unm2l - Man Page

{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.
          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 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 157 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

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK