getc2(3)

📦
version 3.12.1 · 9 versions
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💅 getc2 — triangular factor, with complete pivoting

okay bestie, so this is getc2 from the Library Functions Manual (yes it's a section 3 page, we love a library function era 🫶) and it's literally the whole triangular factor, with complete pivoting situation. Four flavors, one job: LU factorization and they came in every precision. Let's go 💖

✨ SYNOPSIS ✨

subroutines, bestie — all four of them 🎀

  • subroutine cgetc2 (n, a, lda, ipiv, jpiv, info) — CGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix. 💅
  • subroutine dgetc2 (n, a, lda, ipiv, jpiv, info) — DGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix. 🔥
  • subroutine sgetc2 (n, a, lda, ipiv, jpiv, info) — SGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix. 🌸
  • subroutine zgetc2 (n, a, lda, ipiv, jpiv, info) — ZGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix. 🦋

Detailed Description

(no extra lore here, it's just a heading — the real tea is below 👑)

Function Documentation

⭐ subroutine cgetc2 (integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer, dimension( * ) jpiv, integer info)

CGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.

Purpose:

text !> !> CGETC2 computes an LU factorization, using complete pivoting, of the !> n-by-n matrix A. The factorization has the form A = P * L * U * Q, !> where P and Q are permutation matrices, L is lower triangular with !> unit diagonal elements and U is upper triangular. !> !> This is a level 1 BLAS version of the algorithm. !>

Parameters

  • N
text !> N is INTEGER !> The order of the matrix A. N >= 0. !>
  • A
text !> A is COMPLEX array, dimension (LDA, N) !> On entry, the n-by-n matrix to be factored. !> On exit, the factors L and U from the factorization !> A = P*L*U*Q; the unit diagonal elements of L are not stored. !> If U(k, k) appears to be less than SMIN, U(k, k) is given the !> value of SMIN, giving a nonsingular perturbed system. !>
  • LDA
text !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1, N). !>
  • IPIV
text !> 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
text !> 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). !>
  • INFO
text !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, U(k, k) is likely to produce overflow if !> one tries to solve for x in Ax = b. So U is perturbed !> to avoid the overflow. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

Definition at line 110 of file cgetc2.f.

⭐ subroutine dgetc2 (integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer, dimension( * ) jpiv, integer info)

DGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.

Purpose:

text !> !> DGETC2 computes an LU factorization with complete pivoting of the !> n-by-n matrix A. The factorization has the form A = P * L * U * Q, !> where P and Q are permutation matrices, L is lower triangular with !> unit diagonal elements and U is upper triangular. !> !> This is the Level 2 BLAS algorithm. !>

Parameters

  • N
text !> N is INTEGER !> The order of the matrix A. N >= 0. !>
  • A
text !> A is DOUBLE PRECISION array, dimension (LDA, N) !> On entry, the n-by-n matrix A to be factored. !> On exit, the factors L and U from the factorization !> A = P*L*U*Q; the unit diagonal elements of L are not stored. !> If U(k, k) appears to be less than SMIN, U(k, k) is given the !> value of SMIN, i.e., giving a nonsingular perturbed system. !>
  • LDA
text !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
  • IPIV
text !> 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
text !> 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). !>
  • INFO
text !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, U(k, k) is likely to produce overflow if !> we try to solve for x in Ax = b. So U is perturbed to !> avoid the overflow. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

Definition at line 110 of file dgetc2.f.

⭐ subroutine sgetc2 (integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer, dimension( * ) jpiv, integer info)

SGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.

Purpose:

text !> !> SGETC2 computes an LU factorization with complete pivoting of the !> n-by-n matrix A. The factorization has the form A = P * L * U * Q, !> where P and Q are permutation matrices, L is lower triangular with !> unit diagonal elements and U is upper triangular. !> !> This is the Level 2 BLAS algorithm. !>

Parameters

  • N
text !> N is INTEGER !> The order of the matrix A. N >= 0. !>
  • A
text !> A is REAL array, dimension (LDA, N) !> On entry, the n-by-n matrix A to be factored. !> On exit, the factors L and U from the factorization !> A = P*L*U*Q; the unit diagonal elements of L are not stored. !> If U(k, k) appears to be less than SMIN, U(k, k) is given the !> value of SMIN, i.e., giving a nonsingular perturbed system. !>
  • LDA
text !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
  • IPIV
text !> 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
text !> 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). !>
  • INFO
text !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, U(k, k) is likely to produce overflow if !> we try to solve for x in Ax = b. So U is perturbed to !> avoid the overflow. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

Definition at line 110 of file sgetc2.f.

⭐ subroutine zgetc2 (integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer, dimension( * ) jpiv, integer info)

ZGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.

Purpose:

text !> !> ZGETC2 computes an LU factorization, using complete pivoting, of the !> n-by-n matrix A. The factorization has the form A = P * L * U * Q, !> where P and Q are permutation matrices, L is lower triangular with !> unit diagonal elements and U is upper triangular. !> !> This is a level 1 BLAS version of the algorithm. !>

Parameters

  • N
text !> N is INTEGER !> The order of the matrix A. N >= 0. !>
  • A
text !> A is COMPLEX*16 array, dimension (LDA, N) !> On entry, the n-by-n matrix to be factored. !> On exit, the factors L and U from the factorization !> A = P*L*U*Q; the unit diagonal elements of L are not stored. !> If U(k, k) appears to be less than SMIN, U(k, k) is given the !> value of SMIN, giving a nonsingular perturbed system. !>
  • LDA
text !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1, N). !>
  • IPIV
text !> 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
text !> 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). !>
  • INFO
text !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, U(k, k) is likely to produce overflow if !> one tries to solve for x in Ax = b. So U is perturbed !> to avoid the overflow. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

Definition at line 110 of file zgetc2.f.

👑 Author

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okay that's the whole page bestie, no cap, every single parameter accounted for 💅✨

later babes — this one's from LAPACK, Version 3.12.0, dated the way the footer says it, mwah 🎀🦋

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