trsyl(3)

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🦋 trsyl(3) — Library Functions Manual

Okay bestie, buckle up — this is the Library Functions Manual page for trsyl, and it's giving "four subroutines, one very iconic equation" energy. 💅

🌸 NAME 🌸

trsyl — trsyl: the Sylvester equation solver. No cap, that's literally the whole name. 🎀

✨ SYNOPSIS ✨

🫶 Functions

  • subroutine ctrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) — the complex one, CTRSYL 💖
  • subroutine dtrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) — the double precision one, DTRSYL ✨
  • subroutine strsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) — the single precision real one, STRSYL 🌸
  • subroutine ztrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) — the double complex one, ZTRSYL 🦋

💜 Detailed Description 💜

Lowkey there's no extra prose here in the original — the real tea all lives down in the function documentation. Keep scrolling, bestie. 👇

👑 Function Documentation 👑

💅 ctrsyl

subroutine ctrsyl (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, integer info)

CTRSYL — the complex main character. 🧚

🎀 Purpose

CTRSYL 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. 🫶

🌟 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 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 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 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 155 of file ctrsyl.f.

🦋 dtrsyl

subroutine dtrsyl (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 info)

DTRSYL — double precision, double the slay. 💜

🎀 Purpose

DTRSYL 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. ✨

Heads up bestie — 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. Not optional, fr fr. 😭

🌟 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 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.
  • 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 dtrsyl.f.

🌸 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 — single precision, still full of attitude. 🍓

🎀 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. ⭐

Same warning as above, bestie — 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 — INTEGER, the leading dimension of the array C. Gotta be LDC >= max(1,M), no cap 💅
  • SCALE — REAL, the scale factor, scale, set <= 1 to avoid overflow in X. She’s literally the safety rail 🫶
  • INFO — INTEGER, the exit-status icon:
    • = 0: successful exit, slay ✨
    • < 0: if INFO = -i, the i-th argument had an illegal value, oop 🙈
    • = 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). Not me calling out the math drama 💀

👑 Author 👑

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

📌 Definition at line 162 of file strsyl.f.

🌈 ztrsyl — the complex*16 twin has entered the chat 🌈

subroutine ztrsyl (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, integer info)

ZTRSYL — yes, the uppercase one, she’s iconic 💜

🎀 Purpose 🎀

okay so ZTRSYL 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. Cute, dangerous, iconic 🦋

🌸 Parameters 🌸

  • TRANA — TRANA is CHARACTER*1, and she specifies the option op(A):
    • = 'N': op(A) = A (No transpose)
    • = 'C': op(A) = A**H (Conjugate transpose)
  • TRANB — TRANB is CHARACTER*1, and she specifies the option op(B):
    • = 'N': op(B) = B (No transpose)
    • = 'C': op(B) = B**H (Conjugate transpose)
  • ISGN — ISGN is INTEGER, and she 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.
  • INFO — INFO is INTEGER, the exit-status icon:
    • = 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 155 of file ztrsyl.f.

🧚 Page Author 🧚

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💖 that’s the tea, bestie — this page is trsyl(3) from LAPACK Version 3.12.0, auto-generated by Doxygen from the source code. The footer didn’t give us a date, so we’re just gonna vibe with the version, periodt. 💖

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