SRC/sorgtsqr.f(3)

🦋 SRC/sorgtsqr.f 🦋

okay so bestie, this page is from the Library Functions Manual — it’s the SRC/sorgtsqr.f(3) one, and it’s giving LAPACK subroutine main character energy. No cap, we’re covering every single detail together. 💖

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✨ NAME ✨

SRC/sorgtsqr.f — that’s literally the name, bestie. No extra notes. 🎀

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🌸 SYNOPSIS 🌸

Here’s the vibe check on how it’s called:

Functions/Subroutines
    subroutine sorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
        SORGTSQR

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💖 Function/Subroutine Documentation 💖

This is the main character right here — SORGTSQR in all its subroutine glory:

subroutine sorgtsqr (integer m, integer n, integer mb, integer nb, real,
     dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer
     ldt, real, dimension( * ) work, integer lwork, integer info)
     SORGTSQR

🌟 Purpose 🌟

okay so what does it actually do? Obsessed that you asked:

SORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns, which are the first N columns of a product of real orthogonal matrices of order M which are returned by SLATSQR.

Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

See the documentation for SLATSQR. ✨

🎀 Parameters 🎀

okay bestie, here’s the full parameter vibe check. Every single one, no skips:

• M — M is INTEGER. The number of rows of the matrix A. M >= 0. ✅
• N — N is INTEGER. The number of columns of the matrix A. M >= N >= 0. ✅
• MB — MB is INTEGER. The row block size used by SLATSQR to return arrays A and T. MB > N. (Note that if MB > M, then M is used instead of MB as the row block size). 🧱
• NB — NB is INTEGER. The column block size used by SLATSQR to return arrays A and T. NB >= 1. (Note that if NB > N, then N is used instead of NB as the column block size). 🧱
• A — A is REAL array, dimension (LDA,N). On entry:
  • The elements on and above the diagonal are not accessed.
  • The elements below the diagonal represent the unit lower-trapezoidal blocked matrix V computed by SLATSQR that defines the input matrices Q_in(k) (ones on the diagonal are not stored) (same format as the output A below the diagonal in SLATSQR). On exit:
  • The array A contains an M-by-N orthonormal matrix Q_out, i.e the columns of A are orthogonal unit vectors.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• T — T is REAL array, dimension (LDT, N * NIRB) where NIRB = Number_of_input_row_blocks = MAX( 1, CEIL((M-N)/(MB-N)) ). Let NICB = Number_of_input_col_blocks = CEIL(N/NB). The upper-triangular block reflectors used to define the input matrices Q_in(k), k=(1:NIRB*NICB). The block reflectors are stored in compact form in NIRB block reflector sequences. Each of NIRB block reflector sequences is stored in a larger NB-by-N column block of T and consists of NICB smaller NB-by-NB upper-triangular column blocks. (same format as the output T in SLATSQR). ✨
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= max(1,min(NB1,N)). (yes, bestie, it literally says NB1 — keep it exactly like that 💅)
• WORK — (workspace) REAL array, dimension (MAX(2,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= (M+NB)*N. 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.

🧚 Contributors: 🧚

November 2019, Igor Kozachenko, Computer Science Division, University of California, Berkeley. 🍓

Definition at line 174 of file sorgtsqr.f.

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💅 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, source page SRC/sorgtsqr.f(3). Bye! 🫶