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Move ?GELQS and ?GEQRS from TESTING/LIN to DEPRECATED (Reference-LAPACK PR 900)

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Martin Kroeker GitHub 2 years ago
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ab3d6a6604
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  1. +196
    -0
      lapack-netlib/SRC/DEPRECATED/cgelqs.f
  2. +189
    -0
      lapack-netlib/SRC/DEPRECATED/cgeqrs.f
  3. +194
    -0
      lapack-netlib/SRC/DEPRECATED/dgelqs.f
  4. +189
    -0
      lapack-netlib/SRC/DEPRECATED/dgeqrs.f
  5. +194
    -0
      lapack-netlib/SRC/DEPRECATED/sgelqs.f
  6. +189
    -0
      lapack-netlib/SRC/DEPRECATED/sgeqrs.f
  7. +196
    -0
      lapack-netlib/SRC/DEPRECATED/zgelqs.f
  8. +189
    -0
      lapack-netlib/SRC/DEPRECATED/zgeqrs.f

+ 196
- 0
lapack-netlib/SRC/DEPRECATED/cgelqs.f View File

@@ -0,0 +1,196 @@
*> \brief \b CGELQS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the LQ factorization
*> A = L*Q
*> computed by CGELQF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= M >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> Details of the LQ factorization of the original matrix A as
*> returned by CGELQF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (M)
*> Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,NRHS)
*> On entry, the m-by-nrhs right hand side matrix B.
*> On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= N.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK must be at least NRHS,
*> and should be at least NRHS*NB, where NB is the block size
*> for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
* =====================================================================
SUBROUTINE CGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. External Subroutines ..
EXTERNAL CLASET, CTRSM, CUNMLQ, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CGELQS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* Solve L*X = B(1:m,:)
*
CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS,
$ CONE, A, LDA, B, LDB )
*
* Set B(m+1:n,:) to zero
*
IF( M.LT.N )
$ CALL CLASET( 'Full', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ),
$ LDB )
*
* B := Q' * B
*
CALL CUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA,
$ TAU, B, LDB, WORK, LWORK, INFO )
*
RETURN
*
* End of CGELQS
*
END

+ 189
- 0
lapack-netlib/SRC/DEPRECATED/cgeqrs.f View File

@@ -0,0 +1,189 @@
*> \brief \b CGEQRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QR factorization
*> A = Q*R
*> computed by CGEQRF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. M >= N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> Details of the QR factorization of the original matrix A as
*> returned by CGEQRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (N)
*> Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,NRHS)
*> On entry, the m-by-nrhs right hand side matrix B.
*> On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= M.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK must be at least NRHS,
*> and should be at least NRHS*NB, where NB is the block size
*> for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
* =====================================================================
SUBROUTINE CGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. External Subroutines ..
EXTERNAL CTRSM, CUNMQR, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CGEQRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* B := Q' * B
*
CALL CUNMQR( 'Left', 'Conjugate transpose', M, NRHS, N, A, LDA,
$ TAU, B, LDB, WORK, LWORK, INFO )
*
* Solve R*X = B(1:n,:)
*
CALL CTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, NRHS,
$ ONE, A, LDA, B, LDB )
*
RETURN
*
* End of CGEQRS
*
END

+ 194
- 0
lapack-netlib/SRC/DEPRECATED/dgelqs.f View File

@@ -0,0 +1,194 @@
*> \brief \b DGELQS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the LQ factorization
*> A = L*Q
*> computed by DGELQF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= M >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> Details of the LQ factorization of the original matrix A as
*> returned by DGELQF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION array, dimension (M)
*> Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*> On entry, the m-by-nrhs right hand side matrix B.
*> On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= N.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK must be at least NRHS,
*> and should be at least NRHS*NB, where NB is the block size
*> for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. External Subroutines ..
EXTERNAL DLASET, DORMLQ, DTRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGELQS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* Solve L*X = B(1:m,:)
*
CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS,
$ ONE, A, LDA, B, LDB )
*
* Set B(m+1:n,:) to zero
*
IF( M.LT.N )
$ CALL DLASET( 'Full', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB )
*
* B := Q' * B
*
CALL DORMLQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB,
$ WORK, LWORK, INFO )
*
RETURN
*
* End of DGELQS
*
END

+ 189
- 0
lapack-netlib/SRC/DEPRECATED/dgeqrs.f View File

@@ -0,0 +1,189 @@
*> \brief \b DGEQRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QR factorization
*> A = Q*R
*> computed by DGEQRF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. M >= N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> Details of the QR factorization of the original matrix A as
*> returned by DGEQRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION array, dimension (N)
*> Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*> On entry, the m-by-nrhs right hand side matrix B.
*> On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= M.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK must be at least NRHS,
*> and should be at least NRHS*NB, where NB is the block size
*> for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. External Subroutines ..
EXTERNAL DORMQR, DTRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGEQRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* B := Q' * B
*
CALL DORMQR( 'Left', 'Transpose', M, NRHS, N, A, LDA, TAU, B, LDB,
$ WORK, LWORK, INFO )
*
* Solve R*X = B(1:n,:)
*
CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, NRHS,
$ ONE, A, LDA, B, LDB )
*
RETURN
*
* End of DGEQRS
*
END

+ 194
- 0
lapack-netlib/SRC/DEPRECATED/sgelqs.f View File

@@ -0,0 +1,194 @@
*> \brief \b SGELQS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), B( LDB, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the LQ factorization
*> A = L*Q
*> computed by SGELQF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= M >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL array, dimension (LDA,N)
*> Details of the LQ factorization of the original matrix A as
*> returned by SGELQF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is REAL array, dimension (M)
*> Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is REAL array, dimension (LDB,NRHS)
*> On entry, the m-by-nrhs right hand side matrix B.
*> On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= N.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK must be at least NRHS,
*> and should be at least NRHS*NB, where NB is the block size
*> for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. External Subroutines ..
EXTERNAL SLASET, SORMLQ, STRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGELQS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* Solve L*X = B(1:m,:)
*
CALL STRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS,
$ ONE, A, LDA, B, LDB )
*
* Set B(m+1:n,:) to zero
*
IF( M.LT.N )
$ CALL SLASET( 'Full', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB )
*
* B := Q' * B
*
CALL SORMLQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB,
$ WORK, LWORK, INFO )
*
RETURN
*
* End of SGELQS
*
END

+ 189
- 0
lapack-netlib/SRC/DEPRECATED/sgeqrs.f View File

@@ -0,0 +1,189 @@
*> \brief \b SGEQRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), B( LDB, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QR factorization
*> A = Q*R
*> computed by SGEQRF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. M >= N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL array, dimension (LDA,N)
*> Details of the QR factorization of the original matrix A as
*> returned by SGEQRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is REAL array, dimension (N)
*> Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is REAL array, dimension (LDB,NRHS)
*> On entry, the m-by-nrhs right hand side matrix B.
*> On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= M.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK must be at least NRHS,
*> and should be at least NRHS*NB, where NB is the block size
*> for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. External Subroutines ..
EXTERNAL SORMQR, STRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGEQRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* B := Q' * B
*
CALL SORMQR( 'Left', 'Transpose', M, NRHS, N, A, LDA, TAU, B, LDB,
$ WORK, LWORK, INFO )
*
* Solve R*X = B(1:n,:)
*
CALL STRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, NRHS,
$ ONE, A, LDA, B, LDB )
*
RETURN
*
* End of SGEQRS
*
END

+ 196
- 0
lapack-netlib/SRC/DEPRECATED/zgelqs.f View File

@@ -0,0 +1,196 @@
*> \brief \b ZGELQS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Compute a minimum-norm solution
*> min || A*X - B ||
*> using the LQ factorization
*> A = L*Q
*> computed by ZGELQF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= M >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> Details of the LQ factorization of the original matrix A as
*> returned by ZGELQF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX*16 array, dimension (M)
*> Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (LDB,NRHS)
*> On entry, the m-by-nrhs right hand side matrix B.
*> On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= N.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK must be at least NRHS,
*> and should be at least NRHS*NB, where NB is the block size
*> for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZGELQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZLASET, ZTRSM, ZUNMLQ
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZGELQS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* Solve L*X = B(1:m,:)
*
CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', M, NRHS,
$ CONE, A, LDA, B, LDB )
*
* Set B(m+1:n,:) to zero
*
IF( M.LT.N )
$ CALL ZLASET( 'Full', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ),
$ LDB )
*
* B := Q' * B
*
CALL ZUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA,
$ TAU, B, LDB, WORK, LWORK, INFO )
*
RETURN
*
* End of ZGELQS
*
END

+ 189
- 0
lapack-netlib/SRC/DEPRECATED/zgeqrs.f View File

@@ -0,0 +1,189 @@
*> \brief \b ZGEQRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Solve the least squares problem
*> min || A*X - B ||
*> using the QR factorization
*> A = Q*R
*> computed by ZGEQRF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. M >= N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> Details of the QR factorization of the original matrix A as
*> returned by ZGEQRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX*16 array, dimension (N)
*> Details of the orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (LDB,NRHS)
*> On entry, the m-by-nrhs right hand side matrix B.
*> On exit, the n-by-nrhs solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= M.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK must be at least NRHS,
*> and should be at least NRHS*NB, where NB is the block size
*> for this environment.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
$ INFO )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZTRSM, ZUNMQR
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
INFO = -8
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
$ THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZGEQRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* B := Q' * B
*
CALL ZUNMQR( 'Left', 'Conjugate transpose', M, NRHS, N, A, LDA,
$ TAU, B, LDB, WORK, LWORK, INFO )
*
* Solve R*X = B(1:n,:)
*
CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, NRHS,
$ ONE, A, LDA, B, LDB )
*
RETURN
*
* End of ZGEQRS
*
END

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