getri(3)

📦
version 3.12.1 · 9 versions
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getri(3) 💅✨ — LAPACK's triangular inverse bestie

Straight from the Library Functions Manual, no cap: this is the page for the getri family, and it's lowkey iconic.

🌸 NAME 🌸

getri — getri: triangular inverse. Yes bestie, the name is a little redundant, but it ate.

✨ SYNOPSIS ✨

Functions

  • subroutine cgetri (n, a, lda, ipiv, work, lwork, info) — CGETRI
  • subroutine dgetri (n, a, lda, ipiv, work, lwork, info) — DGETRI
  • subroutine sgetri (n, a, lda, ipiv, work, lwork, info) — SGETRI
  • subroutine zgetri (n, a, lda, ipiv, work, lwork, info) — ZGETRI

🦋 DETAILED DESCRIPTION 🦋

okay so this page is the whole getri squad: cgetri, dgetri, sgetri, and zgetri. They all do the triangular inverse thing, and the full function tea is below. 👑

🔥 FUNCTION DOCUMENTATION 🔥

💖 subroutine cgetri (integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info) — CGETRI

Purpose

CGETRI computes the inverse of a matrix using the LU factorization computed by CGETRF.

This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A).

Parameters

  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX array, dimension (LDA,N). On entry, the factors L and U from the factorization A = P*L*U as computed by CGETRF. On exit, if INFO = 0, the inverse of the original matrix A.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). The pivot indices from CGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
  • WORK — COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The dimension of the array WORK. LWORK >= max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV.

If LWORK = -1, then a workspace query is assumed; the routine only calculates 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 — INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, U(i,i) is exactly zero; 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.

Definition at line

113 of file cgetri.f.

💜 subroutine dgetri (integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info) — DGETRI

Purpose

DGETRI computes the inverse of a matrix using the LU factorization computed by DGETRF.

This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A).

Parameters

  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — DOUBLE PRECISION array, dimension (LDA,N). On entry, the factors L and U from the factorization A = P*L*U as computed by DGETRF. On exit, if INFO = 0, the inverse of the original matrix A.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
  • WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The dimension of the array WORK. LWORK >= max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV.

If LWORK = -1, then a workspace query is assumed; the routine only calculates 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 — INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, U(i,i) is exactly zero; 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.

Definition at line

113 of file dgetri.f.

🎀 subroutine sgetri (integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info) — SGETRI

Purpose

SGETRI computes the inverse of a matrix using the LU factorization computed by SGETRF.

This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A).

Parameters

  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — REAL array, dimension (LDA,N). On entry, the factors L and U from the factorization A = P*L*U as computed by SGETRF. On exit, if INFO = 0, the inverse of the original matrix A.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). The pivot indices from SGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
  • WORK — REAL array, dimension (MAX(1,LWORK)). On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The dimension of the array WORK. LWORK >= max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV.

If LWORK = -1, then a workspace query is assumed; the routine only calculates 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 — INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, U(i,i) is exactly zero; 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.

Definition at line

113 of file sgetri.f.

🌈 subroutine zgetri (integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info) — ZGETRI

Purpose

ZGETRI computes the inverse of a matrix using the LU factorization computed by ZGETRF.

This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A).

Parameters

  • N — INTEGER. The order of the matrix A. N >= 0.
  • A — COMPLEX*16 array, dimension (LDA,N). On entry, the factors L and U from the factorization A = P*L*U as computed by ZGETRF. On exit, if INFO = 0, the inverse of the original matrix A.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • IPIV — INTEGER array, dimension (N). The pivot indices from ZGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
  • WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
  • LWORK — INTEGER. The dimension of the array WORK. LWORK >= max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV.

If LWORK = -1, then a workspace query is assumed; the routine only calculates 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 — INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, U(i,i) is exactly zero; 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.

Definition at line

113 of file zgetri.f.

👑 AUTHOR 👑

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💖 Footer tea: LAPACK Version 3.12.0 • getri(3) • date field: not listed, but the vibes are timeless. Mwah! 💖

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