latdf(3)

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💅 latdf(3) — Library Functions Manual

okay so bestie, this page lives in the Library Functions Manual section, and it's the whole latdf girlie family: clatdf, dlatdf, slatdf, zlatdf. Same algorithm, four different precisions/types. It's giving "one brain cell, four outfits" and honestly we love that for her ✨

🎀 NAME 🎀

latdf — latdf: Dif-estimate with complete pivoting LU, step in tgsen

🌸 SYNOPSIS 🌸

Functions

  • subroutine clatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv) — CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
  • subroutine dlatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv) — DLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
  • subroutine slatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv) — SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
  • subroutine zlatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv) — ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

🦋 Detailed Description 🦋

Like, genuinely nothing extra here — the whole page is just the function documentation below. No lore, no backstory, just vibes and pivots 💀

💜 Function Documentation 💜

🌟 clatdf 🌟

subroutine clatdf (integer ijob, integer n, complex, dimension( ldz, * ) z,
    integer ldz, complex, dimension( * ) rhs, real rdsum, real rdscal,
    integer, dimension( * ) ipiv, integer, dimension( * ) jpiv)

CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

⭐ Purpose

CLATDF computes the contribution to the reciprocal Dif-estimate by solving for x in Z * x = b, where b is chosen such that the norm of x is as large as possible. It is assumed that LU decomposition of Z has been computed by CGETC2. On entry RHS = f holds the contribution from earlier solved sub-systems, and on return RHS = x.

The factorization of Z returned by CGETC2 has the form Z = P * L * U * Q, where P and Q are permutation matrices. L is lower triangular with unit diagonal elements and U is upper triangular.

🔥 Parameters

  • IJOB — IJOB is INTEGER.
    • IJOB = 2: First compute an approximative null-vector e of Z using CGECON, e is normalized and solve for Zx = +-e - f with the sign giving the greater value of 2-norm(x). About 5 times as expensive as Default.
    • IJOB .ne. 2: Local look ahead strategy where all entries of the r.h.s. b is chosen as either +1 or -1. Default.
  • N — N is INTEGER. The number of columns of the matrix Z.
  • Z — Z is COMPLEX array, dimension (LDZ, N). On entry, the LU part of the factorization of the n-by-n matrix Z computed by CGETC2: Z = P * L * U * Q.
  • LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDA >= max(1, N).
  • RHS — RHS is COMPLEX array, dimension (N). On entry, RHS contains contributions from other subsystems. On exit, RHS contains the solution of the subsystem with entries according to the value of IJOB (see above).
  • RDSUM — RDSUM is REAL. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by CTGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T' RDSUM is not touched.
NOTE: RDSUM only makes sense when CTGSY2 is called by CTGSYL.
  • RDSCAL — RDSCAL is REAL. On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched.
NOTE: RDSCAL only makes sense when CTGSY2 is called by CTGSYL.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).
  • JPIV — JPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🧚 Further Details

This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization.

🍓 Contributors

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

🌈 References

[1] Bo Kagstrom and Lars Westin, Generalized Schur Methods with Condition Estimators for Solving the Generalized Sylvester Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.

[2] Peter Poromaa, On Efficient and Robust Estimators for the Separation between two Regular Matrix Pairs with Applications in Condition Estimation. Report UMINF-95.05, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

Definition at line 167 of file clatdf.f.

💖 dlatdf 💖

subroutine dlatdf (integer ijob, integer n, double precision, dimension(
    ldz, * ) z, integer ldz, double precision, dimension( * ) rhs, double
    precision rdsum, double precision rdscal, integer, dimension( * ) ipiv,
    integer, dimension( * ) jpiv)

DLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

⭐ Purpose

DLATDF uses the LU factorization of the n-by-n matrix Z computed by DGETC2 and computes a contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and choosing the r.h.s. b such that the norm of x is as large as possible. On entry RHS = b holds the contribution from earlier solved sub-systems, and on return RHS = x.

The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q, where P and Q are permutation matrices. L is lower triangular with unit diagonal elements and U is upper triangular.

🔥 Parameters

  • IJOB — IJOB is INTEGER.
    • IJOB = 2: First compute an approximative null-vector e of Z using DGECON, e is normalized and solve for Zx = +-e - f with the sign giving the greater value of 2-norm(x). About 5 times as expensive as Default.
    • IJOB .ne. 2: Local look ahead strategy where all entries of the r.h.s. b is chosen as either +1 or -1 (Default).
  • N — N is INTEGER. The number of columns of the matrix Z.
  • Z — Z is DOUBLE PRECISION array, dimension (LDZ, N). On entry, the LU part of the factorization of the n-by-n matrix Z computed by DGETC2: Z = P * L * U * Q.
  • LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDA >= max(1, N).
  • RHS — RHS is DOUBLE PRECISION array, dimension (N). On entry, RHS contains contributions from other subsystems. On exit, RHS contains the solution of the subsystem with entries according to the value of IJOB (see above).
  • RDSUM — RDSUM is DOUBLE PRECISION. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by DTGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T' RDSUM is not touched.
NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL.
  • RDSCAL — RDSCAL is DOUBLE PRECISION. On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched.
NOTE: RDSCAL only makes sense when DTGSY2 is called by DTGSYL.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).
  • JPIV — JPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🧚 Further Details

This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization.

🍓 Contributors

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

🌈 References

[1] Bo Kagstrom and Lars Westin, Generalized Schur Methods with Condition Estimators for Solving the Generalized Sylvester Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.

[2] Peter Poromaa, On Efficient and Robust Estimators for the Separation between two Regular Matrix Pairs with Applications in Condition Estimation. Report IMINF-95.05, Departement of Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

Definition at line 169 of file dlatdf.f.

✨ slatdf ✨

subroutine slatdf (integer ijob, integer n, real, dimension( ldz, * ) z,
    integer ldz, real, dimension( * ) rhs, real rdsum, real rdscal, integer,
    dimension( * ) ipiv, integer, dimension( * ) jpiv)

SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

(bestie the slatdf purpose + params are literally right there in part 2, hold on 💅)

SLATDF literally uses the LU factorization of the n-by-n matrix Z computed by SGETC2, and it computes a contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and choosing the r.h.s. b such that the norm of x is as large as possible. On entry RHS = b holds the contribution from earlier solved sub-systems, and on return RHS = x. Periodt. 💅

The factorization of Z returned by SGETC2 has the form Z = P*L*U*Q, where P and Q are permutation matrices. L is lower triangular with unit diagonal elements and U is upper triangular. Iconic. ✨

🎀 Parameters 🎀

  • IJOB — IJOB is INTEGER.
    • IJOB = 2: First compute an approximative null-vector e of Z using SGECON; e is normalized and solve for Zx = +-e - f with the sign giving the greater value of 2-norm(x). About 5 times as expensive as Default. 😭
    • IJOB .ne. 2: Local look ahead strategy where all entries of the r.h.s. b is chosen as either +1 or -1 (Default). Slay.
  • N — N is INTEGER. The number of columns of the matrix Z.
  • Z — Z is REAL array, dimension (LDZ, N). On entry, the LU part of the factorization of the n-by-n matrix Z computed by SGETC2: Z = P * L * U * Q.
  • LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDA >= max(1, N).
  • RHS — RHS is REAL array, dimension N. On entry, RHS contains contributions from other subsystems. On exit, RHS contains the solution of the subsystem with entries according to the value of IJOB (see above).
  • RDSUM — RDSUM is REAL. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by STGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T' RDSUM is not touched. NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL.
  • RDSCAL — RDSCAL is REAL. On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched. NOTE: RDSCAL only makes sense when STGSY2 is called by STGSYL.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).
  • JPIV — JPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

✨ Further Details ✨

This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization.

🫶 Contributors 🫶

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

📚 References 📚

[1] Bo Kagstrom and Lars Westin, Generalized Schur Methods with Condition Estimators for Solving the Generalized Sylvester Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.

[2] Peter Poromaa, On Efficient and Robust Estimators for the Separation between two Regular Matrix Pairs with Applications in Condition Estimation. Report IMINF-95.05, Departement of Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

Definition at line 169 of file slatdf.f.

🦋 subroutine zlatdf 🦋

   subroutine zlatdf (integer ijob, integer n, complex*16, dimension( ldz, * )
       z, integer ldz, complex*16, dimension( * ) rhs, double precision rdsum,
       double precision rdscal, integer, dimension( * ) ipiv, integer,
       dimension( * ) jpiv)

ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. 💜

✨ Purpose ✨

ZLATDF computes the contribution to the reciprocal Dif-estimate by solving for x in Z * x = b, where b is chosen such that the norm of x is as large as possible. It is assumed that LU decomposition of Z has been computed by ZGETC2. On entry RHS = f holds the contribution from earlier solved sub-systems, and on return RHS = x.

The factorization of Z returned by ZGETC2 has the form Z = P * L * U * Q, where P and Q are permutation matrices. L is lower triangular with unit diagonal elements and U is upper triangular.

🎀 Parameters 🎀

  • IJOB — IJOB is INTEGER.
    • IJOB = 2: First compute an approximative null-vector e of Z using ZGECON; e is normalized and solve for Zx = +-e - f with the sign giving the greater value of 2-norm(x). About 5 times as expensive as Default. 😭
    • IJOB .ne. 2: Local look ahead strategy where all entries of the r.h.s. b is chosen as either +1 or -1. Default. Slay.
  • N — N is INTEGER. The number of columns of the matrix Z.
  • Z — Z is COMPLEX*16 array, dimension (LDZ, N). On entry, the LU part of the factorization of the n-by-n matrix Z computed by ZGETC2: Z = P * L * U * Q.
  • LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDA >= max(1, N).
  • RHS — RHS is COMPLEX*16 array, dimension (N). On entry, RHS contains contributions from other subsystems. On exit, RHS contains the solution of the subsystem with entries according to the value of IJOB (see above).
  • RDSUM — RDSUM is DOUBLE PRECISION. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by ZTGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T' RDSUM is not touched. NOTE: RDSUM only makes sense when ZTGSY2 is called by CTGSYL.
  • RDSCAL — RDSCAL is DOUBLE PRECISION. On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched. NOTE: RDSCAL only makes sense when ZTGSY2 is called by ZTGSYL.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).
  • JPIV — JPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

✨ Further Details ✨

This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization.

🫶 Contributors 🫶

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

📚 References 📚

[1] Bo Kagstrom and Lars Westin, Generalized Schur Methods with Condition Estimators for Solving the Generalized Sylvester Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.

[2] Peter Poromaa, On Efficient and Robust Estimators for the Separation between two Regular Matrix Pairs with Applications in Condition Estimation. Report UMINF-95.05, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

Definition at line 167 of file zlatdf.f.

👑 Author 👑

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