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author | julie <julielangou@users.noreply.github.com> | 2008-12-16 17:06:58 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2008-12-16 17:06:58 +0000 |
commit | ff981f106bde4ce6a74aa4f4a572c943f5a395b2 (patch) | |
tree | a386cad907bcaefd6893535c31d67ec9468e693e /SRC/cpftrs.f | |
parent | e58b61578b55644f6391f3333262b72c1dc88437 (diff) | |
download | lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.tar.gz lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.tar.bz2 lapack-ff981f106bde4ce6a74aa4f4a572c943f5a395b2.zip |
Diffstat (limited to 'SRC/cpftrs.f')
-rw-r--r-- | SRC/cpftrs.f | 230 |
1 files changed, 230 insertions, 0 deletions
diff --git a/SRC/cpftrs.f b/SRC/cpftrs.f new file mode 100644 index 00000000..cfddeb6e --- /dev/null +++ b/SRC/cpftrs.f @@ -0,0 +1,230 @@ + SUBROUTINE CPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.2) -- +* +* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- +* -- November 2008 -- +* +* -- 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, LDB, N, NRHS +* .. +* .. Array Arguments .. + COMPLEX A( 0: * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* CPFTRS solves a system of linear equations A*X = B with a Hermitian +* positive definite matrix A using the Cholesky factorization +* A = U**H*U or A = L*L**H computed by CPFTRF. +* +* Arguments +* ========= +* +* TRANSR (input) CHARACTER +* = 'N': The Normal TRANSR of RFP A is stored; +* = 'C': The Conjugate-transpose TRANSR of RFP A is stored. +* +* UPLO (input) CHARACTER +* = 'U': Upper triangle of RFP A is stored; +* = 'L': Lower triangle of RFP A is stored. +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* NRHS (input) INTEGER +* The number of right hand sides, i.e., the number of columns +* of the matrix B. NRHS >= 0. +* +* A (input) COMPLEX array, dimension ( N*(N+1)/2 ); +* The triangular factor U or L from the Cholesky factorization +* of RFP A = U**H*U or RFP A = L*L**H, as computed by CPFTRF. +* See note below for more details about RFP A. +* +* B (input/output) COMPLEX array, dimension (LDB,NRHS) +* On entry, the right hand side matrix B. +* On exit, the solution matrix X. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* Note: +* ===== +* +* We first consider Standard Packed 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 +* conjugate-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 +* conjugate-transpose of the last three columns of AP lower. +* To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- +* 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 next consider Standard Packed 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 +* conjugate-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 +* conjugate-transpose of the last two columns of AP lower. +* To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate- +* 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 +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX CONE + PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL LOWER, NORMALTRANSR +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, CTFSM +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + NORMALTRANSR = LSAME( TRANSR, 'N' ) + LOWER = LSAME( UPLO, 'L' ) + IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN + INFO = -1 + ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -4 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CPFTRS', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 .OR. NRHS.EQ.0 ) + + RETURN +* +* start execution: there are two triangular solves +* + IF( LOWER ) THEN + CALL CTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B, + + LDB ) + CALL CTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B, + + LDB ) + ELSE + CALL CTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B, + + LDB ) + CALL CTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B, + + LDB ) + END IF +* + RETURN +* +* End of CPFTRS +* + END |