SRC/cungtsqr.f(3)

SRC/cungtsqr.f 💅

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SYNOPSIS ✨

Functions/Subroutines 🎀

• subroutine cungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) — CUNGTSQR, the main character of this page 👑

subroutine cungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
    CUNGTSQR

Function/Subroutine Documentation 🫶

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

CUNGTSQR

Purpose 💜

Real talk: CUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal columns. Those columns are the first N columns of a product of comlpex unitary matrices of order M which are returned by CLATSQR.

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

See the documentation for CLATSQR.

Parameters 🌸

• 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 CLATSQR 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 CLATSQR 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 COMPLEX 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 CLATSQR 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 CLATSQR).
  • 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 COMPLEX 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 CLATSQR).

• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= max(1,min(NB1,N)).
• WORK — (workspace) COMPLEX 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 cungtsqr.f.

Author 💖

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