hetri_3(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🦋 hetri_3(3) 🦋

okay so welcome to the Library Functions Manual page for hetri_3(3) — she's a real one, and honestly the whole {he,sy}tri_3 family ate 💅. grab a snack, this one's long so we're splitting it into parts, and this is part 1 🍓.

🎀 NAME 🎀

hetri_3 — {he,sy}tri_3: inverse

✨ SYNOPSIS ✨

Functions

  • subroutine chetri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info) — CHETRI_3
  • subroutine csytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info) — CSYTRI_3
  • subroutine dsytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info) — DSYTRI_3
  • subroutine ssytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info) — SSYTRI_3
  • subroutine zhetri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info) — ZHETRI_3
  • subroutine zsytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info) — ZSYTRI_3

💫 DETAILED DESCRIPTION 💫

like, there's genuinely nothing written here in the source, so this section is lowkey just vibes 🫶. the real tea is all in the function docs below, bestie — keep scrolling 💖.

🌸 FUNCTION DOCUMENTATION 🌸

💜 subroutine chetri_3

subroutine chetri_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)

CHETRI_3

✨ Purpose ✨

okay so CHETRI_3 computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by CHETRF_RK or CHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

CHETRI_3 sets the leading dimension of the workspace before calling CHETRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS. slay 💅.

🎀 Parameters 🎀

  • UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_BK:
    • a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
    • b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.

On exit, if INFO = 0, the Hermitian inverse of the original matrix.

  • If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced;
  • If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • E — E is COMPLEX array, dimension (N). On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where
    • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
    • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHETRF_RK or CHETRF_BK.
  • WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — LWORK is INTEGER. The length of WORK.
    • If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3).

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌈 Contributors

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 169 of file chetri_3.f.

💜 subroutine csytri_3

subroutine csytri_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)

CSYTRI_3

✨ Purpose ✨

CSYTRI_3 computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by CSYTRF_RK or CSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

CSYTRI_3 sets the leading dimension of the workspace before calling CSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS ✨.

🎀 Parameters 🎀

  • UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by CSYTRF_RK and CSYTRF_BK:
    • a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
    • b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.

On exit, if INFO = 0, the symmetric inverse of the original matrix.

  • If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced;
  • If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • E — E is COMPLEX array, dimension (N). On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where
    • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
    • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSYTRF_RK or CSYTRF_BK.
  • WORK — WORK is COMPLEX array, dimension (N+NB+1)*(NB+3). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — LWORK is INTEGER. The length of WORK. LWORK >= (N+NB+1)*(NB+3).

If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌈 Contributors

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 168 of file csytri_3.f.

💜 subroutine dsytri_3

subroutine dsytri_3 (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) e, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRI_3

✨ Purpose ✨

…and that's exactly where part 1 dips bestie — part 2 picks up DSYTRI_3's purpose and the rest 💖✨

💖 dsytri_3 💖

✨ Purpose

Okay bestie, so DSYTRI_3 computes the inverse of a real symmetric indefinite matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

DSYTRI_3 sets the leading dimension of the workspace before calling DSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS. slay.

🎀 Parameters

UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

N — N is INTEGER. The order of the matrix A. N >= 0.

A — A is DOUBLE PRECISION array, dimension (LDA,N).

On entry, diagonal of the block diagonal matrix D and factors U or L as computed by DSYTRF_RK and DSYTRF_BK:

  • a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
  • b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.

On exit, if INFO = 0, the symmetric inverse of the original matrix.

  • If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced;
  • If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).

E — E is DOUBLE PRECISION array, dimension (N).

On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where

  • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
  • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.

IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSYTRF_RK or DSYTRF_BK.

WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK — LWORK is INTEGER. The length of WORK. If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3).

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. (the docs really say "optimal size of the optimal size" — we're just the messengers 💀)

INFO — INFO is INTEGER.

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

🌟 Author

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

💐 Contributors

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 169 of file dsytri_3.f.

🦋 ssytri_3 🦋

subroutine ssytri_3 (character uplo, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real,
    dimension( * ) work, integer lwork, integer info)
SSYTRI_3

✨ Purpose

SSYTRI_3 computes the inverse of a real symmetric indefinite matrix A using the factorization computed by SSYTRF_RK or SSYTRF_BK:

A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

SSYTRI_3 sets the leading dimension of the workspace before calling SSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS. same energy, real precision.

🎀 Parameters

UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

N — N is INTEGER. The order of the matrix A. N >= 0.

A — A is REAL array, dimension (LDA,N).

On entry, diagonal of the block diagonal matrix D and factors U or L as computed by SSYTRF_RK and SSYTRF_BK:

  • a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
  • b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.

On exit, if INFO = 0, the symmetric inverse of the original matrix.

  • If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced;
  • If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).

E — E is REAL array, dimension (N).

On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where

  • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
  • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases.

IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by SSYTRF_RK or SSYTRF_BK.

WORK — WORK is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK — LWORK is INTEGER. The length of WORK. If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3).

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

INFO — INFO is INTEGER.

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.

🌟 Author

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

💐 Contributors

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 169 of file ssytri_3.f.

💜 zhetri_3 💜

subroutine zhetri_3 (character uplo, integer n, complex*16, dimension( lda,
    * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
    ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)
ZHETRI_3

✨ Purpose

ZHETRI_3 computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

ZHETRI_3 sets the leading dimension of the workspace before calling ZHETRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS. complex Hermitian era 💅

🎀 Parameters

UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.

  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
  • N — INTEGER. Lowkey the whole vibe of the matrix: its order. And N >= 0, always. ✨
  • A — COMPLEX*16 array, dimension (LDA,N). Okay so on entry this bad boy is holding the diagonal of the block diagonal matrix D and the factors U or L exactly as ZHETRF_RK and ZHETRF_BK left them 💅
    • a) ONLY the diagonal elements of the Hermitian block diagonal matrix D live on the diagonal of A, i.e. D(k,k) = A(k,k). The superdiagonal (or subdiagonal) elements of D belong in array E on entry — don't leave them here, that's not their home 🏠
    • b) If UPLO = 'U': factor U is chilling in the superdiagonal part of A. If UPLO = 'L': factor L is in the subdiagonal part of A.

On exit, if INFO = 0, you get the Hermitian inverse of the original matrix 🎀

  • If UPLO = 'U': the upper triangular part of the inverse is formed, and the part of A below the diagonal is not referenced (she's off duty).
  • If UPLO = 'L': the lower triangular part of the inverse is formed, and the part of A above the diagonal is not referenced.
  • LDA — INTEGER. The leading dimension of the array A, bestie. LDA >= max(1,N). No exceptions, fr fr.
  • E — COMPLEX*16 array, dimension (N). On entry she carries the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where:
    • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
    • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
🚨 NOTE: for a 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both the UPLO = 'U' or UPLO = 'L' cases. She simply doesn't get invited to that party 🫥
  • IPIV — INTEGER array, dimension (N). All the deets of the interchanges and the block structure of D, exactly as determined by ZHETRF_RK or ZHETRF_BK. Receipts 🔥
  • WORK — COMPLEX*16 array, dimension (N+NB+1)*(NB+3). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. Little overachiever 💖
  • LWORK — INTEGER. The length of WORK. LWORK >= (N+NB+1)*(NB+3).

If LDWORK = -1, then a workspace query is assumed — the routine only calculates the optimal size of the optimal size of the WORK array 😭 (yes, the manpage says it twice, we're keeping it, character for character), returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. So polite of her 💅

  • INFO — INTEGER. The vibe report 📋
    • = 0: successful exit, we ate 👑
    • < 0: if INFO = -i, the i-th argument had an illegal value 🚩
    • > 0: if INFO = i, D(i,i) = 0 — the matrix is singular and its inverse could not be computed. She's not invertible, she's singular, and we respect that 💀

👑 Author

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

🫶 Contributors:

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

📌 Definition

Definition at line 168 of file zhetri_3.f.

🦋 zsytri_3 — the symmetric sibling 🦋

subroutine zsytri_3 (character uplo, integer n, complex*16, dimension( lda,
* ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)

<h2 style="display:none">ZSYTRI_3</h2>

✨ Purpose

ZSYTRI_3 computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:
A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 🌸

ZSYTRI_3 sets the leading dimension of the workspace before calling ZSYTRI_3X that actually computes the inverse. (Yes, two spaces before "before" — we keep the typography, we're not monsters 🎀) This is the blocked version of the algorithm, calling Level 3 BLAS. Iconic behavior, honestly 🔥

💜 Parameters

  • UPLO — CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': Upper triangle of A is stored;
    • = 'L': Lower triangle of A is stored.
  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX*16 array, dimension (LDA,N). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK:
    • a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and
    • b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A.

On exit, if INFO = 0, the symmetric inverse of the original matrix 🦋

  • If UPLO = 'U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced;
  • If UPLO = 'L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • E — COMPLEX*16 array, dimension (N). On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where:
    • If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
    • If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
🚨 NOTE: for 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. Same energy as her Hermitian sister 💅
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK.
  • WORK — COMPLEX*16 array, dimension (N+NB+1)*(NB+3). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The length of WORK. LWORK >= (N+NB+1)*(NB+3).

If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the optimal size of the WORK array (again — twice — keeping it 🫶), returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

  • INFO — INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed 😭

👑 Author

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

🫶 Contributors:

November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

📌 Definition

Definition at line 168 of file zsytri_3.f.

🎀 one last Author moment 🎀

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