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

NAME

       geqrt - geqrt: QR factor, with T

SYNOPSIS

   Functions
       subroutine cgeqrt (m, n, nb, a, lda, t, ldt, work, info)
           CGEQRT
       subroutine dgeqrt (m, n, nb, a, lda, t, ldt, work, info)
           DGEQRT
       subroutine sgeqrt (m, n, nb, a, lda, t, ldt, work, info)
           SGEQRT
       subroutine zgeqrt (m, n, nb, a, lda, t, ldt, work, info)
           ZGEQRT

Detailed Description

Function Documentation

   subroutine cgeqrt (integer m, integer n, integer nb, complex, dimension( lda, * ) a, integer
       lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer
       info)
       CGEQRT

       Purpose:

            CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
            using the compact WY representation of Q.

       Parameters
           M

                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           NB

                     NB is INTEGER
                     The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.

           A

                     A is COMPLEX array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the elements on and above the diagonal of the array
                     contain the min(M,N)-by-N upper trapezoidal matrix R (R is
                     upper triangular if M >= N); the elements below the diagonal
                     are the columns of V.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           T

                     T is COMPLEX array, dimension (LDT,MIN(M,N))
                     The upper triangular block reflectors stored in compact form
                     as a sequence of upper triangular blocks.  See below
                     for further details.

           LDT

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

           WORK

                     WORK is COMPLEX array, dimension (NB*N)

           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.

       Further Details:

             The matrix V stores the elementary reflectors H(i) in the i-th column
             below the diagonal. For example, if M=5 and N=3, the matrix V is

                          V = (  1       )
                              ( v1  1    )
                              ( v1 v2  1 )
                              ( v1 v2 v3 )
                              ( v1 v2 v3 )

             where the vi's represent the vectors which define H(i), which are returned
             in the matrix A.  The 1's along the diagonal of V are not stored in A.

             Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
             block is of order NB except for the last block, which is of order
             IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
             reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
             for the last block) T's are stored in the NB-by-K matrix T as

                          T = (T1 T2 ... TB).

   subroutine dgeqrt (integer m, integer n, integer nb, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision,
       dimension( * ) work, integer info)
       DGEQRT

       Purpose:

            DGEQRT computes a blocked QR factorization of a real M-by-N matrix A
            using the compact WY representation of Q.

       Parameters
           M

                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           NB

                     NB is INTEGER
                     The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the elements on and above the diagonal of the array
                     contain the min(M,N)-by-N upper trapezoidal matrix R (R is
                     upper triangular if M >= N); the elements below the diagonal
                     are the columns of V.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           T

                     T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
                     The upper triangular block reflectors stored in compact form
                     as a sequence of upper triangular blocks.  See below
                     for further details.

           LDT

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension (NB*N)

           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.

       Further Details:

             The matrix V stores the elementary reflectors H(i) in the i-th column
             below the diagonal. For example, if M=5 and N=3, the matrix V is

                          V = (  1       )
                              ( v1  1    )
                              ( v1 v2  1 )
                              ( v1 v2 v3 )
                              ( v1 v2 v3 )

             where the vi's represent the vectors which define H(i), which are returned
             in the matrix A.  The 1's along the diagonal of V are not stored in A.

             Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
             block is of order NB except for the last block, which is of order
             IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
             reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
             for the last block) T's are stored in the NB-by-K matrix T as

                          T = (T1 T2 ... TB).

   subroutine sgeqrt (integer m, integer n, integer nb, real, dimension( lda, * ) a, integer lda,
       real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)
       SGEQRT

       Purpose:

            SGEQRT computes a blocked QR factorization of a real M-by-N matrix A
            using the compact WY representation of Q.

       Parameters
           M

                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           NB

                     NB is INTEGER
                     The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.

           A

                     A is REAL array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the elements on and above the diagonal of the array
                     contain the min(M,N)-by-N upper trapezoidal matrix R (R is
                     upper triangular if M >= N); the elements below the diagonal
                     are the columns of V.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           T

                     T is REAL array, dimension (LDT,MIN(M,N))
                     The upper triangular block reflectors stored in compact form
                     as a sequence of upper triangular blocks.  See below
                     for further details.

           LDT

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

           WORK

                     WORK is REAL array, dimension (NB*N)

           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.

       Further Details:

             The matrix V stores the elementary reflectors H(i) in the i-th column
             below the diagonal. For example, if M=5 and N=3, the matrix V is

                          V = (  1       )
                              ( v1  1    )
                              ( v1 v2  1 )
                              ( v1 v2 v3 )
                              ( v1 v2 v3 )

             where the vi's represent the vectors which define H(i), which are returned
             in the matrix A.  The 1's along the diagonal of V are not stored in A.

             Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
             block is of order NB except for the last block, which is of order
             IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
             reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
             for the last block) T's are stored in the NB-by-K matrix T as

                          T = (T1 T2 ... TB).

   subroutine zgeqrt (integer m, integer n, integer nb, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * )
       work, integer info)
       ZGEQRT

       Purpose:

            ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
            using the compact WY representation of Q.

       Parameters
           M

                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           NB

                     NB is INTEGER
                     The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the elements on and above the diagonal of the array
                     contain the min(M,N)-by-N upper trapezoidal matrix R (R is
                     upper triangular if M >= N); the elements below the diagonal
                     are the columns of V.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           T

                     T is COMPLEX*16 array, dimension (LDT,MIN(M,N))
                     The upper triangular block reflectors stored in compact form
                     as a sequence of upper triangular blocks.  See below
                     for further details.

           LDT

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

           WORK

                     WORK is COMPLEX*16 array, dimension (NB*N)

           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.

       Further Details:

             The matrix V stores the elementary reflectors H(i) in the i-th column
             below the diagonal. For example, if M=5 and N=3, the matrix V is

                          V = (  1       )
                              ( v1  1    )
                              ( v1 v2  1 )
                              ( v1 v2 v3 )
                              ( v1 v2 v3 )

             where the vi's represent the vectors which define H(i), which are returned
             in the matrix A.  The 1's along the diagonal of V are not stored in A.

             Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
             block is of order NB except for the last block, which is of order
             IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
             reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
             for the last block) T's are stored in the NB-by-K matrix T as

                          T = (T1 T2 ... TB).

Author

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