tgsy2(3)

📦

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💖 `tgsy2(3)` — Sylvester equation panel (?) 💖

✨ NAME ✨

tgsy2 — tgsy2: Sylvester equation panel (?)

🌸 SYNOPSIS 🌸

✨ Functions ✨

subroutine ctgsy2 (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, rdsum, rdscal, info) — CTGSY2 solves the generalized Sylvester equation (unblocked algorithm).
subroutine dtgsy2 (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, rdsum, rdscal, iwork, pq, info) — DTGSY2 solves the generalized Sylvester equation (unblocked algorithm).
subroutine stgsy2 (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, rdsum, rdscal, iwork, pq, info) — STGSY2 solves the generalized Sylvester equation (unblocked algorithm).
subroutine ztgsy2 (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, rdsum, rdscal, info) — ZTGSY2 solves the generalized Sylvester equation (unblocked algorithm).

💫 DETAILED DESCRIPTION 💫

Okay so the original gives this section a heading and then literally zero body text — minimalist icon behavior — so we’re moving straight to the function docs. 💅

🎀 FUNCTION DOCUMENTATION 🎀

💖 `subroutine ctgsy2` 💖

subroutine ctgsy2 (character trans, integer ijob, integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( ldd, * ) d, integer ldd, complex, dimension( lde, * ) e, integer lde, complex, dimension( ldf, * ) f, integer ldf, real scale, real rdsum, real rdscal, integer info)

CTGSY2 solves the generalized Sylvester equation (unblocked algorithm).

🧪 Purpose 🧪

Bestie, here’s the main character energy: CTGSY2 solves the generalized Sylvester equation

A * R - L * B = scale *  C               (1)
D * R - L * E = scale * F

using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices, (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M, N-by-N and M-by-N, respectively. A, B, D and E are upper triangular (i.e., (A,D) and (B,E) in generalized Schur form).

The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor chosen to avoid overflow.

In matrix notation solving equation (1) corresponds to solve Zx = scale * b, where Z is defined as

       Z = [ kron(In, A)  -kron(B**H, Im) ]             (2)
           [ kron(In, D)  -kron(E**H, Im) ],

Ik is the identity matrix of size k and X**H is the transpose of X. kron(X, Y) is the Kronecker product between the matrices X and Y.

If TRANS = 'C', y in the conjugate transposed system Z**H*y = scale*b is solved for, which is equivalent to solve for R and L in

            A**H * R  + D**H * L   = scale * C           (3)
            R  * B**H + L  * E**H  = scale * -F

This case is used to compute an estimate of Dif[(A, D), (B, E)] = sigma_min(Z) using reverse communication with CLACON.

CTGSY2 also (IJOB >= 1) contributes to the computation in CTGSYL of an upper bound on the separation between two matrix pairs. Then the input (A, D), (B, E) are sub-pencils of two matrix pairs in CTGSYL.

💅 Parameters 💅

TRANS — is CHARACTER*1 💫 = 'N': solve the generalized Sylvester equation (1). = 'T': solve the 'transposed' system (3).
IJOB — is INTEGER ✨ Specifies what kind of functionality to be performed. = 0: solve (1) only. = 1: A contribution from this subsystem to a Frobenius norm-based estimate of the separation between two matrix pairs is computed. (look ahead strategy is used). = 2: A contribution from this subsystem to a Frobenius norm-based estimate of the separation between two matrix pairs is computed. (SGECON on sub-systems is used.) Not referenced if TRANS = 'T'.
M — is INTEGER. On entry, M specifies the order of A and D, and the row dimension of C, F, R and L.
N — is INTEGER. On entry, N specifies the order of B and E, and the column dimension of C, F, R and L.
A — is COMPLEX array, dimension (LDA, M). On entry, A contains an upper triangular matrix.
LDA — is INTEGER. The leading dimension of the matrix A. LDA >= max(1, M).
B — is COMPLEX array, dimension (LDB, N). On entry, B contains an upper triangular matrix.
LDB — is INTEGER. The leading dimension of the matrix B. LDB >= max(1, N).
C — is COMPLEX array, dimension (LDC, N). On entry, C contains the right-hand-side of the first matrix equation in (1). On exit, if IJOB = 0, C has been overwritten by the solution R.
LDC — is INTEGER. The leading dimension of the matrix C. LDC >= max(1, M).
D — is COMPLEX array, dimension (LDD, M). On entry, D contains an upper triangular matrix.
LDD — is INTEGER. The leading dimension of the matrix D. LDD >= max(1, M).
E — is COMPLEX array, dimension (LDE, N). On entry, E contains an upper triangular matrix.
LDE — is INTEGER. The leading dimension of the matrix E. LDE >= max(1, N).
F — is COMPLEX array, dimension (LDF, N). On entry, F contains the right-hand-side of the second matrix equation in (1). On exit, if IJOB = 0, F has been overwritten by the solution L.
LDF — is INTEGER. The leading dimension of the matrix F. LDF >= max(1, M).
SCALE — is REAL. On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions R and L (C and F on entry) will hold the solutions to a slightly perturbed system but the input matrices A, B, D and E have not been changed. If SCALE = 0, R and L will hold the solutions to the homogeneous system with C = F = 0. Normally, SCALE = 1.
RDSUM — is REAL. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by CTGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T' RDSUM is not touched. NOTE: RDSUM only makes sense when CTGSY2 is called by CTGSYL.
RDSCAL — is REAL. On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched. NOTE: RDSCAL only makes sense when CTGSY2 is called by CTGSYL.
INFO — is INTEGER. On exit, if INFO is set to =0: Successful exit. <0: If INFO = -i, input argument number i is illegal. >0: The matrix pairs (A, D) and (B, E) have common or very close eigenvalues.

👑 Author 👑

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

🌸 Contributors: 🌸

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

Definition at line 256 of file ctgsy2.f.

💙 `subroutine dtgsy2` 💙

subroutine dtgsy2 (character trans, integer ijob, 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, dimension( ldd, * ) d, integer ldd, double precision, dimension( lde, * ) e, integer lde, double precision, dimension( ldf, * ) f, integer ldf, double precision scale, double precision rdsum, double precision rdscal, integer, dimension( * ) iwork, integer pq, integer info)

DTGSY2 solves the generalized Sylvester equation (unblocked algorithm).

🧪 Purpose 🧪

okay so DTGSY2 solves the generalized Sylvester equation:

            A * R - L * B = scale * C                (1)
            D * R - L * E = scale * F,

using Level 1 and 2 BLAS. Here R and L are unknown M-by-N matrices, and (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M, N-by-N and M-by-N, respectively, with real entries. The pairs (A, D) and (B, E) must be in generalized Schur canonical form — that means A, B are upper quasi triangular and D, E are upper triangular. The solution (R, L) overwrites (C, F), and 0 <= SCALE <= 1 is an output scaling factor chosen to avoid overflow. slay.

In matrix notation, solving equation (1) is the same as solving Z*x = scale*b, where Z is defined as:

       Z = [ kron(In, A)  -kron(B**T, Im) ]             (2)
           [ kron(In, D)  -kron(E**T, Im) ],

Ik is the identity matrix of size k, and X**T is the transpose of X. kron(X, Y) is the Kronecker product between the matrices X and Y. In the process of solving (1), we solve a number of such systems where Dim(In), Dim(In) = 1 or 2. iykyk 💅

If TRANS = 'T', solve the transposed system Z**T*y = scale*b for y, which is equivalent to solving for R and L in:

            A**T * R  + D**T * L   = scale * C           (3)
            R  * B**T + L  * E**T  = scale * -F

This case is used to compute an estimate of Dif[(A, D), (B, E)] = sigma_min(Z) using reverse communication with DLACON.

DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL of an upper bound on the separation between two matrix pairs. Then the input (A, D), (B, E) are sub-pencils of the matrix pair in DTGSYL. See DTGSYL for details. periodt 🌿

Parameters 💅

TRANS — is CHARACTER*1.
- = 'N': solve the generalized Sylvester equation (1).
- = 'T': solve the 'transposed' system (3).
IJOB — is INTEGER. Specifies what kind of functionality to be performed.
- = 0: solve (1) only.
- = 1: a contribution from this subsystem to a Frobenius norm-based estimate of the separation between two matrix pairs is computed. (look ahead strategy is used).
- = 2: a contribution from this subsystem to a Frobenius norm-based estimate of the separation between two matrix pairs is computed. (DGECON on sub-systems is used.)
- Not referenced if TRANS = 'T'.
M — is INTEGER. On entry, M specifies the order of A and D, and the row dimension of C, F, R and L.
N — is INTEGER. On entry, N specifies the order of B and E, and the column dimension of C, F, R and L.
A — is DOUBLE PRECISION array, dimension (LDA, M). On entry, A contains an upper quasi triangular matrix.
LDA — is INTEGER. The leading dimension of the matrix A. LDA >= max(1, M).
B — is DOUBLE PRECISION array, dimension (LDB, N). On entry, B contains an upper quasi triangular matrix.
LDB — is INTEGER. The leading dimension of the matrix B. LDB >= max(1, N).
C — is DOUBLE PRECISION array, dimension (LDC, N). On entry, C contains the right-hand-side of the first matrix equation in (1). On exit, if IJOB = 0, C has been overwritten by the solution R.
LDC — is INTEGER. The leading dimension of the matrix C. LDC >= max(1, M).
D — is DOUBLE PRECISION array, dimension (LDD, M). On entry, D contains an upper triangular matrix.
LDD — is INTEGER. The leading dimension of the matrix D. LDD >= max(1, M).
E — is DOUBLE PRECISION array, dimension (LDE, N). On entry, E contains an upper triangular matrix.
LDE — is INTEGER. The leading dimension of the matrix E. LDE >= max(1, N).
F — is DOUBLE PRECISION array, dimension (LDF, N). On entry, F contains the right-hand-side of the second matrix equation in (1). On exit, if IJOB = 0, F has been overwritten by the solution L.
LDF — is INTEGER. The leading dimension of the matrix F. LDF >= max(1, M).
SCALE — is DOUBLE PRECISION. On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions R and L (C and F on entry) will hold the solutions to a slightly perturbed system but the input matrices A, B, D and E have not been changed. If SCALE = 0, R and L will hold the solutions to the homogeneous system with C = F = 0. Normally, SCALE = 1.
RDSUM — is DOUBLE PRECISION. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by DTGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T', RDSUM is not touched.

NOTE: RDSUM only makes sense when DTGSY2 is called by DTGSYL.

RDSCAL — is DOUBLE PRECISION. On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched.

NOTE: RDSCAL only makes sense when DTGSY2 is called by DTGSYL.

IWORK — is INTEGER array, dimension (M+N+2).
PQ — is INTEGER. On exit, the number of subsystems (of size 2-by-2, 4-by-4 and 8-by-8) solved by this routine.
INFO — is INTEGER. On exit, if INFO is set to:
- =0: Successful exit
- <0: If INFO = -i, the i-th argument had an illegal value.
- >0: The matrix pairs (A, D) and (B, E) have common or very close eigenvalues.

Author 🫶

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

Contributors: 🧚

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

Definition at line 271 of file dtgsy2.f.

subroutine `stgsy2` 🌸

   subroutine stgsy2 (character trans, integer ijob, integer m, integer n,
       real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,
       integer ldb, real, dimension( ldc, * ) c, integer ldc, real, dimension(
       ldd, * ) d, integer ldd, real, dimension( lde, * ) e, integer lde, real,
       dimension( ldf, * ) f, integer ldf, real scale, real rdsum, real rdscal,
       integer, dimension( * ) iwork, integer pq, integer info)

STGSY2 solves the generalized Sylvester equation (unblocked algorithm).

Purpose ✨

okay so STGSY2 solves the generalized Sylvester equation:

            A * R - L * B = scale * C                (1)
            D * R - L * E = scale * F,

In matrix notation, solving equation (1) is the same as solving Z*x = scale*b, where Z is defined as:

       Z = [ kron(In, A)  -kron(B**T, Im) ]             (2)
           [ kron(In, D)  -kron(E**T, Im) ],

If TRANS = 'T', solve the transposed system Z**T*y = scale*b for y, which is equivalent to solving for R and L in:

            A**T * R  + D**T * L   = scale * C           (3)
            R  * B**T + L  * E**T  = scale * -F

This case is used to compute an estimate of Dif[(A, D), (B, E)] = sigma_min(Z) using reverse communication with SLACON.

STGSY2 also (IJOB >= 1) contributes to the computation in STGSYL of an upper bound on the separation between two matrix pairs. Then the input (A, D), (B, E) are sub-pencils of the matrix pair in STGSYL. See STGSYL for details. ate 💚

Parameters 🎀

TRANS — is CHARACTER*1.
- = 'N': solve the generalized Sylvester equation (1).
- = 'T': solve the 'transposed' system (3).
IJOB
IJOB — INTEGER, bestie, and it tells us what flavor of work we're doing. = 0: solve (1) only. = 1: a contribution from this subsystem to a Frobenius norm-based estimate of the separation between two matrix pairs is computed (look ahead strategy is used). = 2: same Frobenius norm-based separation contribution, but SGECON on sub-systems is used. Not referenced if TRANS = 'T'. 👑
M — INTEGER. On entry, M specifies the order of A and D, and the row dimension of C, F, R and L. 💅
N — INTEGER. On entry, N specifies the order of B and E, and the column dimension of C, F, R and L. ✨
A — REAL array, dimension (LDA, M). On entry, A contains an upper quasi triangular matrix. 🦋
LDA — INTEGER. The leading dimension of the matrix A. LDA >= max(1, M). 🎀
B — REAL array, dimension (LDB, N). On entry, B contains an upper quasi triangular matrix. 🌸
LDB — INTEGER. The leading dimension of the matrix B. LDB >= max(1, N). 🎀
C — REAL array, dimension (LDC, N). On entry, C contains the right-hand-side of the first matrix equation in (1). On exit, if IJOB = 0, C has been overwritten by the solution R. 💖
LDC — INTEGER. The leading dimension of the matrix C. LDC >= max(1, M). 🎀
D — REAL array, dimension (LDD, M). On entry, D contains an upper triangular matrix. 🌈
LDD — INTEGER. The leading dimension of the matrix D. LDD >= max(1, M). 🎀
E — REAL array, dimension (LDE, N). On entry, E contains an upper triangular matrix. 🌈
LDE — INTEGER. The leading dimension of the matrix E. LDE >= max(1, N). 🎀
F — REAL array, dimension (LDF, N). On entry, F contains the right-hand-side of the second matrix equation in (1). On exit, if IJOB = 0, F has been overwritten by the solution L. 💖
LDF — INTEGER. The leading dimension of the matrix F. LDF >= max(1, M). 🎀
SCALE — REAL. On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions R and L (C and F on entry) will hold the solutions to a slightly perturbed system but the input matrices A, B, D and E have not been changed. If SCALE = 0, R and L will hold the solutions to the homogeneous system with C = F = 0. Normally, SCALE = 1. 🫶
RDSUM — REAL. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by STGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T', RDSUM is not touched. NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL. 😭
RDSCAL — REAL. On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched. NOTE: RDSCAL only makes sense when STGSY2 is called by STGSYL. 😭
IWORK — INTEGER array, dimension (M+N+2). 🧚
PQ — INTEGER. On exit, the number of subsystems (of size 2-by-2, 4-by-4 and 8-by-8) solved by this routine. 👑
INFO — INTEGER. On exit, if INFO is set to =0: successful exit. <0: if INFO = -i, the i-th argument had an illegal value. >0: the matrix pairs (A, D) and (B, E) have common or very close eigenvalues. 💀

✨ Author ✨

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🫶 Contributors: 🫶

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

Definition at line 271 of file stgsy2.f. 🎀

🦋 `subroutine ztgsy2` 🦋

subroutine ztgsy2 (character trans, integer ijob, 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,
    complex*16, dimension( ldd, * ) d, integer ldd, complex*16, dimension(
    lde, * ) e, integer lde, complex*16, dimension( ldf, * ) f, integer ldf,
    double precision scale, double precision rdsum, double precision rdscal,
    integer info)

ZTGSY2 solves the generalized Sylvester equation (unblocked algorithm). 🔥

Purpose: ✨

ZTGSY2 solves the generalized Sylvester equation

A * R - L * B = scale * C               (1)
D * R - L * E = scale * F

using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices, (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M, N-by-N and M-by-N, respectively. A, B, D and E are upper triangular (i.e., (A,D) and (B,E) in generalized Schur form). 💅

The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor chosen to avoid overflow. 🫶

In matrix notation solving equation (1) corresponds to solve Zx = scale * b, where Z is defined as

Z = [ kron(In, A)  -kron(B**H, Im) ]             (2)
    [ kron(In, D)  -kron(E**H, Im) ],

Ik is the identity matrix of size k and X**H is the conjugate transpose of X. kron(X, Y) is the Kronecker product between the matrices X and Y. 🌈

If TRANS = 'C', y in the conjugate transposed system Z**H*y = scale*b is solved for, which is equivalent to solve for R and L in

A**H * R  + D**H * L   = scale * C           (3)
R  * B**H + L  * E**H  = scale * -F

This case is used to compute an estimate of Dif[(A, D), (B, E)] = sigma_min(Z) using reverse communication with ZLACON. 👑

ZTGSY2 also (IJOB >= 1) contributes to the computation in ZTGSYL of an upper bound on the separation between two matrix pairs. Then the input (A, D), (B, E) are sub-pencils of two matrix pairs in ZTGSYL. 🌟

Parameters 🎀

TRANS — CHARACTER*1. = 'N': solve the generalized Sylvester equation (1). = 'T': solve the 'transposed' system (3). fun fact: the Purpose section above says 'C' for the conjugate-transposed case, while this parameter list says 'T' — that's the page's own plot twist, not mine 💀
IJOB — INTEGER. Specifies what kind of functionality to be performed. =0: solve (1) only. =1: a contribution from this subsystem to a Frobenius norm-based estimate of the separation between two matrix pairs is computed (look ahead strategy is used). =2: a contribution from this subsystem to a Frobenius norm-based estimate of the separation between two matrix pairs is computed (DGECON on sub-systems is used). Not referenced if TRANS = 'T'. 💅
M — INTEGER. On entry, M specifies the order of A and D, and the row dimension of C, F, R and L. ✨
N — INTEGER. On entry, N specifies the order of B and E, and the column dimension of C, F, R and L. ✨
A — COMPLEX*16 array, dimension (LDA, M). On entry, A contains an upper triangular matrix. 🦋
LDA — INTEGER. The leading dimension of the matrix A. LDA >= max(1, M). 🎀
B — COMPLEX*16 array, dimension (LDB, N). On entry, B contains an upper triangular matrix. 🌸
LDB — INTEGER. The leading dimension of the matrix B. LDB >= max(1, N). 🎀
C — COMPLEX*16 array, dimension (LDC, N). On entry, C contains the right-hand-side of the first matrix equation in (1). On exit, if IJOB = 0, C has been overwritten by the solution R. 💖
LDC — INTEGER. The leading dimension of the matrix C. LDC >= max(1, M). 🎀
D — COMPLEX*16 array, dimension (LDD, M). On entry, D contains an upper triangular matrix. 🌈
LDD — INTEGER. The leading dimension of the matrix D. LDD >= max(1, M). 🎀
E — COMPLEX*16 array, dimension (LDE, N). On entry, E contains an upper triangular matrix. 🌈
LDE — INTEGER. The leading dimension of the matrix E. LDE >= max(1, N). 🎀
F — COMPLEX*16 array, dimension (LDF, N). On entry, F contains the right-hand-side of the second matrix equation in (1). On exit, if IJOB = 0, F has been overwritten by the solution L. 💖
LDF — INTEGER. The leading dimension of the matrix F. LDF >= max(1, M). 🎀

Last little batch of params, bestie — then you’re literally free 💅

SCALE — DOUBLE PRECISION. On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions R and L (C and F on entry) will hold the solutions to a slightly perturbed system, but the input matrices A, B, D and E have not been changed. If SCALE = 0, R and L will hold the solutions to the homogeneous system with C = F = 0. Normally, SCALE = 1 — so the normal vibe is SCALE = 1, periodt ✨
RDSUM — DOUBLE PRECISION. On entry, the sum of squares of computed contributions to the Dif-estimate under computation by ZTGSYL, where the scaling factor RDSCAL (see below) has been factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T', RDSUM is not touched 🙈

NOTE: RDSUM only makes sense when ZTGSY2 is called by ZTGSYL.

RDSCAL — DOUBLE PRECISION. On entry, scaling factor used to prevent overflow in RDSUM. On exit, RDSCAL is updated w.r.t. the current contributions in RDSUM. If TRANS = 'T', RDSCAL is not touched 🙈

NOTE: RDSCAL only makes sense when ZTGSY2 is called by ZTGSYL.

INFO — INTEGER. On exit, if INFO is set to:
- =0: Successful exit
- <0: If INFO = -i, input argument number i is illegal.
- >0: The matrix pairs (A, D) and (B, E) have common or very close eigenvalues.

✨ Author ✨

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

✨ Contributors ✨

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

Definition at line 256 of file ztgsy2.f.

✨ Author (the Doxygen autogen one) ✨

Generated automatically by Doxygen for LAPACK from the source code.

xoxo, this page is serving LAPACK Version 3.12.0 realness and it’s the tgsy2(3) page — go forth and slay your linear algebra, bestie 💅✨🫶

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

tgsy2(3)

💖 tgsy2(3) — Sylvester equation panel (?) 💖

✨ NAME ✨

🌸 SYNOPSIS 🌸

✨ Functions ✨

💫 DETAILED DESCRIPTION 💫

🎀 FUNCTION DOCUMENTATION 🎀

💖 subroutine ctgsy2 💖

🧪 Purpose 🧪

💅 Parameters 💅

👑 Author 👑

🌸 Contributors: 🌸

💙 subroutine dtgsy2 💙

🧪 Purpose 🧪

Parameters 💅

Author 🫶

Contributors: 🧚

subroutine stgsy2 🌸

Purpose ✨

Parameters 🎀

✨ Author ✨

🫶 Contributors: 🫶

🦋 subroutine ztgsy2 🦋

✨ Author ✨

✨ Contributors ✨

✨ Author (the Doxygen autogen one) ✨

💖 `tgsy2(3)` — Sylvester equation panel (?) 💖

💖 `subroutine ctgsy2` 💖

💙 `subroutine dtgsy2` 💙

subroutine `stgsy2` 🌸

🦋 `subroutine ztgsy2` 🦋