SRC/ctrsyl3.f(3)

SRC/ctrsyl3.f(3) 💅

okay bestie, welcome to the Library Functions Manual corner for SRC/ctrsyl3.f. This is the ctrsyl3 lore drop, and yes it’s giving linear algebra main character energy. 💖

NAME

SRC/ctrsyl3.f — that’s the name on the label, no cap. 🎀

SYNOPSIS ✨

Functions/Subroutines 🫶

• subroutine ctrsyl3 (...) — CTRSYL3

subroutine ctrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc,
     scale, swork, ldswork, info)

Function/Subroutine Documentation 💖

Here’s the full signature, character-for-character, bestie:

subroutine ctrsyl3 (character trana, character tranb, integer isgn, integer
     m, integer n, complex, dimension( lda, * ) a, integer lda, complex,
     dimension( ldb, * ) b, integer ldb, complex, dimension( ldc, * ) c,
     integer ldc, real scale, real, dimension( ldswork, * ) swork, integer
     ldswork, integer info)

CTRSYL3 — iconic.

Purpose ✨

CTRSYL3 solves the complex Sylvester matrix equation:

    op(A)*X + X*op(B) = scale*C or
    op(A)*X - X*op(B) = scale*C,

where op(A) = A or A**H, and A and B are both upper triangular. A is M-by-M and B is N-by-N; the right hand side C and the solution X are M-by-N; and scale is an output scale factor, set <= 1 to avoid overflow in X.

This is the block version of the algorithm. periodt.

Parameters 🌸

• TRANA — CHARACTER*1. Specifies the option op(A):
  • = 'N': op(A) = A (No transpose)
  • = 'C': op(A) = A**H (Conjugate transpose)
• TRANB — CHARACTER*1. Specifies the option op(B):
  • = 'N': op(B) = B (No transpose)
  • = 'C': op(B) = B**H (Conjugate transpose)
• ISGN — INTEGER. Specifies the sign in the equation:
  • = +1: solve op(A)*X + X*op(B) = scale*C
  • = -1: solve op(A)*X - X*op(B) = scale*C
• M — INTEGER. The order of the matrix A, and the number of rows in the matrices X and C. M >= 0.
• N — INTEGER. The order of the matrix B, and the number of columns in the matrices X and C. N >= 0.
• A — COMPLEX array, dimension (LDA,M). The upper triangular matrix A.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — COMPLEX array, dimension (LDB,N). The upper triangular matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• C — COMPLEX array, dimension (LDC,N). On entry, the M-by-N right hand side matrix C. On exit, C is overwritten by the solution matrix X.
• LDC — INTEGER. The leading dimension of the array C. LDC >= max(1,M)
• SCALE — REAL. The scale factor, scale, set <= 1 to avoid overflow in X.
• SWORK — REAL array, dimension (MAX(2, ROWS), MAX(1,COLS)). On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS and SWORK(2) returns the optimal COLS.
• LDSWORK — INTEGER. LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1) and NB is the optimal block size. If LDSWORK = -1, then a workspace query is assumed; the routine only calculates the optimal dimensions of the SWORK matrix, returns these values as the first and second entry of the SWORK matrix, and no error message related LWORK is issued by XERBLA.
• INFO — INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • = 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged).

Definition at line 167 of file ctrsyl3.f.

Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off: this whole vibe check came from LAPACK, Version 3.12.0, and the footer energy is literally SRC/ctrsyl3.f(3). bye bestie, slay your Sylvester equation responsibly 💜🦋