SRC/ztrsyl3.f(3)

Okay so this page is the SRC/ztrsyl3.f(3) entry from LAPACK's Library Functions Manual, and it's lowkey the most iconic block-version Sylvester solver manual page you'll read today. Let's get into it, bestie. 🫶

🌸 NAME 🌸

SRC/ztrsyl3.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine ztrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc,
    scale, swork, ldswork, info)
    ZTRSYL3

🦋 Function/Subroutine Documentation 🦋

subroutine ztrsyl3 (character trana, character tranb, integer isgn, integer
    m, integer n, complex*16, dimension( lda, * ) a, integer lda,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(
    ldc, * ) c, integer ldc, double precision scale, double precision,
    dimension( ldswork, * ) swork, integer ldswork, integer info)
    ZTRSYL3

💅 Purpose 💅

Literally, ZTRSYL3 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 💖

TRANA is CHARACTER*1. Specifies the option op(A):

• = 'N': op(A) = A (No transpose)
• = 'C': op(A) = A**H (Conjugate transpose)

💖 TRANB 💖

TRANB is CHARACTER*1. Specifies the option op(B):

• = 'N': op(B) = B (No transpose)
• = 'C': op(B) = B**H (Conjugate 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 COMPLEX*16 array, dimension (LDA,M). The upper triangular matrix A.

💖 LDA 💖

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).

💖 B 💖

B is COMPLEX*16 array, dimension (LDB,N). The upper triangular matrix B.

💖 LDB 💖

LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

💖 C 💖

C is COMPLEX*16 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 DOUBLE PRECISION. The scale factor, scale, set <= 1 to avoid overflow in X.

💖 SWORK 💖

SWORK is DOUBLE PRECISION 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 💖

LDSWORK is 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 💖

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).

🧚 Definition 🧚

Definition at line 168 of file ztrsyl3.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie! 💖 LAPACK, Version 3.12.0, from SRC/ztrsyl3.f(3) — mwah! 💋