SRC/zungtsqr.f(3)

Bestie, welcome to SRC/zungtsqr.f(3) from the Library Functions Manual — today we're decoding zungtsqr, and honestly? It's giving linear algebra royalty 👑✨.

🌸 NAME 🌸

SRC/zungtsqr.f — that's literally the whole name, bestie. This page is all about the zungtsqr routine.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine zungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) — ZUNGTSQR 🫶

💖 Function/Subroutine Documentation 💖

subroutine zungtsqr (integer m, integer n, integer mb, integer nb,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
    ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer lwork,
    integer info)

ZUNGTSQR — the main character, periodt ✨.

🎀 Purpose 🎀

ZUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal columns, which are the first N columns of a product of comlpex unitary matrices of order M which are returned by ZLATSQR. Yes, comlpex is literally what the source says 😭💀.

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

See the documentation for ZLATSQR.

🫶 Parameters 🫶

• M — INTEGER. The number of rows of the matrix A. M >= 0.
• N — INTEGER. The number of columns of the matrix A. M >= N >= 0.
• MB — INTEGER. The row block size used by ZLATSQR 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 — INTEGER. The column block size used by ZLATSQR 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 — COMPLEX*16 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 ZLATSQR 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 ZLATSQR).
  • On exit: The array A contains an M-by-N orthonormal matrix Q_out, i.e the columns of A are orthogonal unit vectors. Slay 💅.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• T — COMPLEX*16 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 ZLATSQR).

• LDT — INTEGER. The leading dimension of the array T. LDT >= max(1,min(NB1,N)).
• WORK — (workspace) COMPLEX*16 array, dimension (MAX(2,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — 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. Iconic querystyle behavior 💖.

• 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.

🌈 Contributors 🌈

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

Definition at line 174 of file zungtsqr.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the whole page, bestie — LAPACK Version 3.12.0, SRC/zungtsqr.f(3), mwah 💋✨🦋