TESTING/EIG/dlatm4.f(3)

🌸 TESTING/EIG/dlatm4.f — DLATM4 💅

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🎀 NAME

TESTING/EIG/dlatm4.f

✨ SYNOPSIS

🧚 Functions/Subroutines

subroutine dlatm4 (itype, n, nz1, nz2, isign, amagn, rcond, triang,
    idist, iseed, a, lda)

DLATM4

💖 Function/Subroutine Documentation

subroutine dlatm4 (integer itype, integer n, integer nz1, integer nz2,
    integer isign, double precision amagn, double precision rcond, double
    precision triang, integer idist, integer, dimension( 4 ) iseed, double
    precision, dimension( lda, * ) a, integer lda)

DLATM4

🧚 Purpose

okay so DLATM4 generates basic square matrices, which may later be multiplied by others in order to produce test matrices. It is intended mainly to be used to test the generalized eigenvalue routines.

It first generates the diagonal and (possibly) subdiagonal, according to the value of ITYPE, NZ1, NZ2, ISIGN, AMAGN, and RCOND. It then fills in the upper triangle with random numbers, if TRIANG is non-zero.

🍓 Parameters

ITYPE

ITYPE is INTEGER. It picks the type of matrix on the diagonal and subdiagonal.

If ITYPE < 0, then type abs(ITYPE) is generated and then swapped end for end (A(I,J) := A'(N-J,N-I).). See also the description of AMAGN and ISIGN.

Special types:

• = 0: the zero matrix.
• = 1: the identity.
• = 2: a transposed Jordan block.
• = 3: If N is odd, then a k+1 x k+1 transposed Jordan block followed by a k x k identity block, where k=(N-1)/2. If N is even, then k=(N-2)/2, and a zero diagonal entry is tacked onto the end.

Diagonal types. The diagonal consists of NZ1 zeros, then k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE specifies the nonzero diagonal entries as follows:

• = 4: 1, ..., k
• = 5: 1, RCOND, ..., RCOND
• = 6: 1, ..., 1, RCOND
• = 7: 1, a, a^2, ..., a^(k-1)=RCOND
• = 8: 1, 1-d, 1-2*d, ..., 1-(k-1)*d=RCOND
• = 9: random numbers chosen from (RCOND,1)
• = 10: random numbers with distribution IDIST (see DLARND.)

N

N is INTEGER. The order of the matrix.

NZ1

NZ1 is INTEGER. If abs(ITYPE) > 3, then the first NZ1 diagonal entries will be zero.

NZ2

NZ2 is INTEGER. If abs(ITYPE) > 3, then the last NZ2 diagonal entries will be zero.

ISIGN

ISIGN is INTEGER.

• = 0: The sign of the diagonal and subdiagonal entries will be left unchanged.
• = 1: The diagonal and subdiagonal entries will have their sign changed at random.
• = 2: If ITYPE is 2 or 3, then the same as ISIGN=1. Otherwise, with probability 0.5, odd-even pairs of diagonal entries A(2*j-1,2*j-1), A(2*j,2*j) will be converted to a 2x2 block by pre- and post-multiplying by distinct random orthogonal rotations. The remaining diagonal entries will have their sign changed at random.

AMAGN

AMAGN is DOUBLE PRECISION. The diagonal and subdiagonal entries will be multiplied by AMAGN.

RCOND

RCOND is DOUBLE PRECISION. If abs(ITYPE) > 4, then the smallest diagonal entry will be RCOND.

🚨 RCOND must be between 0 and 1.

TRIANG

TRIANG is DOUBLE PRECISION. The entries above the diagonal will be random numbers with magnitude bounded by TRIANG (i.e., random numbers multiplied by TRIANG).

IDIST

IDIST is INTEGER. Specifies the type of distribution to be used to generate a random matrix.

• = 1: UNIFORM( 0, 1 )
• = 2: UNIFORM( -1, 1 )
• = 3: NORMAL ( 0, 1 )

ISEED

ISEED is INTEGER array, dimension (4). On entry ISEED specifies the seed of the random number generator. The values of ISEED are changed on exit, and can be used in the next call to DLATM4 to continue the same random number sequence.

💀 Note: ISEED(4) should be odd, for the random number generator used at present.

A

A is DOUBLE PRECISION array, dimension (LDA, N). Array to be computed.

LDA

LDA is INTEGER. Leading dimension of A. Must be at least 1 and at least N.

👑 Author

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

📌 Definition at line 173 of file dlatm4.f.

🌈 Author

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