SRC/strsyl.f(3)

💖 SRC/strsyl.f 💖

okay bestie, welcome to the SRC/strsyl.f page from the Library Functions Manual ✨ this one is all about the STRSYL subroutine, and yes, it's giving linear algebra main character energy 💅

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🌸 NAME 🌸

SRC/strsyl.f — literally the page name, no cap 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines

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

STRSYL — that's the subroutine, periodt 💫

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🦋 Function/Subroutine Documentation 🦋

💜 subroutine strsyl (...)

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

STRSYL — again, iconic, no notes 👑

🌟 Purpose

STRSYL solves the real 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**T, and A and B are both upper quasi-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.

A and B must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign ✨

🎀 Parameters

• TRANA — TRANA is CHARACTER*1. Specifies the option op(A): = 'N': op(A) = A (No transpose); = 'T': op(A) = A**T (Transpose); = 'C': op(A) = A**H (Conjugate transpose = Transpose).
• TRANB — TRANB is CHARACTER*1. Specifies the option op(B): = 'N': op(B) = B (No transpose); = 'T': op(B) = B**T (Transpose); = 'C': op(B) = B**H (Conjugate transpose = Transpose).
• ISGN — ISGN is 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 — M is INTEGER. The order of the matrix A, and the number of rows in the matrices X and C. M >= 0.
• N — N is INTEGER. The order of the matrix B, and the number of columns in the matrices X and C. N >= 0.
• A — A is REAL array, dimension (LDA,M). The upper quasi-triangular matrix A, in Schur canonical form.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — B is REAL array, dimension (LDB,N). The upper quasi-triangular matrix B, in Schur canonical form.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• C — C is REAL 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 — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M)
• SCALE — SCALE is REAL. The scale factor, scale, set <= 1 to avoid overflow in X.
• INFO — INFO is 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).

👑 Author

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

Definition at line 162 of file strsyl.f. 📌

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🧚 Author

Generated automatically by Doxygen for LAPACK from the source code ✨

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