realGTcomputational(3)

📦

version 3.11.0 · 2 versions

3.11.0 · debian bookworm (latest)
3.10.0 · ubuntu jammy

realGTcomputational(3) 💅

okay so welcome to the LAPACK group chat for realGTcomputational, bestie. This is the real computational crew for GT matrices. No cap, it's giving linear algebra but make it cute. ✨

🌸 NAME 🌸

realGTcomputational — real. That's the name, that's the vibe. Periodt.

✨ SYNOPSIS ✨

Functions:

subroutine sgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, IWORK, INFO) — SGTCON
subroutine sgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) — SGTRFS
subroutine sgttrf (N, DL, D, DU, DU2, IPIV, INFO) — SGTTRF
subroutine sgttrs (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO) — SGTTRS
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.

🦋 Detailed Description 🦋

This is the group of real computational functions for GT matrices. That's it, that's the whole assignment. 💖

🎀 Function Documentation 🎀

💜 subroutine sgtcon 💜

subroutine sgtcon (character NORM, integer N, real, dimension( * ) DL, real,
       dimension( * ) D, real, dimension( * ) DU, real, dimension( * ) DU2,
       integer, dimension( * ) IPIV, real ANORM, real RCOND, real, dimension( *
       ) WORK, integer, dimension( * ) IWORK, integer INFO)
       SGTCON

Purpose

SGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

No cap, it's the condition-number detective. 🔍

Parameters

NORM — NORM is CHARACTER*1. Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
- = '1' or 'O': 1-norm;
- = 'I': Infinity-norm.
N — N is INTEGER. The order of the matrix A. N >= 0.
DL — DL is REAL array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.
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 superdiagonal of U.
DU2 — DU2 is REAL array, dimension (N-2). The (n-2) elements of the second superdiagonal 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.
ANORM — ANORM is REAL. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.
RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
WORK — WORK is REAL array, dimension (2*N)
IWORK — IWORK is INTEGER array, dimension (N)
INFO — INFO is INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value

Author

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

💜 subroutine sgtrfs 💜

subroutine sgtrfs (character TRANS, integer N, integer NRHS, real,
       dimension( * ) DL, real, dimension( * ) D, real, dimension( * ) DU,
       real, dimension( * ) DLF, real, dimension( * ) DF, real, dimension( * )
       DUF, real, dimension( * ) DU2, integer, dimension( * ) IPIV, real,
       dimension( ldb, * ) B, integer LDB, real, dimension( ldx, * ) X, integer
       LDX, real, dimension( * ) FERR, real, dimension( * ) BERR, real,
       dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)
       SGTRFS

Purpose

SGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution.

It's like a glow-up for your solution, plus receipts. 💅

Parameters

TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
- = 'N': A * X = B (No transpose)
- = 'T': A**T * X = B (Transpose)
- = 'C': A**H * X = B (Conjugate transpose = Transpose)
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 REAL array, dimension (N-1). The (n-1) subdiagonal elements of A.
D — D is REAL array, dimension (N). The diagonal elements of A.
DU — DU is REAL array, dimension (N-1). The (n-1) superdiagonal elements of A.
DLF — DLF is REAL array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.
DF — DF is REAL array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUF — DUF is REAL array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
DU2 — DU2 is REAL array, dimension (N-2). The (n-2) elements of the second superdiagonal 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). The right hand side matrix B.
LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
X — X is REAL array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by SGTTRS. On exit, the improved solution matrix X.
LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
FERR — FERR is REAL array, dimension (NRHS). The estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
BERR — BERR is REAL array, dimension (NRHS). The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
WORK — WORK is REAL array, dimension (3*N)
IWORK — IWORK is INTEGER array, dimension (N)
INFO — INFO is INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters

ITMAX is the maximum number of steps of iterative refinement.

Author

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

💜 subroutine sgttrf 💜

subroutine sgttrf (integer N, real, dimension( * ) DL, real, dimension( * )
       D, real, dimension( * ) DU, real, dimension( * ) DU2, integer,
       dimension( * ) IPIV, integer INFO)
       SGTTRF

Purpose

SGTTRF computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges.

The factorization has the form

   A = L * U

where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals.

It's giving factorization realness. 🔥

Parameters

N — N is INTEGER. The order of the matrix A.
DL — DL is 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-1) multipliers that define the matrix L from the LU factorization of A.
D — D is 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 the upper triangular matrix U from the LU factorization of A.
DU — DU is 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.
DU2 — DU2 is REAL array, dimension (N-2). On exit, DU2 is overwritten by 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.
INFO — INFO is INTEGER
- = 0: successful exit
- < 0: if INFO = -k, the k-th argument had an illegal value
- > 0: if INFO = k, U(k,k) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Author

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

💖 `sgttrs` 💖

   subroutine sgttrs (character TRANS, 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, integer INFO)
       SGTTRS

Okay bestie, meet SGTTRS 💅. She solves one of these systems of equations:

A*X = B  or  A**T*X = B,

with a tridiagonal matrix A using the LU factorization computed by SGTTRF. No cap, she's just that girl. ✨

🌸 Purpose 🌸

SGTTRS 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. Periodt.

🎀 Parameters 🎀

TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations.
- = 'N': A * X = B (No transpose)
- = 'T': A**T* X = B (Transpose)
- = 'C': 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). 🌟
INFO — INFO is INTEGER.
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value 😭

👑 Author 👑

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

🌈 `sgtts2` 🌈

   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. Periodt.

🎀 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.

👑 Author 👑

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💖 That's the tea, bestie! This was LAPACK version 3.11.0, generated Sun Nov 27 2022, and you're reading realGTcomputational(3). Byeee! 💅✨

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💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash on 2026-10-14: a language model's rewrite of the original, under its terms

realGTcomputational(3)

realGTcomputational(3) 💅

🌸 NAME 🌸

✨ SYNOPSIS ✨

🦋 Detailed Description 🦋

🎀 Function Documentation 🎀

💜 subroutine sgtcon 💜

Purpose

Parameters

Author

💜 subroutine sgtrfs 💜

Purpose

Parameters

Internal Parameters

Author

💜 subroutine sgttrf 💜

Purpose

Parameters

Author

💖 sgttrs 💖

🌸 Purpose 🌸

🎀 Parameters 🎀

👑 Author 👑

🌈 sgtts2 🌈

🌸 Purpose 🌸

🎀 Parameters 🎀

👑 Author 👑

👑 Author 👑

💖 `sgttrs` 💖

🌈 `sgtts2` 🌈