---
name: "getsqrhrt"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/getsqrhrt"
---

# getsqrhrt(3)

getsqrhrt: tall-skinny QR factor, with Householder reconstruction

## NAME

getsqrhrt - getsqrhrt: tall-skinny QR factor, with Householder reconstruction

## SYNOPSIS

### Functions

subroutine **cgetsqrhrt** (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)\
 **CGETSQRHRT**  subroutine **dgetsqrhrt** (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)\
 **DGETSQRHRT**  subroutine **sgetsqrhrt** (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)\
 **SGETSQRHRT**  subroutine **zgetsqrhrt** (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)\
 **ZGETSQRHRT**

## Detailed Description

## Function Documentation

### 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)

**CGETSQRHRT**

**Purpose:**

```
!>
!> 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.
!>
```

**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.
!>
```

*MB1*

```
!>          MB1 is INTEGER
!>          The row block size to be used in the blocked TSQR.
!>          MB1 > N.
!>
```

*NB1*

```
!>          NB1 is INTEGER
!>          The column block size to be used in the blocked TSQR.
!>          N >= NB1 >= 1.
!>
```

*NB2*

```
!>          NB2 is INTEGER
!>          The block size to be used in the blocked QR that is
!>          output. NB2 >= 1.
!>
```

*A*

```
!>          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).
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
```

*T*

```
!>          T is COMPLEX array, dimension (LDT,N))
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB2.
!>
```

*WORK*

```
!>          (workspace) 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.
!>          If MIN(M,N) = 0, LWORK >= 1, else
!>          LWORK >= MAX( 1, 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.
!>
```

*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 2020, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>
```

Definition at line **180** of file **cgetsqrhrt.f**.

### 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)

**DGETSQRHRT**

**Purpose:**

```
!>
!> 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.
!>
```

**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.
!>
```

*MB1*

```
!>          MB1 is INTEGER
!>          The row block size to be used in the blocked TSQR.
!>          MB1 > N.
!>
```

*NB1*

```
!>          NB1 is INTEGER
!>          The column block size to be used in the blocked TSQR.
!>          N >= NB1 >= 1.
!>
```

*NB2*

```
!>          NB2 is INTEGER
!>          The block size to be used in the blocked QR that is
!>          output. NB2 >= 1.
!>
```

*A*

```
!>          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).
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
```

*T*

```
!>          T is DOUBLE PRECISION array, dimension (LDT,N))
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB2.
!>
```

*WORK*

```
!>          (workspace) DOUBLE PRECISION 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.
!>          If MIN(M,N) = 0, LWORK >= 1, else
!>          LWORK >= MAX( 1, 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.
!>
```

*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 2020, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>
```

Definition at line **180** of file **dgetsqrhrt.f**.

### 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)

**SGETSQRHRT**

**Purpose:**

```
!>
!> 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.
!>
```

**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.
!>
```

*MB1*

```
!>          MB1 is INTEGER
!>          The row block size to be used in the blocked TSQR.
!>          MB1 > N.
!>
```

*NB1*

```
!>          NB1 is INTEGER
!>          The column block size to be used in the blocked TSQR.
!>          N >= NB1 >= 1.
!>
```

*NB2*

```
!>          NB2 is INTEGER
!>          The block size to be used in the blocked QR that is
!>          output. NB2 >= 1.
!>
```

*A*

```
!>          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).
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
```

*T*

```
!>          T is REAL array, dimension (LDT,N))
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB2.
!>
```

*WORK*

```
!>          (workspace) REAL 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.
!>          If MIN(M,N) = 0, LWORK >= 1, else
!>          LWORK >= MAX( 1, 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.
!>
```

*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 2020, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>
```

Definition at line **180** of file **sgetsqrhrt.f**.

### 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)

**ZGETSQRHRT**

**Purpose:**

```
!>
!> 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.
!>
```

**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.
!>
```

*MB1*

```
!>          MB1 is INTEGER
!>          The row block size to be used in the blocked TSQR.
!>          MB1 > N.
!>
```

*NB1*

```
!>          NB1 is INTEGER
!>          The column block size to be used in the blocked TSQR.
!>          N >= NB1 >= 1.
!>
```

*NB2*

```
!>          NB2 is INTEGER
!>          The block size to be used in the blocked QR that is
!>          output. NB2 >= 1.
!>
```

*A*

```
!>          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).
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
```

*T*

```
!>          T is COMPLEX*16 array, dimension (LDT,N))
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB2.
!>
```

*WORK*

```
!>          (workspace) COMPLEX*16 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.
!>          If MIN(M,N) = 0, LWORK >= 1, else
!>          LWORK >= MAX( 1, 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.
!>
```

*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 2020, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!>
```

Definition at line **180** of file **zgetsqrhrt.f**.

## Author

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