Annotation of rpl/lapack/lapack/dpotrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DPOTRF( UPLO, N, A, LDA, 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, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION A( LDA, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DPOTRF computes the Cholesky factorization of a real symmetric
! 20: * positive definite matrix A.
! 21: *
! 22: * The factorization has the form
! 23: * A = U**T * U, if UPLO = 'U', or
! 24: * A = L * L**T, if UPLO = 'L',
! 25: * where U is an upper triangular matrix and L is lower triangular.
! 26: *
! 27: * This is the block version of the algorithm, calling Level 3 BLAS.
! 28: *
! 29: * Arguments
! 30: * =========
! 31: *
! 32: * UPLO (input) CHARACTER*1
! 33: * = 'U': Upper triangle of A is stored;
! 34: * = 'L': Lower triangle of A is stored.
! 35: *
! 36: * N (input) INTEGER
! 37: * The order of the matrix A. N >= 0.
! 38: *
! 39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 40: * On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 41: * N-by-N upper triangular part of A contains the upper
! 42: * triangular part of the matrix A, and the strictly lower
! 43: * triangular part of A is not referenced. If UPLO = 'L', the
! 44: * leading N-by-N lower triangular part of A contains the lower
! 45: * triangular part of the matrix A, and the strictly upper
! 46: * triangular part of A is not referenced.
! 47: *
! 48: * On exit, if INFO = 0, the factor U or L from the Cholesky
! 49: * factorization A = U**T*U or A = L*L**T.
! 50: *
! 51: * LDA (input) INTEGER
! 52: * The leading dimension of the array A. LDA >= max(1,N).
! 53: *
! 54: * INFO (output) INTEGER
! 55: * = 0: successful exit
! 56: * < 0: if INFO = -i, the i-th argument had an illegal value
! 57: * > 0: if INFO = i, the leading minor of order i is not
! 58: * positive definite, and the factorization could not be
! 59: * completed.
! 60: *
! 61: * =====================================================================
! 62: *
! 63: * .. Parameters ..
! 64: DOUBLE PRECISION ONE
! 65: PARAMETER ( ONE = 1.0D+0 )
! 66: * ..
! 67: * .. Local Scalars ..
! 68: LOGICAL UPPER
! 69: INTEGER J, JB, NB
! 70: * ..
! 71: * .. External Functions ..
! 72: LOGICAL LSAME
! 73: INTEGER ILAENV
! 74: EXTERNAL LSAME, ILAENV
! 75: * ..
! 76: * .. External Subroutines ..
! 77: EXTERNAL DGEMM, DPOTF2, DSYRK, DTRSM, XERBLA
! 78: * ..
! 79: * .. Intrinsic Functions ..
! 80: INTRINSIC MAX, MIN
! 81: * ..
! 82: * .. Executable Statements ..
! 83: *
! 84: * Test the input parameters.
! 85: *
! 86: INFO = 0
! 87: UPPER = LSAME( UPLO, 'U' )
! 88: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 89: INFO = -1
! 90: ELSE IF( N.LT.0 ) THEN
! 91: INFO = -2
! 92: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 93: INFO = -4
! 94: END IF
! 95: IF( INFO.NE.0 ) THEN
! 96: CALL XERBLA( 'DPOTRF', -INFO )
! 97: RETURN
! 98: END IF
! 99: *
! 100: * Quick return if possible
! 101: *
! 102: IF( N.EQ.0 )
! 103: $ RETURN
! 104: *
! 105: * Determine the block size for this environment.
! 106: *
! 107: NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 )
! 108: IF( NB.LE.1 .OR. NB.GE.N ) THEN
! 109: *
! 110: * Use unblocked code.
! 111: *
! 112: CALL DPOTF2( UPLO, N, A, LDA, INFO )
! 113: ELSE
! 114: *
! 115: * Use blocked code.
! 116: *
! 117: IF( UPPER ) THEN
! 118: *
! 119: * Compute the Cholesky factorization A = U'*U.
! 120: *
! 121: DO 10 J = 1, N, NB
! 122: *
! 123: * Update and factorize the current diagonal block and test
! 124: * for non-positive-definiteness.
! 125: *
! 126: JB = MIN( NB, N-J+1 )
! 127: CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
! 128: $ A( 1, J ), LDA, ONE, A( J, J ), LDA )
! 129: CALL DPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
! 130: IF( INFO.NE.0 )
! 131: $ GO TO 30
! 132: IF( J+JB.LE.N ) THEN
! 133: *
! 134: * Compute the current block row.
! 135: *
! 136: CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1,
! 137: $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ),
! 138: $ LDA, ONE, A( J, J+JB ), LDA )
! 139: CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
! 140: $ JB, N-J-JB+1, ONE, A( J, J ), LDA,
! 141: $ A( J, J+JB ), LDA )
! 142: END IF
! 143: 10 CONTINUE
! 144: *
! 145: ELSE
! 146: *
! 147: * Compute the Cholesky factorization A = L*L'.
! 148: *
! 149: DO 20 J = 1, N, NB
! 150: *
! 151: * Update and factorize the current diagonal block and test
! 152: * for non-positive-definiteness.
! 153: *
! 154: JB = MIN( NB, N-J+1 )
! 155: CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
! 156: $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
! 157: CALL DPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
! 158: IF( INFO.NE.0 )
! 159: $ GO TO 30
! 160: IF( J+JB.LE.N ) THEN
! 161: *
! 162: * Compute the current block column.
! 163: *
! 164: CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
! 165: $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ),
! 166: $ LDA, ONE, A( J+JB, J ), LDA )
! 167: CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
! 168: $ N-J-JB+1, JB, ONE, A( J, J ), LDA,
! 169: $ A( J+JB, J ), LDA )
! 170: END IF
! 171: 20 CONTINUE
! 172: END IF
! 173: END IF
! 174: GO TO 40
! 175: *
! 176: 30 CONTINUE
! 177: INFO = INFO + J - 1
! 178: *
! 179: 40 CONTINUE
! 180: RETURN
! 181: *
! 182: * End of DPOTRF
! 183: *
! 184: END
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