---
name: "upmtr"
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/upmtr"
---

# upmtr(3)

{up,op}mtr: multiply by Q from hptrd

## NAME

upmtr - {up,op}mtr: multiply by Q from hptrd

## SYNOPSIS

### Functions

subroutine **cupmtr** (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)\
 **CUPMTR**  subroutine **dopmtr** (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)\
 **DOPMTR**  subroutine **sopmtr** (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)\
 **SOPMTR**  subroutine **zupmtr** (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)\
 **ZUPMTR**

## Detailed Description

## Function Documentation

### subroutine cupmtr (character side, character uplo, character trans, integer m, integer n, complex, dimension( \* ) ap, complex, dimension( \* ) tau, complex, dimension( ldc, \* ) c, integer ldc, complex, dimension( \* ) work, integer info)

**CUPMTR**

**Purpose:**

```
!>
!> CUPMTR overwrites the general complex M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'C':      Q**H * C       C * Q**H
!>
!> where Q is a complex unitary matrix of order nq, with nq = m if
!> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
!> nq-1 elementary reflectors, as returned by CHPTRD using packed
!> storage:
!>
!> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
!>
!> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right.
!>
```

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U': Upper triangular packed storage used in previous
!>                 call to CHPTRD;
!>          = 'L': Lower triangular packed storage used in previous
!>                 call to CHPTRD.
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate transpose, apply Q**H.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>
```

*AP*

```
!>          AP is COMPLEX array, dimension
!>                               (M*(M+1)/2) if SIDE = 'L'
!>                               (N*(N+1)/2) if SIDE = 'R'
!>          The vectors which define the elementary reflectors, as
!>          returned by CHPTRD.  AP is modified by the routine but
!>          restored on exit.
!>
```

*TAU*

```
!>          TAU is COMPLEX array, dimension (M-1) if SIDE = 'L'
!>                                     or (N-1) if SIDE = 'R'
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by CHPTRD.
!>
```

*C*

```
!>          C is COMPLEX array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
!>
```

*LDC*

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

*WORK*

```
!>          WORK is COMPLEX array, dimension
!>                                   (N) if SIDE = 'L'
!>                                   (M) if SIDE = 'R'
!>
```

*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.

Definition at line **148** of file **cupmtr.f**.

### subroutine dopmtr (character side, character uplo, character trans, integer m, integer n, double precision, dimension( \* ) ap, double precision, dimension( \* ) tau, double precision, dimension( ldc, \* ) c, integer ldc, double precision, dimension( \* ) work, integer info)

**DOPMTR**

**Purpose:**

```
!>
!> DOPMTR overwrites the general real M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'T':      Q**T * C       C * Q**T
!>
!> where Q is a real orthogonal matrix of order nq, with nq = m if
!> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
!> nq-1 elementary reflectors, as returned by DSPTRD using packed
!> storage:
!>
!> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
!>
!> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**T from the Left;
!>          = 'R': apply Q or Q**T from the Right.
!>
```

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U': Upper triangular packed storage used in previous
!>                 call to DSPTRD;
!>          = 'L': Lower triangular packed storage used in previous
!>                 call to DSPTRD.
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'T':  Transpose, apply Q**T.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>
```

*AP*

```
!>          AP is DOUBLE PRECISION array, dimension
!>                               (M*(M+1)/2) if SIDE = 'L'
!>                               (N*(N+1)/2) if SIDE = 'R'
!>          The vectors which define the elementary reflectors, as
!>          returned by DSPTRD.  AP is modified by the routine but
!>          restored on exit.
!>
```

*TAU*

```
!>          TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
!>                                     or (N-1) if SIDE = 'R'
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by DSPTRD.
!>
```

*C*

```
!>          C is DOUBLE PRECISION array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
!>
```

*LDC*

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

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension
!>                                   (N) if SIDE = 'L'
!>                                   (M) if SIDE = 'R'
!>
```

*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.

Definition at line **148** of file **dopmtr.f**.

### subroutine sopmtr (character side, character uplo, character trans, integer m, integer n, real, dimension( \* ) ap, real, dimension( \* ) tau, real, dimension( ldc, \* ) c, integer ldc, real, dimension( \* ) work, integer info)

**SOPMTR**

**Purpose:**

```
!>
!> SOPMTR overwrites the general real M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'T':      Q**T * C       C * Q**T
!>
!> where Q is a real orthogonal matrix of order nq, with nq = m if
!> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
!> nq-1 elementary reflectors, as returned by SSPTRD using packed
!> storage:
!>
!> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
!>
!> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**T from the Left;
!>          = 'R': apply Q or Q**T from the Right.
!>
```

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U': Upper triangular packed storage used in previous
!>                 call to SSPTRD;
!>          = 'L': Lower triangular packed storage used in previous
!>                 call to SSPTRD.
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'T':  Transpose, apply Q**T.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>
```

*AP*

```
!>          AP is REAL array, dimension
!>                               (M*(M+1)/2) if SIDE = 'L'
!>                               (N*(N+1)/2) if SIDE = 'R'
!>          The vectors which define the elementary reflectors, as
!>          returned by SSPTRD.  AP is modified by the routine but
!>          restored on exit.
!>
```

*TAU*

```
!>          TAU is REAL array, dimension (M-1) if SIDE = 'L'
!>                                     or (N-1) if SIDE = 'R'
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by SSPTRD.
!>
```

*C*

```
!>          C is REAL array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
!>
```

*LDC*

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

*WORK*

```
!>          WORK is REAL array, dimension
!>                                   (N) if SIDE = 'L'
!>                                   (M) if SIDE = 'R'
!>
```

*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.

Definition at line **148** of file **sopmtr.f**.

### subroutine zupmtr (character side, character uplo, character trans, integer m, integer n, complex\*16, dimension( \* ) ap, complex\*16, dimension( \* ) tau, complex\*16, dimension( ldc, \* ) c, integer ldc, complex\*16, dimension( \* ) work, integer info)

**ZUPMTR**

**Purpose:**

```
!>
!> ZUPMTR overwrites the general complex M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'C':      Q**H * C       C * Q**H
!>
!> where Q is a complex unitary matrix of order nq, with nq = m if
!> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
!> nq-1 elementary reflectors, as returned by ZHPTRD using packed
!> storage:
!>
!> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
!>
!> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right.
!>
```

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U': Upper triangular packed storage used in previous
!>                 call to ZHPTRD;
!>          = 'L': Lower triangular packed storage used in previous
!>                 call to ZHPTRD.
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate transpose, apply Q**H.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>
```

*AP*

```
!>          AP is COMPLEX*16 array, dimension
!>                               (M*(M+1)/2) if SIDE = 'L'
!>                               (N*(N+1)/2) if SIDE = 'R'
!>          The vectors which define the elementary reflectors, as
!>          returned by ZHPTRD.  AP is modified by the routine but
!>          restored on exit.
!>
```

*TAU*

```
!>          TAU is COMPLEX*16 array, dimension (M-1) if SIDE = 'L'
!>                                     or (N-1) if SIDE = 'R'
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by ZHPTRD.
!>
```

*C*

```
!>          C is COMPLEX*16 array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
!>
```

*LDC*

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

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension
!>                                   (N) if SIDE = 'L'
!>                                   (M) if SIDE = 'R'
!>
```

*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.

Definition at line **148** of file **zupmtr.f**.

## Author

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