SRC/dsytrs_3.f(3)

SRC/dsytrs_3.f(3) 💖

okay so this page is from the Library Functions Manual, and it is literally all about DSYTRS_3 — no cap, she solves linear systems and she is iconic. 🎀

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NAME ✨

SRC/dsytrs_3.f — bestie, this is the DSYTRS_3 zone. 🦋

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SYNOPSIS 🌸

Functions/Subroutines 🎀

subroutine dsytrs_3 (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)

DSYTRS_3 — yes, the main character is right here. 💅

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Function/Subroutine Documentation 🫶

subroutine dsytrs_3 (character uplo, integer n, integer nrhs, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( * ) e, integer, dimension( * ) ipiv, double precision,
    dimension( ldb, * ) b, integer ldb, integer info)

DSYTRS_3 — she’s giving solver energy. 🔥

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Purpose 🌈

okay so DSYTRS_3 solves a system of linear equations A * X = B with a real symmetric 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.

This algorithm is using Level 3 BLAS. 🫶✨

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Parameters 💜

• UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
  • = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T);
  • = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). 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.
• 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.
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• INFO — INFO is INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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Author 👑

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

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Contributors 🧚

• June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley
• September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

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Definition at line 163 of file dsytrs_3.f. 📌

Definition at line 163 of file dsytrs_3.f.

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Author 💻

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