gtts2(3)

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💖 gtts2(3) — Library Functions Manual 💖

🌸 NAME 🌸

gtts2 — gtts2: triangular solve using factor. That's the whole name, bestie — it's a triangular solve using a factor. 💅

✨ SYNOPSIS ✨

Okay so this page is basically the group chat for four Fortran subroutines. They all do the triangular-solve-with-a-factor thing, just in different numeric flavors. 👑

Functions

  • subroutine cgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb) — CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
  • subroutine dgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb) — DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
  • subroutine sgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb) — SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
  • subroutine zgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb) — ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

🦋 Detailed Description 🦋

This section is literally just a heading in the original — no extra prose dropped here. The functions are documented right below. 🫶

💅 Function Documentation 💅

🧚 cgtts2 🧚

Full signature:

   subroutine cgtts2 (integer itrans, integer n, integer nrhs, complex,
       dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * )
       du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex,
       dimension( ldb, * ) b, integer ldb)

CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose: CGTTS2 solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, with a tridiagonal matrix A using the LU factorization computed by CGTTRF.

Parameters

  • ITRANS — ITRANS is INTEGER. Specifies the form of the system of equations:
    • = 0: A * X = B (No transpose)
    • = 1: A**T * X = B (Transpose)
    • = 2: A**H * X = B (Conjugate transpose)
  • N — N is INTEGER. The order of the matrix A.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • DL — DL is COMPLEX array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A.
  • D — D is COMPLEX array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
  • DU — DU is COMPLEX array, dimension (N-1). The (n-1) elements of the first super-diagonal of U.
  • DU2 — DU2 is COMPLEX array, dimension (N-2). The (n-2) elements of the second super-diagonal of U.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
  • B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the matrix of right hand side vectors B. On exit, B is overwritten by the solution vectors X.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

Author

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

Definition at line 127 of file cgtts2.f.

🧚 dgtts2 🧚

Full signature:

   subroutine dgtts2 (integer itrans, integer n, integer nrhs, double
       precision, dimension( * ) dl, double precision, dimension( * ) d, double
       precision, dimension( * ) du, double precision, dimension( * ) du2,
       integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b,
       integer ldb)

DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose: DGTTS2 solves one of the systems of equations A*X = B or A**T*X = B, with a tridiagonal matrix A using the LU factorization computed by DGTTRF.

Parameters

  • ITRANS — ITRANS is INTEGER. Specifies the form of the system of equations:
    • = 0: A * X = B (No transpose)
    • = 1: A**T* X = B (Transpose)
    • = 2: A**T* X = B (Conjugate transpose = Transpose)
  • N — N is INTEGER. The order of the matrix A.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • DL — DL is DOUBLE PRECISION array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A.
  • D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
  • DU — DU is DOUBLE PRECISION array, dimension (N-1). The (n-1) elements of the first super-diagonal of U.
  • DU2 — DU2 is DOUBLE PRECISION array, dimension (N-2). The (n-2) elements of the second super-diagonal of U.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
  • B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the matrix of right hand side vectors B. On exit, B is overwritten by the solution vectors X.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

Author

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

Definition at line 127 of file dgtts2.f.

🧚 sgtts2 🧚

Full signature:

   subroutine sgtts2 (integer itrans, integer n, integer nrhs, real, dimension(
       * ) dl, real, dimension( * ) d, real, dimension( * ) du, real,
       dimension( * ) du2, integer, dimension( * ) ipiv, real, dimension( ldb,
       * ) b, integer ldb)

SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose: SGTTS2 solves one of the systems of equations A*X = B or A**T*X = B, with a tridiagonal matrix A using the LU factorization computed by SGTTRF.

Parameters

  • ITRANS — ITRANS is INTEGER. Specifies the form of the system of equations:
    • = 0: A * X = B (No transpose)
    • = 1: A**T* X = B (Transpose)
    • = 2: A**T* X = B (Conjugate transpose = Transpose)
  • N — N is INTEGER. The order of the matrix A.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • DL — DL is REAL array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A.
  • D — D is REAL array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
  • DU — DU is REAL array, dimension (N-1). The (n-1) elements of the first super-diagonal of U.
  • DU2 — DU2 is REAL array, dimension (N-2). The (n-2) elements of the second super-diagonal of U.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
  • B — B is REAL array, dimension (LDB,NRHS). On entry, the matrix of right hand side vectors B. On exit, B is overwritten by the solution vectors X.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

Author

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

Definition at line 127 of file sgtts2.f.

🧚 zgtts2 🧚

Full signature:

   subroutine zgtts2 (integer itrans, integer n, integer nrhs, complex*16,
       dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension(
       * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv,
       complex*16, dimension( ldb, * ) b, integer ldb)

ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose: ZGTTS2 solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, with a tridiagonal matrix A using the LU factorization computed by ZGTTRF.

Parameters

  • ITRANS — ITRANS is INTEGER. Specifies the form of the system of equations:
    • = 0: A * X = B (No transpose)
    • = 1: A**T * X = B (Transpose)
    • = 2: A**H * X = B (Conjugate transpose)
  • N — N is INTEGER. The order of the matrix A.
  • NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • DL — DL is COMPLEX*16 array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A.
  • D —
  • D — bestie this one's a COMPLEX*16 array, dimension (N), and it holds the n diagonal elements of the upper triangular matrix U from the LU factorization of A. 👑
  • DU — COMPLEX*16 array, dimension (N-1), carrying the (n-1) elements of the first super-diagonal of U. the way it's literally one shorter than D… iconic behavior. ✨
  • DU2 — COMPLEX*16 array, dimension (N-2), holding the (n-2) elements of the second super-diagonal of U. shrinking again, it's giving diminishing returns 💅
  • IPIV — INTEGER array, dimension (N), the pivot indices, no cap. for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). and here's the tea: IPIV(i) will always be either i or i+1, and IPIV(i) = i indicates a row interchange was not required. so it's either "swapped" or "we were fine actually." 🫶
  • B — COMPLEX*16 array, dimension (LDB,NRHS). on entry, it's the matrix of right hand side vectors B. on exit? B is overwritten by the solution vectors X. so like… glow-up in place, the original is gone, don't come looking for it 😭
  • LDB — INTEGER, the leading dimension of the array B, and it has one rule: LDB >= max(1,N). that's it. that's the whole vibe check. ✅

👑 Author 👑

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

four absolute legends, all credited, all respected 🫡

Definition at line 127 of file zgtts2.f. — yes, that's literally where it lives, bestie, go look 🔍

🌸 Author 🌸 (yes, again — the docs said it twice, so we say it twice)

Generated automatically by Doxygen for LAPACK from the source code. like, the robots made this one. respect to the robots honestly 🤖💖

okay that's the whole page!! you made it to the end, I'm so proud of you 🎀 this was LAPACK, Version 3.12.0, and the page is gtts2(3) — no date stamp on this one, just the version and the vibes. now go forth and factorize, bestie, you're literally the main character of linear algebra 💜🦋✨

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