gtsvx(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

🎀 gtsvx(3) — Library Functions Manual 🎀

Bestie, this is the gtsvx(3) page, and the name is gtsvx — gtsvx: factor and solve, expert ✨. It’s giving “linear algebra but make it expert mode,” and honestly? Iconic.

✨ NAME ✨

gtsvx — gtsvx: factor and solve, expert

🌈 SYNOPSIS 🌈

💅 Functions 💅

subroutine cgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) — CGTSVX computes the solution to system of linear equations A * X = B for GT matrices
subroutine dgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) — DGTSVX computes the solution to system of linear equations A * X = B for GT matrices
subroutine sgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info) — SGTSVX computes the solution to system of linear equations A * X = B for GT matrices
subroutine zgtsvx (fact, trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info) — ZGTSVX computes the solution to system of linear equations A * X = B for GT matrices

🦋 Detailed Description 🦋

Okay so this is the detailed-description zone, and it rolls straight into the function documentation. Let’s get into the cgtsvx of it all. 💖

💜 Function Documentation 💜

🧚 subroutine cgtsvx 🧚

subroutine cgtsvx (character fact, character trans, integer n, integer nrhs,
    complex, dimension( * ) dl, complex, dimension( * ) d, complex,
    dimension( * ) du, complex, dimension( * ) dlf, complex, dimension( * )
    df, complex, dimension( * ) duf, complex, dimension( * ) du2, integer,
    dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,
    complex, dimension( ldx, * ) x, integer ldx, real rcond, real,
    dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * )
    work, real, dimension( * ) rwork, integer info)

CGTSVX computes the solution to system of linear equations A * X = B for GT matrices

🎯 Purpose 🎯

Bestie, CGTSVX is out here using the LU factorization to solve a complex system of linear equations:

A * X = B
A**T * X = B
A**H * X = B

…where A is a tridiagonal matrix of order N, and X and B are N-by-NRHS matrices. It also provides error bounds on the solution and a condition estimate. Obsessed. ✨

🌸 Description 🌸

Here’s the step-by-step, bestie:

If FACT = 'N', the LU decomposition is used to factor the matrix A as 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. 💅
If some U(i,i)=0, so that U is exactly singular, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below. 🫶
The system of equations is solved for X using the factored form of A.
Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it. 🌟

🧸 Parameters 🧸

FACT — FACT is CHARACTER*1. It specifies whether or not the factored form of A has been supplied on entry.
- = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not be modified.
- = 'N': The matrix will be copied to DLF, DF, and DUF and factored.
TRANS — TRANS is CHARACTER*1. It 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)
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 COMPLEX array, dimension (N-1). The (n-1) subdiagonal elements of A.
D — D is COMPLEX array, dimension (N). The n diagonal elements of A.
DU — DU is COMPLEX array, dimension (N-1). The (n-1) superdiagonal elements of A.
DLF — DLF is COMPLEX array, dimension (N-1).
- If FACT = 'F', then DLF is an input argument and on entry contains the (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.
- If FACT = 'N', then DLF is an output argument and on exit contains the (n-1) multipliers that define the matrix L from the LU factorization of A.
DF — DF is COMPLEX array, dimension (N).
- If FACT = 'F', then DF is an input argument and on entry contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
- If FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUF — DUF is COMPLEX array, dimension (N-1).
- If FACT = 'F', then DUF is an input argument and on entry contains the (n-1) elements of the first superdiagonal of U.
- If FACT = 'N', then DUF is an output argument and on exit contains the (n-1) elements of the first superdiagonal of U.
DU2 — DU2 is COMPLEX array, dimension (N-2).
- If FACT = 'F', then DU2 is an input argument and on entry contains the (n-2) elements of the second superdiagonal of U.
- If FACT = 'N', then DU2 is an output argument and on exit contains the (n-2) elements of the second superdiagonal of U.
IPIV — IPIV is INTEGER array, dimension (N).
- If FACT = 'F', then IPIV is an input argument and on entry contains the pivot indices from the LU factorization of A as computed by CGTTRF.
- If FACT = 'N', then IPIV is an output argument and on exit contains the pivot indices from the LU factorization of A; 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). The N-by-NRHS right hand side matrix B.
LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
X — X is COMPLEX array, dimension (LDX,NRHS). If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
RCOND — RCOND is REAL. The estimate of the reciprocal condition number of the matrix A. If RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. This condition is indicated by a return code of INFO > 0.
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 COMPLEX array, dimension (2*N).
RWORK — RWORK is REAL array, dimension (N).
INFO — INFO is INTEGER.
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, and i is
  - <= N: U(i,i) is exactly zero. The factorization has not been completed unless i = N, but the factor U is exactly singular, so the solution and error bounds could not be computed. RCOND = 0 is returned.
  - = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. Nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest.

🌟 Author 🌟

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

Definition at line 291 of file cgtsvx.f.

   subroutine dgtsvx (character fact, character trans, integer n, integer nrhs,
       double precision, dimension( * ) dl, double precision, dimension( * ) d,
       double precision, dimension( * ) du, double precision, dimension( * )
       dlf, double precision, dimension( * ) df, double precision, dimension( *
       ) duf, double precision, dimension( * ) du2, integer, dimension( * )
       ipiv, double precision, dimension( ldb, * ) b, integer ldb, double
       precision, dimension( ldx, * ) x, integer ldx, double precision rcond,
       double precision, dimension( * ) ferr, double precision, dimension( * )
       berr, double precision, dimension( * ) work, integer, dimension( * )
       iwork, integer info)

DGTSVX computes the solution to system of linear equations A * X = B for GT matrices. iconic behavior, honestly 💅

🎯 Purpose

Okay so DGTSVX uses the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, where A is a tridiagonal matrix of order N and X and B are N-by-NRHS matrices.

Error bounds on the solution and a condition estimate are also provided. the full package, bestie ✨

🔍 Description

The following steps are performed:

If FACT = 'N', the LU decomposition is used to factor the matrix A as 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.
If some U(i,i)=0, so that U is exactly singular, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below.
The system of equations is solved for X using the factored form of A.
Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it. glow-up era 🦋

🧩 Parameters

FACT — is CHARACTER*1, and it specifies whether or not the factored form of A has been supplied on entry.
- = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not be modified.
- = 'N': The matrix will be copied to DLF, DF, and DUF and factored.
TRANS — is CHARACTER*1, and it 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 — is INTEGER, and it is the order of the matrix A. N >= 0.
NRHS — is INTEGER, and it is the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
DL — is DOUBLE PRECISION array, dimension (N-1). The (n-1) subdiagonal elements of A. the under-edge crew 🌊
D — is DOUBLE PRECISION array, dimension (N). The n diagonal elements of A. main character diagonal ⭐
DU — is DOUBLE PRECISION array, dimension (N-1). The (n-1) superdiagonal elements of A.
DLF — is DOUBLE PRECISION array, dimension (N-1).
- If FACT = 'F', then DLF is an input argument and on entry contains the (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF.
- If FACT = 'N', then DLF is an output argument and on exit contains the (n-1) multipliers that define the matrix L from the LU factorization of A.
DF — is DOUBLE PRECISION array, dimension (N).
- If FACT = 'F', then DF is an input argument and on entry contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
- If FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUF — is DOUBLE PRECISION array, dimension (N-1).
- If FACT = 'F', then DUF is an input argument and on entry contains the (n-1) elements of the first superdiagonal of U.
- If FACT = 'N', then DUF is an output argument and on exit contains the (n-1) elements of the first superdiagonal of U.
DU2 — is DOUBLE PRECISION array, dimension (N-2).
- If FACT = 'F', then DU2 is an input argument and on entry contains the (n-2) elements of the second superdiagonal of U.
- If FACT = 'N', then DU2 is an output argument and on exit contains the (n-2) elements of the second superdiagonal of U.
IPIV — is INTEGER array, dimension (N).
- If FACT = 'F', then IPIV is an input argument and on entry contains the pivot indices from the LU factorization of A as computed by DGTTRF.
- If FACT = 'N', then IPIV is an output argument and on exit contains the pivot indices from the LU factorization of A; 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. pivot tea, spilled 🫖
B — is DOUBLE PRECISION array, dimension (LDB,NRHS). The N-by-NRHS right hand side matrix B.
LDB — is INTEGER, and it is the leading dimension of the array B. LDB >= max(1,N).
X — is DOUBLE PRECISION array, dimension (LDX,NRHS). If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. the answer matrix, periodt 💖
LDX — is INTEGER, and it is the leading dimension of the array X. LDX >= max(1,N).
RCOND — is DOUBLE PRECISION. The estimate of the reciprocal condition number of the matrix A. If RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. This condition is indicated by a return code of INFO > 0.
FERR — is DOUBLE PRECISION 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. she’s reliable but dramatic 😭
BERR — is DOUBLE PRECISION 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 — is DOUBLE PRECISION array, dimension (3*N).
IWORK — is INTEGER array, dimension (N).
INFO — is INTEGER.
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, and i is
  - <= N: U(i,i) is exactly zero. The factorization has not been completed unless i = N, but the factor U is exactly singular, so the solution and error bounds could not be computed. RCOND = 0 is returned.
  - = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. Nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest. so we still compute, bestie 💅

👑 Author

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

Definition at line 290 of file dgtsvx.f.

   subroutine sgtsvx (character fact, 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 rcond, real, dimension( * ) ferr, real, dimension( * ) berr,
       real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SGTSVX computes the solution to system of linear equations A * X = B for GT matrices. single precision, same slay ✨

🎯 Purpose

SGTSVX uses the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, where A is a tridiagonal matrix of order N and X and B are N-by-NRHS matrices.

Error bounds on the solution and a condition estimate are also provided. she’s thorough 🦋

🧠 Description

okay so here's the step-by-step of what actually goes down:

if FACT = 'N', the LU decomposition is used to factor the matrix A as 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. slay.
if some U(i,i)=0, so that U is exactly singular, then the routine returns with INFO = i. otherwise, the factored form of A is used to estimate the condition number of the matrix A. if the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but bestie the routine still goes on to solve for X and compute error bounds as described below. no cap.
the system of equations is solved for X using the factored form of A. periodt.
iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it. iconic.

💅 Parameters

FACT — this is CHARACTER*1. it tells us whether or not the factored form of A has been supplied on entry. = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not be modified. = 'N': the matrix will be copied to DLF, DF, and DUF and factored.
TRANS — 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 — INTEGER. the order of the matrix A. N >= 0.
NRHS — INTEGER. the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
DL — REAL array, dimension (N-1). the (n-1) subdiagonal elements of A.
D — REAL array, dimension (N). the n diagonal elements of A.
DU — REAL array, dimension (N-1). the (n-1) superdiagonal elements of A.
DLF — REAL array, dimension (N-1). if FACT = 'F', then DLF is an input argument and on entry contains the (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. if FACT = 'N', then DLF is an output argument and on exit contains the (n-1) multipliers that define the matrix L from the LU factorization of A.
DF — REAL array, dimension (N). if FACT = 'F', then DF is an input argument and on entry contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A. if FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUF — REAL array, dimension (N-1). if FACT = 'F', then DUF is an input argument and on entry contains the (n-1) elements of the first superdiagonal of U. if FACT = 'N', then DUF is an output argument and on exit contains the (n-1) elements of the first superdiagonal of U.
DU2 — REAL array, dimension (N-2). if FACT = 'F', then DU2 is an input argument and on entry contains the (n-2) elements of the second superdiagonal of U. if FACT = 'N', then DU2 is an output argument and on exit contains the (n-2) elements of the second superdiagonal of U.
IPIV — INTEGER array, dimension (N). if FACT = 'F', then IPIV is an input argument and on entry contains the pivot indices from the LU factorization of A as computed by SGTTRF. if FACT = 'N', then IPIV is an output argument and on exit contains the pivot indices from the LU factorization of A; 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 — REAL array, dimension (LDB,NRHS). the N-by-NRHS right hand side matrix B.
LDB — INTEGER. the leading dimension of the array B. LDB >= max(1,N).
X — REAL array, dimension (LDX,NRHS). if INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
LDX — INTEGER. the leading dimension of the array X. LDX >= max(1,N).
RCOND — REAL. the estimate of the reciprocal condition number of the matrix A. if RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. this condition is indicated by a return code of INFO > 0.
FERR — 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. lowkey useful.
BERR — 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 — REAL array, dimension (3*N).
IWORK — INTEGER array, dimension (N).
INFO — INTEGER. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

0: if INFO = i, and i is

    <= N: U(i,i) is exactly zero. the factorization has not been completed unless i = N, but the factor U is exactly singular, so the solution and error bounds could not be computed. RCOND = 0 is returned.     = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest. 💀

🫶 Author

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

Definition at line 290 of file sgtsvx.f.

🦋 `zgtsvx`

subroutine zgtsvx (character fact, character trans, integer n, integer nrhs,
    complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16,
    dimension( * ) du, complex*16, dimension( * ) dlf, complex*16,
    dimension( * ) df, complex*16, dimension( * ) duf, complex*16,
    dimension( * ) du2, integer, dimension( * ) ipiv, complex*16, dimension(
    ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx,
    double precision rcond, double precision, dimension( * ) ferr, double
    precision, dimension( * ) berr, complex*16, dimension( * ) work, double
    precision, dimension( * ) rwork, integer info)

ZGTSVX computes the solution to system of linear equations A * X = B for GT matrices. periodt.

✨ Purpose

okay so ZGTSVX uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, where A is a tridiagonal matrix of order N and X and B are N-by-NRHS matrices.

error bounds on the solution and a condition estimate are also provided. we love a thorough queen. 💅

🌸 Description

the following steps are performed:

if FACT = 'N', the LU decomposition is used to factor the matrix A as 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. slay.
if some U(i,i)=0, so that U is exactly singular, then the routine returns with INFO = i. otherwise, the factored form of A is used to estimate the condition number of the matrix A. if the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below. no cap.
the system of equations is solved for X using the factored form of A. periodt.
iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it. iconic.

💅 Parameters

FACT

Picking up right at FACT, bestie:

FACT — CHARACTER*1. Specifies whether or not the factored form of A has been supplied on entry. = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not be modified. = 'N': the matrix will be copied to DLF, DF, and DUF and factored. 🫶
TRANS — 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). 🔥
N — INTEGER. The order of the matrix A. N >= 0. ✨
NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. 💖
DL — COMPLEX*16 array, dimension (N-1). The (n-1) subdiagonal elements of A. 🦋
D — COMPLEX*16 array, dimension (N). The n diagonal elements of A. 🎀
DU — COMPLEX*16 array, dimension (N-1). The (n-1) superdiagonal elements of A. 🌸
DLF — COMPLEX*16 array, dimension (N-1). If FACT = 'F', then DLF is an input argument and on entry contains the (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF. If FACT = 'N', then DLF is an output argument and on exit contains the (n-1) multipliers that define the matrix L from the LU factorization of A. 💅
DF — COMPLEX*16 array, dimension (N). If FACT = 'F', then DF is an input argument and on entry contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A. If FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A. 👑
DUF — COMPLEX*16 array, dimension (N-1). If FACT = 'F', then DUF is an input argument and on entry contains the (n-1) elements of the first superdiagonal of U. If FACT = 'N', then DUF is an output argument and on exit contains the (n-1) elements of the first superdiagonal of U. 🌈
DU2 — COMPLEX*16 array, dimension (N-2). If FACT = 'F', then DU2 is an input argument and on entry contains the (n-2) elements of the second superdiagonal of U. If FACT = 'N', then DU2 is an output argument and on exit contains the (n-2) elements of the second superdiagonal of U. ⭐
IPIV — INTEGER array, dimension (N). If FACT = 'F', then IPIV is an input argument and on entry contains the pivot indices from the LU factorization of A as computed by ZGTTRF. If FACT = 'N', then IPIV is an output argument and on exit contains the pivot indices from the LU factorization of A; 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 — COMPLEX*16 array, dimension (LDB,NRHS). The N-by-NRHS right hand side matrix B. 🍓
LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🧚
X — COMPLEX*16 array, dimension (LDX,NRHS). If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. 💜
LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N). 🙈
RCOND — DOUBLE PRECISION. The estimate of the reciprocal condition number of the matrix A. If RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. This condition is indicated by a return code of INFO > 0. 😭
FERR — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — COMPLEX*16 array, dimension (2*N). 🫶
RWORK — DOUBLE PRECISION array, dimension (N). ✨
INFO — INTEGER.
- = 0: successful exit.
- < 0: if INFO = -i, the i-th argument had an illegal value.
- > 0: if INFO = i, and i is:
  - <= N: U(i,i) is exactly zero. The factorization has not been completed unless i = N, but the factor U is exactly singular, so the solution and error bounds could not be computed. RCOND = 0 is returned.
  - = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. Nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest.

Author 👑

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

Definition at line 291 of file zgtsvx.f.

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gtsvx(3)

🎀 gtsvx(3) — Library Functions Manual 🎀

✨ NAME ✨

🌈 SYNOPSIS 🌈

💅 Functions 💅

🦋 Detailed Description 🦋

💜 Function Documentation 💜

🧚 subroutine cgtsvx 🧚

🎯 Purpose 🎯

🌸 Description 🌸

🧸 Parameters 🧸

🌟 Author 🌟

🎯 Purpose

🔍 Description

🧩 Parameters

👑 Author

🎯 Purpose

🧠 Description

💅 Parameters

🫶 Author

🦋 zgtsvx

✨ Purpose

🌸 Description

💅 Parameters

Author 👑

Author (Doxygen's little note) 🌸

🦋 `zgtsvx`