# gemlqt - Man Page

gemlqt: multiply by Q from gelqt

## Synopsis

### Functions

subroutine **cgemlqt** (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)**CGEMLQT**

subroutine **dgemlqt** (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)**DGEMLQT**

subroutine **sgemlqt** (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)**SGEMLQT**

subroutine **zgemlqt** (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)**ZGEMLQT**

## Detailed Description

## Function Documentation

### subroutine cgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

**CGEMLQT**

**Purpose:**

CGEMLQT 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 defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by CGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

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

*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.

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

*MB*MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in CGELQT.

*V*V is COMPLEX array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGELQT in the first K rows of its array argument A.

*LDV*LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K).

*T*T is COMPLEX array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CGELQT, stored as a MB-by-K matrix.

*LDT*LDT is INTEGER The leading dimension of the array T. LDT >= MB.

*C*C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**H C, 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. The dimension of WORK is N*MB if SIDE = 'L', or M*MB 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 **151** of file **cgemlqt.f**.

### subroutine dgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

**DGEMLQT**

**Purpose:**

DGEMLQT 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 defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by DGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

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

*TRANS*TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': 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.

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

*MB*MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in DGELQT.

*V*V is DOUBLE PRECISION array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQT in the first K rows of its array argument A.

*LDV*LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K).

*T*T is DOUBLE PRECISION array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by DGELQT, stored as a MB-by-K matrix.

*LDT*LDT is INTEGER The leading dimension of the array T. LDT >= MB.

*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, Q**T C, 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. The dimension of WORK is N*MB if SIDE = 'L', or M*MB 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 **166** of file **dgemlqt.f**.

### subroutine sgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

**SGEMLQT**

**Purpose:**

DGEMLQT 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 defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by SGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

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

*TRANS*TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': 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.

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

*MB*MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in SGELQT.

*V*V is REAL array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQT in the first K rows of its array argument A.

*LDV*LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K).

*T*T is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by SGELQT, stored as a MB-by-K matrix.

*LDT*LDT is INTEGER The leading dimension of the array T. LDT >= MB.

*C*C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**T C, 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. The dimension of WORK is N*MB if SIDE = 'L', or M*MB 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 **151** of file **sgemlqt.f**.

### subroutine zgemlqt (character side, character trans, integer m, integer n, integer k, integer mb, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)

**ZGEMLQT**

**Purpose:**

ZGEMLQT 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 defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by ZGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

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

*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.

*K**MB*MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in ZGELQT.

*V*V is COMPLEX*16 array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGELQT in the first K rows of its array argument A.

*LDV*LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K).

*T*T is COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by ZGELQT, stored as a MB-by-K matrix.

*LDT*LDT is INTEGER The leading dimension of the array T. LDT >= MB.

*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, Q**H C, 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. The dimension of WORK is N*MB if SIDE = 'L', or M*MB 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 **166** of file **zgemlqt.f**.

## Author

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