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authorjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
committerjulie <julielangou@users.noreply.github.com>2008-12-16 17:06:58 +0000
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+ 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