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wrappers for dgetri and dgetrf

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edoapra 2022-03-29 16:19:47 -07:00
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1
src/64to32blas/GNUmakefile
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@ -10,6 +10,7 @@
ypotri.o ypotrf.o ysygv.o ygeev.o ygeevx.o \
ygels.o ygelss.o ygtsv.o\
ypftrf.o ypftri.o ytfsm.o \
ygetrf.o ygetri.o \
ifily.o\
jscal.o jaxpy.o jgemm.o jheev.o jcopy.o jdotc.o \
ijamax.o jgesvd.o jgeev.o jgetrs.o jgetrf.o \

20
src/64to32blas/ygetrf.F Normal file
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@ -0,0 +1,20 @@
SUBROUTINE ygetrf( M, N, A, LDA, ipiv, INFO )
*
* $id$
*
implicit none
#include "y64.fh"
integer ipiv(*)
integer info, lda, m, n
double precision a( lda, * )
c
INTGR4 m4,n4,info4,lda4
c
n4=n
m4=n
lda4=lda
c
call dgetrf( m4, n4, a, lda4, ipiv, info4 )
info=info4
return
end

21
src/64to32blas/ygetri.F Normal file
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@ -0,0 +1,21 @@
SUBROUTINE ygetri( N, A, LDA, ipiv, WORK, LWORK, INFO )
*
* $id$
*
implicit none
#include "y64.fh"
integer ipiv(*)
integer info, lda, n, lwork
double precision a( lda, * )
double precision work(*)
c
INTGR4 n4,info4,lda4,lwork4
c
n4=n
lda4=lda
lwork4=lwork
c
call dgetri( n4, a, lda4, ipiv, work, lwork4, info4 )
info=info4
return
end

2
src/lapack/GNUmakefile
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@ -84,7 +84,7 @@ OBJ_OPTIMIZE = dbdsqr.o dgebd2.o dgebrd.o dgelq2.o \
dlanhs.o dlarfx.o dlahrd.o dlanv2.o \
dlarra.o dlarrb.o dlarrc.o dlarrd.o dlarrf.o dlarrk.o dlarrv.o\
dlar1v.o dlaneg.o dgelss.o dormtr.o dormql.o dorm2l.o \
dsfrk.o dsytrf.o \
dsfrk.o dsytrf.o dgetri.o dtrsm.o dtrmv.o dtrmm.o\
dpftrf.o dpftri.o dtfsm.o dtftri.o zlacp2.o \
zsysv.o zsytrf.o zsytf2.o zsytrs.o zsytrs2.o zsyr.o \
zsyconv.o zlasyf.o

258
src/lapack/double/dgetri.f Normal file
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*> \brief \b DGETRI
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DGETRI + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetri.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetri.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetri.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LWORK, N
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGETRI computes the inverse of a matrix using the LU factorization
*> computed by DGETRF.
*>
*> This method inverts U and then computes inv(A) by solving the system
*> inv(A)*L = inv(U) for inv(A).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, the factors L and U from the factorization
*> A = P*L*U as computed by DGETRF.
*> On exit, if INFO = 0, the inverse of the original matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices from DGETRF; for 1<=i<=N, row i of the
*> matrix was interchanged with row IPIV(i).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*> On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK. LWORK >= max(1,N).
*> For optimal performance LWORK >= N*NB, where NB is
*> the optimal blocksize returned by ILAENV.
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns
*> this value as the first entry of the WORK array, and no error
*> message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
*> singular and its inverse could not be computed.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup doubleGEcomputational
*
* =====================================================================
SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* -- LAPACK computational 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, LWORK, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB,
$ NBMIN, NN
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DGEMV, DSWAP, DTRSM, DTRTRI, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 )
LWKOPT = N*NB
WORK( 1 ) = LWKOPT
LQUERY = ( LWORK.EQ.-1 )
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -3
ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGETRI', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Form inv(U). If INFO > 0 from DTRTRI, then U is singular,
* and the inverse is not computed.
*
CALL DTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO )
IF( INFO.GT.0 )
$ RETURN
*
NBMIN = 2
LDWORK = N
IF( NB.GT.1 .AND. NB.LT.N ) THEN
IWS = MAX( LDWORK*NB, 1 )
IF( LWORK.LT.IWS ) THEN
NB = LWORK / LDWORK
NBMIN = MAX( 2, ILAENV( 2, 'DGETRI', ' ', N, -1, -1, -1 ) )
END IF
ELSE
IWS = N
END IF
*
* Solve the equation inv(A)*L = inv(U) for inv(A).
*
IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN
*
* Use unblocked code.
*
DO 20 J = N, 1, -1
*
* Copy current column of L to WORK and replace with zeros.
*
DO 10 I = J + 1, N
WORK( I ) = A( I, J )
A( I, J ) = ZERO
10 CONTINUE
*
* Compute current column of inv(A).
*
IF( J.LT.N )
$ CALL DGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ),
$ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 )
20 CONTINUE
ELSE
*
* Use blocked code.
*
NN = ( ( N-1 ) / NB )*NB + 1
DO 50 J = NN, 1, -NB
JB = MIN( NB, N-J+1 )
*
* Copy current block column of L to WORK and replace with
* zeros.
*
DO 40 JJ = J, J + JB - 1
DO 30 I = JJ + 1, N
WORK( I+( JJ-J )*LDWORK ) = A( I, JJ )
A( I, JJ ) = ZERO
30 CONTINUE
40 CONTINUE
*
* Compute current block column of inv(A).
*
IF( J+JB.LE.N )
$ CALL DGEMM( 'No transpose', 'No transpose', N, JB,
$ N-J-JB+1, -ONE, A( 1, J+JB ), LDA,
$ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA )
CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB,
$ ONE, WORK( J ), LDWORK, A( 1, J ), LDA )
50 CONTINUE
END IF
*
* Apply column interchanges.
*
DO 60 J = N - 1, 1, -1
JP = IPIV( J )
IF( JP.NE.J )
$ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
60 CONTINUE
*
WORK( 1 ) = IWS
RETURN
*
* End of DGETRI
*
END

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src/lapack/double/dtrmm.f Normal file
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*> \brief \b DTRMM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA
* INTEGER LDA,LDB,M,N
* CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A(LDA,*),B(LDB,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTRMM performs one of the matrix-matrix operations
*>
*> B := alpha*op( A )*B, or B := alpha*B*op( A ),
*>
*> where alpha is a scalar, B is an m by n matrix, A is a unit, or
*> non-unit, upper or lower triangular matrix and op( A ) is one of
*>
*> op( A ) = A or op( A ) = A**T.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> On entry, SIDE specifies whether op( A ) multiplies B from
*> the left or right as follows:
*>
*> SIDE = 'L' or 'l' B := alpha*op( A )*B.
*>
*> SIDE = 'R' or 'r' B := alpha*B*op( A ).
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> On entry, UPLO specifies whether the matrix A is an upper or
*> lower triangular matrix as follows:
*>
*> UPLO = 'U' or 'u' A is an upper triangular matrix.
*>
*> UPLO = 'L' or 'l' A is a lower triangular matrix.
*> \endverbatim
*>
*> \param[in] TRANSA
*> \verbatim
*> TRANSA is CHARACTER*1
*> On entry, TRANSA specifies the form of op( A ) to be used in
*> the matrix multiplication as follows:
*>
*> TRANSA = 'N' or 'n' op( A ) = A.
*>
*> TRANSA = 'T' or 't' op( A ) = A**T.
*>
*> TRANSA = 'C' or 'c' op( A ) = A**T.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> On entry, DIAG specifies whether or not A is unit triangular
*> as follows:
*>
*> DIAG = 'U' or 'u' A is assumed to be unit triangular.
*>
*> DIAG = 'N' or 'n' A is not assumed to be unit
*> triangular.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of B. M must be at
*> least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of B. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION.
*> On entry, ALPHA specifies the scalar alpha. When alpha is
*> zero then A is not referenced and B need not be set before
*> entry.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m
*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
*> Before entry with UPLO = 'U' or 'u', the leading k by k
*> upper triangular part of the array A must contain the upper
*> triangular matrix and the strictly lower triangular part of
*> A is not referenced.
*> Before entry with UPLO = 'L' or 'l', the leading k by k
*> lower triangular part of the array A must contain the lower
*> triangular matrix and the strictly upper triangular part of
*> A is not referenced.
*> Note that when DIAG = 'U' or 'u', the diagonal elements of
*> A are not referenced either, but are assumed to be unity.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. When SIDE = 'L' or 'l' then
*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
*> then LDA must be at least max( 1, n ).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension ( LDB, N )
*> Before entry, the leading m by n part of the array B must
*> contain the matrix B, and on exit is overwritten by the
*> transformed matrix.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> On entry, LDB specifies the first dimension of B as declared
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_blas_level3
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 3 Blas routine.
*>
*> -- Written on 8-February-1989.
*> Jack Dongarra, Argonne National Laboratory.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER LDA,LDB,M,N
CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION A(LDA,*),B(LDB,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I,INFO,J,K,NROWA
LOGICAL LSIDE,NOUNIT,UPPER
* ..
* .. Parameters ..
DOUBLE PRECISION ONE,ZERO
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
* ..
*
* Test the input parameters.
*
LSIDE = LSAME(SIDE,'L')
IF (LSIDE) THEN
NROWA = M
ELSE
NROWA = N
END IF
NOUNIT = LSAME(DIAG,'N')
UPPER = LSAME(UPLO,'U')
*
INFO = 0
IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
INFO = 1
ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
INFO = 2
ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
+ (.NOT.LSAME(TRANSA,'T')) .AND.
+ (.NOT.LSAME(TRANSA,'C'))) THEN
INFO = 3
ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
INFO = 4
ELSE IF (M.LT.0) THEN
INFO = 5
ELSE IF (N.LT.0) THEN
INFO = 6
ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
INFO = 9
ELSE IF (LDB.LT.MAX(1,M)) THEN
INFO = 11
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DTRMM ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (M.EQ.0 .OR. N.EQ.0) RETURN
*
* And when alpha.eq.zero.
*
IF (ALPHA.EQ.ZERO) THEN
DO 20 J = 1,N
DO 10 I = 1,M
B(I,J) = ZERO
10 CONTINUE
20 CONTINUE
RETURN
END IF
*
* Start the operations.
*
IF (LSIDE) THEN
IF (LSAME(TRANSA,'N')) THEN
*
* Form B := alpha*A*B.
*
IF (UPPER) THEN
DO 50 J = 1,N
DO 40 K = 1,M
IF (B(K,J).NE.ZERO) THEN
TEMP = ALPHA*B(K,J)
DO 30 I = 1,K - 1
B(I,J) = B(I,J) + TEMP*A(I,K)
30 CONTINUE
IF (NOUNIT) TEMP = TEMP*A(K,K)
B(K,J) = TEMP
END IF
40 CONTINUE
50 CONTINUE
ELSE
DO 80 J = 1,N
DO 70 K = M,1,-1
IF (B(K,J).NE.ZERO) THEN
TEMP = ALPHA*B(K,J)
B(K,J) = TEMP
IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
DO 60 I = K + 1,M
B(I,J) = B(I,J) + TEMP*A(I,K)
60 CONTINUE
END IF
70 CONTINUE
80 CONTINUE
END IF
ELSE
*
* Form B := alpha*A**T*B.
*
IF (UPPER) THEN
DO 110 J = 1,N
DO 100 I = M,1,-1
TEMP = B(I,J)
IF (NOUNIT) TEMP = TEMP*A(I,I)
DO 90 K = 1,I - 1
TEMP = TEMP + A(K,I)*B(K,J)
90 CONTINUE
B(I,J) = ALPHA*TEMP
100 CONTINUE
110 CONTINUE
ELSE
DO 140 J = 1,N
DO 130 I = 1,M
TEMP = B(I,J)
IF (NOUNIT) TEMP = TEMP*A(I,I)
DO 120 K = I + 1,M
TEMP = TEMP + A(K,I)*B(K,J)
120 CONTINUE
B(I,J) = ALPHA*TEMP
130 CONTINUE
140 CONTINUE
END IF
END IF
ELSE
IF (LSAME(TRANSA,'N')) THEN
*
* Form B := alpha*B*A.
*
IF (UPPER) THEN
DO 180 J = N,1,-1
TEMP = ALPHA
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 150 I = 1,M
B(I,J) = TEMP*B(I,J)
150 CONTINUE
DO 170 K = 1,J - 1
IF (A(K,J).NE.ZERO) THEN
TEMP = ALPHA*A(K,J)
DO 160 I = 1,M
B(I,J) = B(I,J) + TEMP*B(I,K)
160 CONTINUE
END IF
170 CONTINUE
180 CONTINUE
ELSE
DO 220 J = 1,N
TEMP = ALPHA
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 190 I = 1,M
B(I,J) = TEMP*B(I,J)
190 CONTINUE
DO 210 K = J + 1,N
IF (A(K,J).NE.ZERO) THEN
TEMP = ALPHA*A(K,J)
DO 200 I = 1,M
B(I,J) = B(I,J) + TEMP*B(I,K)
200 CONTINUE
END IF
210 CONTINUE
220 CONTINUE
END IF
ELSE
*
* Form B := alpha*B*A**T.
*
IF (UPPER) THEN
DO 260 K = 1,N
DO 240 J = 1,K - 1
IF (A(J,K).NE.ZERO) THEN
TEMP = ALPHA*A(J,K)
DO 230 I = 1,M
B(I,J) = B(I,J) + TEMP*B(I,K)
230 CONTINUE
END IF
240 CONTINUE
TEMP = ALPHA
IF (NOUNIT) TEMP = TEMP*A(K,K)
IF (TEMP.NE.ONE) THEN
DO 250 I = 1,M
B(I,K) = TEMP*B(I,K)
250 CONTINUE
END IF
260 CONTINUE
ELSE
DO 300 K = N,1,-1
DO 280 J = K + 1,N
IF (A(J,K).NE.ZERO) THEN
TEMP = ALPHA*A(J,K)
DO 270 I = 1,M
B(I,J) = B(I,J) + TEMP*B(I,K)
270 CONTINUE
END IF
280 CONTINUE
TEMP = ALPHA
IF (NOUNIT) TEMP = TEMP*A(K,K)
IF (TEMP.NE.ONE) THEN
DO 290 I = 1,M
B(I,K) = TEMP*B(I,K)
290 CONTINUE
END IF
300 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of DTRMM
*
END

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*> \brief \b DTRMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,LDA,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A(LDA,*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTRMV performs one of the matrix-vector operations
*>
*> x := A*x, or x := A**T*x,
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> On entry, UPLO specifies whether the matrix is an upper or
*> lower triangular matrix as follows:
*>
*> UPLO = 'U' or 'u' A is an upper triangular matrix.
*>
*> UPLO = 'L' or 'l' A is a lower triangular matrix.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> On entry, TRANS specifies the operation to be performed as
*> follows:
*>
*> TRANS = 'N' or 'n' x := A*x.
*>
*> TRANS = 'T' or 't' x := A**T*x.
*>
*> TRANS = 'C' or 'c' x := A**T*x.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> On entry, DIAG specifies whether or not A is unit
*> triangular as follows:
*>
*> DIAG = 'U' or 'u' A is assumed to be unit triangular.
*>
*> DIAG = 'N' or 'n' A is not assumed to be unit
*> triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension ( LDA, N )
*> Before entry with UPLO = 'U' or 'u', the leading n by n
*> upper triangular part of the array A must contain the upper
*> triangular matrix and the strictly lower triangular part of
*> A is not referenced.
*> Before entry with UPLO = 'L' or 'l', the leading n by n
*> lower triangular part of the array A must contain the lower
*> triangular matrix and the strictly upper triangular part of
*> A is not referenced.
*> Note that when DIAG = 'U' or 'u', the diagonal elements of
*> A are not referenced either, but are assumed to be unity.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. LDA must be at least
*> max( 1, n ).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the n
*> element vector x. On exit, X is overwritten with the
*> transformed vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_blas_level2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- Written on 22-October-1986.
*> Jack Dongarra, Argonne National Lab.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,LDA,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION A(LDA,*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER (ZERO=0.0D+0)
* ..
* .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I,INFO,IX,J,JX,KX
LOGICAL NOUNIT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
*
* Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
INFO = 1
ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
+ .NOT.LSAME(TRANS,'C')) THEN
INFO = 2
ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (LDA.LT.MAX(1,N)) THEN
INFO = 6
ELSE IF (INCX.EQ.0) THEN
INFO = 8
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DTRMV ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
IF (INCX.LE.0) THEN
KX = 1 - (N-1)*INCX
ELSE IF (INCX.NE.1) THEN
KX = 1
END IF
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through A.
*
IF (LSAME(TRANS,'N')) THEN
*
* Form x := A*x.
*
IF (LSAME(UPLO,'U')) THEN
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
DO 10 I = 1,J - 1
X(I) = X(I) + TEMP*A(I,J)
10 CONTINUE
IF (NOUNIT) X(J) = X(J)*A(J,J)
END IF
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = X(JX)
IX = KX
DO 30 I = 1,J - 1
X(IX) = X(IX) + TEMP*A(I,J)
IX = IX + INCX
30 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*A(J,J)
END IF
JX = JX + INCX
40 CONTINUE
END IF
ELSE
IF (INCX.EQ.1) THEN
DO 60 J = N,1,-1
IF (X(J).NE.ZERO) THEN
TEMP = X(J)
DO 50 I = N,J + 1,-1
X(I) = X(I) + TEMP*A(I,J)
50 CONTINUE
IF (NOUNIT) X(J) = X(J)*A(J,J)
END IF
60 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 80 J = N,1,-1
IF (X(JX).NE.ZERO) THEN
TEMP = X(JX)
IX = KX
DO 70 I = N,J + 1,-1
X(IX) = X(IX) + TEMP*A(I,J)
IX = IX - INCX
70 CONTINUE
IF (NOUNIT) X(JX) = X(JX)*A(J,J)
END IF
JX = JX - INCX
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := A**T*x.
*
IF (LSAME(UPLO,'U')) THEN
IF (INCX.EQ.1) THEN
DO 100 J = N,1,-1
TEMP = X(J)
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 90 I = J - 1,1,-1
TEMP = TEMP + A(I,J)*X(I)
90 CONTINUE
X(J) = TEMP
100 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 120 J = N,1,-1
TEMP = X(JX)
IX = JX
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 110 I = J - 1,1,-1
IX = IX - INCX
TEMP = TEMP + A(I,J)*X(IX)
110 CONTINUE
X(JX) = TEMP
JX = JX - INCX
120 CONTINUE
END IF
ELSE
IF (INCX.EQ.1) THEN
DO 140 J = 1,N
TEMP = X(J)
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 130 I = J + 1,N
TEMP = TEMP + A(I,J)*X(I)
130 CONTINUE
X(J) = TEMP
140 CONTINUE
ELSE
JX = KX
DO 160 J = 1,N
TEMP = X(JX)
IX = JX
IF (NOUNIT) TEMP = TEMP*A(J,J)
DO 150 I = J + 1,N
IX = IX + INCX
TEMP = TEMP + A(I,J)*X(IX)
150 CONTINUE
X(JX) = TEMP
JX = JX + INCX
160 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of DTRMV
*
END

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@ -0,0 +1,440 @@
*> \brief \b DTRSM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA
* INTEGER LDA,LDB,M,N
* CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A(LDA,*),B(LDB,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTRSM solves one of the matrix equations
*>
*> op( A )*X = alpha*B, or X*op( A ) = alpha*B,
*>
*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or
*> non-unit, upper or lower triangular matrix and op( A ) is one of
*>
*> op( A ) = A or op( A ) = A**T.
*>
*> The matrix X is overwritten on B.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> On entry, SIDE specifies whether op( A ) appears on the left
*> or right of X as follows:
*>
*> SIDE = 'L' or 'l' op( A )*X = alpha*B.
*>
*> SIDE = 'R' or 'r' X*op( A ) = alpha*B.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> On entry, UPLO specifies whether the matrix A is an upper or
*> lower triangular matrix as follows:
*>
*> UPLO = 'U' or 'u' A is an upper triangular matrix.
*>
*> UPLO = 'L' or 'l' A is a lower triangular matrix.
*> \endverbatim
*>
*> \param[in] TRANSA
*> \verbatim
*> TRANSA is CHARACTER*1
*> On entry, TRANSA specifies the form of op( A ) to be used in
*> the matrix multiplication as follows:
*>
*> TRANSA = 'N' or 'n' op( A ) = A.
*>
*> TRANSA = 'T' or 't' op( A ) = A**T.
*>
*> TRANSA = 'C' or 'c' op( A ) = A**T.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> On entry, DIAG specifies whether or not A is unit triangular
*> as follows:
*>
*> DIAG = 'U' or 'u' A is assumed to be unit triangular.
*>
*> DIAG = 'N' or 'n' A is not assumed to be unit
*> triangular.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of B. M must be at
*> least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of B. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION.
*> On entry, ALPHA specifies the scalar alpha. When alpha is
*> zero then A is not referenced and B need not be set before
*> entry.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension ( LDA, k ),
*> where k is m when SIDE = 'L' or 'l'
*> and k is n when SIDE = 'R' or 'r'.
*> Before entry with UPLO = 'U' or 'u', the leading k by k
*> upper triangular part of the array A must contain the upper
*> triangular matrix and the strictly lower triangular part of
*> A is not referenced.
*> Before entry with UPLO = 'L' or 'l', the leading k by k
*> lower triangular part of the array A must contain the lower
*> triangular matrix and the strictly upper triangular part of
*> A is not referenced.
*> Note that when DIAG = 'U' or 'u', the diagonal elements of
*> A are not referenced either, but are assumed to be unity.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. When SIDE = 'L' or 'l' then
*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
*> then LDA must be at least max( 1, n ).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension ( LDB, N )
*> Before entry, the leading m by n part of the array B must
*> contain the right-hand side matrix B, and on exit is
*> overwritten by the solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> On entry, LDB specifies the first dimension of B as declared
*> in the calling (sub) program. LDB must be at least
*> max( 1, m ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_blas_level3
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 3 Blas routine.
*>
*>
*> -- Written on 8-February-1989.
*> Jack Dongarra, Argonne National Laboratory.
*> Iain Duff, AERE Harwell.
*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
*> Sven Hammarling, Numerical Algorithms Group Ltd.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER LDA,LDB,M,N
CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION A(LDA,*),B(LDB,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I,INFO,J,K,NROWA
LOGICAL LSIDE,NOUNIT,UPPER
* ..
* .. Parameters ..
DOUBLE PRECISION ONE,ZERO
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
* ..
*
* Test the input parameters.
*
LSIDE = LSAME(SIDE,'L')
IF (LSIDE) THEN
NROWA = M
ELSE
NROWA = N
END IF
NOUNIT = LSAME(DIAG,'N')
UPPER = LSAME(UPLO,'U')
*
INFO = 0
IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
INFO = 1
ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
INFO = 2
ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
+ (.NOT.LSAME(TRANSA,'T')) .AND.
+ (.NOT.LSAME(TRANSA,'C'))) THEN
INFO = 3
ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
INFO = 4
ELSE IF (M.LT.0) THEN
INFO = 5
ELSE IF (N.LT.0) THEN
INFO = 6
ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
INFO = 9
ELSE IF (LDB.LT.MAX(1,M)) THEN
INFO = 11
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DTRSM ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (M.EQ.0 .OR. N.EQ.0) RETURN
*
* And when alpha.eq.zero.
*
IF (ALPHA.EQ.ZERO) THEN
DO 20 J = 1,N
DO 10 I = 1,M
B(I,J) = ZERO
10 CONTINUE
20 CONTINUE
RETURN
END IF
*
* Start the operations.
*
IF (LSIDE) THEN
IF (LSAME(TRANSA,'N')) THEN
*
* Form B := alpha*inv( A )*B.
*
IF (UPPER) THEN
DO 60 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 30 I = 1,M
B(I,J) = ALPHA*B(I,J)
30 CONTINUE
END IF
DO 50 K = M,1,-1
IF (B(K,J).NE.ZERO) THEN
IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
DO 40 I = 1,K - 1
B(I,J) = B(I,J) - B(K,J)*A(I,K)
40 CONTINUE
END IF
50 CONTINUE
60 CONTINUE
ELSE
DO 100 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 70 I = 1,M
B(I,J) = ALPHA*B(I,J)
70 CONTINUE
END IF
DO 90 K = 1,M
IF (B(K,J).NE.ZERO) THEN
IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
DO 80 I = K + 1,M
B(I,J) = B(I,J) - B(K,J)*A(I,K)
80 CONTINUE
END IF
90 CONTINUE
100 CONTINUE
END IF
ELSE
*
* Form B := alpha*inv( A**T )*B.
*
IF (UPPER) THEN
DO 130 J = 1,N
DO 120 I = 1,M
TEMP = ALPHA*B(I,J)
DO 110 K = 1,I - 1
TEMP = TEMP - A(K,I)*B(K,J)
110 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(I,I)
B(I,J) = TEMP
120 CONTINUE
130 CONTINUE
ELSE
DO 160 J = 1,N
DO 150 I = M,1,-1
TEMP = ALPHA*B(I,J)
DO 140 K = I + 1,M
TEMP = TEMP - A(K,I)*B(K,J)
140 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(I,I)
B(I,J) = TEMP
150 CONTINUE
160 CONTINUE
END IF
END IF
ELSE
IF (LSAME(TRANSA,'N')) THEN
*
* Form B := alpha*B*inv( A ).
*
IF (UPPER) THEN
DO 210 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 170 I = 1,M
B(I,J) = ALPHA*B(I,J)
170 CONTINUE
END IF
DO 190 K = 1,J - 1
IF (A(K,J).NE.ZERO) THEN
DO 180 I = 1,M
B(I,J) = B(I,J) - A(K,J)*B(I,K)
180 CONTINUE
END IF
190 CONTINUE
IF (NOUNIT) THEN
TEMP = ONE/A(J,J)
DO 200 I = 1,M
B(I,J) = TEMP*B(I,J)
200 CONTINUE
END IF
210 CONTINUE
ELSE
DO 260 J = N,1,-1
IF (ALPHA.NE.ONE) THEN
DO 220 I = 1,M
B(I,J) = ALPHA*B(I,J)
220 CONTINUE
END IF
DO 240 K = J + 1,N
IF (A(K,J).NE.ZERO) THEN
DO 230 I = 1,M
B(I,J) = B(I,J) - A(K,J)*B(I,K)
230 CONTINUE
END IF
240 CONTINUE
IF (NOUNIT) THEN
TEMP = ONE/A(J,J)
DO 250 I = 1,M
B(I,J) = TEMP*B(I,J)
250 CONTINUE
END IF
260 CONTINUE
END IF
ELSE
*
* Form B := alpha*B*inv( A**T ).
*
IF (UPPER) THEN
DO 310 K = N,1,-1
IF (NOUNIT) THEN
TEMP = ONE/A(K,K)
DO 270 I = 1,M
B(I,K) = TEMP*B(I,K)
270 CONTINUE
END IF
DO 290 J = 1,K - 1
IF (A(J,K).NE.ZERO) THEN
TEMP = A(J,K)
DO 280 I = 1,M
B(I,J) = B(I,J) - TEMP*B(I,K)
280 CONTINUE
END IF
290 CONTINUE
IF (ALPHA.NE.ONE) THEN
DO 300 I = 1,M
B(I,K) = ALPHA*B(I,K)
300 CONTINUE
END IF
310 CONTINUE
ELSE
DO 360 K = 1,N
IF (NOUNIT) THEN
TEMP = ONE/A(K,K)
DO 320 I = 1,M
B(I,K) = TEMP*B(I,K)
320 CONTINUE
END IF
DO 340 J = K + 1,N
IF (A(J,K).NE.ZERO) THEN
TEMP = A(J,K)
DO 330 I = 1,M
B(I,J) = B(I,J) - TEMP*B(I,K)
330 CONTINUE
END IF
340 CONTINUE
IF (ALPHA.NE.ONE) THEN
DO 350 I = 1,M
B(I,K) = ALPHA*B(I,K)
350 CONTINUE
END IF
360 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of DTRSM
*
END