Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       unm2r - {un,or}m2r: multiply by Q from geqrf, level 2

SYNOPSIS

   Functions
       subroutine cunm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
           CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization
           determined by cgeqrf (unblocked algorithm).
       subroutine dorm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
           DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization
           determined by sgeqrf (unblocked algorithm).
       subroutine sorm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
           SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization
           determined by sgeqrf (unblocked algorithm).
       subroutine zunm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
           ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization
           determined by cgeqrf (unblocked algorithm).

Detailed Description

Function Documentation

   subroutine cunm2r (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)
       CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization
       determined by cgeqrf (unblocked algorithm).

       Purpose:

            CUNM2R 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(2) . . . H(k)

            as returned by CGEQRF. 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
                     CGEQRF in the first 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 CGEQRF.

           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.

   subroutine dorm2r (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)
       DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization
       determined by sgeqrf (unblocked algorithm).

       Purpose:

            DORM2R 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 DGEQRF. 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
                     DGEQRF in the first 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 DOUBLE PRECISION array, dimension (K)
                     TAU(i) must contain the scalar factor of the elementary
                     reflector H(i), as returned by DGEQRF.

           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.

   subroutine sorm2r (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)
       SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization
       determined by sgeqrf (unblocked algorithm).

       Purpose:

            SORM2R 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 SGEQRF. 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
                     SGEQRF in the first 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 SGEQRF.

           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.

   subroutine zunm2r (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)
       ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization
       determined by cgeqrf (unblocked algorithm).

       Purpose:

            ZUNM2R 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(2) . . . H(k)

            as returned by ZGEQRF. 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
                     ZGEQRF in the first 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 ZGEQRF.

           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.

Author

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