TESTING/EIG/clatm4.f(3)

💅 TESTING/EIG/clatm4.f(3) 💅

From the Library Functions Manual, bestie — this page is all about the CLATM4 subroutine. It's giving test-matrix construction realness, so let's go. ✨

🎀 NAME 🎀

TESTING/EIG/clatm4.f

✨ SYNOPSIS ✨

🌀 Functions/Subroutines 🌀

subroutine clatm4 (itype, n, nz1, nz2, rsign, amagn, rcond, triang,
    idist, iseed, a, lda)

CLATM4

🌈 Function/Subroutine Documentation 🌈

subroutine clatm4 (integer itype, integer n, integer nz1, integer nz2,
    logical rsign, real amagn, real rcond, real triang, integer idist,
    integer, dimension( 4 ) iseed, complex, dimension( lda, * ) a, integer
    lda)

CLATM4

🎯 Purpose 🎯

Okay so CLATM4 generates basic square matrices, which may later be multiplied by others in order to produce test matrices. The main-character use? It's intended mainly to be used to test the generalized eigenvalue routines. 🫶

First it generates the diagonal and (possibly) subdiagonal, according to the value of ITYPE, NZ1, NZ2, RSIGN, AMAGN, and RCOND. Then it fills in the upper triangle with random numbers, if TRIANG is non-zero. Slay. 💅

🧸 Parameters 🧸

• ITYPE — ITYPE is INTEGER. It's the type-of-matrix selector for the diagonal and sub-diagonal. 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 RSIGN. 👀
  • 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 CLARND.)
• N — N is INTEGER. The order of the matrix. The size. The moment. 💫
• 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.
• RSIGN — RSIGN is LOGICAL. It controls the sign/magnitude randomizing vibe:
  • = .TRUE.: The diagonal and subdiagonal entries will be multiplied by random numbers of magnitude 1.
  • = .FALSE.: The diagonal and subdiagonal entries will be left as they are (usually non-negative real.)
• AMAGN — AMAGN is REAL. The diagonal and subdiagonal entries will be multiplied by AMAGN.
• RCOND — RCOND is REAL. If abs(ITYPE) > 4, then the smallest diagonal entry will be RCOND. RCOND must be between 0 and 1. No cap.
• TRIANG — TRIANG is REAL. 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. On entry, DIST specifies the type of distribution to be used to generate a random matrix .
  • = 1: real and imaginary parts each UNIFORM( 0, 1 )
  • = 2: real and imaginary parts each UNIFORM( -1, 1 )
  • = 3: real and imaginary parts each NORMAL( 0, 1 )
  • = 4: complex number uniform in DISK( 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 CLATM4 to continue the same random number sequence. Note: ISEED(4) should be odd, for the random number generator used at present. 🍓
• A — A is COMPLEX 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 169 of file clatm4.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo bestie 💖 — source/version energy: LAPACK, Version 3.12.0, and the file tag TESTING/EIG/clatm4.f(3). The footer doesn't list a date, so we're not inventing one. Periodt. 🌈