TESTING/EIG/chet21.f(3)

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💖 NAME 💖

TESTING/EIG/chet21.f

hey bestie 💖 this is the TESTING/EIG/chet21.f(3) page from the Library Functions Manual — and yes, we’re going through the whole chet21 moment with zero details left behind. periodt.

✨ 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 🦋

🫶 subroutine 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)

CHET21

🎀 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).

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 . We shall use the letter to refer to the product of Householder transformations (which should be equal to U).

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).

🍓 Parameters 🍓

💅 ITYPE 💅

ITYPE is INTEGER Specifies the type of tests to be performed.

  1. 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 )
  1. 2: U expressed as a product V of Housholder transformations:
RESULT(1) = | A - V S V**H | / ( |A| n ulp )
  1. 3: U expressed both as a dense unitary matrix and as a product of Housholder 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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