SUBROUTINE SPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
*
* -- LAPACK routine (version 3.2.2) --
*
* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
* -- June 2010 --
*
* -- 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 ..
REAL A( 0: * ), B( LDB, * )
* ..
*
* Purpose
* =======
*
* SPFTRS solves a system of linear equations A*X = B with a symmetric
* positive definite matrix A using the Cholesky factorization
* A = U**T*U or A = L*L**T computed by SPFTRF.
*
* Arguments
* =========
*
* TRANSR (input) CHARACTER
* = 'N': The Normal TRANSR of RFP A is stored;
* = 'T': The 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) REAL 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**T, as computed by SPFTRF.
* See note below for more details about RFP A.
*
* B (input/output) REAL 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
*
* Further Details
* ===============
*
* 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
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL LOWER, NORMALTRANSR
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, STFSM
* ..
* .. 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, 'T' ) ) 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( 'SPFTRS', -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 STFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
+ LDB )
CALL STFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
+ LDB )
ELSE
CALL STFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
+ LDB )
CALL STFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
+ LDB )
END IF
*
RETURN
*
* End of SPFTRS
*
END