phynexis-deps/lapack
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
e2428ec4cbbbfb86fb48a67a0696347f73aebc21
lapack/SRC/stfttp.f
T
Julie e18d437924 Making LAPACK's code eternal... no more version and date in source files. 
GitHub is now enabling us to track accurately version and date.
No need for this anymore.
2021-03-25 10:16:58 -07:00

515 lines
14 KiB
FortranFixed
Raw Blame History

*> \brief \b STFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download STFTTP + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stfttp.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stfttp.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stfttp.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE STFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
*
* .. Scalar Arguments ..
* CHARACTER TRANSR, UPLO
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* REAL AP( 0: * ), ARF( 0: * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> STFTTP copies a triangular matrix A from rectangular full packed
*> format (TF) to standard packed format (TP).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANSR
*> \verbatim
*> TRANSR is CHARACTER*1
*> = 'N': ARF is in Normal format;
*> = 'T': ARF is in Transpose format;
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': A is upper triangular;
*> = 'L': A is lower triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] ARF
*> \verbatim
*> ARF is REAL array, dimension ( N*(N+1)/2 ),
*> On entry, the upper or lower triangular matrix A stored in
*> RFP format. For a further discussion see Notes below.
*> \endverbatim
*>
*> \param[out] AP
*> \verbatim
*> AP is REAL array, dimension ( N*(N+1)/2 ),
*> On exit, the upper or lower triangular matrix A, packed
*> columnwise in a linear array. The j-th column of A is stored
*> in the array AP as follows:
*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
*> \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 realOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> We first consider Rectangular Full Packed (RFP) Format when N is
*> even. We give an example where N = 6.
*>
*> AP is Upper AP is Lower
*>
*> 00 01 02 03 04 05 00
*> 11 12 13 14 15 10 11
*> 22 23 24 25 20 21 22
*> 33 34 35 30 31 32 33
*> 44 45 40 41 42 43 44
*> 55 50 51 52 53 54 55
*>
*>
*> Let TRANSR = 'N'. RFP holds AP as follows:
*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
*> the transpose of the first three columns of AP upper.
*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
*> the transpose of the last three columns of AP lower.
*> This covers the case N even and TRANSR = 'N'.
*>
*> RFP A RFP A
*>
*> 03 04 05 33 43 53
*> 13 14 15 00 44 54
*> 23 24 25 10 11 55
*> 33 34 35 20 21 22
*> 00 44 45 30 31 32
*> 01 11 55 40 41 42
*> 02 12 22 50 51 52
*>
*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
*> transpose of RFP A above. One therefore gets:
*>
*>
*> RFP A RFP A
*>
*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
*>
*>
*> We then consider Rectangular Full Packed (RFP) Format when N is
*> odd. We give an example where N = 5.
*>
*> AP is Upper AP is Lower
*>
*> 00 01 02 03 04 00
*> 11 12 13 14 10 11
*> 22 23 24 20 21 22
*> 33 34 30 31 32 33
*> 44 40 41 42 43 44
*>
*>
*> Let TRANSR = 'N'. RFP holds AP as follows:
*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
*> the transpose of the first two columns of AP upper.
*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
*> the transpose of the last two columns of AP lower.
*> This covers the case N odd and TRANSR = 'N'.
*>
*> RFP A RFP A
*>
*> 02 03 04 00 33 43
*> 12 13 14 10 11 44
*> 22 23 24 20 21 22
*> 00 33 34 30 31 32
*> 01 11 44 40 41 42
*>
*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
*> transpose of RFP A above. One therefore gets:
*>
*> RFP A RFP A
*>
*> 02 12 22 00 01 00 10 20 30 40 50
*> 03 13 23 33 11 33 11 21 31 41 51
*> 04 14 24 34 44 43 44 22 32 42 52
*> \endverbatim
*>
* =====================================================================
SUBROUTINE STFTTP( TRANSR, UPLO, N, ARF, AP, 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 ..
CHARACTER TRANSR, UPLO
INTEGER INFO, N
* ..
* .. Array Arguments ..
REAL AP( 0: * ), ARF( 0: * )
* ..
*
* =====================================================================
*
* .. Parameters ..
* ..
* .. Local Scalars ..
LOGICAL LOWER, NISODD, NORMALTRANSR
INTEGER N1, N2, K, NT
INTEGER I, J, IJ
INTEGER IJP, JP, LDA, JS
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NORMALTRANSR = LSAME( TRANSR, 'N' )
LOWER = LSAME( UPLO, 'L' )
IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
INFO = -1
ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'STFTTP', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( N.EQ.1 ) THEN
IF( NORMALTRANSR ) THEN
AP( 0 ) = ARF( 0 )
ELSE
AP( 0 ) = ARF( 0 )
END IF
RETURN
END IF
*
* Size of array ARF(0:NT-1)
*
NT = N*( N+1 ) / 2
*
* Set N1 and N2 depending on LOWER
*
IF( LOWER ) THEN
N2 = N / 2
N1 = N - N2
ELSE
N1 = N / 2
N2 = N - N1
END IF
*
* If N is odd, set NISODD = .TRUE.
* If N is even, set K = N/2 and NISODD = .FALSE.
*
* set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
* where noe = 0 if n is even, noe = 1 if n is odd
*
IF( MOD( N, 2 ).EQ.0 ) THEN
K = N / 2
NISODD = .FALSE.
LDA = N + 1
ELSE
NISODD = .TRUE.
LDA = N
END IF
*
* ARF^C has lda rows and n+1-noe cols
*
IF( .NOT.NORMALTRANSR )
$ LDA = ( N+1 ) / 2
*
* start execution: there are eight cases
*
IF( NISODD ) THEN
*
* N is odd
*
IF( NORMALTRANSR ) THEN
*
* N is odd and TRANSR = 'N'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
* T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
*
IJP = 0
JP = 0
DO J = 0, N2
DO I = J, N - 1
IJ = I + JP
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JP = JP + LDA
END DO
DO I = 0, N2 - 1
DO J = 1 + I, N2
IJ = I + J*LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
*
ELSE
*
* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
* T1 -> a(n2), T2 -> a(n1), S -> a(0)
*
IJP = 0
DO J = 0, N1 - 1
IJ = N2 + J
DO I = 0, J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
IJ = IJ + LDA
END DO
END DO
JS = 0
DO J = N1, N - 1
IJ = JS
DO IJ = JS, JS + J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA
END DO
*
END IF
*
ELSE
*
* N is odd and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, TRANSPOSE and N is odd
* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
* T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
*
IJP = 0
DO I = 0, N2
DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
JS = 1
DO J = 0, N2 - 1
DO IJ = JS, JS + N2 - J - 1
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA + 1
END DO
*
ELSE
*
* SRPA for UPPER, TRANSPOSE and N is odd
* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
* T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
*
IJP = 0
JS = N2*LDA
DO J = 0, N1 - 1
DO IJ = JS, JS + J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA
END DO
DO I = 0, N1
DO IJ = I, I + ( N1+I )*LDA, LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
*
END IF
*
END IF
*
ELSE
*
* N is even
*
IF( NORMALTRANSR ) THEN
*
* N is even and TRANSR = 'N'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
* T1 -> a(1), T2 -> a(0), S -> a(k+1)
*
IJP = 0
JP = 0
DO J = 0, K - 1
DO I = J, N - 1
IJ = 1 + I + JP
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JP = JP + LDA
END DO
DO I = 0, K - 1
DO J = I, K - 1
IJ = I + J*LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
*
ELSE
*
* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
* T1 -> a(k+1), T2 -> a(k), S -> a(0)
*
IJP = 0
DO J = 0, K - 1
IJ = K + 1 + J
DO I = 0, J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
IJ = IJ + LDA
END DO
END DO
JS = 0
DO J = K, N - 1
IJ = JS
DO IJ = JS, JS + J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA
END DO
*
END IF
*
ELSE
*
* N is even and TRANSR = 'T'
*
IF( LOWER ) THEN
*
* SRPA for LOWER, TRANSPOSE and N is even (see paper)
* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
*
IJP = 0
DO I = 0, K - 1
DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
JS = 0
DO J = 0, K - 1
DO IJ = JS, JS + K - J - 1
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA + 1
END DO
*
ELSE
*
* SRPA for UPPER, TRANSPOSE and N is even (see paper)
* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
*
IJP = 0
JS = ( K+1 )*LDA
DO J = 0, K - 1
DO IJ = JS, JS + J
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
JS = JS + LDA
END DO
DO I = 0, K - 1
DO IJ = I, I + ( K+I )*LDA, LDA
AP( IJP ) = ARF( IJ )
IJP = IJP + 1
END DO
END DO
*
END IF
*
END IF
*
END IF
*
RETURN
*
* End of STFTTP
*
END
Reference in New Issue View Git Blame Copy Permalink