ggsvp3(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

, in arch rolling

okay bestie, welcome to ggsvp3(3) from the Library Functions Manual — and yes, it’s giving “step in ggsvd” energy 💅

🌸 NAME 🌸

ggsvp3 — ggsvp3: step in ggsvd

✨ SYNOPSIS ✨

✨ Functions ✨

CGGSVP3 — subroutine cggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)
DGGSVP3 — subroutine dggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, tau, work, lwork, info)
SGGSVP3 — subroutine sggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, tau, work, lwork, info)
ZGGSVP3 — subroutine zggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)

💅 Detailed Description 💅

No extra little summary here, bestie — it jumps straight into the function docs.

👑 Function Documentation 👑

💖 subroutine `cggsvp3` 💖

subroutine cggsvp3 (character jobu, character jobv, character jobq, integer
    m, integer p, integer n, complex, dimension( lda, * ) a, integer lda,
    complex, dimension( ldb, * ) b, integer ldb, real tola, real tolb,
    integer k, integer l, complex, dimension( ldu, * ) u, integer ldu,
    complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldq, *
    ) q, integer ldq, integer, dimension( * ) iwork, real, dimension( * )
    rwork, complex, dimension( * ) tau, complex, dimension( * ) work,
    integer lwork, integer info)

CGGSVP3

🎀 Purpose 🎀

Okay so CGGSVP3 computes unitary matrices U, V and Q such that:

                   N-K-L  K    L
 U**H*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
                L ( 0     0   A23 )
            M-K-L ( 0     0    0  )

                 N-K-L  K    L
        =     K ( 0    A12  A13 )  if M-K-L < 0;
            M-K ( 0     0   A23 )

                 N-K-L  K    L
 V**H*B*Q =   L ( 0     0   B13 )
            P-L ( 0     0    0  )

Where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.

This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine CGGSVD3.

🧸 Parameters 🧸

JOBU — JOBU is CHARACTER*1; 'U': Unitary matrix U is computed; 'N': U is not computed.
JOBV — JOBV is CHARACTER*1; 'V': Unitary matrix V is computed; 'N': V is not computed.
JOBQ — JOBQ is CHARACTER*1; 'Q': Unitary matrix Q is computed; 'N': Q is not computed.
M — M is INTEGER. The number of rows of the matrix A. M >= 0.
P — P is INTEGER. The number of rows of the matrix B. P >= 0.
N — N is INTEGER. The number of columns of the matrices A and B. N >= 0.
A — A is COMPLEX array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
B — B is COMPLEX array, dimension (LDB,N). On entry, the P-by-N matrix B. On exit, B contains the triangular matrix described in the Purpose section.
LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,P).
TOLA — TOLA is REAL.
TOLB — TOLB is REAL.

TOLA and TOLB are the thresholds to determine the effective numerical rank of matrix B and a subblock of A. Generally, they are set to TOLA = MAX(M,N)*norm(A)*MACHEPS, TOLB = MAX(P,N)*norm(B)*MACHEPS. The size of TOLA and TOLB may affect the size of backward errors of the decomposition.

K — K is INTEGER.
L — L is INTEGER. On exit, K and L specify the dimension of the subblocks described in the Purpose section. K + L = effective numerical rank of (A**H,B**H)**H.
U — U is COMPLEX array, dimension (LDU,M). If JOBU = 'U', U contains the unitary matrix U. If JOBU = 'N', U is not referenced.
LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
V — V is COMPLEX array, dimension (LDV,P). If JOBV = 'V', V contains the unitary matrix V. If JOBV = 'N', V is not referenced.
LDV — LDV is INTEGER. The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
Q — Q is COMPLEX array, dimension (LDQ,N). If JOBQ = 'Q', Q contains the unitary matrix Q. If JOBQ = 'N', Q is not referenced.
LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK — IWORK is INTEGER array, dimension (N).
RWORK — RWORK is REAL array, dimension (2*N).
TAU — TAU is COMPLEX array, dimension (N).
WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.

🌟 Author 🌟

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

🔥 Further Details 🔥

The subroutine uses LAPACK subroutine CGEQP3 for the QR factorization with column pivoting to detect the effective numerical rank of a matrix. It may be replaced by a better rank determination strategy.

CGGSVP3 replaces the deprecated subroutine CGGSVP.

Definition at line 275 of file cggsvp3.f.

💜 subroutine `dggsvp3` 💜

subroutine dggsvp3 (character jobu, character jobv, character jobq, integer
    m, integer p, integer n, double precision, dimension( lda, * ) a,
    integer lda, double precision, dimension( ldb, * ) b, integer ldb,
    double precision tola, double precision tolb, integer k, integer l,
    double precision, dimension( ldu, * ) u, integer ldu, double precision,
    dimension( ldv, * ) v, integer ldv, double precision, dimension( ldq, *
    ) q, integer ldq, integer, dimension( * ) iwork, double precision,
    dimension( * ) tau, double precision, dimension( * ) work, integer
    lwork, integer info)

DGGSVP3

🎀 Purpose 🎀

Okay so DGGSVP3 computes orthogonal matrices U, V and Q such that:

                   N-K-L  K    L
 U**T*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
                L ( 0     0   A23 )
            M-K-L ( 0     0    0  )

                 N-K-L  K    L
        =     K ( 0    A12  A13 )  if M-K-L < 0;
            M-K ( 0     0   A23 )

                 N-K-L  K    L
 V**T*B*Q =   L ( 0     0   B13 )
            P-L ( 0     0    0  )

This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine DGGSVD3.

🧸 Parameters 🧸

JOBU — JOBU is CHARACTER*1; 'U': Orthogonal matrix U is computed; 'N': U is not computed.
JOBV — JOBV is CHARACTER*1; 'V': Orthogonal matrix V is computed; 'N': V is not computed.
JOBQ — JOBQ is CHARACTER*1; 'Q': Orthogonal matrix Q is computed; 'N': Q is not computed.
M — M is INTEGER. The number of rows of the matrix A. M >= 0.
P — P is INTEGER. The number of rows of the matrix B. P >= 0.
N — N is INTEGER. The number of columns of the matrices A and B. N >= 0.
A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
B
B — DOUBLE PRECISION array, dimension (LDB,N). On entry, it’s the P-by-N matrix B. On exit, B contains the triangular matrix described in the Purpose section. 🫶
LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,P). no cap.
TOLA — DOUBLE PRECISION.
TOLB — DOUBLE PRECISION.

TOLA and TOLB are the thresholds that determine the effective numerical rank of matrix B and a subblock of A. Generally, they’re set to:

TOLA = MAX(M,N)*norm(A)*MACHEPS
TOLB = MAX(P,N)*norm(B)*MACHEPS

The size of TOLA and TOLB may affect the size of backward errors of the decomposition. 🎀

K — INTEGER.
L — INTEGER. On exit, K and L specify the dimension of the subblocks described in the Purpose section. K + L = effective numerical rank of (A**T,B**T)**T. ✨
U — DOUBLE PRECISION array, dimension (LDU,M). If JOBU = 'U', U contains the orthogonal matrix U. If JOBU = 'N', U is not referenced. 💅
LDU — INTEGER. The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
V — DOUBLE PRECISION array, dimension (LDV,P). If JOBV = 'V', V contains the orthogonal matrix V. If JOBV = 'N', V is not referenced. 🦋
LDV — INTEGER. The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
Q — DOUBLE PRECISION array, dimension (LDQ,N). If JOBQ = 'Q', Q contains the orthogonal matrix Q. If JOBQ = 'N', Q is not referenced. 🌸
LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK — INTEGER array, dimension (N).
TAU — DOUBLE PRECISION array, dimension (N).
WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 👑
LWORK — INTEGER. The dimension of the array WORK. LWORK >= 1.

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

INFO — INTEGER.
- = 0: successful exit.
- < 0: if INFO = -i, the i-th argument had an illegal value.

💖 Author 💖

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

🫶 Further Details: 🫶

The subroutine uses LAPACK subroutine DGEQP3 for the QR factorization with column pivoting to detect the effective numerical rank of the a matrix. It may be replaced by a better rank determination strategy.

DGGSVP3 replaces the deprecated subroutine DGGSVP. periodt.

Definition at line 269 of file dggsvp3.f.

🌈 `subroutine sggsvp3` 🌈

subroutine sggsvp3 (character jobu, character jobv, character jobq, integer
m, integer p, integer n, real, dimension( lda, * ) a, integer lda, real,
dimension( ldb, * ) b, integer ldb, real tola, real tolb, integer k,
integer l, real, dimension( ldu, * ) u, integer ldu, real, dimension(
ldv, * ) v, integer ldv, real, dimension( ldq, * ) q, integer ldq,
integer, dimension( * ) iwork, real, dimension( * ) tau, real,
dimension( * ) work, integer lwork, integer info)
SGGSVP3

🎯 Purpose: 🎯

SGGSVP3 computes orthogonal matrices U, V and Q such that:

                   N-K-L  K    L
 U**T*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
                L ( 0     0   A23 )
            M-K-L ( 0     0    0  )

                 N-K-L  K    L
        =     K ( 0    A12  A13 )  if M-K-L < 0;
            M-K ( 0     0   A23 )

                 N-K-L  K    L
 V**T*B*Q =   L ( 0     0   B13 )
            P-L ( 0     0    0  )

where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T.

This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine SGGSVD3. 💜

🧮 Parameters 🧮

JOBU — CHARACTER*1.
- = 'U': Orthogonal matrix U is computed;
- = 'N': U is not computed.
JOBV — CHARACTER*1.
- = 'V': Orthogonal matrix V is computed;
- = 'N': V is not computed.
JOBQ — CHARACTER*1.
- = 'Q': Orthogonal matrix Q is computed;
- = 'N': Q is not computed.
M — INTEGER. The number of rows of the matrix A. M >= 0.
P — INTEGER. The number of rows of the matrix B. P >= 0.
N — INTEGER. The number of columns of the matrices A and B. N >= 0.
A — REAL array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section. 🌟
LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
B — REAL array, dimension (LDB,N). On entry, the P-by-N matrix B. On exit, B contains the triangular matrix described in the Purpose section.
LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,P).
TOLA — REAL.
TOLB — REAL.

TOLA and TOLB are the thresholds to determine the effective numerical rank of matrix B and a subblock of A. Generally, they are set to:

TOLA = MAX(M,N)*norm(A)*MACHEPS
TOLB = MAX(P,N)*norm(B)*MACHEPS

The size of TOLA and TOLB may affect the size of backward errors of the decomposition.

K — INTEGER.
L — INTEGER. On exit, K and L specify the dimension of the subblocks described in Purpose section. K + L = effective numerical rank of (A**T,B**T)**T. ✨
U — REAL array, dimension (LDU,M). If JOBU = 'U', U contains the orthogonal matrix U. If JOBU = 'N', U is not referenced. 💅
LDU — INTEGER. The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
V — REAL array, dimension (LDV,P). If JOBV = 'V', V contains the orthogonal matrix V. If JOBV = 'N', V is not referenced. 🦋
LDV — INTEGER. The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
Q — REAL array, dimension (LDQ,N). If JOBQ = 'Q', Q contains the orthogonal matrix Q. If JOBQ = 'N', Q is not referenced. 🌸
LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK — INTEGER array, dimension (N).
TAU — REAL array, dimension (N).
WORK — REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 👑
LWORK — INTEGER. The dimension of the array WORK. LWORK >= 1.

INFO — INTEGER.
- = 0: successful exit.
- < 0: if INFO = -i, the i-th argument had an illegal value.

💖 Author 💖

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

🫶 Further Details: 🫶

The subroutine uses LAPACK subroutine SGEQP3 for the QR factorization with column pivoting to detect the effective numerical rank of the a matrix. It may be replaced by a better rank determination strategy.

SGGSVP3 replaces the deprecated subroutine SGGSVP. periodt.

Definition at line 269 of file sggsvp3.f.

okay bestie, no intro needed — here's the exact signature for ZGGSVP3, and yes you can copy-paste this, it's precious:

   subroutine zggsvp3 (character jobu, character jobv, character jobq, integer
       m, integer p, integer n, complex*16, dimension( lda, * ) a, integer lda,
       complex*16, dimension( ldb, * ) b, integer ldb, double precision tola,
       double precision tolb, integer k, integer l, complex*16, dimension( ldu,
       * ) u, integer ldu, complex*16, dimension( ldv, * ) v, integer ldv,
       complex*16, dimension( ldq, * ) q, integer ldq, integer, dimension( * )
       iwork, double precision, dimension( * ) rwork, complex*16, dimension( *
       ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

the routine is literally called ZGGSVP3 — all caps, main character energy, periodt.

✨ Purpose ✨

ZGGSVP3 computes unitary matrices U, V and Q such that

                   N-K-L  K    L
 U**H*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
                L ( 0     0   A23 )
            M-K-L ( 0     0    0  )

                 N-K-L  K    L
        =     K ( 0    A12  A13 )  if M-K-L < 0;
            M-K ( 0     0   A23 )

                 N-K-L  K    L
 V**H*B*Q =   L ( 0     0   B13 )
            P-L ( 0     0    0  )

This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine ZGGSVD3.

🫶 Parameters 🫶

okay, parameter dump time — every single one matters, no skipping 💅

JOBU — CHARACTER*1. = 'U': unitary matrix U is computed; = 'N': U is not computed.
JOBV — CHARACTER*1. = 'V': unitary matrix V is computed; = 'N': V is not computed.
JOBQ — CHARACTER*1. = 'Q': unitary matrix Q is computed; = 'N': Q is not computed.
M — INTEGER. The number of rows of the matrix A. M >= 0.
P — INTEGER. The number of rows of the matrix B. P >= 0.
N — INTEGER. The number of columns of the matrices A and B. N >= 0.
A — COMPLEX*16 array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, A contains the triangular (or trapezoidal) matrix described in the Purpose section.
LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
B — COMPLEX*16 array, dimension (LDB,N). On entry, the P-by-N matrix B. On exit, B contains the triangular matrix described in the Purpose section.
LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,P).
TOLA — DOUBLE PRECISION.
TOLB — DOUBLE PRECISION. TOLA and TOLB are the thresholds to determine the effective numerical rank of matrix B and a subblock of A. Generally, they are set to TOLA = MAX(M,N)*norm(A)*MAZHEPS, TOLB = MAX(P,N)*norm(B)*MAZHEPS. The size of TOLA and TOLB may affect the size of backward errors of the decomposition.
K — INTEGER.
L — INTEGER. On exit, K and L specify the dimension of the subblocks described in the Purpose section. K + L = effective numerical rank of (A**H,B**H)**H.
U — COMPLEX*16 array, dimension (LDU,M). If JOBU = 'U', U contains the unitary matrix U. If JOBU = 'N', U is not referenced.
LDU — INTEGER. The leading dimension of the array U. LDU >= max(1,M) if JOBU = 'U'; LDU >= 1 otherwise.
V — COMPLEX*16 array, dimension (LDV,P). If JOBV = 'V', V contains the unitary matrix V. If JOBV = 'N', V is not referenced.
LDV — INTEGER. The leading dimension of the array V. LDV >= max(1,P) if JOBV = 'V'; LDV >= 1 otherwise.
Q — COMPLEX*16 array, dimension (LDQ,N). If JOBQ = 'Q', Q contains the unitary matrix Q. If JOBQ = 'N', Q is not referenced.
LDQ — INTEGER. The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK — INTEGER array, dimension (N).
RWORK — DOUBLE PRECISION array, dimension (2*N).
TAU — COMPLEX*16 array, dimension (N).
WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK — INTEGER. The dimension of the array WORK. LWORK >= 1. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
INFO — INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.

👑 Author 👑

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

🔥 Further Details 🔥

The subroutine uses LAPACK subroutine ZGEQP3 for the QR factorization with column pivoting to detect the effective numerical rank of the a matrix. It may be replaced by a better rank determination strategy.

ZGGSVP3 replaces the deprecated subroutine ZGGSVP.

deprecated means don't use the old one, bestie — she's been replaced 👑

📌 Definition at line 📌

Definition at line 275 of file zggsvp3.f.

🎀 Author (generated) 🎀

Generated automatically by Doxygen for LAPACK from the source code.

that's the whole page, bestie — LAPACK Version 3.12.0, page ggsvp3(3), signed sealed and slaying 💖💅

📦 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

ggsvp3(3)

🌸 NAME 🌸

✨ SYNOPSIS ✨

✨ Functions ✨

💅 Detailed Description 💅

👑 Function Documentation 👑

💖 subroutine cggsvp3 💖

🎀 Purpose 🎀

🧸 Parameters 🧸

🌟 Author 🌟

🔥 Further Details 🔥

💜 subroutine dggsvp3 💜

🎀 Purpose 🎀

🧸 Parameters 🧸

💖 Author 💖

🫶 Further Details: 🫶

🌈 subroutine sggsvp3 🌈

🎯 Purpose: 🎯

🧮 Parameters 🧮

💖 Author 💖

🫶 Further Details: 🫶

✨ Purpose ✨

🫶 Parameters 🫶

👑 Author 👑

🔥 Further Details 🔥

📌 Definition at line 📌

🎀 Author (generated) 🎀

💖 subroutine `cggsvp3` 💖

💜 subroutine `dggsvp3` 💜

🌈 `subroutine sggsvp3` 🌈