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Annotation of rpl/lapack/lapack/zpotrs.f, revision 1.4

1.1       bertrand    1:       SUBROUTINE ZPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
                      2: *
                      3: *  -- LAPACK routine (version 3.2) --
                      4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                      6: *     November 2006
                      7: *
                      8: *     .. Scalar Arguments ..
                      9:       CHARACTER          UPLO
                     10:       INTEGER            INFO, LDA, LDB, N, NRHS
                     11: *     ..
                     12: *     .. Array Arguments ..
                     13:       COMPLEX*16         A( LDA, * ), B( LDB, * )
                     14: *     ..
                     15: *
                     16: *  Purpose
                     17: *  =======
                     18: *
                     19: *  ZPOTRS solves a system of linear equations A*X = B with a Hermitian
                     20: *  positive definite matrix A using the Cholesky factorization
                     21: *  A = U**H*U or A = L*L**H computed by ZPOTRF.
                     22: *
                     23: *  Arguments
                     24: *  =========
                     25: *
                     26: *  UPLO    (input) CHARACTER*1
                     27: *          = 'U':  Upper triangle of A is stored;
                     28: *          = 'L':  Lower triangle of A is stored.
                     29: *
                     30: *  N       (input) INTEGER
                     31: *          The order of the matrix A.  N >= 0.
                     32: *
                     33: *  NRHS    (input) INTEGER
                     34: *          The number of right hand sides, i.e., the number of columns
                     35: *          of the matrix B.  NRHS >= 0.
                     36: *
                     37: *  A       (input) COMPLEX*16 array, dimension (LDA,N)
                     38: *          The triangular factor U or L from the Cholesky factorization
                     39: *          A = U**H*U or A = L*L**H, as computed by ZPOTRF.
                     40: *
                     41: *  LDA     (input) INTEGER
                     42: *          The leading dimension of the array A.  LDA >= max(1,N).
                     43: *
                     44: *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
                     45: *          On entry, the right hand side matrix B.
                     46: *          On exit, the solution matrix X.
                     47: *
                     48: *  LDB     (input) INTEGER
                     49: *          The leading dimension of the array B.  LDB >= max(1,N).
                     50: *
                     51: *  INFO    (output) INTEGER
                     52: *          = 0:  successful exit
                     53: *          < 0:  if INFO = -i, the i-th argument had an illegal value
                     54: *
                     55: *  =====================================================================
                     56: *
                     57: *     .. Parameters ..
                     58:       COMPLEX*16         ONE
                     59:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
                     60: *     ..
                     61: *     .. Local Scalars ..
                     62:       LOGICAL            UPPER
                     63: *     ..
                     64: *     .. External Functions ..
                     65:       LOGICAL            LSAME
                     66:       EXTERNAL           LSAME
                     67: *     ..
                     68: *     .. External Subroutines ..
                     69:       EXTERNAL           XERBLA, ZTRSM
                     70: *     ..
                     71: *     .. Intrinsic Functions ..
                     72:       INTRINSIC          MAX
                     73: *     ..
                     74: *     .. Executable Statements ..
                     75: *
                     76: *     Test the input parameters.
                     77: *
                     78:       INFO = 0
                     79:       UPPER = LSAME( UPLO, 'U' )
                     80:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
                     81:          INFO = -1
                     82:       ELSE IF( N.LT.0 ) THEN
                     83:          INFO = -2
                     84:       ELSE IF( NRHS.LT.0 ) THEN
                     85:          INFO = -3
                     86:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
                     87:          INFO = -5
                     88:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
                     89:          INFO = -7
                     90:       END IF
                     91:       IF( INFO.NE.0 ) THEN
                     92:          CALL XERBLA( 'ZPOTRS', -INFO )
                     93:          RETURN
                     94:       END IF
                     95: *
                     96: *     Quick return if possible
                     97: *
                     98:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
                     99:      $   RETURN
                    100: *
                    101:       IF( UPPER ) THEN
                    102: *
                    103: *        Solve A*X = B where A = U'*U.
                    104: *
                    105: *        Solve U'*X = B, overwriting B with X.
                    106: *
                    107:          CALL ZTRSM( 'Left', 'Upper', 'Conjugate transpose', 'Non-unit',
                    108:      $               N, NRHS, ONE, A, LDA, B, LDB )
                    109: *
                    110: *        Solve U*X = B, overwriting B with X.
                    111: *
                    112:          CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N,
                    113:      $               NRHS, ONE, A, LDA, B, LDB )
                    114:       ELSE
                    115: *
                    116: *        Solve A*X = B where A = L*L'.
                    117: *
                    118: *        Solve L*X = B, overwriting B with X.
                    119: *
                    120:          CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N,
                    121:      $               NRHS, ONE, A, LDA, B, LDB )
                    122: *
                    123: *        Solve L'*X = B, overwriting B with X.
                    124: *
                    125:          CALL ZTRSM( 'Left', 'Lower', 'Conjugate transpose', 'Non-unit',
                    126:      $               N, NRHS, ONE, A, LDA, B, LDB )
                    127:       END IF
                    128: *
                    129:       RETURN
                    130: *
                    131: *     End of ZPOTRS
                    132: *
                    133:       END