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SUBROUTINE SPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
* * -- LAPACK routine (version 3.3.1) -- * * -- Contributed by Fred Gustavson of the IBM Watson Research Center -- * -- April 2011 -- * * -- 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*1 * = 'N': The Normal TRANSR of RFP A is stored; * = 'T': The Transpose TRANSR of RFP A is stored. * * UPLO (input) CHARACTER*1 * = '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 |