dblgesylv(3)

📦
version 1.1.2 · 3 versions
, in fedora 43

💅 dblgesylv(3) 💅

okay bestie, you clicked into the MEPACK page for dblgesylv(3) and honestly? it's giving ✨linear algebra main character energy✨. it's a long one so we're doing this in parts — this is part 1, don't wander off 🫶

🎀 NAME 🎀

  • dblgesylv — Double Precision
  • Double Precision routines for standard Sylvester equations.

🦋 SYNOPSIS 🦋

Functions

subroutine dla_gesylv (facta, factb, transa, transb, sgn, m, n, a, lda,
    b, ldb, qa, ldqa, qb, ldqb, x, ldx, scale, work, ldwork, info)

Frontend for the solution of Standard Sylvester Equations. 👑

subroutine dla_gesylv2 (facta, factb, transa, transb, sgn, m, n, a, lda,
    b, ldb, qa, ldqa, qb, ldqb, x, ldx, scale, work, ldwork, info)

Frontend for the solution of Standard Sylvester Equations. 💖

subroutine dla_gesylv2_refine (transa, transb, guess, sgn, m, n, a, lda,
    b, ldb, x, ldx, y, ldy, as, ldas, bs, ldbs, q, ldq, u, ldu, maxit,
    tau, convlog, work, ldwork, info)

Iterative Refinement for the standard Sylvester Equations. 🔁

subroutine dla_gesylv_refine (transa, transb, guess, sgn, m, n, a, lda,
    b, ldb, x, ldx, y, ldy, as, ldas, bs, ldbs, q, ldq, u, ldu, maxit,
    tau, convlog, work, ldwork, info)

Iterative Refinement for the standard Sylvester Equations. 🔁

🌈 Detailed Description 🌈

Double Precision routines for standard Sylvester equations. yes bestie, that's literally it — the name is the whole vibe.

This subsection contains the solvers for standard Sylvester equations with general coefficient matrices in double precision arithmetic. The Schur decompositions are computed in double precision with the help of LAPACK. 🧮✨

📚 Function Documentation 📚

subroutine dla_gesylv (... )

Frontend for the solution of Standard Sylvester Equations.

💫 Purpose

DLA_GESYLV solves a Sylvester equation of the following forms:

op1(A) * X  +  X * op2(B) = SCALE * Y                              (1)

or

op1(A) * X  -  X * op2(B) = SCALE * Y                              (2)

where A is a M-by-M matrix and B is a N-by-N matrix. The right hand side Y and the solution X are M-by-N matrices. The matrices A and B can be either a general unreduced matrix or an upper Hessenberg form or a (quasi-) upper triangular factor. In the later case QA and QB provide the Schur-vectors of the matrices A and B. 🦋

🌸 Parameters

  • FACTA — CHARACTER. Tells you how matrix A is handed to you.
    • == 'N': The matrix A is given as a general matrix and its Schur decomposition A = QA*S*QA**T will be computed.
    • == 'F': The matrix A is given as its Schur decomposition in terms of S and QA, form A = QA*S*QA**T.
    • == 'H': The matrix A is given as an upper Hessenberg form and its Schur decomposition A = QA*S*QA**T will be computed.
  • FACTB — CHARACTER. Tells you how matrix B is handed to you.
    • == 'N': The matrix B is given as a general matrix and its Schur decomposition B = QB*R*QB**T will be computed.
    • == 'F': The matrix B is given as its Schur decomposition in terms of R and QB, form B = QB*R*QB**T.
    • == 'H': The matrix B is given as an upper Hessenberg form and its Schur decomposition B = QB*R*QB**T will be computed.
  • TRANSA — CHARACTER. Specifies the form of the system of equations with respect to A:
    • == 'N': op1(A) = A
    • == 'T': op1(A) = A**T
  • TRANSB — CHARACTER. Specifies the form of the system of equations with respect to B:
    • == 'N': op2(B) = B,
    • == 'T': op2(B) = B**T
  • SGN — DOUBLE PRECISION, allowed values: +/-1. Specifies the sign between the two parts of the Sylvester equation. 💅
    • = 1 : Solve Equation (1)
    • == -1: Solve Equation (2)
  • M — INTEGER. The order of the matrices A and C. M >= 0.
  • N — INTEGER. The order of the matrices B and D. N >= 0.
  • A — DOUBLE PRECISION array, dimension (LDA,M).
    • If FACTA == , the matrix A is a general matrix and it is overwritten with its schur decomposition S.
    • If FACTA == , the matrix A contains its (quasi-) upper triangular matrix S being the Schur decomposition of A.
    • If FACTA == , the matrix A is an upper Hessenberg matrix and it is overwritten with its schur decomposition S.
not me noticing the character after FACTA == is just… missing in the source, bestie 😭 that's literally how the page ships, so that's how it stays.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • B — DOUBLE PRECISION array, dimension (LDB,N).
    • If FACTB == , the matrix B is a general matrix and it is overwritten with its schur decomposition R.
    • If FACTB == , the matrix B contains its (quasi-) upper triangular matrix R being the Schur decomposition of B.
    • If FACTB == , the matrix B is an upper Hessenberg matrix and it is overwritten with its schur decomposition R.
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • QA — DOUBLE PRECISION array, dimension (LDQA,M).
    • If FACTA == , the matrix QA is an empty M-by-M matrix on input and contains the Schur vectors of A on output.
    • If FACTA == , the matrix QA contains the Schur vectors of A.
    • If FACTA == , the matrix QA is an empty M-by-M matrix on input and contains the Schur vectors of A on output.
  • LDQA — INTEGER. The leading dimension of the array QA. LDQA >= max(1,M).
  • QB — DOUBLE PRECISION array, dimension (LDQB,N).
    • If FACTB == , the matrix QB is an empty N-by-N matrix on input and contains the Schur vectors of B on output.
    • If FACTB == , the matrix QB contains the Schur vectors of B.
    • If FACTB == , the matrix QB is an empty N-by-N matrix on input and contains the Schur vectors of B on output.
  • LDQB — INTEGER. The leading dimension of the array QB. LDQB >= max(1,N).
  • X — DOUBLE PRECISION array, dimension (LDX,N).
    • On input, the matrix X contains the right hand side Y.
    • On output, the matrix X contains the solution of Equation (1) or (2).
    • Right hand side Y and the solution X are M-by-N matrices.
  • LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,M).
  • SCALE — DOUBLE PRECISION. SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true. 🫶
  • WORK — DOUBLE PRECISION array, dimension (MAX(1,LDWORK)). Workspace for the algorithm. The optmimal workspace is given either by \ref mepack_memory_frontend or a previous call to the this routine with LDWORK === -1.
  • LDWORK — INTEGER. Size of the workspace for the algorithm. This can be determined by a call \ref mepack_memory_frontend. Alternatively, if LDWORK == -1 on input, the subroutine will return the required size of the workspace in LDWORK without performing any computations. 🧠
  • INFO — INTEGER.
    • == 0: successful exit 🎉
    • = 1: DHGEES failed
    • = 2: DLA_SORT_EV failed
    • = 3: DLA_TRLYAP_DAG failed
    • < 0: if INFO = -i, the i-th argument had an illegal value

👀 See also

  • DLA_TRSYLV_L3
  • DLA_TRSYLV_L3_2S
  • DLA_TRSYLV_DAG
  • DLA_TRSYLV_L2_UNOPT
  • DLA_TRSYLV_L2
  • DLA_TRSYLV_L2_REORDER
  • DLA_TRSYLV_L2_LOCAL_COPY
  • DLA_TRSYLV_L2_LOCAL_COPY_32
  • DLA_TRSYLV_L2_LOCAL_COPY_64
  • DLA_TRSYLV_L2_LOCAL_COPY_96
  • DLA_TRSYLV_L2_LOCAL_COPY_128

✍️ Author

Martin Koehler, MPI Magdeburg

📅 Date

October 2025

📍 Definition

Definition at line 250 of file dla_gesylv.f90.

subroutine dla_gesylv2 (... )

Frontend for the solution of Standard Sylvester Equations.

💫 Purpose

DLA_GESYLV2 solves a Sylvester equation of the following forms:

op1(A) * X * op2(B) +  X  = SCALE * Y                              (1)

or

op1(A) * X * op2(B) -  X  = SCALE * Y                              (2)

where A is a M-by-M matrix and B is a N-by-N matrix. The right hand side Y and the solution X are M-by-N matrices. The matrices A and B can be either a general unreduced matrix or an upper Hessenberg form or a (quasi-) upper triangular factor. In the later case QA and QB provide the Schur-vectors of the matrices A and B. 🦋

🌸 Parameters

  • FACTA
  • FACTA — CHARACTER 💅 okay so this one tells you how the matrix A is given, aka A's whole origin story.
    • == 'N': The matrix A is given as a general matrix and its Schur decomposition A = QA*S*QA**T will be computed. 🫶
    • == 'F': The matrix A is given as its Schur decomposition in terms of S and QA form A = QA*S*QA**T.
    • == 'H': The matrix A is given as an upper Hessenberg form and its Schur decomposition A = QA*S*QA**T will be computed.
  • FACTB — CHARACTER ✨ same energy as FACTA but for the matrix B, bestie.
    • == 'N': The matrix B is given as a general matrix and its Schur decomposition B = QB*R*QB**T will be computed.
    • == 'F': The matrix B is given as its Schur decomposition in terms of R and QB form B = QB*R*QB**T.
    • == 'H': The matrix B is given as an upper Hessenberg form and its Schur decomposition B = QB*R*QB**T will be computed.
  • TRANSA — CHARACTER 🌸 Specifies the form of the system of equations with respect to A:
    • == 'N': op1(A) = A
    • == 'T': op1(A) = A**T
  • TRANSB — CHARACTER 🦋 Specifies the form of the system of equations with respect to B:
    • == 'N': op2(B) = B,
    • == 'T': op2(B) = B**T
  • SGN — DOUBLE PRECISION, allowed values: +/-1 🎀 Specifies the sign between the two parts of the Sylvester equation, like which side of the relationship we're on.
    • = 1 : Solve Equation (1)
    • == -1: Solve Equation (2)
  • M — INTEGER 💜 The order of the matrices A and C. M >= 0.
  • N — INTEGER 💜 The order of the matrices B and D. N >= 0.
  • A — DOUBLE PRECISION array, dimension (LDA,M) ⭐
    • If FACTA == , the matrix A is a general matrix and it is overwritten with its schur decomposition S.
    • If FACTA == , the matrix A contains its (quasi-) upper triangular matrix S being the Schur decomposition of A.
    • If FACTA == , the matrix A is an upper Hessenberg matrix and it is overwritten with its schur decomposition S.
  • LDA — INTEGER 💅 The leading dimension of the array A. LDA >= max(1,M).
  • B — DOUBLE PRECISION array, dimension (LDB,N) ⭐
    • If FACTB == , the matrix B is a general matrix and it is overwritten with its schur decomposition R.
    • If FACTB == , the matrix B contains its (quasi-) upper triangular matrix R being the Schur decomposition of B.
    • If FACTB == , the matrix B is an upper Hessenberg matrix and it is overwritten with its schur decomposition R.
  • LDB — INTEGER 💅 The leading dimension of the array B. LDB >= max(1,N).
  • QA — DOUBLE PRECISION array, dimension (LDQA,M) 🌈
    • If FACTA == , the matrix QA is an empty M-by-M matrix on input and contains the Schur vectors of A on output.
    • If FACTA == , the matrix QA contains the Schur vectors of A.
    • If FACTA == , the matrix QA is an empty M-by-M matrix on input and contains the Schur vectors of A on output.
  • LDQA — INTEGER 💅 The leading dimension of the array QA. LDQA >= max(1,M).
  • QB — DOUBLE PRECISION array, dimension (LDQB,N) 🌈
    • If FACTB == , the matrix QB is an empty N-by-N matrix on input and contains the Schur vectors of B on output.
    • If FACTB == , the matrix QB contains the Schur vectors of B.
    • If FACTB == , the matrix QB is an empty N-by-N matrix on input and contains the Schur vectors of B on output.
  • LDQB — INTEGER 💅 The leading dimension of the array QB. LDQB >= max(1,N).
  • X — DOUBLE PRECISION array, dimension (LDX,N) 👑 On input, the matrix X contains the right hand side Y. On output, the matrix X contains the solution of Equation (1) or (2). Right hand side Y and the solution X are M-by-N matrices.
  • LDX — INTEGER 💅 The leading dimension of the array X. LDX >= max(1,M).
  • SCALE — DOUBLE PRECISION 🍓 SCALE is a scaling factor to prevent the overflow in the result. If INFO == 0 then SCALE is 1.0D0 otherwise if one of the inner systems could not be solved correctly, 0 < SCALE <= 1 holds true.
  • WORK — DOUBLE PRECISION array, dimension (MAX(1,LDWORK)) 🧚 Workspace for the algorithm. The optmimal workspace is given either by \ref mepack_memory_frontend or a previous call to the this routine with LDWORK === -1.
  • LDWORK — INTEGER 🌸 Size of the workspace for the algorithm. This can be determined by a call \ref mepack_memory_frontend. Alternatively, if LDWORK == -1 on input the subroutine will return the required size of the workspace in LDWORK without performing any computations.
  • INFO — INTEGER 💀 the receipts, bestie:
    • == 0: successful exit ✨
    • = 1: DHGEES failed
    • = 2: DLA_SORT_EV failed
    • = 3: DLA_TRLYAP_DAG failed
    • < 0: if INFO = -i, the i-th argument had an illegal value

🫶 See also 🫶

  • DLA_TRSYLV2_L3
  • DLA_TRSYLV2_L3_2S
  • DLA_TRSYLV2_DAG
  • DLA_TRSYLV2_L2_UNOPT
  • DLA_TRSYLV2_L2
  • DLA_TRSYLV2_L2_REORDER
  • DLA_TRSYLV2_L2_LOCAL_COPY
  • DLA_TRSYLV2_L2_LOCAL_COPY_32
  • DLA_TRSYLV2_L2_LOCAL_COPY_64
  • DLA_TRSYLV2_L2_LOCAL_COPY_96
  • DLA_TRSYLV2_L2_LOCAL_COPY_128

👑 Author 👑

Martin Koehler, MPI Magdeburg

🌸 Date 🌸

October 2025

Definition at line 250 of file dla_gesylv2.f90.

💖 subroutine dla_gesylv2_refine 💖

subroutine dla_gesylv2_refine (character, dimension(1) transa, character,
    dimension(1) transb, character, dimension(1) guess, double precision
    sgn, integer m, integer n, double precision, dimension(lda, *) a,
    integer lda, double precision, dimension(ldb, *) b, integer ldb, double
    precision, dimension ( ldx , * ) x, integer ldx, double precision,
    dimension(ldy, *) y, integer ldy, double precision, dimension(ldas, *)
    as, integer ldas, double precision, dimension(ldbs,*) bs, integer ldbs,
    double precision, dimension(ldq, *) q, integer ldq, double precision,
    dimension(ldu, *) u, integer ldu, integer maxit, double precision tau,
    double precision, dimension(*) convlog, double precision, dimension(*)
    work, integer ldwork, integer info)

Iterative Refinement for the Standard Sylvester Equations.

✨ Purpose ✨

DLA_GESYLV2_REFINE solves a Sylvester equation of the following forms

op1(A) * X * op2(B)  +  X = Y                              (1)

or

op1(A) * X * op2(B)  -  X = Y                              (2)

where A is a M-by-M matrix and B is a N-by-N matrix using iterative refinement. 🌀 The right hand side Y and the solution X are M-by-N matrices. The matrix A and B need to be given in the original form as well as in their Schur decomposition since both are required in the iterative refinement procedure. Like, both fits, both serve. No shortcuts. 💅

🎀 Parameters 🎀

  • TRANSA — CHARACTER 🌸 Specifies the form of the system of equations with respect to A:
    • == 'N': op1(A) = A
    • == 'T': op1(A) = A**T
  • TRANSB — CHARACTER 🌸 Specifies the form of the system of equations with respect to B:
    • == 'N': op2(B) = B,
    • == 'T': op2(B) = B**T
  • GUESS — CHARACTER ✨ Specifies whether X contains an initial guess or nor not.
    • = 'I': X contains an initial guess
    • = 'N': No initial guess, X is set to zero at the begin of the iteration.
  • SGN — DOUBLE PRECISION, allowed values: +/-1 🎀 Specifies the sign between both terms.
  • M — INTEGER 💜 The order of the matrix A. M >= 0.
  • N — INTEGER 💜 The order of the matrix B. N >= 0.
  • A — DOUBLE PRECISION array, dimension (LDA,M) ⭐ The array A contains the original matrix A defining the eqaution.
  • LDA — INTEGER 💅 The leading dimension of the array A. LDA >= max(1,M).
  • B — DOUBLE PRECISION array, dimension (LDB,N) ⭐ The array B contains the original matrix B defining the eqaution.
  • LDB — INTEGER 💅 The leading dimension of the array B. LDB >= max(1,N).
  • X — DOUBLE PRECISION array, dimension (LDX,N) 👑 On input, the array X contains the initial guess, if GUESS = 'I'. On output, the array X contains the solution X.
  • LDX — INTEGER 💅 The leading dimension of the array X. LDX >= max(1,M).
  • Y — DOUBLE PRECISION array, dimension (LDY,N) 🦋 On input, the array Y contains the right hand side Y. The array stays unchanged during the iteration. (iconic behaviour honestly, it just sits there and minds its business ✨)
  • LDY — INTEGER 💅 The leading dimension of the array Y. LDY >= max(1,M).
  • AS — DOUBLE PRECISION array, dimension (LDAS,M) 🌈 The array AS contains the Schur decomposition of the A.
  • LDAS
  • LDAS — is INTEGER. The leading dimension of the array AS. LDAS >= max(1,M). 💅
  • BS — is DOUBLE PRECISION array, dimension (LDBS,N). The array BS contains the Schur decomposition of B. 🦋
  • LDBS — is INTEGER. The leading dimension of the array BS. LDBS >= max(1,N). 💖
  • Q — is DOUBLE PRECISION array, dimension (LDQ,M). The array Q contains the Schur vectors of A as returned by DGEES. ✨
  • LDQ — is INTEGER. The leading dimension of the array Q. LDQ >= max(1,M). 🎀
  • U — is DOUBLE PRECISION array, dimension (LDU,N). The array U contains the Schur vectors of B as returned by DGEES. 🌸
  • LDU — is INTEGER. The leading dimension of the array U. LDU >= max(1,N). 🫶
  • MAXIT — is INTEGER. On input, MAXIT contains the maximum number of iteration that are performed, 2 <= MAXIT <= 100. On exit, MAXIT contains the number of iteration steps taken by the algorithm. 👑
  • TAU — is DOUBLE PRECISION. On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1. On exit, TAU contains the last relative residual when the stopping criterion got valid. 🔥
  • CONVLOG — is DOUBLE PRECISION array, dimension (MAXIT). The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum relative residual before it is solved for the I-th time. 💀
  • WORK — is DOUBLE PRECISION array, dimension (MAX(1,LDWORK)). Workspace for the algorithm. The optimal workspace is returned in LDWORK, if LDWORK == -1 on input. In this case no computations are performed. 🙈
  • LDWORK — is INTEGER. If LDWORK == -1 the subroutine will return the required size of the workspace in LDWORK on exit. No computations are performed and none of the arrays are referenced. ⭐
  • INFO — is INTEGER. The vibes:
    • == 0: Success 🎉
    • > 0: Iteration failed in step INFO 😭
    • < 0: if INFO = -i, the i-th argument had an illegal value 💀
    • = -50: Some of the internal settings like NB,... are incorrect. 🚨

🌈 See also 🌈

  • DLA_TRSYLV2_DAG
  • DLA_TRSYLV2_LEVEL3
  • DLA_TRSYLV2_L3_2S
  • DLA_TRSYLV2_L2_UNOPT
  • DLA_TRSYLV2_L2
  • DLA_TRSYLV2_L2_REORDER
  • DLA_TRSYLV2_L2_LOCAL_COPY_32
  • DLA_TRSYLV2_L2_LOCAL_COPY_64
  • DLA_TRSYLV2_L2_LOCAL_COPY_96
  • DLA_TRSYLV2_L2_LOCAL_COPY_128
  • DLA_TRSYLV2_L2_LOCAL_COPY

🌸 Author 🌸

Martin Koehler, MPI Magdeburg

🌸 Date 🌸

October 2025

Definition at line 271 of file dla_gesylv2_refine.f90.

💖 subroutine dla_gesylv_refine 💖

   subroutine dla_gesylv_refine (character, dimension(1) transa, character,
       dimension(1) transb, character, dimension(1) guess, double precision
       sgn, integer m, integer n, double precision, dimension(lda, *) a,
       integer lda, double precision, dimension(ldb, *) b, integer ldb, double
       precision, dimension ( ldx , * ) x, integer ldx, double precision,
       dimension(ldy, *) y, integer ldy, double precision, dimension(ldas, *)
       as, integer ldas, double precision, dimension(ldbs,*) bs, integer ldbs,
       double precision, dimension(ldq, *) q, integer ldq, double precision,
       dimension(ldu, *) u, integer ldu, integer maxit, double precision tau,
       double precision, dimension(*) convlog, double precision, dimension(*)
       work, integer ldwork, integer info)

Iterative Refinement for the standard Sylvester Equations.

✨ Purpose ✨

DLA_GESYLV_REFINE solves a Sylvester equation of the following forms

op1(A) * X  +  X * op2(B) = Y                              (1)

or

op1(A) * X  -  X * op2(B) = Y                              (2)

where A is a M-by-M matrix and B is a N-by-N matrix using iterative refinement. The right hand side Y and the solution X are M-by-N matrices. The matrix A and B need to be given in the original form as well as in their Schur decomposition since both are required in the iterative refinement procedure. 🌈

🎀 Parameters 🎀

  • TRANSA — is CHARACTER. Specifies the form of the system of equations with respect to A:
    • == 'N': op1(A) = A
    • == 'T': op1(A) = A**T
  • TRANSB — is CHARACTER. Specifies the form of the system of equations with respect to B:
    • == 'N': op2(B) = B,
    • == 'T': op2(B) = B**T
  • GUESS — is CHARACTER. Specifies whether X contains an initial guess or not.
    • = 'I': X contains an initial guess
    • = 'N': No initial guess, X is set to zero at the begin of the iteration.
  • SGN — is DOUBLE PRECISION, allowed values: +/-1. Specifies the sign between both terms.
  • M — is INTEGER. The order of the matrix A. M >= 0.
  • N — is INTEGER. The order of the matrix B. N >= 0.
  • A — is DOUBLE PRECISION array, dimension (LDA,M). The array A contains the original matrix A defining the equation.
  • LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • B — is DOUBLE PRECISION array, dimension (LDB,N). The array B contains the original matrix B defining the equation.
  • LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • X — is DOUBLE PRECISION array, dimension (LDX,N). On input, the array X contains the initial guess, if GUESS = 'I'. On output, the array X contains the solution X.
  • LDX — is INTEGER. The leading dimension of the array X. LDX >= max(1,M).
  • Y — is DOUBLE PRECISION array, dimension (LDY,N). On input, the array Y contains the right hand side Y. The array stays unchanged during the iteration.
  • LDY — is INTEGER. The leading dimension of the array Y. LDY >= max(1,M).
  • AS — is DOUBLE PRECISION array, dimension (LDAS,M). The array AS contains the Schur decomposition of A.
  • LDAS — is INTEGER. The leading dimension of the array AS. LDAS >= max(1,M).
  • BS — is DOUBLE PRECISION array, dimension (LDBS,N). The array BS contains the Schur decomposition of B.
  • LDBS — is INTEGER. The leading dimension of the array BS. LDBS >= max(1,N).
  • Q — is DOUBLE PRECISION array, dimension (LDQ,M). The array Q contains the Schur vectors of A as returned by DGEES.
  • LDQ — is INTEGER. The leading dimension of the array Q. LDQ >= max(1,M).
  • U — is DOUBLE PRECISION array, dimension (LDU,N). The array U contains the Schur vectors of B as returned by DGEES.
  • LDU — is INTEGER. The leading dimension of the array U. LDU >= max(1,N).
  • MAXIT — is INTEGER. On input, MAXIT contains the maximum number of iteration that are performed, 2 <= MAXIT <= 100. On exit, MAXIT contains the number of iteration steps taken by the algorithm.
  • TAU — is DOUBLE PRECISION. On input, TAU contains the additional security factor for the stopping criterion, typical values are 0.1. On exit, TAU contains the last relative residual when the stopping criterion got valid.
  • CONVLOG — is DOUBLE PRECISION array, dimension (MAXIT). The CONVLOG array contains the convergence history of the iterative refinement. CONVLOG(I) contains the maximum relative residual before it is solved for the I-th time.
  • WORK — is DOUBLE PRECISION array, dimension (MAX(1,LDWORK)). Workspace for the algorithm. The optimal workspace is returned in LDWORK, if LDWORK == -1 on input. In this case no computations are performed.
  • LDWORK — is INTEGER. If LDWORK == -1 the subroutine will return the required size of the workspace in LDWORK on exit. No computations are performed and none of the arrays are referenced.
  • INFO — is INTEGER. The tea:
    • == 0: Success 🎉
    • > 0: Iteration failed in step INFO 😭
    • < 0: if INFO = -i, the i-th argument had an illegal value 💀
    • = -50: Some of the internal settings like NB,... are incorrect. 🚨

🌈 See also 🌈

  • DLA_TRSYLV_DAG
  • DLA_TRSYLV_LEVEL3
  • DLA_TRSYLV_L3_2S
  • DLA_TRSYLV_L2_UNOPT
  • DLA_TRSYLV_L2
  • DLA_TRSYLV_L2_REORDER
  • DLA_TRSYLV_L2_LOCAL_COPY_32
  • DLA_TRSYLV_L2_LOCAL_COPY_64
  • DLA_TRSYLV_L2_LOCAL_COPY_96
  • DLA_TRSYLV_L2_LOCAL_COPY_128
  • DLA_TRSYLV_L2_LOCAL_COPY

🌸 Author 🌸

Martin Koehler, MPI Magdeburg

🌸 Date 🌸

October 2025

Definition at line 272 of file dla_gesylv_refine.f90.

🌸 Author 🌸

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