.TH "getsqrhrt" 3 "Sat Dec 9 2023 21:42:18" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
getsqrhrt \- getsqrhrt: tall-skinny QR factor, with Householder reconstruction
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcgetsqrhrt\fP (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)"
.br
.RI "\fBCGETSQRHRT\fP "
.ti -1c
.RI "subroutine \fBdgetsqrhrt\fP (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)"
.br
.RI "\fBDGETSQRHRT\fP "
.ti -1c
.RI "subroutine \fBsgetsqrhrt\fP (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)"
.br
.RI "\fBSGETSQRHRT\fP "
.ti -1c
.RI "subroutine \fBzgetsqrhrt\fP (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)"
.br
.RI "\fBZGETSQRHRT\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgetsqrhrt (integer m, integer n, integer mb1, integer nb1, integer nb2, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer lwork, integer info)"

.PP
\fBCGETSQRHRT\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CGETSQRHRT computes a NB2-sized column blocked QR-factorization
 of a complex M-by-N matrix A with M >= N,

    A = Q * R\&.

 The routine uses internally a NB1-sized column blocked and MB1-sized
 row blocked TSQR-factorization and perfors the reconstruction
 of the Householder vectors from the TSQR output\&. The routine also
 converts the R_tsqr factor from the TSQR-factorization output into
 the R factor that corresponds to the Householder QR-factorization,

    A = Q_tsqr * R_tsqr = Q * R\&.

 The output Q and R factors are stored in the same format as in CGEQRT
 (Q is in blocked compact WY-representation)\&. See the documentation
 of CGEQRT for more details on the format\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&. M >= N >= 0\&.
.fi
.PP
.br
\fIMB1\fP 
.PP
.nf
          MB1 is INTEGER
          The row block size to be used in the blocked TSQR\&.
          MB1 > N\&.
.fi
.PP
.br
\fINB1\fP 
.PP
.nf
          NB1 is INTEGER
          The column block size to be used in the blocked TSQR\&.
          N >= NB1 >= 1\&.
.fi
.PP
.br
\fINB2\fP 
.PP
.nf
          NB2 is INTEGER
          The block size to be used in the blocked QR that is
          output\&. NB2 >= 1\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)

          On entry: an M-by-N matrix A\&.

          On exit:
           a) the elements on and above the diagonal
              of the array contain the N-by-N upper-triangular
              matrix R corresponding to the Householder QR;
           b) the elements below the diagonal represent Q by
              the columns of blocked V (compact WY-representation)\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is COMPLEX array, dimension (LDT,N))
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= NB2\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          (workspace) COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          The dimension of the array WORK\&.
          LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
          where
             NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
             NB1LOCAL = MIN(NB1,N)\&.
             LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
             LW1 = NB1LOCAL * N,
             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4

.PP
.nf
 November 2020, Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley
.fi
.PP
 
.RE
.PP

.SS "subroutine dgetsqrhrt (integer m, integer n, integer mb1, integer nb1, integer nb2, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer lwork, integer info)"

.PP
\fBDGETSQRHRT\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DGETSQRHRT computes a NB2-sized column blocked QR-factorization
 of a real M-by-N matrix A with M >= N,

    A = Q * R\&.

 The routine uses internally a NB1-sized column blocked and MB1-sized
 row blocked TSQR-factorization and perfors the reconstruction
 of the Householder vectors from the TSQR output\&. The routine also
 converts the R_tsqr factor from the TSQR-factorization output into
 the R factor that corresponds to the Householder QR-factorization,

    A = Q_tsqr * R_tsqr = Q * R\&.

 The output Q and R factors are stored in the same format as in DGEQRT
 (Q is in blocked compact WY-representation)\&. See the documentation
 of DGEQRT for more details on the format\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&. M >= N >= 0\&.
.fi
.PP
.br
\fIMB1\fP 
.PP
.nf
          MB1 is INTEGER
          The row block size to be used in the blocked TSQR\&.
          MB1 > N\&.
.fi
.PP
.br
\fINB1\fP 
.PP
.nf
          NB1 is INTEGER
          The column block size to be used in the blocked TSQR\&.
          N >= NB1 >= 1\&.
.fi
.PP
.br
\fINB2\fP 
.PP
.nf
          NB2 is INTEGER
          The block size to be used in the blocked QR that is
          output\&. NB2 >= 1\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)

          On entry: an M-by-N matrix A\&.

          On exit:
           a) the elements on and above the diagonal
              of the array contain the N-by-N upper-triangular
              matrix R corresponding to the Householder QR;
           b) the elements below the diagonal represent Q by
              the columns of blocked V (compact WY-representation)\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is DOUBLE PRECISION array, dimension (LDT,N))
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= NB2\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          The dimension of the array WORK\&.
          LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
          where
             NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
             NB1LOCAL = MIN(NB1,N)\&.
             LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
             LW1 = NB1LOCAL * N,
             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4

.PP
.nf
 November 2020, Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley
.fi
.PP
 
.RE
.PP

.SS "subroutine sgetsqrhrt (integer m, integer n, integer mb1, integer nb1, integer nb2, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer lwork, integer info)"

.PP
\fBSGETSQRHRT\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SGETSQRHRT computes a NB2-sized column blocked QR-factorization
 of a complex M-by-N matrix A with M >= N,

    A = Q * R\&.

 The routine uses internally a NB1-sized column blocked and MB1-sized
 row blocked TSQR-factorization and perfors the reconstruction
 of the Householder vectors from the TSQR output\&. The routine also
 converts the R_tsqr factor from the TSQR-factorization output into
 the R factor that corresponds to the Householder QR-factorization,

    A = Q_tsqr * R_tsqr = Q * R\&.

 The output Q and R factors are stored in the same format as in SGEQRT
 (Q is in blocked compact WY-representation)\&. See the documentation
 of SGEQRT for more details on the format\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&. M >= N >= 0\&.
.fi
.PP
.br
\fIMB1\fP 
.PP
.nf
          MB1 is INTEGER
          The row block size to be used in the blocked TSQR\&.
          MB1 > N\&.
.fi
.PP
.br
\fINB1\fP 
.PP
.nf
          NB1 is INTEGER
          The column block size to be used in the blocked TSQR\&.
          N >= NB1 >= 1\&.
.fi
.PP
.br
\fINB2\fP 
.PP
.nf
          NB2 is INTEGER
          The block size to be used in the blocked QR that is
          output\&. NB2 >= 1\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)

          On entry: an M-by-N matrix A\&.

          On exit:
           a) the elements on and above the diagonal
              of the array contain the N-by-N upper-triangular
              matrix R corresponding to the Householder QR;
           b) the elements below the diagonal represent Q by
              the columns of blocked V (compact WY-representation)\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is REAL array, dimension (LDT,N))
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= NB2\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          (workspace) REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          The dimension of the array WORK\&.
          LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
          where
             NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
             NB1LOCAL = MIN(NB1,N)\&.
             LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
             LW1 = NB1LOCAL * N,
             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4

.PP
.nf
 November 2020, Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley
.fi
.PP
 
.RE
.PP

.SS "subroutine zgetsqrhrt (integer m, integer n, integer mb1, integer nb1, integer nb2, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer lwork, integer info)"

.PP
\fBZGETSQRHRT\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZGETSQRHRT computes a NB2-sized column blocked QR-factorization
 of a complex M-by-N matrix A with M >= N,

    A = Q * R\&.

 The routine uses internally a NB1-sized column blocked and MB1-sized
 row blocked TSQR-factorization and perfors the reconstruction
 of the Householder vectors from the TSQR output\&. The routine also
 converts the R_tsqr factor from the TSQR-factorization output into
 the R factor that corresponds to the Householder QR-factorization,

    A = Q_tsqr * R_tsqr = Q * R\&.

 The output Q and R factors are stored in the same format as in ZGEQRT
 (Q is in blocked compact WY-representation)\&. See the documentation
 of ZGEQRT for more details on the format\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&. M >= N >= 0\&.
.fi
.PP
.br
\fIMB1\fP 
.PP
.nf
          MB1 is INTEGER
          The row block size to be used in the blocked TSQR\&.
          MB1 > N\&.
.fi
.PP
.br
\fINB1\fP 
.PP
.nf
          NB1 is INTEGER
          The column block size to be used in the blocked TSQR\&.
          N >= NB1 >= 1\&.
.fi
.PP
.br
\fINB2\fP 
.PP
.nf
          NB2 is INTEGER
          The block size to be used in the blocked QR that is
          output\&. NB2 >= 1\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)

          On entry: an M-by-N matrix A\&.

          On exit:
           a) the elements on and above the diagonal
              of the array contain the N-by-N upper-triangular
              matrix R corresponding to the Householder QR;
           b) the elements below the diagonal represent Q by
              the columns of blocked V (compact WY-representation)\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is COMPLEX*16 array, dimension (LDT,N))
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= NB2\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          The dimension of the array WORK\&.
          LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
          where
             NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
             NB1LOCAL = MIN(NB1,N)\&.
             LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
             LW1 = NB1LOCAL * N,
             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4

.PP
.nf
 November 2020, Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.