gtsv(3)

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version 3.12.1 · 9 versions
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💖 gtsv(3) — factor and solve 💖

from the Library Functions Manual, bestie, and this page is literally the tridiagonal solver headquarters. ✨

✨ NAME ✨

gtsv - gtsv: factor and solve 💅

🦋 SYNOPSIS 🦋

🌸 Functions 🌸

  • subroutine cgtsv (n, nrhs, dl, d, du, b, ldb, info) — CGTSV computes the solution to system of linear equations A * X = B for GT matrices. ✨
  • subroutine dgtsv (n, nrhs, dl, d, du, b, ldb, info) — DGTSV computes the solution to system of linear equations A * X = B for GT matrices. 💫
  • subroutine sgtsv (n, nrhs, dl, d, du, b, ldb, info) — SGTSV computes the solution to system of linear equations A * X = B for GT matrices. 🌟
  • subroutine zgtsv (n, nrhs, dl, d, du, b, ldb, info) — ZGTSV computes the solution to system of linear equations A * X = B for GT matrices. 🎀

🌈 Detailed Description 🌈

okay so this is the big “where the functions actually live” zone. no extra lore here, just the docs. 🫶

💅 Function Documentation 💅

💜 cgtsv — the COMPLEX one 💜

subroutine cgtsv (integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( ldb, * ) b, integer ldb, integer info)

CGTSV computes the solution to system of linear equations A * X = B for GT matrices. slay. ✨

Purpose: 🎯

CGTSV solves the equation

A*X = B,

where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting.

Note that the equation A**T *X = B may be solved by interchanging the order of the arguments DU and DL. 👀

Parameters 🧸

  • N — N is INTEGER. The order of the matrix A. N >= 0. 💅
  • 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 a COMPLEX array, dimension (N-1). On entry, DL must contain the (n-1) subdiagonal elements of A. On exit, DL is overwritten by the (n-2) elements of the second superdiagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2). 🌀
  • D — D is a COMPLEX array, dimension (N). On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of U. 🌟
  • DU — DU is a COMPLEX array, dimension (N-1). On entry, DU must contain the (n-1) superdiagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first superdiagonal of U. 💫
  • B — B is a COMPLEX array, dimension (LDB,NRHS). On entry, this is the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, it’s the N-by-NRHS solution matrix X. 🎉
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🫶
  • INFO — INFO is INTEGER. The receipts:
    • = 0: successful exit 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value 🚨
    • > 0: if INFO = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = N. 😭

Author 👑

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

Definition: at line 123 of file cgtsv.f. 📌

💙 dgtsv — the DOUBLE PRECISION one 💙

subroutine dgtsv (integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DGTSV computes the solution to system of linear equations A * X = B for GT matrices. no cap. 💫

Purpose: 🎯

DGTSV solves the equation

A*X = B,

where A is an n by n tridiagonal matrix, by Gaussian elimination with partial pivoting.

Note that the equation A**T*X = B may be solved by interchanging the order of the arguments DU and DL. 👀

Parameters 🧸

  • N — N is INTEGER. The order of the matrix A. N >= 0. 💅
  • 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 a DOUBLE PRECISION array, dimension (N-1). On entry, DL must contain the (n-1) sub-diagonal elements of A. On exit, DL is overwritten by the (n-2) elements of the second super-diagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2). 🌀
  • D — D is a DOUBLE PRECISION array, dimension (N). On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of U. 🌟
  • DU — DU is a DOUBLE PRECISION array, dimension (N-1). On entry, DU must contain the (n-1) super-diagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first super-diagonal of U. 💫
  • B — B is a DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, this is the N by NRHS matrix of right hand side matrix B. On exit, if INFO = 0, it’s the N by NRHS solution matrix X. 🎉
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🫶
  • INFO — INFO is INTEGER. The receipts:
    • = 0: successful exit 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value 🚨
    • > 0: if INFO = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = N. 😭

Author 👑

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

Definition: at line 126 of file dgtsv.f. 📌

💚 sgtsv — the REAL one 💚

subroutine sgtsv (integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( ldb, * ) b, integer ldb, integer info)

SGTSV computes the solution to system of linear equations A * X = B for GT matrices. iconic. 🌟

Purpose: 🎯

SGTSV solves the equation

A*X = B,

where A is an n by n tridiagonal matrix, by Gaussian elimination with partial pivoting.

Note that the equation A**T*X = B may be solved by interchanging the order of the arguments DU and DL. 👀

Parameters 🧸

  • N — N is INTEGER. The order of the matrix A. N >= 0. 💅
  • 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 a REAL array, dimension (N-1). On entry, DL must contain the (n-1) sub-diagonal elements of A. On exit, DL is overwritten by the (n-2) elements of the second super-diagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2). 🌀
  • D — D is a REAL array, dimension (N). On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of U. 🌟
  • DU — DU is a REAL array, dimension (N-1). On entry, DU must contain the (n-1) super-diagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first super-diagonal of U. 💫
  • B — B is a REAL array, dimension (LDB,NRHS). On entry, this is the N by NRHS matrix of right hand side matrix B. On exit, if INFO = 0, it’s the N by NRHS solution matrix X. 🎉
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🫶
  • INFO — INFO is INTEGER. The receipts:
    • = 0: successful exit 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value 🚨
    • > 0: if INFO = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = N. 😭

Author 👑

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

Definition: at line 126 of file sgtsv.f. 📌

💜 zgtsv — the COMPLEX*16 one 💜

subroutine zgtsv (integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZGTSV computes the solution to system of linear equations A * X = B for GT matrices. main character energy. ✨

Purpose: 🎯

ZGTSV solves the equation

A*X = B,

where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting.

Note that the equation A**T *X = B may be solved by interchanging the order of the arguments DU and DL. 👀

Parameters 🧸

  • N — N is INTEGER. The order of the matrix A. N >= 0. 💅
  • 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 a COMPLEX*16 array, dimension (N-1). On entry, DL must contain the (n-1) subdiagonal elements of A. On exit, DL is overwritten by the (n-2) elements of the second superdiagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2). 🌀
  • D — D is a COMPLEX*16 array, dimension (N). On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of U. 🌟
  • DU

Here’s the rest of the parameter cast, bestie — every detail intact, no cap:

  • DU — COMPLEX*16 array, dimension (N-1). On entry, DU must contain the (n-1) superdiagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first superdiagonal of U. 💅
  • B — COMPLEX*16 array, dimension (LDB,NRHS). On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. ✨
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🫶
  • INFO — INTEGER. The exit-status vibe check:
    • = 0: successful exit — slay. 👑
    • < 0: if INFO = -i, the i-th argument had an illegal value — not iconic. 😭
    • > 0: if INFO = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = N. 🚨

🎀 Author 🎀

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

Definition at line 123 of file zgtsv.f. 📌

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. 💻

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