literally appears twice in the header because it’s dramatic like that 💅.

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ssyt22.f

That long beautiful path is the NAME, no cap. 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine SSYT22 (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, result) — SSYT22

This is the whole function vibe, bestie.

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💖 Function/Subroutine Documentation 💖

subroutine SSYT22 (integer itype, character uplo, integer n, integer m,
       integer kband, real, dimension( lda, * ) a, integer lda, real,
       dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u,
       integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension(
       * ) tau, real, dimension( * ) work, real, dimension( 2 ) result)
       SSYT22

The routine’s name is SSYT22, periodt. 👑

🦋 Purpose 🦋

SSYT22 generally checks a decomposition of the form

A U = U S

where A is symmetric, 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 and whose scaling constants are in we shall use the letter to refer to the product of Householder transformations (which should be equal to U).

Yes, the source text has those blank-ish spots where names would go — I’m keeping the blanks, bestie, because inventing names would be a no-no 🙈.

Specifically, if ITYPE=1, then:

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

💅 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**T | / ( |A| n ulp ) and RESULT(2) = | I - U U**T | / ( 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, SSYT22 does nothing. It must be at least zero. Not modified.
• M — INTEGER. The number of columns of U. If it is zero, SSYT22 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 — REAL 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 — REAL array, dimension (LDU, N). If ITYPE=1 or 3, this contains the orthogonal matrix in the decomposition, expressed as a dense matrix. If ITYPE=2, then it is not referenced. Not modified.
• LDU — INTEGER. The leading dimension of U. LDU must be at least N and at least 1. Not modified.
• V — REAL 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 — REAL array, dimension (N). If ITYPE >= 2, then TAU(j) is the scalar factor of v(j) v(j)**T 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 — REAL array, dimension (2*N**2). 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 155 of file ssyt22.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Signed, sealed, and slaying: LAPACK Version 3.12.0, footer path /home/abui...IG/ssyt22.f(3). Mwah 💋✨