--- name: "unmr2" 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/unmr2" --- # unmr2(3) {un,or}mr2: step in unmrq ## NAME unmr2 - {un,or}mr2: step in unmrq ## SYNOPSIS ### Functions subroutine **cunmr2** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\ **CUNMR2** multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm). subroutine **dormr2** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\ **DORMR2** multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). subroutine **sormr2** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\ **SORMR2** multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). subroutine **zunmr2** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\ **ZUNMR2** multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm). ## Detailed Description ## Function Documentation ### subroutine cunmr2 (character side, character trans, integer m, integer n, integer k, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) tau, complex, dimension( ldc, \* ) c, integer ldc, complex, dimension( \* ) work, integer info) **CUNMR2** multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm). **Purpose:** ``` !> !> CUNMR2 overwrites the general complex m-by-n matrix C with !> !> Q * C if SIDE = 'L' and TRANS = 'N', or !> !> Q**H* C if SIDE = 'L' and TRANS = 'C', or !> !> C * Q if SIDE = 'R' and TRANS = 'N', or !> !> C * Q**H if SIDE = 'R' and TRANS = 'C', !> !> where Q is a complex unitary matrix defined as the product of k !> elementary reflectors !> !> Q = H(1)**H H(2)**H . . . H(k)**H !> !> as returned by CGERQF. 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': apply Q (No transpose) !> = 'C': apply Q**H (Conjugate transpose) !> ``` *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. !> ``` *A* ``` !> A is COMPLEX array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,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 !> CGERQF in the last k rows of its array argument A. !> A is modified by the routine but restored on exit. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !> ``` *TAU* ``` !> TAU is COMPLEX array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by CGERQF. !> ``` *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 **157** of file **cunmr2.f**. ### subroutine dormr2 (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) tau, double precision, dimension( ldc, \* ) c, integer ldc, double precision, dimension( \* ) work, integer info) **DORMR2** multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). **Purpose:** ``` !> !> DORMR2 overwrites the general real m by n matrix C with !> !> Q * C if SIDE = 'L' and TRANS = 'N', or !> !> Q**T* C if SIDE = 'L' and TRANS = 'T', or !> !> C * Q if SIDE = 'R' and TRANS = 'N', or !> !> C * Q**T if SIDE = 'R' and TRANS = 'T', !> !> where Q is a real orthogonal matrix defined as the product of k !> elementary reflectors !> !> Q = H(1) H(2) . . . H(k) !> !> as returned by DGERQF. 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': apply Q (No transpose) !> = 'T': apply Q' (Transpose) !> ``` *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. !> ``` *A* ``` !> A is DOUBLE PRECISION array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,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 !> DGERQF in the last k rows of its array argument A. !> A is modified by the routine but restored on exit. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !> ``` *TAU* ``` !> TAU is DOUBLE PRECISION array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by DGERQF. !> ``` *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 **157** of file **dormr2.f**. ### subroutine sormr2 (character side, character trans, integer m, integer n, integer k, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( ldc, \* ) c, integer ldc, real, dimension( \* ) work, integer info) **SORMR2** multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). **Purpose:** ``` !> !> SORMR2 overwrites the general real m by n matrix C with !> !> Q * C if SIDE = 'L' and TRANS = 'N', or !> !> Q**T* C if SIDE = 'L' and TRANS = 'T', or !> !> C * Q if SIDE = 'R' and TRANS = 'N', or !> !> C * Q**T if SIDE = 'R' and TRANS = 'T', !> !> where Q is a real orthogonal matrix defined as the product of k !> elementary reflectors !> !> Q = H(1) H(2) . . . H(k) !> !> as returned by SGERQF. 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': apply Q (No transpose) !> = 'T': apply Q' (Transpose) !> ``` *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. !> ``` *A* ``` !> A is REAL array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,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 !> SGERQF in the last k rows of its array argument A. !> A is modified by the routine but restored on exit. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !> ``` *TAU* ``` !> TAU is REAL array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by SGERQF. !> ``` *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 **157** of file **sormr2.f**. ### subroutine zunmr2 (character side, character trans, integer m, integer n, integer k, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( ldc, \* ) c, integer ldc, complex\*16, dimension( \* ) work, integer info) **ZUNMR2** multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm). **Purpose:** ``` !> !> ZUNMR2 overwrites the general complex m-by-n matrix C with !> !> Q * C if SIDE = 'L' and TRANS = 'N', or !> !> Q**H* C if SIDE = 'L' and TRANS = 'C', or !> !> C * Q if SIDE = 'R' and TRANS = 'N', or !> !> C * Q**H if SIDE = 'R' and TRANS = 'C', !> !> where Q is a complex unitary matrix defined as the product of k !> elementary reflectors !> !> Q = H(1)**H H(2)**H . . . H(k)**H !> !> as returned by ZGERQF. 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': apply Q (No transpose) !> = 'C': apply Q**H (Conjugate transpose) !> ``` *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. !> ``` *A* ``` !> A is COMPLEX*16 array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,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 !> ZGERQF in the last k rows of its array argument A. !> A is modified by the routine but restored on exit. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !> ``` *TAU* ``` !> TAU is COMPLEX*16 array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by ZGERQF. !> ``` *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 **157** of file **zunmr2.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.