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SUBROUTINE CPSTRF( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
* * -- LAPACK routine (version 3.2.2) -- * Craig Lucas, University of Manchester / NAG Ltd. * October, 2008 * * .. Scalar Arguments .. REAL TOL INTEGER INFO, LDA, N, RANK CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX A( LDA, * ) REAL WORK( 2*N ) INTEGER PIV( N ) * .. * * Purpose * ======= * * CPSTRF computes the Cholesky factorization with complete * pivoting of a complex Hermitian positive semidefinite matrix A. * * The factorization has the form * P**T * A * P = U**H * U , if UPLO = 'U', * P**T * A * P = L * L**H, if UPLO = 'L', * where U is an upper triangular matrix and L is lower triangular, and * P is stored as vector PIV. * * This algorithm does not attempt to check that A is positive * semidefinite. This version of the algorithm calls level 3 BLAS. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * symmetric matrix A is stored. * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The order of the matrix A. N >= 0. * * A (input/output) COMPLEX array, dimension (LDA,N) * On entry, the symmetric matrix A. If UPLO = 'U', the leading * n by n upper triangular part of A contains the upper * triangular part of the matrix A, and the strictly lower * triangular part of A is not referenced. If UPLO = 'L', the * leading n by n lower triangular part of A contains the lower * triangular part of the matrix A, and the strictly upper * triangular part of A is not referenced. * * On exit, if INFO = 0, the factor U or L from the Cholesky * factorization as above. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * PIV (output) INTEGER array, dimension (N) * PIV is such that the nonzero entries are P( PIV(K), K ) = 1. * * RANK (output) INTEGER * The rank of A given by the number of steps the algorithm * completed. * * TOL (input) REAL * User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) * will be used. The algorithm terminates at the (K-1)st step * if the pivot <= TOL. * * WORK (workspace) REAL array, dimension (2*N) * Work space. * * INFO (output) INTEGER * < 0: If INFO = -K, the K-th argument had an illegal value, * = 0: algorithm completed successfully, and * > 0: the matrix A is either rank deficient with computed rank * as returned in RANK, or is indefinite. See Section 7 of * LAPACK Working Note #161 for further information. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) COMPLEX CONE PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. COMPLEX CTEMP REAL AJJ, SSTOP, STEMP INTEGER I, ITEMP, J, JB, K, NB, PVT LOGICAL UPPER * .. * .. External Functions .. REAL SLAMCH INTEGER ILAENV LOGICAL LSAME, SISNAN EXTERNAL SLAMCH, ILAENV, LSAME, SISNAN * .. * .. External Subroutines .. EXTERNAL CGEMV, CHERK, CLACGV, CPSTF2, CSSCAL, CSWAP, $ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, MIN, REAL, SQRT, MAXLOC * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CPSTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Get block size * NB = ILAENV( 1, 'CPOTRF', UPLO, N, -1, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL CPSTF2( UPLO, N, A( 1, 1 ), LDA, PIV, RANK, TOL, WORK, $ INFO ) GO TO 230 * ELSE * * Initialize PIV * DO 100 I = 1, N PIV( I ) = I 100 CONTINUE * * Compute stopping value * DO 110 I = 1, N WORK( I ) = REAL( A( I, I ) ) 110 CONTINUE PVT = MAXLOC( WORK( 1:N ), 1 ) AJJ = REAL( A( PVT, PVT ) ) IF( AJJ.EQ.ZERO.OR.SISNAN( AJJ ) ) THEN RANK = 0 INFO = 1 GO TO 230 END IF * * Compute stopping value if not supplied * IF( TOL.LT.ZERO ) THEN SSTOP = N * SLAMCH( 'Epsilon' ) * AJJ ELSE SSTOP = TOL END IF * * IF( UPPER ) THEN * * Compute the Cholesky factorization P**T * A * P = U**H * U * DO 160 K = 1, N, NB * * Account for last block not being NB wide * JB = MIN( NB, N-K+1 ) * * Set relevant part of first half of WORK to zero, * holds dot products * DO 120 I = K, N WORK( I ) = 0 120 CONTINUE * DO 150 J = K, K + JB - 1 * * Find pivot, test for exit, else swap rows and columns * Update dot products, compute possible pivots which are * stored in the second half of WORK * DO 130 I = J, N * IF( J.GT.K ) THEN WORK( I ) = WORK( I ) + $ REAL( CONJG( A( J-1, I ) )* $ A( J-1, I ) ) END IF WORK( N+I ) = REAL( A( I, I ) ) - WORK( I ) * 130 CONTINUE * IF( J.GT.1 ) THEN ITEMP = MAXLOC( WORK( (N+J):(2*N) ), 1 ) PVT = ITEMP + J - 1 AJJ = WORK( N+PVT ) IF( AJJ.LE.SSTOP.OR.SISNAN( AJJ ) ) THEN A( J, J ) = AJJ GO TO 220 END IF END IF * IF( J.NE.PVT ) THEN * * Pivot OK, so can now swap pivot rows and columns * A( PVT, PVT ) = A( J, J ) CALL CSWAP( J-1, A( 1, J ), 1, A( 1, PVT ), 1 ) IF( PVT.LT.N ) $ CALL CSWAP( N-PVT, A( J, PVT+1 ), LDA, $ A( PVT, PVT+1 ), LDA ) DO 140 I = J + 1, PVT - 1 CTEMP = CONJG( A( J, I ) ) A( J, I ) = CONJG( A( I, PVT ) ) A( I, PVT ) = CTEMP 140 CONTINUE A( J, PVT ) = CONJG( A( J, PVT ) ) * * Swap dot products and PIV * STEMP = WORK( J ) WORK( J ) = WORK( PVT ) WORK( PVT ) = STEMP ITEMP = PIV( PVT ) PIV( PVT ) = PIV( J ) PIV( J ) = ITEMP END IF * AJJ = SQRT( AJJ ) A( J, J ) = AJJ * * Compute elements J+1:N of row J. * IF( J.LT.N ) THEN CALL CLACGV( J-1, A( 1, J ), 1 ) CALL CGEMV( 'Trans', J-K, N-J, -CONE, A( K, J+1 ), $ LDA, A( K, J ), 1, CONE, A( J, J+1 ), $ LDA ) CALL CLACGV( J-1, A( 1, J ), 1 ) CALL CSSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA ) END IF * 150 CONTINUE * * Update trailing matrix, J already incremented * IF( K+JB.LE.N ) THEN CALL CHERK( 'Upper', 'Conj Trans', N-J+1, JB, -ONE, $ A( K, J ), LDA, ONE, A( J, J ), LDA ) END IF * 160 CONTINUE * ELSE * * Compute the Cholesky factorization P**T * A * P = L * L**H * DO 210 K = 1, N, NB * * Account for last block not being NB wide * JB = MIN( NB, N-K+1 ) * * Set relevant part of first half of WORK to zero, * holds dot products * DO 170 I = K, N WORK( I ) = 0 170 CONTINUE * DO 200 J = K, K + JB - 1 * * Find pivot, test for exit, else swap rows and columns * Update dot products, compute possible pivots which are * stored in the second half of WORK * DO 180 I = J, N * IF( J.GT.K ) THEN WORK( I ) = WORK( I ) + $ REAL( CONJG( A( I, J-1 ) )* $ A( I, J-1 ) ) END IF WORK( N+I ) = REAL( A( I, I ) ) - WORK( I ) * 180 CONTINUE * IF( J.GT.1 ) THEN ITEMP = MAXLOC( WORK( (N+J):(2*N) ), 1 ) PVT = ITEMP + J - 1 AJJ = WORK( N+PVT ) IF( AJJ.LE.SSTOP.OR.SISNAN( AJJ ) ) THEN A( J, J ) = AJJ GO TO 220 END IF END IF * IF( J.NE.PVT ) THEN * * Pivot OK, so can now swap pivot rows and columns * A( PVT, PVT ) = A( J, J ) CALL CSWAP( J-1, A( J, 1 ), LDA, A( PVT, 1 ), LDA ) IF( PVT.LT.N ) $ CALL CSWAP( N-PVT, A( PVT+1, J ), 1, $ A( PVT+1, PVT ), 1 ) DO 190 I = J + 1, PVT - 1 CTEMP = CONJG( A( I, J ) ) A( I, J ) = CONJG( A( PVT, I ) ) A( PVT, I ) = CTEMP 190 CONTINUE A( PVT, J ) = CONJG( A( PVT, J ) ) * * Swap dot products and PIV * STEMP = WORK( J ) WORK( J ) = WORK( PVT ) WORK( PVT ) = STEMP ITEMP = PIV( PVT ) PIV( PVT ) = PIV( J ) PIV( J ) = ITEMP END IF * AJJ = SQRT( AJJ ) A( J, J ) = AJJ * * Compute elements J+1:N of column J. * IF( J.LT.N ) THEN CALL CLACGV( J-1, A( J, 1 ), LDA ) CALL CGEMV( 'No Trans', N-J, J-K, -CONE, $ A( J+1, K ), LDA, A( J, K ), LDA, CONE, $ A( J+1, J ), 1 ) CALL CLACGV( J-1, A( J, 1 ), LDA ) CALL CSSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 ) END IF * 200 CONTINUE * * Update trailing matrix, J already incremented * IF( K+JB.LE.N ) THEN CALL CHERK( 'Lower', 'No Trans', N-J+1, JB, -ONE, $ A( J, K ), LDA, ONE, A( J, J ), LDA ) END IF * 210 CONTINUE * END IF END IF * * Ran to completion, A has full rank * RANK = N * GO TO 230 220 CONTINUE * * Rank is the number of steps completed. Set INFO = 1 to signal * that the factorization cannot be used to solve a system. * RANK = J - 1 INFO = 1 * 230 CONTINUE RETURN * * End of CPSTRF * END |