--- name: "unm2l" 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/unm2l" --- # unm2l(3) {un,or}m2l: step in unmql ## NAME unm2l - {un,or}m2l: step in unmql ## SYNOPSIS ### Functions subroutine **cunm2l** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\ **CUNM2L** multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm). subroutine **dorm2l** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\ **DORM2L** multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). subroutine **sorm2l** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\ **SORM2L** multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). subroutine **zunm2l** (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)\ **ZUNM2L** multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm). ## Detailed Description ## Function Documentation ### subroutine cunm2l (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) **CUNM2L** multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm). **Purpose:** ``` !> !> CUNM2L 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(k) . . . H(2) H(1) !> !> as returned by CGEQLF. 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,K) !> The i-th column must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> CGEQLF in the last k columns 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. !> If SIDE = 'L', LDA >= max(1,M); !> if SIDE = 'R', LDA >= max(1,N). !> ``` *TAU* ``` !> TAU is COMPLEX array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by CGEQLF. !> ``` *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 **cunm2l.f**. ### subroutine dorm2l (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) **DORM2L** multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). **Purpose:** ``` !> !> DORM2L 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(k) . . . H(2) H(1) !> !> as returned by DGEQLF. 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**T (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,K) !> The i-th column must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> DGEQLF in the last k columns of its array argument A. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. !> If SIDE = 'L', LDA >= max(1,M); !> if SIDE = 'R', LDA >= max(1,N). !> ``` *TAU* ``` !> TAU is DOUBLE PRECISION array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by DGEQLF. !> ``` *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 **156** of file **dorm2l.f**. ### subroutine sorm2l (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) **SORM2L** multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). **Purpose:** ``` !> !> SORM2L 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(k) . . . H(2) H(1) !> !> as returned by SGEQLF. 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**T (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,K) !> The i-th column must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> SGEQLF in the last k columns 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. !> If SIDE = 'L', LDA >= max(1,M); !> if SIDE = 'R', LDA >= max(1,N). !> ``` *TAU* ``` !> TAU is REAL array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by SGEQLF. !> ``` *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 **sorm2l.f**. ### subroutine zunm2l (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) **ZUNM2L** multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm). **Purpose:** ``` !> !> ZUNM2L 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(k) . . . H(2) H(1) !> !> as returned by ZGEQLF. 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,K) !> The i-th column must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> ZGEQLF in the last k columns 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. !> If SIDE = 'L', LDA >= max(1,M); !> if SIDE = 'R', LDA >= max(1,N). !> ``` *TAU* ``` !> TAU is COMPLEX*16 array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by ZGEQLF. !> ``` *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 **zunm2l.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.