Annotation of rpl/lapack/lapack/zpotrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPOTRF( 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: COMPLEX*16 A( LDA, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZPOTRF computes the Cholesky factorization of a complex Hermitian
! 20: * positive definite matrix A.
! 21: *
! 22: * The factorization has the form
! 23: * A = U**H * U, if UPLO = 'U', or
! 24: * A = L * L**H, 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) COMPLEX*16 array, dimension (LDA,N)
! 40: * On entry, the Hermitian 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**H*U or A = L*L**H.
! 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: COMPLEX*16 CONE
! 66: PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ) )
! 67: * ..
! 68: * .. Local Scalars ..
! 69: LOGICAL UPPER
! 70: INTEGER J, JB, NB
! 71: * ..
! 72: * .. External Functions ..
! 73: LOGICAL LSAME
! 74: INTEGER ILAENV
! 75: EXTERNAL LSAME, ILAENV
! 76: * ..
! 77: * .. External Subroutines ..
! 78: EXTERNAL XERBLA, ZGEMM, ZHERK, ZPOTF2, ZTRSM
! 79: * ..
! 80: * .. Intrinsic Functions ..
! 81: INTRINSIC MAX, MIN
! 82: * ..
! 83: * .. Executable Statements ..
! 84: *
! 85: * Test the input parameters.
! 86: *
! 87: INFO = 0
! 88: UPPER = LSAME( UPLO, 'U' )
! 89: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 90: INFO = -1
! 91: ELSE IF( N.LT.0 ) THEN
! 92: INFO = -2
! 93: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 94: INFO = -4
! 95: END IF
! 96: IF( INFO.NE.0 ) THEN
! 97: CALL XERBLA( 'ZPOTRF', -INFO )
! 98: RETURN
! 99: END IF
! 100: *
! 101: * Quick return if possible
! 102: *
! 103: IF( N.EQ.0 )
! 104: $ RETURN
! 105: *
! 106: * Determine the block size for this environment.
! 107: *
! 108: NB = ILAENV( 1, 'ZPOTRF', UPLO, N, -1, -1, -1 )
! 109: IF( NB.LE.1 .OR. NB.GE.N ) THEN
! 110: *
! 111: * Use unblocked code.
! 112: *
! 113: CALL ZPOTF2( UPLO, N, A, LDA, INFO )
! 114: ELSE
! 115: *
! 116: * Use blocked code.
! 117: *
! 118: IF( UPPER ) THEN
! 119: *
! 120: * Compute the Cholesky factorization A = U'*U.
! 121: *
! 122: DO 10 J = 1, N, NB
! 123: *
! 124: * Update and factorize the current diagonal block and test
! 125: * for non-positive-definiteness.
! 126: *
! 127: JB = MIN( NB, N-J+1 )
! 128: CALL ZHERK( 'Upper', 'Conjugate transpose', JB, J-1,
! 129: $ -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA )
! 130: CALL ZPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
! 131: IF( INFO.NE.0 )
! 132: $ GO TO 30
! 133: IF( J+JB.LE.N ) THEN
! 134: *
! 135: * Compute the current block row.
! 136: *
! 137: CALL ZGEMM( 'Conjugate transpose', 'No transpose', JB,
! 138: $ N-J-JB+1, J-1, -CONE, A( 1, J ), LDA,
! 139: $ A( 1, J+JB ), LDA, CONE, A( J, J+JB ),
! 140: $ LDA )
! 141: CALL ZTRSM( 'Left', 'Upper', 'Conjugate transpose',
! 142: $ 'Non-unit', JB, N-J-JB+1, CONE, A( J, J ),
! 143: $ LDA, A( J, J+JB ), LDA )
! 144: END IF
! 145: 10 CONTINUE
! 146: *
! 147: ELSE
! 148: *
! 149: * Compute the Cholesky factorization A = L*L'.
! 150: *
! 151: DO 20 J = 1, N, NB
! 152: *
! 153: * Update and factorize the current diagonal block and test
! 154: * for non-positive-definiteness.
! 155: *
! 156: JB = MIN( NB, N-J+1 )
! 157: CALL ZHERK( 'Lower', 'No transpose', JB, J-1, -ONE,
! 158: $ A( J, 1 ), LDA, ONE, A( J, J ), LDA )
! 159: CALL ZPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
! 160: IF( INFO.NE.0 )
! 161: $ GO TO 30
! 162: IF( J+JB.LE.N ) THEN
! 163: *
! 164: * Compute the current block column.
! 165: *
! 166: CALL ZGEMM( 'No transpose', 'Conjugate transpose',
! 167: $ N-J-JB+1, JB, J-1, -CONE, A( J+JB, 1 ),
! 168: $ LDA, A( J, 1 ), LDA, CONE, A( J+JB, J ),
! 169: $ LDA )
! 170: CALL ZTRSM( 'Right', 'Lower', 'Conjugate transpose',
! 171: $ 'Non-unit', N-J-JB+1, JB, CONE, A( J, J ),
! 172: $ LDA, A( J+JB, J ), LDA )
! 173: END IF
! 174: 20 CONTINUE
! 175: END IF
! 176: END IF
! 177: GO TO 40
! 178: *
! 179: 30 CONTINUE
! 180: INFO = INFO + J - 1
! 181: *
! 182: 40 CONTINUE
! 183: RETURN
! 184: *
! 185: * End of ZPOTRF
! 186: *
! 187: END
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