SRC/dtrsyl3.f(3)

💖 SRC/dtrsyl3.f 💖

Okay bestie, welcome to SRC/dtrsyl3.f from the Library Functions Manual. This is LAPACK Version 3.12.0 energy, and we’re reading the whole thing like it’s the group chat. 🫶

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🌸 NAME 🌸

SRC/dtrsyl3.f — that’s it, that’s the name, periodt. 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine dtrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info) — DTRSYL3

subroutine dtrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc,
    scale, iwork, liwork, swork, ldswork, info)

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🫶 Function/Subroutine Documentation 🫶

💅 subroutine dtrsyl3 💅

Here’s the full signature, bb — keep it exactly as written:

subroutine dtrsyl3 (character trana, character tranb, integer isgn, integer
       m, integer n, double precision, dimension( lda, * ) a, integer lda,
       double precision, dimension( ldb, * ) b, integer ldb, double precision,
       dimension( ldc, * ) c, integer ldc, double precision scale, integer,
       dimension( * ) iwork, integer liwork, double precision, dimension(
       ldswork, * ) swork, integer ldswork, integer info)

DTRSYL3, bb. 👑

💫 Purpose 💫

Okay so DTRSYL3 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 DHSEQR), 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.

This is the block version of the algorithm.

🎀 Parameters 🎀

• TRANA — TRANA is CHARACTER*1. This is the op(A) selector, bestie:
  • = '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. This is the op(B) selector:
  • = 'N': op(B) = B (No transpose)
  • = 'T': op(B) = B**T (Transpose)
  • = 'C': op(B) = B**H (Conjugate transpose = Transpose)
• ISGN — ISGN is INTEGER. It sets 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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.
• IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
• LIWORK — IWORK is INTEGER. The dimension of the array IWORK. LIWORK >= ((M + NB - 1) / NB + 1) + ((N + NB - 1) / NB + 1), where NB is the optimal block size.

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal dimension of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA.

• 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).

The INFO = 1 case is the “uh oh, close eigenvalues” warning, bestie — but the matrices A and B are unchanged. 💀

📍 Definition at line 197 of file dtrsyl3.f.

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🌈 Author 🌈

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