SRC/zgesv.f(3)

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✨ NAME ✨

SRC/zgesv.f — that's the name section, no extra lore. 🎀

🧩 SYNOPSIS 🧩

🧩 Functions/Subroutines

       subroutine zgesv (n, nrhs, a, lda, ipiv, b, ldb, info)

📚 Function/Subroutine Documentation 📚

Here's the full signature, bestie — yes, it's a lot, but it's iconic:

   subroutine zgesv (integer n, integer nrhs, complex*16, dimension( lda, * )
       a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension(
       ldb, * ) b, integer ldb, integer info)

🎯 Purpose

ZGESV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as

A = P * L * U,

where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

🎛️ Parameters

• N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• A — COMPLEX*16 array, dimension (LDA,N). On entry, the N-by-N coefficient matrix A. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• IPIV — INTEGER array, dimension (N). The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).
• B — COMPLEX*16 array, dimension (LDB,NRHS). On entry, the N-by-NRHS matrix of right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• 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 factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.

👑 Author

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

📍 Definition at line 123 of file zgesv.f.

That's literally where it's defined. ✨

🪄 Author

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